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0903.2320v2 | Witness for an entangled state with positive partial transpose | In this letter we have analyzed an entangled state in $C^{3} \bigotimes C^{3}$ having a positive partial transposition and have shown that it is an edge state. Further we have constructed explicitly a witness operator $W$ which detects the entanglement. | Quantum Physics (quant-ph) | The paper is withdrawn after noticing some errors | factual/methodological/other critical errors in manuscript | 377 |
0903.2488v2 | Schwarzschild-type solution in an effective gravitational theory with local Galilean invariance | We construct a Schwarzschild-type exact external solution for a theory of gravity admitting local Galilean invariance. In order to realize the Galilean invariance we need to adopt a five-dimensional manifold. The solution for the gravitational field equations obeys a Birkhoff-like theorem. Three classic tests of general relativity are analyzed in detail: the perihelion shift of the planet Mercury, the deflection of light by the Sun, and the gravitational redshift of atomic spectral lines. The Galilean version of these tests exhibits an additional parameter $b$ related to the fifth-coordinate. This constant $b$ can be estimated by a comparison with observational data. We observe that the Galilean theory is able to reproduce the results traditionally predicted by general relativity in the limit of negligible $b$. This shows that the tests are not specifically Lorentz invariant. | General Relativity and Quantum Cosmology (gr-qc) | This paper has been withdrawn by the authors due to a mistaken interpretation of the solution's group of symmetry | factual/methodological/other critical errors in manuscript | 378 |
0903.3616v2 | A dual characterization of the C^1 harmonic capacity and applications | The Lipschitz and C^1 harmonic capacities K and K_c in R^n can be considered as high-dimensional versions of the so-called analytic and continuous analytic capacities G and A (respectively). In this paper we provide a dual characterization of K_c in the spirit of the classical one for the capacity A by means of the Garabedian function. | Analysis of PDEs (math.AP) | This paper has been withdrawn by the author due to a crucial sign error in Proposition 3.2 17 pages | factual/methodological/other critical errors in manuscript | 379 |
0903.4295v6 | The Tracy--Widom law for some sparse random matrices | Consider the random matrix obtained from the adjacency matrix of a random d-regular graph by multiplying every entry by a random sign. The largest eigenvalue converges, after proper scaling, to the Tracy--Widom distribution. | Mathematical Physics (math-ph) | The proof contains a serious mistake, and Lemma 5 can not be true as stated. For example, the probability that the graph is not connected tends to zero slower than eq. 4 would imply. I am grateful to [REDACTED-NAME] and Sandrine Péché who brought this to my attention | factual/methodological/other critical errors in manuscript | 380 |
0903.4974v3 | What is realism and how can it be non-local? | The quantum theory predictions about entanglements contradict the assumptions of realism and locality when these two are taken together, the so-called non-local realism. Groblacher et al. took one step further and examined the concept of realism while admitting that entangled quantum systems are influenced not only by local parameters but also by distant parameters. Groblacher et al. called that non-local realism and tried to prove that it is still contradicted by the quantum this http URL present text analyses the consistency of the concept of non-local realism, before questioning whether the experiment contradicts it or not. The realism supposes that macroscopic apparatuses don't enforce one result or another in measurements, but only reveal pre-existent values of properties of the measured systems. However, it is shown here that if factors situated at a distance from a system are assumed to influence the system response to measurements, the wave function may be not unique. It's the macroscopic objects that pick one wave function from the different possible wave functions. So, their influence on the results cannot be denied s.t. the realism is not tenable. | Quantum Physics (quant-ph) | This paper was withdrawn by the author because since its publication, new facts and conclusions appeared, s.t. part of the arguments presented here are no more tenable. An updated account of the realism hypothesis in QM vs. non-locality can be found at arXiv:1009.2986v2 [this http URL-ph] | factual/methodological/other critical errors in manuscript | 383 |
0904.0684v10 | On Codimension Two Ribbon Embeddings | We consider ribbon n-knots for n\geq 2. For such knots we define a set of moves on ribbon disks, and show that any two ribbon disks for isotopic knots are related by a finite sequence of such moves and ambient isotopies. Using this we are able to prove that there is a natural geometric correspondence between ribbon n-knots and ribbon m-knots which is bijective. We also explore a diagrammatic calculus for such knots. In addition we show that for such knots, any two band presentations for the same knot are stably equivalent. | Geometric Topology (math.GT) | Withdrawn due to possible hole in proof | factual/methodological/other critical errors in manuscript | 390 |
0904.0757v3 | Higher regulators, periods and special values of the degree four L-function of GSp(4) | We consider the degree 4 L-function associated to an automorphic representation of the symplectic group GSp(4). Starting with Beilinson's Eisenstien symbol we construct some motivic cohomology classes on the Shimura variety of GSp(4). We show that the image of these classes under the absolute Hodge regulator vanishes on the boundary of the Baily-Borel compactification of the Shimura variety. This allows to relate these classes to the product of an archimedean integral, Harris' occcult period invariant, a Deligne period and the special value of the L-function predicted by Beilinson's conjecture. The considered representation is assumed to have a Bessel model with respect to an isotropic symmetric matrix. | Number Theory (math.NT) | Withdrawn because of the presence of several mistakes. In particular, the proof of the first stated theorem is false. A slight variant of this theorem has been proven in the publication "On higher regulators of Siegel threefolds I: the vanishing on the boundary", by the author | factual/methodological/other critical errors in manuscript | 391 |
0904.1628v2 | Asymptotic Efficiency and Finite Sample Performance of Frequentist Quantum State Estimation | We undertake a detailed study of the performance of maximum likelihood (ML) estimators of the density matrix of finite-dimensional quantum systems, in order to interrogate generic properties of frequentist quantum state estimation. Existing literature on frequentist quantum estimation has not rigorously examined the finite sample performance of the estimators and associated methods of hypothesis testing. While ML is usually preferred on the basis of its asymptotic properties - it achieves the Cramer-Rao (CR) lower bound - the finite sample properties are often less than optimal. We compare the asymptotic and finite-sample properties of the ML estimators and test statistics for two different choices of measurement bases: the average case optimal or mutually unbiased bases (MUB) and a representative set of suboptimal bases, for spin-1/2 and spin-1 systems. We show that, in both cases, the standard errors of the ML estimators sometimes do not contain the true value of the parameter, which can render inference based on the asymptotic properties of the ML unreliable for experimentally realistic sample sizes. The results indicate that in order to fully exploit the information geometry of quantum states and achieve smaller reconstruction errors, the use of Bayesian state reconstruction methods - which, unlike frequentist methods, do not rely on asymptotic properties - is desirable, since the estimation error is typically lower due to the incorporation of prior knowledge. | Quantum Physics (quant-ph) | This paper has been withdrawn by the author due to a bug in the estimation code | factual/methodological/other critical errors in manuscript | 396 |
0904.1746v4 | Linear in temperature resistivity of scalar fermions: application to high Tc cuprates | no longer applicable | Strongly Correlated Electrons (cond-mat.str-el) | The analysis of the Kubo formula was not properly carried out | factual/methodological/other critical errors in manuscript | 398 |
0904.3281v2 | Some norm relations of the Eisenstein classes of GSp(4) | We construct a norm compatible system of Galois cohomology classes in the cyclotomic extension of the field of rationnals giving rise (conjecturally) to the degree four p-adic L-function of the symplectic group GSp(4). These classes are defined as cup products of torsion sections of the elliptic polylogarithm pro-sheaf. We rely on the norm compatibility of the elliptic polylogarithm and on some weight computations in the cohomology of Siegel threefolds. | Number Theory (math.NT) | The integrality statement is false. See the publication "A norm compatible system of Galois cohomology classes for GSp(4)" of the author for a correct statement and proof | factual/methodological/other critical errors in manuscript | 406 |
0904.3407v2 | 3D nanostructuring of La0.7Sr0.3MnO3 thin film surfaces by scanning tunnelling microscopy | Nanoscale 3D surface modifications, by scanning tunneling microscopy under ambient conditions, of La0.7Sr0.3MnO3 thin films have been performed. It was demonstrated that there are well defined combinations of bias voltages and scan speeds which allow for controlled surface structuring. Lateral structures with sizes down to 1.5 nm are possible to obtain. Moreover, it is possible to reproducibly control the depth of etching with half a unit cell precision, enabling design of 3D surface structures and control of the surface termination of La0.7Sr0.3MnO3 through etching. | Mesoscale and Nanoscale Physics (cond-mat.mes-hall) | This paper has been withdrawn by the author due to a error fig1 | factual/methodological/other critical errors in manuscript | 407 |
0904.3516v4 | Piecewise Analytic Subactions for Analytic Dynamics | We consider a piecewise analytic expanding map f: [0,1]-> [0,1] of degree d which preserves orientation, and an analytic positive potential g: [0,1] -> R. We address the analysis of the following problem: for a given analytic potential beta log g, where beta is a real constant, it is well known that there exists a real analytic (with a complex analytic extension to a small complex neighborhood of [0,1]) eigenfunction phi_beta for the Ruelle operator. One can ask: what happen with the function phi_beta, when beta goes to infinity. The domain of analyticity can change with beta. The correct question should be: is 1/ beta log phi_beta analytic in the limit, when beta goes to infinity ? Under a uniqueness assumption, this limit, when beta goes to infinity, is in fact a calibrated subaction V (see bellow definition). We show here that under certain conditions and for a certain class of generic potentials this continuous function is piecewise analytic (but not analytic). In a few examples one can get that the subaction is analytic (we need at least to assume that the maximizing probability has support in a unique fixed point). | Dynamical Systems (math.DS) | This paper has been withdrawn by the authors. The present version has several results that are correct, but, there is a problem in the use of sections 7 and 8 to derive generic properties for the set of analytic potentials g. All sections before this are OK | factual/methodological/other critical errors in manuscript | 408 |
0905.0165v3 | Magnetohydrodynamics, Dark Energy and Closed Null Curves: Towards a Family of Astrophysical Compact Objects | Starting with a static, spherically symmetric spacetime incorporating critical (unstable) closed null geodesics, a family of models for equilibrium states of non-isolated compact objects is obtained by solving the Einstein equations for an energy-momentum tensor featuring a perfect fluid with ideal-gas equation of state, dark energy, and a magnetic field. All of these source fields are described by simple, monotonically decreasing mathematical functions. No ansatz is made for either of the two unknown metric elements;the null curve geometry yields one, and the other follows from a simplification of the magnetic field vector. The metric elements are free of singularities and horizons everywhere, although their inverses are singular at the origin. The entire metric assumes its Lorentzian form at infinity. The geometry of this model, as well as fundamental quantum considerations, require that the radial coordinate must always be greater than zero, thereby obviating the physical singularity at the origin. | General Relativity and Quantum Cosmology (gr-qc) | Paper withdrawn due to a small but crucial technical error | factual/methodological/other critical errors in manuscript | 412 |
0905.0647v2 | Quasilocal Energy in General Relativity | We show that the quasilocal mass defined by Wang and Yau is not well-defined at spatial infinity. It approaches neither the ADM mass nor the ADM energy. We suggest an alternative scheme which retains all the desirable characteristics of the Wang-Yau mass and, in addition, asymptotes to the ADM energy at infinity. | General Relativity and Quantum Cosmology (gr-qc) | This paper has been withdrawn. We find that there are significant difficulties with the computation and we are currently not happy with the results presented in this article. | factual/methodological/other critical errors in manuscript | 416 |
0905.2472v2 | Long-range Ferromagnetic Ordering and Magnetic Phase Transition in Metal-organic Frameworks | The new version will be updated soon. | Materials Science (cond-mat.mtrl-sci) | This paper has been withdrawn by the author due to the limitation of the theoratical model in this version and a crucial error in the experiment part. The model has been updated and extended to most Metal-[REDACTED-NAME] with [REDACTED-NAME]-Cu(II) [REDACTED-NAME]. Moreover, the corresponding experiment also has been updated | factual/methodological/other critical errors in manuscript | 426 |
0905.2510v3 | The Semiring Properties of Fuzzy Algebras | The relationship between fuzzy algebras and semirings is explored with fuzzy algebra operators replacing the arithmetic operators of semirings. A new class of fuzzy structures which are similar to semirings is defined. Results of partial ordering on fuzzy algebras are shown. The zero-sum free property of semirings on fuzzy structures is shown. The semiring property of homomorphism is mapped to fuzzy structures and results like order- and operator-preservation are described. | Rings and Algebras (math.RA) | The paper is withdrawn due to multiple errors that have been pointed to us by referees. | factual/methodological/other critical errors in manuscript | 427 |
0905.2866v2 | The Artin Symbol as a Canonical Capitulation Map | We show that there is a canonical, order preserving map $\psi$ of lattices of subgroups, which maps the lattice $\Sub(A)$ of subgroups of the ideal class group of a galois number field $\K$ into the lattice $\Sub(\KH/\K)$ of subfields of the Hilbert class field. Furthermore, this map is a capitulation map in the sense that all the primes in the classes of $A' \subset A$ capitulate in $\psi(A')$. In particular we have a new, strong version of the generalized Hilbert 94 Theorem, which confirms the result of Myiake and adds more structure to (part) of the capitulation kernel of subfields of $\KH$. | Number Theory (math.NT) | Erroneous, withdrawn! | factual/methodological/other critical errors in manuscript | 429 |
0905.2888v2 | The self-gravity model of longitudinal span of Neptune main arc Fraternite | According to recent works [Tsui PSS \textbf{55}, 237-242 (2007), \textbf{55}, 2042-2044 (2007)], the Neptune Adams ring main arc Fraternite is regarded as captured by the corotation elliptic resonance (CER) potential of Galatea. The minor arcs Egalite(2,1), Liberte, and Courage are located at positions where the time averaged forces, due to the 42-43 corotation-Lindblad resonances under the central field of Neptune, vanish. With adequately chosen Fraternite mass and Galatea eccentricity, this model gives minor arc locations compatible to observed positions, and allows a dynamic transport of materials among arcs. To complement this model, the effect of self-gravity of Fraternite, with a distributed mass, is evaluated together with the CER potential to account for its $10^{0}$ longitudinal span. Although self-gravity is the collective action of all the particles in the arc, each individual particle will see the self-potential with a central maximum as an external potential generated by other particles. | Earth and Planetary Astrophysics (astro-ph.EP) | I have come to the conclusion that the model was incorrect | factual/methodological/other critical errors in manuscript | 430 |
0905.3213v2 | Multipolar interactions and complex phases in ferromagnetic ultrathin films | We present a model to describe complex phases observed at mesoscopic scales in ultrathin magnetic films. The model is based on the interaction between dipolar as well as quadrupolar magnetic moments. In the special case of strong perpendicular crystal anisotropy, we show that quadrupolar degrees of freedom associated with orientation of domain walls are essential in order to correctly describe the observed phenomenology of domain formation. A nematic phase characterized by orientational order of domain walls (stripe-like) but without translational order is predicted. This isotropic-nematic transition belongs to the Kosterlitz-Thouless type in the thermodynamic limit. However, we found that in actual experimental scales, the fluctuations of the nematic order parameter are regularized by the sample size, and orientational long range order, as predicted by mean field, should be observable. The transition may be completely characterized experimentally from measurements of the magnetic structure factor as well as from the non-linear in-plane magnetic susceptibility. | Statistical Mechanics (cond-mat.stat-mech) | This paper has been withdrawn by the authors due to conceptual problems in the definition of the model | factual/methodological/other critical errors in manuscript | 432 |
0905.3781v2 | A Proof of the Strengthened Hanna Neumann Conjecture | We prove the Strengthened Hanna Neumann Conjecture. We give a more direct cohomological interpretation of the conjecture in terms of "typical" covering maps, and use graph Galois theory to "symmetrize" the conjecture. The conjecture is then related to certain kernel of a morphism of sheaves, and is implied provided these kernels are co-acyclic in the covering cohomology theory. This allows us to prove a slightly generalized Strengthened Hanna Neumann Conjecture; this conjecture is false if generalized to all sheaves. The kernels we use do not exist in the theory of graphs, so our use of sheaf theory seems essential to this approach. | Group Theory (math.GR) | This paper was been withdrawn by the author due to a crucial error in thinking that it is immediate that the vanishing of rho kernels of a direct sum of sheaves is equivalent to the individual vanishing. A corrected version of the proof is available as "[REDACTED-NAME] [REDACTED-NAME] Conjecture I", which gives a proof without sheaf theory (really translating the sheaf theory to combinatorics). A sequel to this paper, "[REDACTED-NAME] [REDACTED-NAME] Conjecture II" is in preparation; this will develop sheaf theory and give a simple proof of the conjecture (simple assuming the sheaf theory is in place). | factual/methodological/other critical errors in manuscript | 434 |
0905.3862v2 | Infinite families of regular expanders of arbitrary constant degree obtained via the modified zig-zag product | We generalize the zig-zag product construction to produce infinite families of regular graphs of any constant degree. We analyze the second largest eigenvalue of this new zig-zag product to show that the modified zig-zag product of good expanders is again a good expander (yet not Ramanujan). | Combinatorics (math.CO) | Paper withdrawn due to error in main theorem | factual/methodological/other critical errors in manuscript | 435 |
0905.4317v2 | A chord-arc covering theorem in Hilbert space | We prove that there exists $M>0$ such that for any closed rectifiable curve $\Gamma$ in Hilbert space, almost every point in $\Gamma$ is contained in a countable union of $M$ chord-arc curves whose total length is no more than $M$ times the length of $\Gamma$. | Metric Geometry (math.MG) | Withdrawn due to an error | factual/methodological/other critical errors in manuscript | 438 |
0905.4682v3 | On the order of vanishing of the cyclotomic p-adic L-function | For a newform for Gamma_0(N) of even weight k, we prove that its attached p-adic L-function is not identically zero on the group Z_p of the p-adic units. If p >3, we prove that the order of vanishing at any p-adic integer is finite. | Number Theory (math.NT) | This paper has been withdrawn by the author due to a mistake concerning the non-vanishing mod p | factual/methodological/other critical errors in manuscript | 439 |
0906.0593v3 | On the modified Basis Pursuit reconstruction for Compressed Sensing with partially known support | The goal of this short note is to present a refined analysis of the modified Basis Pursuit ($\ell_1$-minimization) approach to signal recovery in Compressed Sensing with partially known support, as introduced by Vaswani and Lu. The problem is to recover a signal $x \in \mathbb R^p$ using an observation vector $y=Ax$, where $A \in \mathbb R^{n\times p}$ and in the highly underdetermined setting $n\ll p$. Based on an initial and possibly erroneous guess $T$ of the signal's support ${\rm supp}(x)$, the Modified Basis Pursuit method of Vaswani and Lu consists of minimizing the $\ell_1$ norm of the estimate over the indices indexed by $T^c$ only. We prove exact recovery essentially under a Restricted Isometry Property assumption of order 2 times the cardinal of $T^c \cap {\rm supp}(x)$, i.e. the number of missed components. | Statistics Theory (math.ST) | Withdrawn due to an error in the proof. A new version will be submitted as a section in a future paper | factual/methodological/other critical errors in manuscript | 442 |
0906.1303v2 | A note on Stanley's conjecture for monomial ideals | We prove that the Stanley's conjecture holds for monomial ideals $I\subset K[x_1,...,x_n]$ generated by at most $2n-1$ monomials, i.e. $sdepth(I)\geq depth(I)$. | Commutative Algebra (math.AC) | This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 1.5 | factual/methodological/other critical errors in manuscript | 443 |
0906.1481v3 | Amalgamated free products of topological groups being Hausdorff -- a new approach | The paper deals with the problem posed by Katz and Morris whether the free product with amalgamation of any Hausdorff topological groups is Hausdorff, the negative solution of which (even for the particular case of a closed amalgamated subgroup) easily follows from the relevant result by Uspenskij. The topology of such a product is characterized by proving that it coincides with the so-called $X_0$-topology in the sense of Mal'tsev for the corresponding pushout $X$ in the category of Hausdorff topological spaces. Applying this characterization, it is proved that the canonical mappings of Hausdorff groups into their amalgamated free product are open homeomorphic embeddings if an amalgamated subgroup is open. This immediately implies that in that case this product is Hausdorff. | General Topology (math.GN) | The proof of the main result of the paper uses the other mathematician's theorem (published in Dokl. Akad. Nauk SSSR) which turns out to be false | factual/methodological/other critical errors in manuscript | 444 |
0906.1631v2 | Detection of Large-Scale Cosmic Magnetic Fields | Observational evidence for the existence of cosmic magnetic fields in intergalactic space coherent over Mpc scales is presented. Using an unprecedentedly large sample of Faraday rotation measures of radio sources from the NRAO VLA Sky Survey data and the photometric redshift galaxy catalog from the sixth Data Release of the Sloan Digital Sky Survey (SDSS), we measure the cross-correlations between the rotation measures and the galaxy density field distributed along the source sightlines. It is shown that the rotation measures for sightlines passing through high density regions at separation r >= 1 Mpc/h from the locations of background radio sources are significantly enhanced. We discuss possible generators of this enhancement and interpret it to be intergalactic magnetic fields coherent over 1 Mpc/h with mean field strength B~30 nG. | Cosmology and Nongalactic Astrophysics (astro-ph.CO) | This paper has been withdrawn by the author because the measured cross-correlation signals have been found to be spurious after thorough reanalysis. The rotation measures have been now found to be correlated not only with the galaxy density along the source sightlines but also with the errors, which demonstrated that the measured cross-correlations do not indicate the existence of the cosmic magnetic field. Thus, we withdraw the paper | factual/methodological/other critical errors in manuscript | 445 |
0906.2965v8 | Gauge Theory of the full Lorentz Group on flat Spacetime | We compute gauge theories of the Lorentz group. We discuss non-interacting, and interacting fermionic systems. The interacting system combines a local with a global Lorentz group, i.e, discusses a $SO(3,1)_{l}\times SO(3,1)_{g}$-theory. We compute the equations of motion and conservation laws for the fermionic matter current. The core of our work is the prediction of some new form of monopoles we call 'Dirac-Clifford-'t Hooft-Polyakov'-monopole. It resides in a state similar to color-flavor locking. Dirac-Clifford-'t Hooft-Polyakov-monopoles are invariant under global Lorentz transformations and are predicted to form vortices. The theory is renormalizable, since all Goldstone-Nambu modes are converted into massive vector gauge fields. | High Energy Physics - Theory (hep-th) | This paper has been withdrawn due to crucial errors | factual/methodological/other critical errors in manuscript | 453 |
0906.3533v19 | On the Distribution of Carmichael numbers | Erdős conjectured in 1956 that there are $x^{1-o(1)}$ Carmichael numbers up to $x$. Pomerance made this conjecture more precise and proposed that there are $x^{1-{\frac{\{1+o(1)\}\log\log\log x}{\log\log x}}}$ Carmichael numbers up to $x$. At the time, his data tables up to $25 \cdot 10^{9}$ appeared to support his conjecture. However, Pinch extended this data and showed that up to $10^{21}$, Pomerance's conjecture did not appear well-supported. Thus, the purpose of this paper is two-fold. First, we build upon the work of Pomerance and others to present an alternate conjecture regarding the distribution of Carmichael numbers that fits proven bounds and is better supported by Pinch's new data. Second, we provide another conjecture concerning the distribution of Carmichael numbers that significantly sharpens Pomerance's heuristic arguments. We also extend and update counts pertaining to pseudoprimes and Carmichael numbers, and discuss the distribution of One-Parameter Quadratic-Base Test pseudoprimes. | Number Theory (math.NT) | This paper has been withdrawn by the author because in [15] the authors show that if one assumes the widely believed Elliott-Halberstam conjecture then for any constant a<1 there exists C>0 such that there are more than x^a Carmichael numbers up to x, once x>C. Conjecture 1.0.2 and Corollary 1.0.3 contradict this conjecture (as well as the less well justified (1.0.7)). There is little mathematical basis for the Conjecture 1.0.2 but there is little here, except that it fits data in the limited range in which there is data; there are many functions one could construct that would do this. Corollary 1.0.3 is extremely unlikely to be true, if only for the reason that it postulates an asymptotic formula for C(x), the number of Carmichael numbers up to x, while no other conjecture makes such a strong statement(these conjectures all have a (1+o(1)) somewhere in an exponent, meaning that they assert asymptotic formulas for log(x/C(x)) rather than for C(x) itself). Also, in the second conjecture, Conjecture 1.0.4, the secondary terms proven by the author are washed out by the (1+o(1)) factor anyway. However, the tables and related data can be of some use to researchers | factual/methodological/other critical errors in manuscript | 455 |
0906.4604v19 | On Riemann and Generalized Riemann Hypotheses | The research on zeros of special functions is a very active and important topics in mathematics, and the most famous problem of this field is the Riemann hypothesis. In this work we present a possible proof to the Riemann hypothesis and the generalized Riemann hypothesis by reducing them to certain Gamma functions that have no zeros in the critical strip. At the heart of this proof is essentially a Tauberian type argument and a crucial estimate depends on the asymptotic behaviors of the Riemann $\Xi(s)$ and character $\Xi\left(s;\chi,a\right)$ function of a non-principal primitive character in a horizontal strip, and the fact that partial sums of $\frac{1}{\zeta(s)}$ and $\frac{1}{L\left(s,\chi\right)}$ are norm-bounded almost periodic functions to the right of the critical line. | General Mathematics (math.GM) | due to some errors in the estimates | factual/methodological/other critical errors in manuscript | 462 |
0906.5247v4 | Measured Quantum Groupoids Associated with Matched Pairs of Locally Compact Groupoids | Generalizing the notion of matched pair of groups, we define and study matched pairs of locally compact groupoids endowed with Haar systems, in order to give new examples of measured quantum groupoids. This article has been withdrawn due to some gap in a lemma although the principal result is surely true and the demonstration will be specified in a former paper. | Operator Algebras (math.OA) | A gap in demonstration of Lemma 4.3.5 which may be false, although theorem 4.3.7 is surely correct but its demonstration must be specified | factual/methodological/other critical errors in manuscript | 464 |
0906.5331v2 | A one dimensional model showing a quantum phase transition based on a singular potential | We study a one-dimensional singular potential plus three types of regular interactions: constant electric field, harmonic oscillator and infinite square well. We use the Lippman-Schwinger Green function technique in order to search for the bound state energies. In the electric field case the unique bound state coincides with that found in an earlier study as the field is switched off. For non-zero field the ground state is shifted and positive energy "quasibound states" appear. For the harmonic oscillator we find a quantum phase transition of a novel type. This behavior does not occur in the corresponding case of an infinite square well and demonstrates the influence of quantum non-locality. | Quantum Physics (quant-ph) | We have realized that one of the main conclusions of the paper is wrong: Due to an erroneous calculation, we have concluded that some states in the harmonic oscillator with a point interaction evaporate, which is simple impossible due to the structure of the potential. As this manuscript contains major errors, we consider convenient its withdrawal | factual/methodological/other critical errors in manuscript | 466 |
0906.5472v4 | Gromov-Witten Invariants of Stabilizations of Symplectic 4-Manifolds | We relate the Gromov-Witten invariants of $X\times S^2$ to the Seiberg-Witten invariants of $X$ where $X$ is a simply-connected symplectic 4-manifold. We also give examples that expose the similarity between the classification of smooth 4-manifolds and some classification problems regarding symplectic 6-manifolds. | Symplectic Geometry (math.SG) | This paper has been withdrawn by the author due to an error in the proof of main theorem part 2. | factual/methodological/other critical errors in manuscript | 467 |
0906.5563v3 | The integral property of the spheroidal wave functions | The perturbation method in supersymmetric quantum mechanics (SUSYQM) is used to study whether the spheroidal equations have the shape-invariance property. Expanding the super-potential term by term in the parameter alpha and solving it, we find that the superpotential loses its shape-invariance property upon to the second term. This first means that we could not solve the spheroidal problems by the SUSQM; further it is not unreasonable to say they are non-solvable in some sense. | Quantum Physics (quant-ph) | This paper has been withdrawn by the authors. In later study, we found the conclusion is wrong in some way | factual/methodological/other critical errors in manuscript | 469 |
0907.0953v3 | On some moduli spaces of bundles on K3 surfaces, II | We give many examples in which there exist infinitely many divisorial conditions on the moduli space of polarized K3 surfaces $(S,H)$ of degree $H^2=2g-2$, $g \geq 3$, and Picard number $rk N(S)=\rho(S)=2$ such that for a general K3 surface $S$ satisfying these conditions the moduli space of sheaves $M_S(r,H,s)$ is birationally equivalent to the Hilbert scheme $S[g-rs]$ of zero-dimensional subschemes of $S$ of lenght equal to $g-rs$. This result generalizes the main result of \cite{Nik1} when $g=rs+1$ and of \cite{Monat} when $r=s=2$, $g \geq 5$. | Algebraic Geometry (math.AG) | I withdraw my paper from arXiv because there is an error in the proof of the main result of
the paper.
I am very sorry for this. I hope to submit a corrected version soon. | factual/methodological/other critical errors in manuscript | 472 |
0907.1250v2 | An existence result for the infinity laplacian with non-homogeneous Neumann boundary conditions using Tug-of-War games | In this paper we show how to use a Tug-of-War game to obtain existence of a viscosity solution to the infinity laplacian with non-homogeneous mixed boundary conditions. For a Lipschitz and positive function $g$ there exists a viscosity solution of the mixed boundary value problem, $$ \{\begin{array}{ll} \displaystyle -\Delta_{\infty}u(x)=0\quad & \text{in} \Omega, \displaystyle \frac{\partial u}{\partial n}(x)= g (x)\quad & \text{on} \Gamma_N, \displaystyle u(x)= 0 \quad & \text{on} \Gamma_D. \end{array}. $$ | Analysis of PDEs (math.AP) | This paper has been withdrawn due to some errors in some of the proofs | factual/methodological/other critical errors in manuscript | 476 |
0907.1413v2 | Privacy constraints in regularized convex optimization | This paper is withdrawn due to some errors, which are corrected in arXiv:0912.0071v4 [cs.LG]. | Cryptography and Security (cs.CR) | This paper has been withdrawn by the authors due to some errors. Corrections have been included in arXiv:0912.0071v4 | factual/methodological/other critical errors in manuscript | 477 |
0907.1997v2 | Statistical estimation requires unbounded memory | We investigate the existence of bounded-memory consistent estimators of various statistical functionals. This question is resolved in the negative in a rather strong sense. We propose various bounded-memory approximations, using techniques from automata theory and stochastic processes. Some questions of potential interest are raised for future work. | Computation (stat.CO) | this is an old version, with a mistake in the proof of Thm. 6.1. Please see my homepage for an updated version | factual/methodological/other critical errors in manuscript | 481 |
0907.2544v2 | Higgs mechanism SU(24)#SU(24)->U(1)EM | The suggested model permits to construct gauge-invariant expressions bringing to the masses of all the fermions, included the neutrinos. The model realizes Higgs mechanism. It is based on the presence of non-trivial ground states of a scalar field. An arbitrary fixed ground state generates the masses of all the particles. The selected symmetry is based on the fact that the sum of the electric charges of all the well-known fermions (taking into account the partition of the quarks by colors) is equal to 0. As a result of the Higgs mechanism massive vector bosons appear. They bring the charges: 0,\pm 1/3,\pm 2/3,\pm 1. It may be, the model will be of interest from the point of view of the unification of all the vector interactions. | General Physics (physics.gen-ph) | 7 pages This article has been withdrawn by the author because after the spontaneous breaking of symmetry the terms of interaction of fermions with gauge vector bosons do not correspond to the SM | factual/methodological/other critical errors in manuscript | 486 |
0907.3063v3 | Nih-3T3 Fibroblast Studied by Fourier Transform Infrared Spectroscopy | This paper has been withdrawn by the author due to a crucial sign error in some equations | Biological Physics (physics.bio-ph) | This paper has been withdrawn by the author, due a crucial sign error in Table 4. 31 pages, 20 figures | factual/methodological/other critical errors in manuscript | 487 |
0907.3211v4 | Equivariant cohomology and resolution | The `Folk Theorem' that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a `resolution tower' which projects to a resolution, with iterated boundary fibration, of the quotient. Equivariant K-theory and the Cartan model for equivariant cohomology are tracked under the resolution procedure as is the delocalized equivariant cohomology of Baum, Brylinski and MacPherson. This leads to resolved models for each of these cohomology theories, in terms of relative objects over the resolution tower and hence to reduced models as flat-twisted relative objects over the resolution of the quotient. As a result an explicit equivariant Chern character is constructed, essentially as in the non-equivariant case, over the resolution of the quotient. | Differential Geometry (math.DG) | Mistake found, under revision | factual/methodological/other critical errors in manuscript | 488 |
0907.4754v2 | Transonicity in black hole accretion -- A mathematical study using the generalized Sturm chains | By applying the theory of algebraic polynomials and the theory of dynamical systems, we construct the generalized Sturm sequences/chains to investigate the transonic properties of hydrodynamic accretion onto non-rotating astrophysical black holes, to demonstrate, completely analytically, how many critical point such an accretion flow can have. Our work is significantly important, because for the first time in the literature, we provide a purely analytical method, by applying certain powerful theorem of algebraic polynomials in pure mathematics, to check whether certain astrophysical hydrodynamic accretion may undergo more than one sonic transitions. Our work can be generalized to analytically calculate the maximal number of equilibrium points certain autonomous dynamical systems can have in general (Abridged). | High Energy Astrophysical Phenomena (astro-ph.HE) | This paper has been withdrawn by the authors due to a major algebraic error recently identified in one of the main equations used to evaluate the communicated result | factual/methodological/other critical errors in manuscript | 497 |
0908.0147v2 | An independent link model of simple fluids; random close packing limit | A new approach to modelling the behaviour of simple fluids is presented. Starting from the usual expression of the partition function of N molecules, a Fourier transformation is performed. It is argued that the N(N-1)/2 dynamical variables kpq in the reciprocal space featuring the link between 2 molecules p and q can reasonably be considered independent in the thermodynamical limit. Treated as a set of effective independent particles, their statistical behaviour is analogous to a Bose-Einstein gas. Expressions of the partition function, of the radial pair correlation function and of the pressure are derived, and a special attention is given to the mathematical inter-consistency of those quantities. The results, which are independent of the exact shape of the intermolecular potential, are applied to the simple case of hard sphere fluids. An analytical expression of the radial pair correlation function is derived as well as of the equation of state. The model predicts a qualitatively satisfactory behaviour for g(R), and it provides numerically correct values for the equation of state at low and medium densities, although at higher densities the contact value of g(R)is underestimated. Quite interestingly it predicts for the maximum random close packing density the correct value 0.637 . | Fluid Dynamics (physics.flu-dyn) | 35 pages, 5 figures The paper has been withdrawn by the author since the model does not account for the radial pair distribution function at high density | factual/methodological/other critical errors in manuscript | 501 |
0908.0498v3 | On the homotopy exact sequence for Nori's fundamental group | Unlike Grothendieck's étale fundamental group, Nori's fundamental group does not fulfill the homotopy exact sequence in general. We give necessary and sufficient conditions which force exactness of the sequence. | Algebraic Geometry (math.AG) | [REDACTED-NAME] found a gap in the proof of Proposition 3.4. We withdraw the article, at least for the time being | factual/methodological/other critical errors in manuscript | 502 |
0908.1140v2 | Frequency dependent negative capacitance of (Ba0.6Sr0.4)(ZrxTi1-x)O3 thin films grown on La0.9Sr1.1NiO4 buffered SrTiO3 substrate | Ba0.6Sr0.4TiO3 and (Ba0.6Sr0.4)(Zr0.3Ti0.7)O3 thin films were deposited on La0.9Sr1.1NiO4 buffered SrTiO3 substrates. (Ba0.6Sr0.4)(Zr0.3Ti0.7)O3 film (2.77 nF) showed one order large capacitance compared to that of Ba0.6Sr0.4TiO3 film (270 pF) at 100 kHz. (Ba0.6Sr0.4)(Zr0.3Ti0.7)O3 film showed negative capacitance at f >3 MHz except for f=5.05 to 7.36 MHz, and 10.4 to 13.4 MHz, where it showed positive capacitance. Tunability of the Ba0.6Sr0.4TiO3 film (~15%) is much lower than that of the (Ba0.6Sr0.4)(Zr0.3Ti0.7)O3 film (30 to 65%, both normal and inverse). A significant change of the tunability was observed at frequencies f>500 kHz for the (Ba0.6Sr0.4)(Zr0.3Ti0.7)O3 film showing inverse tunability, this can be attributed to the negative capacitance effect, where current lags behind the voltage. (Ba0.6Sr0.4)(Zr0.3Ti0.7)O3 film (6.87x10-6 A/cm2) showing one order high leakage current density than BST film (1.32x10-7 A/cm2). Ba0.6Sr0.4TiO3 film showed large grain size (140 nm) and surface roughness (11.5 nm) and (Ba0.6Sr0.4)(Zr0.3Ti0.7)O3 film showed small grain size (80 nm) and roughness (2.3 nm). | Materials Science (cond-mat.mtrl-sci) | This paper has been withdrawn by the author due to some misinterpretation of the results. | factual/methodological/other critical errors in manuscript | 509 |
0908.1259v4 | Minimal Lie group homomorphisms | Let $G_1$ and $G_2$ be Lie groups furnished with bi-invariant metrics and $f:G_1\rightarrow G_2$ be a Lie group homomorphism which is also a minimal isometric immersion. If $G_1$ is compact and connected, we prove that either $G_1$ is isometric to a flat torus or $f$ is unstable as a harmonic map. We also apply this result to the case in which $f$ is the inclusion of a compact, connected Lie subgroup of a Lie group, as well as to construct several examples of unstable harmonic maps into the orthogonal group. | Differential Geometry (math.DG) | This paper has been withdraw due to a crucial sign error in the proof of the theorem | factual/methodological/other critical errors in manuscript | 511 |
0908.1939v3 | A Characterization Theorem for the Distribution of a Continuous Local Martingale and Related Limit Theorems | The main result of the article reads: the distribution of a continuous starting from zero local martingale whose quadratic characteristic is almost surely absolutely continuous with respect to some non-random increasing continuous function is determined by the distribution of the quadratic characteristic. Functional limit theorem based on this characterization are proved. | Probability (math.PR) | This paper has been withdrawn by the author, because the characterization theorem is incorrect (though the author results sustain with minor changes) | factual/methodological/other critical errors in manuscript | 515 |
0908.3033v2 | Intrinsic instability at the Bose-Einstein condensation of bosonic quasiparticles in magnetic insulators | Starting from a phenomenological standard energy functional to describe the condensation of a dilute gas of bosonic quasiparticles in magnetic insulators, we find that the inclusion of a perturbation term that explicitly violates the axial symmetry significantly modifies the details of the resulting Bose Einstein condensation. Systems with an originally axial symmetry must show an intrinsic tendency to spontaneously violate this symmetry as soon as the condensation sets in, and the phase transition at the respective critical field may even become of first order. We can explain a number of features in the experimental data of various insulating spin systems, such as a slightly nonlinear magnetization near the critical field as well as hysteresis effects and peculiarities in the energy-level scheme of TlCuCl3. We also offer a consistent explanation for certain anomalies in the magnetocaloric effect and in the magnetization of BaCuSi2O6 by assuming a spontaneous violation of axial symmetry at the magnetic phase transition on an energy scale of about 1 micro-eV. The resulting anisotropy gap in the magnetic excitation spectrum, that inevitably forms at the critical field of all such systems, lifts the linear Goldstone mode and is therefore seriously limiting the lifetime of magnetic condensates to a few nanoseconds at most. | Strongly Correlated Electrons (cond-mat.str-el) | This paper has been withdrawn in present form because ch. 4.1 contains an invalid interpretation of M(H) below Hc, and because the "rounding" in M(H) discussed in 4.3. must be taken with more caution when comparing it to experimental data in ch. 5. Other valid explanations for such a rounding do exist. However, the rest of the manuscript and the main conclusions are still valid and can be cited | factual/methodological/other critical errors in manuscript | 519 |
0908.3267v11 | Representations of Hermitian Commutative *-Algebras by Unbounded Operators | We give a spectral theorem for unital representations of Hermitian commutative unital *-algebras by possibly unbounded operators in a pre-Hilbert space. A more general result is known for the case in which the *-algebra is countably generated. | Operator Algebras (math.OA) | Section 3.1 should not say that $1$ is never in the spectrum of a Cayley transform | factual/methodological/other critical errors in manuscript | 521 |
0908.4394v3 | A Dual CFT for Schwarzschild Black Hole | This paper has been withdrawn by the author due to an error in the computation of the central charge. | High Energy Physics - Theory (hep-th) | This paper has been withdrawn by the author due to an error in the computation of the central charge | factual/methodological/other critical errors in manuscript | 528 |
0909.0137v2 | Theoretical Derivation of $Σ$-$D$ Relation of Galactic SNRs | We derive the $\Sigma$-$D$ relation of Galactic supernova remnants of shell-type separately at adiabatic-phase and at radiative-phase through two sets of different formulas, considering the different physical processes of shell-type remnants at both stages. Also statistics on Galactic shell-type remnants about 57 was made. Then we do some comparison with other results obtained before. It shows that all the best fit lines in the $\Sigma$-$D$ relation plots newly are to some extent flatter than those derived by some authors at early time. Our theoretical and statistical outcomes are in somewhat good consistency. | High Energy Astrophysical Phenomena (astro-ph.HE) | This paper has been withdrawn by the author due to the crucial sign errors in Eqs.(12),(26) | factual/methodological/other critical errors in manuscript | 533 |
0909.0570v3 | On induced locally analytic representations of locally analytic groups | Let G be a locally analytic group and H < G - a locally analytic subgroup. The main result is the condition (similar to Frommer-Orlik-Strauch theorem) for induction of locally analytic H-representation to G to be irreducible. Also this paper contains a (new) series of locally analytic representations which do not arise in this way. | Representation Theory (math.RT) | This paper has been withdrawn by the author due a crucial error which cannot be repaired immediately | factual/methodological/other critical errors in manuscript | 536 |
0909.1823v2 | Weak Approximations for Wiener functionals | In this paper we introduce a simple space-filtration discretization scheme on Wiener space which allows us to study weak decompositions of a large class of Wiener functionals. We show that any Wiener functional has an underlying robust semimartingale skeleton which under mild conditions converges to it. The approximation is given in terms of discrete-jumping filtrations which allow us to approximate irregular processes by means of a stochastic derivative operator on Wiener space introduced in this work. As a by-product, we prove that continuous paths and a suitable notion of energy are sufficient in order to get a unique orthogonal decomposition similar to weak Dirichlet processes. In this direction, we generalize the main results given in Graversen and Rao and Coquet et al in the particular Brownian filtration case. The second part of this paper is devoted to the application of these abstract results to concrete irregular processes. We show that our embedded semimartingale structure allows a very explicit and sharp approximation scheme for densities of square-integrable Brownian martingales in full generality. In the last part, we provide new approximations for integrals w.r.t the Brownian local-time. | Probability (math.PR) | This paper has been withdrawn due to mistakes in Prop. 4.1 and Lemma 2.3 | factual/methodological/other critical errors in manuscript | 539 |
0909.3090v2 | On The Origin of Neutrino Mass and Mixing in the Standard Model | One can describe cosmological relic neutrinos by adding Lagrange multipliers to the Standard Model Lagrangian for them. The two possible Lagrange multipliers are a chemical potential, which fixes the mean neutrino/anti-neutrino asymmetry, and a Majorana mass, which fixes the mean spin-entropy. Because these neutrinos originated from a thermal bath, their entropy should be maximal, implying that each state in the background is a symmetric superposition of a neutrino and anti-neutrino. Therefore the Standard Model must be augmented by a flavor-diagonal Majorana neutrino mass matrix. This impacts the propagator via tadpole diagrams due to self-interactions. In the low-energy limit, neutrino self-interactions are entirely off-diagonal because same-flavor four-fermion operators vanish by Pauli exclusion. These interactions must be diagonalized when propagating through a bath of neutrinos, using the U(3) global flavor symmetry. U(3) gets broken broken down to SO(3) by Majorana masses, and down to $A_4$ if the three masses are different. Thus our universe today contains tri-bimaximal mixing and Majorana neutrinos. Neutrino mixing is due to the mismatch between the flavor-diagonal Majorana mass matrix arising at finite density and the self-interaction diagonal finite density propagator. The mass hierarchy is inverted and Majorana phases are absent. Lepton number is conserved and the neutrino-less double beta decay experiment absorbs a pair of neutrinos from the relic background and will prove their Majorana nature. | High Energy Physics - Phenomenology (hep-ph) | Withdrawn because of an error in Eq.13 (prediction of neutrino mixings) | factual/methodological/other critical errors in manuscript | 545 |
0909.3466v3 | Résolution du "partition problem" par une approche arithmétique | This article has been withdrawn | Computational Complexity (cs.CC) | This paper has been withdrawn by the author due to a crucial error (in one of the quadratic forms introduced) | factual/methodological/other critical errors in manuscript | 546 |
0909.3549v3 | A smooth codimension-one foliation of the five-sphere by symplectic leaves | We construct a smooth codimension-one foliation on the five-sphere in which every leaf is a symplectic four-manifold and such that the symplectic structure varies smoothly. Our construction implies the existence of a complete regular Poisson structure on the five-sphere. | Symplectic Geometry (math.SG) | We have withdrawn our paper due to a mistake in the main reference paper and errors in our construction. More over our result has been superseded by Y. Mitsumatsu (arXiv:1101.2319 [REDACTED-NAME] Structures on Lawson's Foliation) | factual/methodological/other critical errors in manuscript | 547 |
0909.4980v5 | On a characterization of dual Banach spaces through determinant subspaces of norm-attaining linear forms | Necessary and sufficient conditions for Banach space to be(isometrically isomorphic to) a dual space will be given. | Functional Analysis (math.FA) | This paper has been withdrawn by the author for some diffused error | factual/methodological/other critical errors in manuscript | 551 |
0909.5521v3 | Clique and Vertex Cover are solvable in polynomial time if the input structure is ordered and contains a successor predicate | In this manuscript, assuming that Graedel's 1991 results are correct (which implies that bounds on the solution values for optimization problems can be expressed in existential second order logic where the first order part is universal Horn), I will show that Clique and Vertex Cover can be solved in polynomial time if the input structure is ordered and contains a successor predicate. In the last section, we will argue about the validity of Graedel's 1991 results. Update: Manuscript withdrawn, because results are incorrect. If phi = phi_1 AND phi_2, and phi is a Horn formula, it does NOT mean that both phi_1 and phi_2 are Horn formulae. Furthermore, the cardinality constraint CANNOT be expressed as a universal Horn sentence in ESO (NOT even when the structure is ordered). | Computational Complexity (cs.CC) | Manuscript withdrawn, because results are incorrect. If phi = phi_1 AND phi_2, and phi is a Horn formula, it does NOT mean that both phi_1 and phi_2 are Horn formulae. Furthermore, the cardinality constraint CANNOT be expressed as a universal Horn sentence in ESO (NOT even when the structure is ordered) | factual/methodological/other critical errors in manuscript | 553 |
0910.1370v2 | Hamiltonian displacement of bidisks inside cylinders | We estimate the Hamiltonian displacement energy of a bidisk inside a cylinder. | Symplectic Geometry (math.SG) | The paper has a flaw in the construction. The correct theorem about displacing bidisks can be found in the paper of Fukaya, Oh, Ohta and Ono, `Displacement of polydisks and [REDACTED-NAME] theory', J. [REDACTED-NAME]., 11(2013), 231-268 | factual/methodological/other critical errors in manuscript | 561 |
0910.2648v2 | Reflectance of a quantum mirror | The problem of the reflectance of a photon by a metallic mirror whose position is treated quantum mechanically is considered. The interaction between the metallic surface and the light is treated classically. It is shown that the reflectance depends on the spread of the wavefunction describing the reflecting surface along its normal. Considering this decrease on the mirror reflectance, it is shown by first principles that it is impossible to achieve a highly entangled state between a photon and a mirror when the photon can be reflected only once. | Quantum Physics (quant-ph) | This paper has been withdrawn by the author due to an error on the treatment that invalidates the conclusions of the paper. | factual/methodological/other critical errors in manuscript | 566 |
0910.3478v2 | On the prolongation structures of Petrov type III vacuum spacetime equations | The universal covering symmetry algebra of the Robinson-Trautman equations of Petrov Type III is shown to include the infinite-dimensional affine Kac-Moody algebra A_1 as a prolongation algebra. This algebra has slower growth than the contragradient algebra K_2 obtained previously for this equation. | Mathematical Physics (math-ph) | Problems with the classification of the infinite-dimensional algebra | factual/methodological/other critical errors in manuscript | 568 |
0910.3866v2 | The Nonlocal Involutive Charges of the CFT ${\cal M}_{3,4}$ | We consider continuum minimal ${\cal M}_{3,4} $ with central charge $c=1/2$. The eigenvalues of the known local involutive charges are known to be related to spectral zeta functions of suitable one dimensional shroedinger hamiltonians. We investigate this connection. We Propose analytic formulae for the eigenvalues of Nonlocal Involutive Charges. We also propose an exact formula for the eigenvalues of the $\Psi$ function of BLZ at central charge $c=1/2$ which reduces to the local non local and dual non local involutive charges for special values on the imaginary axis. | Mathematical Physics (math-ph) | This paper has been withdrawn by the author. Contains false statements. The formulas for the nonlocal IOM is neither proved nor disproved | factual/methodological/other critical errors in manuscript | 570 |
0910.4101v2 | Eigenvalue estimates for the higher order buckling problem | In this paper, we consider lower order eigenvalues of Laplacian operator with any order in Euclidean domains. By choosing special rectangular coordinates, we obtain two estimates for lower order eigenvalues. | Differential Geometry (math.DG) | This article has an error | factual/methodological/other critical errors in manuscript | 571 |
0910.4274v2 | Driven 3D Ising Interface: its fluctuation, Devil's staircase, and effect of interface geometry | Enchanting ripple pattern exist on interface, and manifest them self in it's fluctuation profile as well. These ripples apparently flow as the interface struck with inhomogeneous externally driven field interface, moves fluctuating about it on a rectangular 3D Ising system. Ripple structure and flow have temporal periodicity, eventually with some modulation, and have signature of geometry of field interface. Dramatic transitions occur in fluctuation profile as a function of dynamics and geometry of the force field interface and is divided into two spatial regions : rippled and smooth. For the velocity we are concerned with, the interface is pinned with field interface, and for arbitrary orientations of the field profile local slope of the rippled part of the interface gets locked in to a combination of few rational values (Devil's staircase) which most closely approximate the profile, thereby generating specular pattern of patches. | Statistical Mechanics (cond-mat.stat-mech) | This article has been withdrawn because of critical errors in the manuscript | factual/methodological/other critical errors in manuscript | 572 |
0910.5047v2 | Khovanov homology of alternating links and SU(2) representations of the link group | We prove that the Khovanov homology of alternating knots and 2-component links is equal (as a singly graded group) to the singular homology of a certain space of trace- free, binary dihedral representations of the link group. More generally, it was suggested by Kronheimer and Mrowka that the Khovanov homology of any knot might be related via gauge theory to the space of all trace-free SU(2) representations. Our result suggests that when the knot is alternating, Khovanov homology only sees the trace-free representations which are binary dihedral. The proof we give is completely elementary, using the skein exact sequence, so it does not explain why Khovanov homology should have this topological significance. In addition, we prove a conjecture of Shumakovitch that the Khovanov homology of alternating knots and 2-component links contains no n-torsion for n > 2. We also point out a relationship between the grading in Khovanov homology and the Casson-Walker invariant of the branched double cover. | General Topology (math.GN) | This paper has been withdrawn by the author due to a crucial algebraic error in the proof of the main theorem over \Z. The result is still true, however, by more recent work of Shumakovitch. A fixed and substantially different paper will be uploaded as soon as possible | factual/methodological/other critical errors in manuscript | 580 |
0910.5283v2 | Resonance free regions for nontrapping manifolds with cusps | This paper has been withdrawn because of a mistake in Lemma 7.4. For a corrected version of the main theorem, as well as various further developments and applications, see arXiv:1210.7736 . For nonpositively curved perturbations of parabolic cylinders we establish the existence of a logarithmically large resonance free region. We use an escape function construction in a compact part of the manifold and near infinity we use the method of complex scaling. To the author's knowledge this is the first proof of a large resonance free region for manifolds with cusps. | Analysis of PDEs (math.AP) | This paper has been withdrawn because of a mistake in Lemma 7.4. For a corrected version of the main theorem, as well as various further developments and applications, see arXiv:1210.7736 | factual/methodological/other critical errors in manuscript | 585 |
0910.5848v4 | Abelianization of p-groups with derived subgroup of prime order | In this paper, we arrive at the structure for $G^{ab}(= G/G')$ from a presentation for $G$. We also prove that the frattini subgroup of the abelianization is $G^p$ or the quotient of $G^p$ by the derived subgroup $G'$. | Group Theory (math.GR) | The 'conjecture' stated in this paper is false | factual/methodological/other critical errors in manuscript | 589 |
0911.1507v2 | MAC Layer Hurdles in BSNs | The last few decades have seen considerable research progress in microelectronics and integrated circuits, system-on-chip design, wireless communication, and sensor technology. This progress has enabled the seamless integration of autonomous wireless sensor nodes around a human body to create a Body Sensor Network (BSN). The development of a proactive and ambulatory BSN induces a number of enormous issues and challenges. This paper presents the technical hurdles during the design and implementation of a low-power Medium Access Control (MAC) protocol for in-body and on-body sensor networks. We analyze the performance of IEEE 802.15.4 protocol for the on-body sensor network. We also provide a comprehensive insight into the heterogeneous characteristics of the in-body sensor network. A low-power technique called Pattern-Based Wake-up Table is proposed to handle the normal traffic in a BSN. The proposed technique provides a reliable solution towards low-power communication in the in-body sensor network. | Networking and Internet Architecture (cs.NI) | This paper has been withdrawn by the author due to crucial problems with the results | factual/methodological/other critical errors in manuscript | 599 |
0911.1509v3 | On the Development of Low Power MAC Protocol for WBANs | Current advances in wireless communication, microelectronics, semiconductor technologies, and intelligent sensors have contributed to the development of unobtrusive WBANs. These networks provide long term health monitoring of patients without any constraint in their normal activities. Traditional MAC protocols do not accommodate the assorted WBAN traffic requirements in a power efficient manner. In this paper, we present a brief discussion on the development process of a low power MAC protocol for WBANs. We observe the behavior of a beacon-enabled IEEE 802.15.4 for on-body sensor networks. We further propose a low power technique called traffic based wakeup mechanism for a WBAN that exploits the traffic patterns of the BAN Nodes to ensure power efficient and reliable communication. | Networking and Internet Architecture (cs.NI) | This paper has been withdrawn by the author due to crucial problems with the results | factual/methodological/other critical errors in manuscript | 600 |
0911.1540v5 | Third potential evidence for the new area spectrum based on the Einstein-Kaufman pseudo tensor, a conjecture | This paper has been withdrawn by the authors. In our earlier paper "Corrections to the Bekenstein-Hawking entropy and the Hawking radiation spectrum", arXiv:0910.2755 , we provided two concrete numerical evidences for the new area spectrum based on the Einstein-Kaufman pseudo tensor as opposed to the Ashtekar variables: namely, the reproduction of the Bekenstein-Hawking entropy without fixing Immirzi parameter and the reproduction of the Hawking radiation spectrum. In this article, we provide another potential, albeit not concrete, numerical evidence for this new area spectrum; there was a constant in our earlier article, which was inversely proportional to the density of state, and which we could not fix a priori. Nevertheless, in our earlier article, we obtained this constant to be around 172$\sim$173 by fitting it to the Planck radiation spectrum. In this article, we propose a mathematical formula that reproduces this value. According to this formula, this constant is around 172.8. Nevertheless, we failed to concretely derive this mathematical formula. Therefore, it is a conjecture. | General Physics (physics.gen-ph) | This paper has been withdrawn by the authors. We couldn't find any supporting arguments for the conjecture. Moreover, a real third evidence for the new area spectrum was recently found | factual/methodological/other critical errors in manuscript | 601 |
0911.2487v3 | Mixing of Bose and Fermi Superfluids | Trapped ultra-cold atom experiments provide a unique opportunity to understand Bose-Fermi superfluid mixtures occurring in contrasting areas of physics. At present there are several atom-trap experiments that could potentially explore this superfluid-mixture regime, thus warranting a detailed understanding of the occurrence and stability of various possible thermodynamic phases in the mixture. In the present work, we therefore construct the finite temperature phase diagram of an interacting atomic mixture of Bose and Fermi superfluids. Our study reveals a unique region of phase space, where the BCS instability of the Fermi surface coincides with dynamical instability of the homogeneous mixture towards phase separation through a first-order transition. We illustrate how this intriguing interplay manifests in a trapped configuration, thereby providing important constraints for observing superfluidity in experiments. | Quantum Gases (cond-mat.quant-gas) | This paper has been withdrawn by the authors. Analysis leading to the Phase diagram has a crucial mistake. We are resubmitting the manuscript by making the required changes and also expanding the work considerably. We apologize for any inconvenience caused. The resubmitted manuscript is titled as "Finite-temperature study of Bose-Fermi superfluid mixtures" | factual/methodological/other critical errors in manuscript | 605 |
0911.2865v2 | Neural Networks for Dynamic Shortest Path Routing Problems - A Survey | This paper reviews the overview of the dynamic shortest path routing problem and the various neural networks to solve it. Different shortest path optimization problems can be solved by using various neural networks algorithms. The routing in packet switched multi-hop networks can be described as a classical combinatorial optimization problem i.e. a shortest path routing problem in graphs. The survey shows that the neural networks are the best candidates for the optimization of dynamic shortest path routing problems due to their fastness in computation comparing to other softcomputing and metaheuristics algorithms | Neural and Evolutionary Computing (cs.NE) | This article has been withdrawn by the authors. Misplaced equation 1 | factual/methodological/other critical errors in manuscript | 607 |
0911.3073v2 | The planar algebra of a fixed point subfactor | This paper has been withdrawn by the author due to several mistakes and unclarities. | Operator Algebras (math.OA) | This paper has been withdrawn by the author due to several mistakes and unclarities. | factual/methodological/other critical errors in manuscript | 609 |
0911.3669v2 | The Erdos-Ko-Rado theorem for perfect matchings | A $2k$-matching is a perfect matching of the complete graph on $2k$ vertices. Two $2k$-matchings are defined to be $t$-intersecting if they have at least $t$ edges in common. The main result in this paper is that if $k \geq 3t/2+1$, then the largest system of $t$-intersecting $2k$-matchings has size $(2(k-t)-1)!! = \prod_{i=0}^{k-t-1}(2k-2t-2i-1)$ and the only systems that meet this bound consist of all $2k$-matchings that contain a set of $t$ disjoint edges. Further, this bound on $k$ is sharp for $t\geq 6$. The method used is this paper is similar to the proof of the complete Erdős-Ko-Rado theorem given by Ahlswede and Khachatrian. | Combinatorics (math.CO) | This paper has been withdrawn by the author due to an error in Theorem 2.1, an important case was not considered in this theorem | factual/methodological/other critical errors in manuscript | 617 |
0911.4572v2 | Regeneration for interacting particle systems with interactions of infinite range | We consider an interacting particle system on $\Z^d$ with finite state space and interactions of infinite range in a high-noise regime. Assuming that the rate of change is continuous and that a Dobrushin-like condition holds, we show that the process is recurrent in the sense of Harris and construct explicit regeneration times for the process in restriction to finite cylinder sets. We show that the length of a regeneration period admits exponential moments. The proof that regeneration times are almost surely finite relies on a coupled construction of generalized house-of-cards chains. | Probability (math.PR) | This paper has been withdrawn by the author due to an error in proposition 2 | factual/methodological/other critical errors in manuscript | 621 |
0911.4971v3 | Radiatively enhanced elasticity and turbulence in clumpy tori of Active Galactic Nuclei | The paper assumes radiation forces proportional to distance between equal temperature clouds. However, we assume there are clouds in any direction. The forces then cancel almost entirely, besides small velocity effects. Therefore, the presented theory is inadequate. | Cosmology and Nongalactic Astrophysics (astro-ph.CO) | 10 pages, 5 figures, accepted by MNRAS, this paper has been withdrawn by the authors due to an essential flaw in the assumptions | factual/methodological/other critical errors in manuscript | 623 |
0911.5031v2 | An $O(n^2)$ Algorithm for Computing Longest Common Cyclic Subsequence | The {\em longest common subsequence (LCS)} problem is a classic and well-studied problem in computer science. LCS is a central problem in stringology and finds broad applications in text compression, error-detecting codes and biological sequence comparison. However, in numerous contexts, words represent cyclic sequences of symbols and LCS must be generalized to consider all circular shifts of the strings. This occurs especially in computational biology when genetic material is sequenced form circular DNA or RNA molecules. This initiates the problem of {\em longest common cyclic subsequence (LCCS)} which finds the longest subsequence between all circular shifts of two strings. In this paper, we give an $O(n^2)$ algorithm for solving LCCS problem where $n$ is the number of symbols in the strings. | Data Structures and Algorithms (cs.DS) | This paper has been withdrawn by the author due to a crucial error in the proofs | factual/methodological/other critical errors in manuscript | 624 |
0911.5086v3 | Convex hulls of hyperspheres and convex hulls of convex polytopes lying on parallel hyperplanes | The paper has been withdrawn | Computational Geometry (cs.CG) | The paper has been withdrawn due to an error in the proof of Proposition 6 | factual/methodological/other critical errors in manuscript | 625 |
0911.5459v3 | Shortest Two-way Linear Recurrences | Let $s$ be a finite sequence over a field of length $n$. It is well-known that if $s$ satisfies a linear recurrence of order $d$ with non-zero constant term, then the reverse of $s$ also satisfies a recurrence of order $d$ (with coefficients in reverse order). A recent article of A. Salagean proposed an algorithm to find such a shortest 'two-way' recurrence -- which may be longer than a linear recurrence for $s$ of shortest length $\LC_n$. We give a new and simpler algorithm to compute a shortest two-way linear recurrence. First we show that the pairs of polynomials we use to construct a minimal polynomial iteratively are always relatively prime; we also give the extended multipliers. Then we combine degree lower bounds with a straightforward rewrite of a published algorithm due to the author to obtain our simpler algorithm. The increase in shortest length is $\max\{n+1-2\LC_n,0\}$. | Information Theory (cs.IT) | This paper has been withdrawn by the author as the proof of Part (b) of Theorem 4.10(ii) is incorrect | factual/methodological/other critical errors in manuscript | 628 |
0912.0059v6 | On the semi-direct product structure of CAT(0) groups | In this paper, we investigate finitely generated groups of isometries of CAT(0) spaces containing some central hyperbolic isometry, and study CAT(0) groups. We show that every CAT(0) group $\Gamma$ has the semi-direct product structure $\Gamma=(\cdots(((\Gamma'\rtimes\langle\delta_{n}\rangle)\rtimes\langle\delta_{n-1}\rangle)\rtimes\langle\delta_{n-2}\rangle)\cdots)\rtimes\langle\delta_{1}\rangle$ where $\Gamma'$ is a CAT(0) group with finite center and $\delta_i\in \Gamma$ for $i=1,\dots,n$, and $\Gamma$ contains a finite-index subgroup $\Gamma'\times A$ where $A$ is isomorphic to ${\mathbb{Z}}^n$. We introduce some examples and remarks. Also we provide an example of a virtually irreducible CAT(0) group with trivial-center that acts geometrically on some CAT(0) space that splits as a product $T \times {\mathbb{R}}$. | Group Theory (math.GR) | This paper has been withdrawn by the author due to a crucial error in the example of a virtually irreducible CAT(0) group with trivial-center that acts geometrically on some CAT(0) space that splits as a product $T \times {\mathbb{R}}$ | factual/methodological/other critical errors in manuscript | 633 |
0912.0118v3 | Distribution of Action Potential Duration and T-wave Morphology: a Simulation Study | The results of a simulation study of the action potential duration (APD) distribution and T-wave morphology taking into account the midmyocardial cells (M-cells) concept are described. To investigate the effect of M-cells we present a computer model in which ion channel action potential formulations are incorporated into three-dimensional whole heart model. We implemented inhomogeneous continuous action potential duration distribution based on different distributions of maximal slow delayed rectifier current conductance. Using the proposed action potential distribution procedure midmural zeniths with longest action potential length were created as islands of model cells in the depth of thickest areas of ventricular tissue. Different spatial functions on layer indexes were simulated and their influences on electrocardiogram waveforms were analyzed. Changing parameters of ion channel model we varied duration of minimal and maximal action potential and investigated T-wave amplitude, Q-Tpeak and QT intervals variations. The study demonstrated that the proposed original APD distribution is reasonable and produces realistic electrocardiographic waveforms. | Medical Physics (physics.med-ph) | The paper is not valid | factual/methodological/other critical errors in manuscript | 636 |
0912.0750v2 | Parallel DNA implementation of fast matrix multiplication techniques based on an $n$-moduli set | On distributed memory computers, the implementation and association of fast parallel matrix multiplication algorithms has yielded astounding results and insights. In this discourse, we use the tools of molecular biology to demonstrate the feasibility of performing Strassen's fast matrix multiplication algorithm with DNA based on an $n$-moduli set in the residue number system, thereby demonstrating the viability of computational mathematics with DNA. As a result, a general scalable implementation of this model in the DNA computing paradigm is presented and can be generalized to the application of \emph{all} fast matrix multiplication algorithms on a DNA computer. Fast methods of matrix computations with DNA are important because they also allow for the efficient implementation of other algorithms (i.e. inversion, computing determinants, and graph theory) on a DNA computer. | Quantitative Methods (q-bio.QM) | This paper has been withdrawn for the time being by the author because it has been shown that the use of bio-molecular operations suggested by the Adleman-Lipton model is not very reliable in practice. The massive ligation step cannot produce longer molecules (certainly not more than 10-15 ligations in a row), both the complexity of the tube content and the efficiency of the enzyme are obscuring the results. The streptavidin based separations, as used by Adleman's initial experiment, are also with questionable success when applied to a complex test tube. So, at least the operations "Annealing(T)" and "Separation(T1,X, T2)" proposed in the paper cannot be used reliably (even less when recursion is needed). Thus, until this issue is resolved, the algorithm presented cannot work in practice, yet does have some theoretical use to it. If the pseudocode is more standardized and made more clear, the paper can be viewed as a theoretical exercise showing how using residue number system to represent numbers and parallel algorithms could improve the complexity of solving matrix multiplication. However, I would much rather the paper present a pragmatic insight into matrix multiplication with DNA. If anyone would like to provide assistance or any form of advice, please feel free to contact me at this http [REDACTED-EMAIL] | factual/methodological/other critical errors in manuscript | 646 |
0912.1214v2 | Homotopical Aspects of Commutative Algebras II: Freeness Conditions for Quadratic Modules | This article investigates the homotopy theory of simplicial commutative algebras with a view to homological applications. | Commutative Algebra (math.AC) | This paper has been withdrawn by the author due to some error in the text | factual/methodological/other critical errors in manuscript | 654 |
0912.1574v3 | From the Anderson model on a strip to the DMPK equation and random matrix theory | We study weakly disordered quantum wires whose width is large compared to the Fermi wavelength. It is conjectured that such wires diplay universal metallic behaviour as long as their length is shorter than the localization length (which increases with the width). The random matrix theory that accounts for this behaviour - the DMPK theory- rests on assumptions that are in general not satisfied by realistic microscopic models. Starting from the Anderson model on a strip, we show that a twofold scaling limit nevertheless allows to recover rigorously the fundaments of DMPK theory, thus opening a way to settle some conjectures on universal metallic behaviour. | Mathematical Physics (math-ph) | We withdraw the paper because it contains an essential error, as pointed out to us by [REDACTED-NAME]. Whereas the main conclusion ("random matrix predictions can be checked on a microscopic (Hamiltonian) model") is correct, the result, in particular Proposition 3, is not true in the form as stated. A corrected and expanded treatment will appear shortly | factual/methodological/other critical errors in manuscript | 657 |
0912.1795v4 | Adjunctions between Hopf Galois Theories | We prove that a flat Hopf Galois extension over a ring admits a Galois correspondence between complete lattice of subalgebras and the complete lattice of general quotients of the Hopf algebra. We also construct such a Galois Theory in the dual setting: of module coalgebras over a Hopf algebra, which is essentially easier to obtain. Furthermore, we show that the map which associates to a subalgebra of a comodule algebra over a Hopf algebra a quotient of the associated Hopf algebra (as defined by this http URL ) has both right and left adjoints. This new result leads to an adjunction between Hopf Galois theories of the Hopf algebra and the associated Hopf algebra, which we use to compare these two theories. | Quantum Algebra (math.QA) | This paper has been withdrawn by the authors. The main theorem of this paper was based on a false result given by this http URL (see version 1 of this paper) on faithfully flat descent | factual/methodological/other critical errors in manuscript | 660 |
0912.1910v3 | Fermi-surface instabilities in nuclear matter from angle-correlated particle-particle propagation | Angular correlations arising from particle-particle (pp) propagation in nuclear matter are investigated. Their account follows an exact treatment of the Pauli exclusion principle on intermediate states in the Bruekner-Bethe-Goldstone (BBG) equation. As a result, a correlation form factor emerges from the Cauchy principal-value of the pp propagator, while the imaginary part becomes structurally different from those in Lippmann-Schwinger-type equations. These novel features modify drastically the behaviour of the mass operator near the Fermi surface, reshaping the phase-space where its imaginary part vanishes and sliding down the saturation point of symmetric nuclear matter along the Coester band. The correlation structures found here --which go beyond angle-averaged (or effective-mass type) energy denominators-- may impact present day model predictions for neutron stars based on the BBG equation, and for scattering and reaction observables in full folding optical model calculations | Nuclear Theory (nucl-th) | This paper has been withdrawn due to an incomplete treatment of the pp propagator, neglecting 'double-zero' contributions in Eq. (7) | factual/methodological/other critical errors in manuscript | 661 |
0912.3901v2 | Spin gravity: a non-Abelian gauge theory on a flat spacetime | In this paper, I show that a Yang-Mills force with a U(1)$\timesSU(2)\times$SU(2) group symmetry predicts solar system observations of gravitational behavior as well as binary pulsar precession provided that mass is redefined as intrinsic static pressure and all stress-energy-momentum tensors are, thus, traceless. Using a homogeneous, isotropic universe model, I show that this theory explains the accelerating expansion of the universe directly from group symmetry with no ad hoc constants and predicts that antimatter and matter gravitationally repel one another (antimatter "falls" up). In addition, because it is a generic massless Yang-Mills theory, it is a renormalizable quantum theory. | Mathematical Physics (math-ph) | This paper has been withdrawn because of mathematical errors | factual/methodological/other critical errors in manuscript | 668 |
0912.4084v3 | Computing an Integer Prime Factoring in O(n^2.5) | Paper is withdrawn. On review the paper contributes little of significance. The runtime analysis of the algorithms presented, while correct in terms of number of operations, does not represent the complexity of the algorithms in terms of "bits input". A naive mistake in reasoning. | Data Structures and Algorithms (cs.DS) | This paper has been withdrawn by the author. Paper is withdrawn. On review the paper contributes nothing of significance. The runtime analysis of the algorithms presented, while correct in terms of number of operations, does not represent the complexity of the algorithms in terms of "bits input". A naive mistake in reasoning | factual/methodological/other critical errors in manuscript | 669 |
1001.0181v3 | The entropy and mean separation between energy levels of black hole | According to the widely accepted statistical interpretation of black hole entropy the mean separation between energy levels of black hole should be exponentially small. But this sharply disagrees with the value obtained from the quantization of black hole area. It is shown that the new statistical interpretation of black hole entropy proposed in my paper arXiv:0911.5635 gives the correct value. | General Relativity and Quantum Cosmology (gr-qc) | Withdrawn because the author no longer thinks it is correct | factual/methodological/other critical errors in manuscript | 690 |
1001.0716v2 | Totally Asynchronous Interference Channels | This paper addresses an interference channel consisting of $\mathbf{n}$ active users sharing $u$ frequency sub-bands. Users are asynchronous meaning there exists a mutual delay between their transmitted codes. A stationary model for interference is considered by assuming the starting point of an interferer's data is uniformly distributed along the codeword of any user. The spectrum is divided to private and common bands each containing $v_{\mathrm{p}}$ and $v_{\mathrm{c}}$ frequency sub-bands respectively. We consider a scenario where all transmitters are unaware of the number of active users and the channel gains. The optimum $v_{\mathrm{p}}$ and $v_{\mathrm{c}}$ are obtained such that the so-called outage capacity per user is maximized. If $\Pr\{\mathbf{n}\leq 2\}=1$, upper and lower bounds on the mutual information between the input and output of the channel for each user are derived using a genie-aided technique. The proposed bounds meet each other as the code length grows to infinity yielding a closed expression for the achievable rates. If $\Pr\{\mathbf{n}>2\}>0$, all users follow a locally Randomized On-Off signaling scheme on the common band where each transmitter quits transmitting its Gaussian signals independently from transmission to transmission. Using a conditional version of Entropy Power Inequality (EPI) and an upper bound on the differential entropy of a mixed Gaussian random variable, lower bounds on the achievable rates of users are developed. Thereafter, the activation probability on each transmission slot is designed resulting in the largest outage capacity. | Information Theory (cs.IT) | This paper is withdrawn due to some technicality regarding ergodicity. The corrected version will be submitted under the title "[REDACTED-NAME]-Off signaling in [REDACTED-NAME] Networks" | factual/methodological/other critical errors in manuscript | 693 |
1001.1042v2 | A Graphical representation of the grand canonical partition function | In this paper we consider a stochastic partial differential equation defined on a Lattice $L_\delta$ with coefficients of non-linearity with degree $p$. An analytic solution in the sense of formal power series is given. The obtained series can be re-expressed in terms of rooted trees with two types of leaves. Under the use of the so-called Cole-Hopf transformation and for the particular case $p=2$, one thus get the generalized Burger equation. A graphical representation of the solution and its logarithm is done in this paper. A discussion of the summability of the previous formal solutions is done in this paper using Borel sum. A graphical calculus of the correlation function is given. The special case when the noise is of Lévy type gives a simplified representations of the solution of the generalized Burger equation. From the previous results we recall a graphical representation of the grand canonical partition function. | Mathematical Physics (math-ph) | 20 pages, 1 figure This paper has been withdrawn by the author due to a crucial sign error in equation 15 | factual/methodological/other critical errors in manuscript | 697 |
1001.1267v4 | On Mannheim Partner Curves of $AW(k)-$type | In this study, firstly, Mannheim curves with $\kappa_1 (s) \ne 0$, $\kappa_2 (s) \ne 0$ are considered and the conditions are obtained for Mannheim curve to be slant helix. Moreover, the necessary and sufficient conditions are investigated for Mannheim curve to be AW(2), AW(3) and weak AW(2)-types, respectively. Lastly, it is shown that there is no such a Mannheim curve of AW(1)-type. | Differential Geometry (math.DG) | This paper has been withdrawn by the author due to a crucial sign error in equation 1 | factual/methodological/other critical errors in manuscript | 698 |
1001.1440v2 | A note about algebras obtained by the Cayley-Dickson process | In this paper, we generalize the concepts of level and sublevels of a composition algebra to algebras obtained by the Cayley-Dickson process. In 1967, R. B. Brown constructed, for every $t\in \Bbb{N},$ a division algebra $A_{t}$ of dimension $2^{t}$ over the power-series field $K\{X_{1},X_{2},...,X_{t}\}.$ This gives us the possibility to construct a division algebra of dimension 2$^{t}$ and prescribed level 2$^{k}$ $ k, t\in \Bbb{N}^{*}.$ | Rings and Algebras (math.RA) | This paper has been withdrawn by the author due to some errors. A new version will be update soon | factual/methodological/other critical errors in manuscript | 699 |
1001.2024v2 | Wireless Networks with Asynchronous Users | This paper addresses an interference channel consisting of $\mathbf{n}$ active users sharing $u$ frequency sub-bands. Users are asynchronous meaning there exists a mutual delay between their transmitted codes. A stationary model for interference is considered by assuming the starting point of an interferer's data is uniformly distributed along the codeword of any user. This model is not ergodic, however, we show that the noise plus interference process satisfies an Asymptotic Equipartition Property (AEP) under certain conditions. This enables us to define achievable rates in the conventional Shannon sense. The spectrum is divided to private and common bands. Each user occupies its assigned private band and the common band upon activation. In a scenario where all transmitters are unaware of the number of active users and the channel gains, the optimum spectrum assignment is obtained such that the so-called outage capacity per user is maximized. If $\Pr\{\mathbf{n}>2\}>0$, all users follow a locally Randomized On-Off signaling scheme on the common band where each transmitter quits transmitting its Gaussian signals independently from transmission to transmission. Achievable rates are developed using a conditional version of Entropy Power Inequality (EPI) and an upper bound on the differential entropy of a mixed Gaussian random variable. Thereafter, the activation probability on each transmission slot together with the spectrum assignment are designed resulting in the largest outage capacity. | Information Theory (cs.IT) | This paperi is withdrawn by the author due to a crucial technicality regarding ergodicity. It will be soon corrected and replaced by a draft called "[REDACTED-NAME]-[REDACTED-NAME] n [REDACTED-NAME] Networks" | factual/methodological/other critical errors in manuscript | 701 |
1001.2063v3 | Regularity of the extremal solution for a fourth-order elliptic problem with singular nonlinearity | In this paper, we consider the relation between $p > 1$ and critical dimension of the extremal solution of the semilinear equation $$\{\begin{array}{lllllll} \beta \Delta^{2}u-\tau \Delta u=\frac{\lambda}{(1-u)^{p}} & in\ \ B, 0<u\leq 1 & in\ \ B, u=\Delta u=0 & on\ \ \partial B, \end{array} . $$ where $B$ is the unit ball in $R^{n}$, $\lambda>0$ is a parameter, $\tau>0, \beta>0,p>1$ are fixed constants. By Hardy-Rellich inequality, we find that when $p$ is large enough, the critical dimension is 13.} | Analysis of PDEs (math.AP) | 13 | factual/methodological/other critical errors in manuscript | 702 |
1001.2910v4 | A Subconvexity Bound for Automorphic $L$-functions for $SL(3,Z)$ | In this paper, we develop a conditional subconvexity bound for Godement-Jacquet $L$-functions associated with Maass forms for $SL(3,Z)$. | Number Theory (math.NT) | A subtle mistake in Lemma 3 has been found and it does not appear that it can be easily fixed. | factual/methodological/other critical errors in manuscript | 709 |
1001.3973v2 | Photo-induced high-temperature order-disorder phase transition in CaSnO3 perovskite revealed by Raman spectroscopy | Calcium stannate perovskite (CaSnO3) has been studied by Raman spectroscopy at two excitation wavelengths (514.5 nm and 632.8 nm). A new first-order order-disorder phase transition induces Raman frequency shifts and line width doubling at 121C on heating (94C on cooling), seen in experiments using the 514.5 nm line of an Ar+-ion laser. The transition is also seen when using a 623.8 nm He-Ne laser and by differential scanning calorimetry (DSC), but without strong order-disorder character, indicating that the phase transition is dependent on photo-excitation. High-temperature powder X-ray diffraction measurements provide thermal expansion coefficients of ax = 13.9 x 10-6 K-1, ay = 2.7 x 10-6 K-1, az = 14.3 x 10-6 K-1. The phase transition is postulated to be associated with photo-excited charged and conductive nanoscale ferroelectric order-disorder. As such, CaSnO3 could represent the first in a new class of optoelectronic materials with additional potential photocatalytic properties. | Materials Science (cond-mat.mtrl-sci) | Data questionable after several repeat experiments | factual/methodological/other critical errors in manuscript | 718 |
1001.4237v5 | A priori bounds for Gevrey-Sobolev norms of space-periodic solutions to equations of hydrodynamic type | We present a technique for derivation of a priori bounds for Gevrey-Sobolev norms of space-periodic three-dimensional solutions to evolutionary partial differential equations of hydrodynamic type. It involves a transformation of the flow velocity in the Fourier space, which introduces a feedback between the index of the norm and the norm of the transformed solution, and results in emergence of a mildly dissipative term. To illustrate the technique, we derive finite-time bounds for Gevrey-Sobolev norms of solutions to the Euler and inviscid Burgers equations, and global in time bounds for the Voigt-type regularisations of the Euler and Navier-Stokes equation (assuming that the respective norm of the initial condition is bounded). The boundedness of the norms implies analyticity of the solutions in space. | Analysis of PDEs (math.AP) | version 4 withdrawn due to an error | factual/methodological/other critical errors in manuscript | 723 |
1002.0181v2 | Noncommutative resolution of toric singularities: An application of Frobenius morphism of noncommutative blowup | Using Frobenius morphisms of noncommutative blowups, we prove that every normal toric singularity has a standard noncommutative resolution. | Algebraic Geometry (math.AG) | This paper has been withdrawn by the author due to a crucial error, which was pointed out by a referee. The error lies in the assertion in page 8 that $\mathfrak{C}_{G}$ is a translation of the cone $\mathfrak{C}$. It is not a cone in general. Accordingly an assertion about the preservation of projective modules over a noncommutative ring associated to a toric singularity is no longer valid | factual/methodological/other critical errors in manuscript | 735 |
1002.0459v2 | Effective phase dynamics of noise-induced oscillations in excitable systems | We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest one-dimensional case the effective phase equation is obtained analytically, whereas for more complex situations a simple method of data processing is suggested. As an application an effective coupling function is constructed that quantitatively describes periodically forced noise-induced oscillations. | Chaotic Dynamics (nlin.CD) | This paper has been withdrawn by the author due to errors in Fig. 3 and faulty conclusions drawn from Fig. 4 | factual/methodological/other critical errors in manuscript | 738 |
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