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0704.0840v3 | Associated production of the charged Higgs boson and single top quark at the LHC | The left-right twin Higgs(LRTH) model predicts the existence of the charged Higgs $\phi^{\pm}$. In this paper, we study the production of the charged Higgs boson $\phi^{-}$ with single top quark via the process $bg\to t\phi^{-}$ at the $CERN$ Large Hadron Collider(LHC). The numerical results show that the production cross section can reach the level of $10 pb$ in the reasonable parameter space of the LRTH model. We expect that, as long as it is not too heavy, the possible signatures of the heavy charged Higgs boson $\phi^{-}$ might be detected via the decay mode $\phi^{-}\to \bar{t}b$ at the LHC experiments. | High Energy Physics - Phenomenology (hep-ph) | This paper has been withdrawn by the author(s) due to some mistakes in this paper | factual/methodological/other critical errors in manuscript | 1 |
0704.1180v2 | Full Additivity of the Entanglement of Formation | We present a general strategy that allows a more flexible method for the construction of fully additive multipartite entanglement monotones than the ones so far reported in the literature of axiomatic entanglement measures. Within this framework we give a proof of a conjecture of outstanding implications in information theory: the full additivity of the Entanglement of Formation. | Quantum Physics (quant-ph) | Paper withdrawn. The result regarding the additivity of EoF was not as general as initially considered. Apologies to our colleagues | factual/methodological/other critical errors in manuscript | 3 |
0705.0134v2 | Semiclassical wave propagation for large times | We study solutions of the time dependent Schrödinger equation on Riemannian manifolds with oscillatory initial conditions given by Lagrangian states. Semiclassical approximations describe these solutions for small h (where h is the semiclassical parameter), but their accuracy for large times is in general only understood up to the Ehrenfest time T ~ ln(1/h), and the most difficult case is the one where the underlying classical system is chaotic. We show that on surfaces of constant negative curvature semiclassical approximations remain accurate for times at least up to T ~ h^(-1/2) in the case that the Lagrangian state is associated with an unstable manifold of the geodesic flow. | Mathematical Physics (math-ph) | 40 pages, 1 figure, This paper has been withdrawn by the author due to a gap in the proof of the dispersive estimates | factual/methodological/other critical errors in manuscript | 13 |
0705.0619v4 | Optical detection of anyons in an integer quantum Hall system | We have studied an in-plane resonant photo-response of an integer quantum Hall system in which time-reversal and parity symmetries are broken. The response of initially homogeneous system exhibits a complicate spatial structure sensitive to the system macroscopic sizes. Conceptually, the effect is explained by the large-scale quantum entanglement originated from an indistinguishable particle statistics. The concept is supported by the demonstration of entanglement-related transfer of information in the system interior. | Mesoscale and Nanoscale Physics (cond-mat.mes-hall) | This paper has been withdrawn by the author because further experiments show incorrectness of the proposed interpretation. | factual/methodological/other critical errors in manuscript | 14 |
0705.3667v3 | Classification of singularities in the complete conformally flat Yamabe flow | We show that an eternal solution to a complete, locally conformally flat Yamabe flow, $\frac{\partial}{\partial t} g = -Rg$, with uniformly bounded scalar curvature and positive Ricci curvature at $t = 0$, where the scalar curvature assumes its maximum is a gradient steady soliton. As an application of that, we study the blow up behavior of $g(t)$ at the maximal time of existence, $T < \infty$. We assume that $(M,g(\cdot, t))$ satisfies (i) the injectivity radius bound {\bf or} (ii) the Schouten tensor is positive at time $t = 0$ and the scalar curvature bounded at each time-slice. We show that the singularity the flow develops at time $T$ is always of type I. | Differential Geometry (math.DG) | The paper has been withdrawn due to a crucial error in the argument | factual/methodological/other critical errors in manuscript | 21 |
0706.0357v22 | Generalized Riemann Hypothesis | Withdrawn | General Mathematics (math.GM) | This paper has been withdrawn by the author. A mistake was found at the equation (24) of the original paper. We must consider the terms Mq, q|L for the divisors of LM^2, which the author did not notice. Unfortunately, this leads to a new situation in which the function R(x) now is also a hard-to-analyze term | factual/methodological/other critical errors in manuscript | 23 |
0706.0548v2 | More spectral bounds on the clique and independence numbers | We give some new bounds for the clique and independence numbers of a graph in terms of its eigenvalues. | Combinatorics (math.CO) | This paper has been withdrawn by the author due to a crucial mistake | factual/methodological/other critical errors in manuscript | 31 |
0706.0859v2 | Profinite complexes of curves, their automorphisms and anabelian properties of moduli stacks of curves | Let ${\cal M}_{g,[n]}$, for $2g-2+n>0$, be the D-M moduli stack of smooth curves of genus $g$ labeled by $n$ unordered distinct points. The main result of the paper is that a finite, connected étale cover ${\cal M}^ł$ of ${\cal M}_{g,[n]}$, defined over a sub-$p$-adic field $k$, is "almost" anabelian in the sense conjectured by Grothendieck for curves and their moduli spaces. The precise result is the following. Let $\pi_1({\cal M}^ł_{\ol{k}})$ be the geometric algebraic fundamental group of ${\cal M}^ł$ and let ${Out}^*(\pi_1({\cal M}^ł_{\ol{k}}))$ be the group of its exterior automorphisms which preserve the conjugacy classes of elements corresponding to simple loops around the Deligne-Mumford boundary of ${\cal M}^ł$ (this is the "$\ast$-condition" motivating the "almost" above). Let us denote by ${Out}^*_{G_k}(\pi_1({\cal M}^ł_{\ol{k}}))$ the subgroup consisting of elements which commute with the natural action of the absolute Galois group $G_k$ of $k$. Let us assume, moreover, that the generic point of the D-M stack ${\cal M}^ł$ has a trivial automorphisms group. Then, there is a natural isomorphism: $${Aut}_k({\cal M}^ł)\cong{Out}^*_{G_k}(\pi_1({\cal M}^ł_{\ol{k}})).$$ This partially extends to moduli spaces of curves the anabelian properties proved by Mochizuki for hyperbolic curves over sub-$p$-adic fields. | Algebraic Geometry (math.AG) | This paper has been withdrawn because of a flaw in the paper "Profinite Teichmüller theory" of the first author, on which this paper built on | factual/methodological/other critical errors in manuscript | 33 |
0706.1138v74 | An Approach to the Jacobian Conjecture by Use of Galois group actions | Our final target is a faded result, the Jacobian Conjecture : If $f_1,..., f_n$ be elements in a polynomial ring $k[X_1,..., X_n]$ over a field $k$ of characteristic zero such that $ \det(\partial f_i/ \partial X_j) $ is a nonzero constant, then $k[f_1,..., f_n] = k[X_1,..., X_n]$. | Commutative Algebra (math.AC) | This paper has been withdrawn by the author due to a crucial sign error | factual/methodological/other critical errors in manuscript | 34 |
0706.1359v2 | Evidence for high-temperature topological order in an asymmetric quantum Hall system | An original photo-electric method is applied to study InAs-based quantum Hall system in which time-reversal and parity symmetries are broken by a combination of in-plane magnetic field and built-in electric field. The experiments were performed in the regime of Shubnikov-de Haas oscillations at the temperature as high as about 2K. Under the so mild conditions, the system reveals a topological order manifested itself in an inseparable behaviour of quantum particles on the length as long as about 20mm. | Mesoscale and Nanoscale Physics (cond-mat.mes-hall) | This paper has been withdrawn by the author because further experiments show incorrectness of the proposed interpretation. | factual/methodological/other critical errors in manuscript | 35 |
0707.1462v2 | Non-Uniqueness of Gibbs measures relative to Brownian motion | We consider Gibbs measures relative to Brownian motion of Feynman-Kac type, with single site potential V. We show that for a large class of V, including the Coulomb potential, there exist infinitely many infinite volume Gibbs measures. | Probability (math.PR) | This paper has been withdrawn by the author due to a fatal error in Theorem 3.5 (the main theorem, unfortunately) | factual/methodological/other critical errors in manuscript | 46 |
0707.2445v2 | The Wigner-Fokker-Planck equation: Stationary states and large time behavior | We consider the Wigner-Fokker-Planck equation subject to confining potentials which are smooth perturbations of the harmonic oscillator. For a certain class of these perturbations we prove that the equation admits a unique stationary solution in a weighted L^2-space. Moreover, we show that the solutions of the time-dependent problem converge towards this steady state with an exponential rate. | Quantum Physics (quant-ph) | This paper has been withdrawn by the author due to a crucial error in the proof of the main result. in a new paper (with two new authors) this problem has been resolved | factual/methodological/other critical errors in manuscript | 47 |
0708.0291v2 | Quantum Entanglement of Neutrino Pairs | It is practically shown that a pair of neutrinos from tau decay can form a flavor entangled state. With this kind of state we show that the locality constrains imposed by Bell inequality are violated by the quantum mechanics, and an experimental test of this effect is feasible within the earth's length scale. Theoretically, the quantum entanglement of neutrino pairs can be employed to the use of long distance cryptography distribution in a protocol similar to the BB84. | Quantum Physics (quant-ph) | 7 pages, 5 eps figures; This paper has been withdrawn by the author due to the efficiency of detections | factual/methodological/other critical errors in manuscript | 51 |
0708.0359v3 | Geometric proof of Thom conjecture | This paper has been withdrawn by the author due a crucial sign error in Theorem B. We present a geometric proof of Thom conjecture, which uses Khovanov homology. Our approach doesn't use any analytic methods and is quite different from proof given by Kronheimer and Mrowka in 1994. | Geometric Topology (math.GT) | This paper has been withdrawn by the author due a crucial sign error in Theorem B | factual/methodological/other critical errors in manuscript | 52 |
0709.0883v5 | Liquid State Machines in Adbiatic Quantum Computers for General Computation | Major mistakes do not read | Computational Complexity (cs.CC) | Totally wrong | factual/methodological/other critical errors in manuscript | 60 |
0710.1087v2 | $Z^{'0}Z^{'0}$, $K^{+}K^{-}$ and $K^{0}\bar{K}^{0}$ boson production with definite helicity amplitudes through $e^{+}e^{-}$ collisions in the 3-3-1 models without exotic electric charges | A detailed analysis of $Z^{'0}Z^{'0}$, $K^{+}K^{-}$ and $K^{0}\bar{K}^{0}$ pair production in $e^{+}e^{-}$ collisions is presented by using helicity amplitudes. The trilinear bosons couplings in the $SU(3)_{C}\otimes SU(3)_{L}\otimes U(1)_{X}$ models without exotic electric charges are also calculated. We carry out the mentioned analysis for two models, one of them is a one family model which is an $E_6$ subgroup \cite{b1} and the other one is a three family model with right handed neutrinos\cite{b2,b3}. These models do not contain exotic electric charges. For them, we give explicit formulae and the corresponding numerical estimates of the cross-sections and angular distributions occurred in the processes $e^{+}e^{-}\to Z^{'0}Z^{'0}$, $e^{+}e^{-} \to K^{+}K^{-}$ and $e^{+}e^{-}\to K^{0}\bar{K}^{0}$ present in our models. We suppose these processes are invariant under $C$, $P$ and $T$ transformation. | High Energy Physics - Phenomenology (hep-ph) | This paper has been withdrawn by the author due to: 1.) There are many typos and shortcomings in the English language. 2.) It is not clear the content of the sum rules used to check the unitarity conditions. There is a chaotic mixture between different sum rules. 3.) There is a basic difference between beam energy and cms energy (sqrt(s) = 2E). Which was not clarified everywhere | factual/methodological/other critical errors in manuscript | 75 |
0710.1419v3 | Gelfand-Kirillov conjecture for symplectic reflection algebras | We construct functorially a class of algebras using the formalism of double derivations. These algebras extend to higher dimensions Crawley-Boevey and Holland's construction of deformed preprojective algebras and encompass symplectic reflection algebras associated to wreath products. We use this construction to show that the quotient field of a symplectic reflection algebra is "rational", confirming a pair of conjectures of Etingof and Ginzburg. | Rings and Algebras (math.RA) | The generators and relations given in 2.4 are not correct. Specifically the commutation relation (3) needs to be changed. I do not know how to do this in general, and so the preprint is incorrect as it stands. Corollary 6.3 is correct, however, and is used in arXiv:0709.2338 | factual/methodological/other critical errors in manuscript | 76 |
0710.2117v5 | Gravitation in 4D Euclidean Space-Time Geometry | The Euclidean interpretation of special relativity which has been suggested by the author is a formulation of special relativity in ordinary 4D Euclidean space-time geometry. The natural and geometrically intuitive generalization of this view involves variations of the speed of light (depending on location and direction) and a Euclidean principle of general covariance. In this article, a gravitation model by Jan Broekaert, which implements a view of relativity theory in the spirit of Lorentz and Poincare, is reconstructed and shown to fulfill the principles of the Euclidean approach after an appropriate reinterpretation. | General Physics (physics.gen-ph) | This paper has been withdrawn by the author due to a critical error in the geometric formulation of the principle of inertial motion | factual/methodological/other critical errors in manuscript | 77 |
0710.2663v3 | A State Sum Link Invariant of Regular Isotopy | This paper has been withdrawn because there is a fundamental error in the computations; with the right computational scheme it seems to be just a version of the Jones polynomial | Geometric Topology (math.GT) | This paper has been withdrawn because there is a fundamental error in the computations; with the right computational scheme it seems to be just a version of the Jones polynomial | factual/methodological/other critical errors in manuscript | 78 |
0710.3550v3 | Free frobenius algebra on the differential forms of a manifold | We construct an action of a free resolution of the Frobenius properad on the differential forms of a closed oriented manifold. As a consequence, the forms of a manifold with values in a semi-simple Lie algebra have an additional structure given by an action of a free resolution of the properad describing Lie di-algebras with module compatibility. | Quantum Algebra (math.QA) | This paper has been withdrawn by the author. The definition given for the Frobenius properad is incorrect, i.e. what is stated is not a properad. For sign reasons following from the permutation group actions, in odd degree n, there should be no positive genus operations. The error in that definition invalidates the proof of the main claim in Theorem 4 (even for a proper definition of Frobenius properad). Theorem 8 is also affected similarly | factual/methodological/other critical errors in manuscript | 82 |
0710.5224v2 | Ostwald Ripening on Nanoscale | Applicability of classical Lifshitz-Slyozov theory of Ostwald ripening is analyzed and found limited by relatively large cluster sizes due to restrictions imposed by theoretical assumptions. An assumption about the steady state ripening regime poses an upper limit, while another, implicit assumption of continuous description poses a cluster size-dependent lower limit on the supersaturation level. These two limits mismatch for the clusters under certain size in the nanometer scale making the theory inapplicable. We present a more generic, molecular theory of Ostwald ripening, which reproduces classical Lifshitz-Slyozov and Wagner theories in appropriate extreme cases. This theory has a wider applicability than classical theories, especially at lower supersaturation levels, and is more suitable for nanoscale systems. | Materials Science (cond-mat.mtrl-sci) | Found incorrections | factual/methodological/other critical errors in manuscript | 87 |
0711.0429v2 | Equivalence of types and Catlin boundary systems | The D'Angelo finite type is shown to be equivalent to the Kohn finite ideal type on smooth, pseudoconvex domains in complex n space. This is known as the Kohn Conjecture. The argument uses Catlin's notion of a boundary system as well as methods from subanalytic and semialgebraic geometry. When a subset of the boundary contains only two level sets of the Catlin multitype, a lower bound for the subelliptic gain in the \bar\partial-Neumann problem is obtained in terms of the D'Angelo type, the dimension of the ambient space, and the level of forms. | Complex Variables (math.CV) | Paper withdrawn by the author due to the fact that a Catlin type truncation that is used in the argument may lose finite type, in which case the Levi determinant could be identically zero in the domain of the truncation. An example of this kind and the proof that the Levi determinant only vanishes to an effective order for smooth domains of finite type appears in arXiv:1102.0356 | factual/methodological/other critical errors in manuscript | 89 |
0711.1208v2 | Finite dimensional subspaces of noncommutative $L_p$ spaces | We prove the following noncommutative version of Lewis's classical result. Every n-dimensional subspace E of Lp(M) (1<p<\infty) for a von Neumann algebra M satisfies d_{cb}(E, RC^n_{p'}) \leq c_p n^{\abs{1/2-1/p}} for some constant c_p depending only on $p$, where $1/p +1/p' =1$ and $RC^n_{p'} = [R_n\cap C_n, R_n+C_n]_{1/p'}$. Moreover, there is a projection $P:Lp(M) --> Lp(M)$ onto E with $\norm{P}_{cb} \leq c_p n^{\abs{1/2-1/p}}.$ We follow the classical change of density argument with appropriate noncommutative variations in addition to the opposite trick. | Functional Analysis (math.FA) | This paper has been withdrawn due to a crucial error in the proof of Proposition 3.2 | factual/methodological/other critical errors in manuscript | 90 |
0711.1247v2 | Discovery of Quantum Hidden Variable | The first clue, in the theory of relativity, the 4-vector force acting on a particle is orthogonal to the 4-vector velocity of the particle, this orthogonality means that there is some difference between the orthogonality and the usual statement: the Coulomb's force (or gravitational force) acts along the line joining a couple of particles (in usual 3D space), so the direction of 4-vector Coulomb's force is carefully investigated, it is found that Maxwell's equations can be derived from classical Coulomb's force and the orthogonality. The second clue, a 4-vector force has 4 components, because of the orthogonality of 4-vector force and 4-vector velocity, the number of independent components of the 4-vector force reduces to 3, however we prove that 4-vector Coulomb's force can merely provide 2 independent components, this situation means that there is an undefined component accompanying the 4-vector Coulomb's force, hinting that this missing undefined component is a hidden variable. The third clue, the best way to study the hidden variable is to establish a new concept: Z-space, in which the undefined component of 4-vector Coulomb's force can be clearly defined as the hidden variable for the quantum mechanics. At the last, the undefined component is regarded as a fluctuating source that contributes to Lorentz force, so that the quantum wave equation can be derived out in the ensemble space of particle motion from the relativistic Newton's second law. | General Physics (physics.gen-ph) | This paper has been withdrawn by the author due to some wrong in its chapter 7, conflicting with the current gravitational wave discovery | factual/methodological/other critical errors in manuscript | 91 |
0711.3942v2 | Electronic structures and lattice dynamics of BaTiO3 and BiFeO3 : a comparative first-principles study | First-principles calculations were performed to investigate the ferroelectric properties of barium titanate and bismuth ferrite, as well as phonon dispersion of BaTiO3, using density functional theory and density functional perturbation theory. Results show that the strong hybridization of Ti-O and Bi-O lead to the corresponding mechanisms for stabilizing the distorted structure. The spontaneous polarization of 59.4 \mu C/cm2 and 27.6 \mu C/cm2 were calculated for BiFeO3 and BaTiO3 respectively, using berry phase method within the modern theory of polarization. The stereochemical activity of Bi-6s long-pair, which was the driven mechanism for ferroelectricity in BiFeO3, was able to produce greater polarization than the Ti off-centring displacement in BaTiO3. New multiferroic perovskite type materials combined with these two ferroelectric instabilities were predicted to have a better ferromagnetic ordering in comparison with BiFeO3. | Materials Science (cond-mat.mtrl-sci) | This paper has been withdrawn by the author due to crucial errors | factual/methodological/other critical errors in manuscript | 94 |
0712.0940v3 | Inducing periodicity and chaos by negative feedback | This paper has been withdrawn due to an error in the proof of the main theorem. | Chaotic Dynamics (nlin.CD) | This paper has been withdrawn due to an error in the proof of the main theorem | factual/methodological/other critical errors in manuscript | 98 |
0801.0258v2 | On the Maximum Span of Fixed-Angle Chains | Soss proved that it is NP-hard to find the maximum 2D span of a fixed-angle polygonal chain: the largest distance achievable between the endpoints in a planar embedding. These fixed-angle chains can serve as models of protein backbones. The corresponding problem in 3D is open. We show that three special cases of particular relevance to the protein model are solvable in polynomial time. When all link lengths and all angles are equal, the maximum 3D span is achieved in a flat configuration and can be computed in constant time. When all angles are equal and the chain is simple (non-self-crossing), the maximum flat span can be found in linear time. In 3D, when all angles are equal to 90 deg (but the link lengths arbitrary), the maximum 3D span is in general nonplanar but can be found in quadratic time. | Computational Geometry (cs.CG) | 28 pages, 21 figures. Preliminary version appeared in Proc. 18th Canad. Conf. Comput. Geom., pages 93-96, 2006. This paper has been withdrawn by the authors. Lemma 15 as stated is incorrect, and although we believe the main theorems following (Thms. 17 & 18) are true, the proofs relying on Lem.15 are not valid | factual/methodological/other critical errors in manuscript | 106 |
0801.0370v2 | Funnelling related phase transitions in networks | Funnelling effect, in the context of searching on networks, precisely indicates that the search takes place through a few specific nodes. We define the funnelling capacity $f$ of a node as the fraction of successful dynamic paths through it with a fixed target. We claim that there is a funnelling effect if the distribution $D(f)$ of the fraction of nodes with funnelling capacity $f$ shows a power law behaviour. We find that a transition from a search with funnelling effect to that without any such effect can exist and is driven by the parameters defining the network. | Disordered Systems and Neural Networks (cond-mat.dis-nn) | 4 pages, revtex4, 6 figures
This paper is withdrawn as it required some correction | factual/methodological/other critical errors in manuscript | 107 |
0801.0495v3 | Toric Ideals of Flow Polytopes | A referee found an error in the proof of the Main Theorem ("toric ideals of flow polytopes are generated in degree 3") that we could not fix.
More precisely, the proof of Lemma 4.2.(ii) is incorrect. The results on Gröbner bases are untouched by this. ----- We show that toric ideals of flow polytopes are generated in degree 3. This was conjectured by Diaconis and Eriksson for the special case of the Birkhoff polytope. Our proof uses a hyperplane subdivision method developed by Haase and Paffenholz. It is known that reduced revlex Gröbner bases of the toric ideal of the Birkhoff polytope $B_n$ have at most degree $n$. We show that this bound is sharp for some revlex term orders. For $(m\times n)$-transportation polytopes, a similar result holds: they have Gröbner bases of at most degree $\lfloor mn/2\rfloor$. We construct a family of examples, where this bound is sharp. | Combinatorics (math.CO) | Withdrawn due to an error in the proof of the [REDACTED-NAME] | factual/methodological/other critical errors in manuscript | 108 |
0801.2550v3 | Moduli spaces of framed instanton sheaves on projective spaces | We introduce a generalization of the Atiyah-Drinfeld-Hitchin-Manin linear algebraic data and a generalization of Atiyah-Drinfeld-Hitchin-Manin equation, which are subsequently used to construct all framed instanton bundles on complex projective spaces. Using geometric invariant theory, we prove that the moduli spaces of framed instanton sheaves is a quasi-projective variety. We also provide a link between the generalized ADHM data introduced here and certain representations of quivers, and introduce the notion of perverse instanton sheaves. | Algebraic Geometry (math.AG) | This paper has been withdraw. Even though the mais results are correct, some of the secondary claims are false. A fully revised version, with a new co-author, will be submitted soon. | factual/methodological/other critical errors in manuscript | 113 |
0801.3487v2 | Rayleigh's Stretched String | We obtain rigorous a priori upper and lower bounds to the exact period of the celebrated Rayleigh stretched string differential equation. | Classical Analysis and ODEs (math.CA) | This paper has been withdrawn. There was an error in the proof of theorem 1 | factual/methodological/other critical errors in manuscript | 116 |
0802.1195v2 | Numerical Solution of the Beltrami Equation | An effective algorithm is presented for solving the Beltrami equation fzbar = mu fz in a planar disk. The algorithm involves no evaluation of singular integrals. The strategy, working in concentric rings, is to construct a piecewise linear mu-conformal mapping and then correct the image using a known algorithm for conformal mappings. Numerical examples are provided and the computational complexity is analyzed. | Complex Variables (math.CV) | This paper has been withdrawn by the author due to many critical errors, including the fact that the algorithm converges to a wrong result | factual/methodological/other critical errors in manuscript | 125 |
0802.4391v3 | Evidence for a string-net matter | String-net theory by Xiao-Gang Wen and Michael Levin predicts a new type of matter - string-net matter - and puts forward an original guess regarding the structure of our universe. Here we provide experimental evidence for this matter. It is revealed in a familiar system - InAs-based asymmetric quantum well at tilted quantizing magnetic fields. By an original method we demonstrate the existence of peculiar charged particles those differ in principle from underlying electrons. In accordance with the theory, the particles are found to be strongly entangled on a macroscopic lengthscale but the entanglement differs fundamentally from the "classic" one in the sense that it is unrelated to particles' wavefunctions but is provided by a spesific mediating entity - a network of long-range strings. We argue that the peculiar charged particles are the string ends and, as an extreme of our argumentation, we provide strong evidence for "artificial" photons those are collective excitations of the strings. | Mesoscale and Nanoscale Physics (cond-mat.mes-hall) | This paper has been withdrawn by the author because further experiments have shown incorrectness of the proposed interpretation. | factual/methodological/other critical errors in manuscript | 132 |
0803.0105v3 | A note on the rank of Heegaard Floer homology | We show that if K is a non-trivial knot inside a homology sphere Y, then the rank of knot Floer homology associated with K is strictly bigger than the rank of Heegaard Floer homology of Y. | Geometric Topology (math.GT) | This paper has been withdrawn by the author. The surgery formulas are used incorrectly for proving the main result of the paper | factual/methodological/other critical errors in manuscript | 133 |
0803.0973v3 | The Chabauty-Coleman bound at a prime of bad reduction | We extend the refined version of the Chabauty-Coleman bound on the number of rational points on a curve of genus g>1 to the case of bad reduction. | Number Theory (math.NT) | 10 pages; this paper has been withdrawn by the author due to an error in Lemma 3.4. | factual/methodological/other critical errors in manuscript | 136 |
0803.3112v10 | Unconditional Proof of the Boltzmann-Sinai Ergodic Hypothesis | We consider the system of $N$ ($\ge2$) elastically colliding hard balls of masses $m_1,...,m_N$ and radius $r$ on the flat unit torus $\Bbb T^\nu$, $\nu\ge2$. We prove the so called Boltzmann-Sinai Ergodic Hypothesis, i. e. the full hyperbolicity and ergodicity of such systems for every selection $(m_1,...,m_N;r)$ of the external geometric parameters. The present proof does not use the formerly developed, rather involved algebraic techniques, instead it employs exclusively dynamical methods and tools from geometric analysis. | Dynamical Systems (math.DS) | The paper is withdrawn due to an error | factual/methodological/other critical errors in manuscript | 139 |
0804.1956v2 | The Hausdorff dimension of self-affine Sierpinski sponges | We compute the Hausdorff dimension of limit sets generated by 3-dimensional self-affine mappings with diagonal matrices of the form A_{ijk}=Diag(a_{ijk}, b_{ij}, c_{i}), where 0<a_{ijk}\le b_{ij}\le c_i<1. By doing so we show that the variational principle for the dimension holds for this class. | Dynamical Systems (math.DS) | Lemma 8 is wrong which invalidates the trueness of the main result of the paper | factual/methodological/other critical errors in manuscript | 149 |
0804.3440v2 | Localization Study of a Non-Local Energetic Damage Model | The contribution presents an analysis of a rate-independent non-local damage model, recently proposed by (Mielke and Roubicek, 2006). An analytical as well as numerical solution of a simple one-dimensional bifurcation problem is performed, demonstrating that, for the elementary localization test, the model is free of pathological features. | Materials Science (cond-mat.mtrl-sci) | This paper has been withdrawn by the authors due incorrect form of the local-displacement diagram shown in Figure 3(b); the correct solution always exhibits snapback at the structural level. The corrected and significantly expanded version of the manuscript is available at arXiv:1412.5539. The authors would like to apologize for any inconvenience caused | factual/methodological/other critical errors in manuscript | 155 |
0804.4876v3 | On Splitting Types, Discriminant Bounds, and Conclusive Tests for the Galois Group | Using the action of the Galois group of a normal extension of number fields, we generalize and symmetrize various fundamental statements in algebra and algebraic number theory concerning splitting types of prime ideals, factorization types of polynomials modulo primes, and cycle types of the Galois groups of polynomials. One remarkable example is the removal of all artificial constraints from the Kummer-Dedekind Theorem that relates splitting and factorization patterns. Finally, we present an elementary proof that the discriminant of the splitting field of a monic irreducible polynomial with integer coefficients has a computable upper bound in terms of the coefficients. This result, combined with one of Lagarias et al., shows that tests of polynomials for the cycle types of the Galois group are conclusive. In particular, the Galois groups of monic irreducible cubics, quartics, and quintics with integer coefficients can be completely determined in finitely many steps (though not necessarily in one's lifetime). | Number Theory (math.NT) | A counterexample to Theorem 1.2 has been pointed out to the author (x^2+3 reduced modulo 2). The mistake cannot be corrected at this time | factual/methodological/other critical errors in manuscript | 158 |
0805.0284v2 | Convolution and Cross-Correlation of Ramanujan-Fourier Series | This paper uses the machinery of almost periodic functions to prove that even without uniform convergence the connection between a pair of almost periodic functions and the constants of the associated Fourier series exists for both the convolution and cross-correlation. The general results for two almost periodic functions are narrowed and applied to Ramanujan sums and finally applied to support the specific relation of the Wiener-Khinchin formula for arithemic functions with a Ramanujan-Fourier Series. | Number Theory (math.NT) | The paper fails to establish the continuity of the a.p. functions involved required to uniformly approximate the a.p. function with the Bochner-Fejer polynomials. Without this uniform convergence the key interchange of limits is not justified | factual/methodological/other critical errors in manuscript | 159 |
0805.1877v2 | Perfect tag identification protocol in RFID networks | Radio Frequency IDentification (RFID) systems are becoming more and more popular in the field of ubiquitous computing, in particular for objects identification. An RFID system is composed by one or more readers and a number of tags. One of the main issues in an RFID network is the fast and reliable identification of all tags in the reader range. The reader issues some queries, and tags properly answer. Then, the reader must identify the tags from such answers. This is crucial for most applications. Since the transmission medium is shared, the typical problem to be faced is a MAC-like one, i.e. to avoid or limit the number of tags transmission collisions. We propose a protocol which, under some assumptions about transmission techniques, always achieves a 100% perfomance. It is based on a proper recursive splitting of the concurrent tags sets, until all tags have been identified. The other approaches present in literature have performances of about 42% in the average at most. The counterpart is a more sophisticated hardware to be deployed in the manufacture of low cost tags. | Networking and Internet Architecture (cs.NI) | There is a technical error | factual/methodological/other critical errors in manuscript | 164 |
0805.3573v3 | Averages of ratios of characteristic polynomials in circular beta-ensembles and super-Jack polynomials | We study the averages of ratios of characteristic polynomials over circular $\beta$-ensembles, where $\beta$ is a positive real number. Using Jack polynomial theory, we obtain three expressions for ratio averages. Two of them are given as sums of super-Jack polynomials and another one is given by a hyperdeterminant. As applications, we give dual relations for ratio averages between $\beta$ and $4/\beta$. | Probability (math.PR) | This paper has been withdrawn by the author due to a crucial error | factual/methodological/other critical errors in manuscript | 167 |
0806.0557v4 | An efficient and provably secure arbitrated quantum signature scheme | In this paper, an efficient arbitrated quantum signature scheme is proposed by combining quantum cryptographic techniques and some ideas in classical cryptography. In the presented scheme, the signatory and the receiver can share a long-term secret key with the arbitrator by utilizing the key together with a random number. While in previous quantum signature schemes, the key shared between the signatory and the arbitrator or between the receiver and the arbitrator could be used only once, and thus each time when a signatory needs to sign, the signatory and the receiver have to obtain a new key shared with the arbitrator through a quantum key distribution protocol. Detailed theoretical analysis shows that the proposed scheme is efficient and provably secure. | Quantum Physics (quant-ph) | some contents are wrong | factual/methodological/other critical errors in manuscript | 175 |
0806.0731v4 | Chow Stability of Curves of Genus 4 in P^3 | In the paper, we study the GIT construction of the moduli space of Chow semistable curves of genus 4 in P^3. By using the GIT method developed by Mumford and a deformation theoretic argument, we give a modular description of this moduli space. We classify Chow stable or Chow semistable curves when they are irreducible or nonreduced. Then we work out the case when a curve has two components. Our classification provides some clues to understand the birational map from the moduli space of stable curves of genus 4 to the moduli space of Chow semistable curves of genus 4 in P^3. | Algebraic Geometry (math.AG) | This paper has been withdrawn by the author due to a crucial error | factual/methodological/other critical errors in manuscript | 177 |
0806.1571v4 | On a certain asymptotic relationship involving $\vartheta(t) - \lfloor t \rfloor$ and $t^{1/2}$ | Let $\lfloor t \rfloor$ denote the greatest positive integer less than or equal to a given positive real number $t$ and $\vartheta(t)$ the Chebyshev $\vartheta$-function. In this paper, we prove a certain asymptotic relationship involving $\vartheta(t) - \lfloor t \rfloor $ and $t^{1/2}$. | General Mathematics (math.GM) | Withdrawn; this work is completely nonsense | factual/methodological/other critical errors in manuscript | 181 |
0806.2350v3 | A sharp uniform bound for the distribution of sums of Bernoullis | In this paper we establish a uniform bound for the distribution of a sum $S_n=X_1+...+X_n$ of independent non-homogeneous Bernoulli trials. Specifically, we prove that $\sigma_n P(S_n=j)\leq \eta$ where $\sigma_n$ denotes the standard deviation of $S_n$ and $\eta$ is a universal constant. We compute the best possible constant \eta~0.4688 and we show that the bound also holds for limits of sums and differences of Bernoullis. An application to estimate the rate of convergence of Mann's fixed point iterations is also presented. | Probability (math.PR) | This paper has been withdrawn by the author due to a crucial sign error in $h"(u)$ in Proposition 7 | factual/methodological/other critical errors in manuscript | 182 |
0806.3587v3 | A Maximum Principle for Elliptic Pseudo-differential Operators on Closed, Riemannian Manifolds | In this note we establish the positivity of Green's functions for a class of elliptic differential operators on closed, Riemannian manifolds. | Analysis of PDEs (math.AP) | This paper has been withdrawn due to an error in a reference. | factual/methodological/other critical errors in manuscript | 184 |
0806.3790v3 | Prescription of Q-curvature on closed Riemannian manifolds | In this paper it is hown that given any smooth, positive function f on a closed, smooth manifold of dimension greater than four and with positive Paneitz invariant, there exists a metric on M such that $Q_g$ = f. | Differential Geometry (math.DG) | This paper has been withdrawn due to an error in a reference. | factual/methodological/other critical errors in manuscript | 185 |
0806.4829v3 | Selberg's zeta functions for congruence subgroups of modular groups in SL(2,R) and SL(2,C) | It is known that the Selberg zeta function for the modular group has an expression in terms of the class numbers and the fundamental units of the indefinite binary quadratic forms. In the present paper, we generalize such a expression to any congruence subgroup of the modular groups in SL(2,R) and SL(2,C). | Number Theory (math.NT) | 12 pages. This paper has been withdrawn by the author due to several wrong descriptions | factual/methodological/other critical errors in manuscript | 192 |
0807.1606v4 | Homogeneity of proper complex equifocal submanifolds | In this paper, we show that an irreducible proper complex equifocal submanifold of codimension greater than one in a symmetric space of non-compact type. The proof is performed by showing the homogeneity of the lift of the complexification of the original submanifold to some infinite dimensional anti-Kahelerian space. | Differential Geometry (math.DG) | I found many misses in this paper | factual/methodological/other critical errors in manuscript | 197 |
0807.1607v4 | On equifocal submanifolds with non-flat section in symmetric spaces of rank two | In this paper, we show that there exists no equifocal submanifold with non-flat section in four irreducible simply connected symmetric spaces of compact type and rank two. Also, we show a fact for the sections of equifocal submanifolds with non-flat section in other irreducible simply connected symmetric spaces of compact type and rank two. | Differential Geometry (math.DG) | In this paper, we found important misses | factual/methodological/other critical errors in manuscript | 198 |
0807.1662v2 | A note on two-positive Ricci curvature and positive Einstein curvature | In this short note we discuss some recent results about two-positive Ricci curvature and their applications to positive Einstein curvature. | Differential Geometry (math.DG) | This paper has been withdrawn by the author due to an error in Theorem 2.2 | factual/methodological/other critical errors in manuscript | 199 |
0807.2326v2 | Floer homology and existence of incompressible tori in homology spheres | We show that if a prime homology sphere has the same Floer homology as the standard three-sphere, it does not contain any incompressible tori. | Geometric Topology (math.GT) | This paper has been withdrawn by the author. The results are based on the (incorrect) splicing formula of the initial version of arXiv:0802.2874. The correct splicing formula gives partial results instead, which will appear in a revision | factual/methodological/other critical errors in manuscript | 200 |
0807.2554v2 | Statistical tools used to identify scientific misconduct in mobile phone research (REFLEX program) | A severe case of scientific misconduct was discovered in a paper from 2005 allegedly showing harmful effects (DNA breakage) of non-thermal mobile phone electromagnetic field exposure on human and rat cells. Here we describe the way how the fraudulent data were identified. The low variations of the reported biological data are shown to be below theoretical lower limits (multinomial distributions). Another reason for doubts was highly significant non-equal distributions of last digits, a known hint towards data fabrication. The Medical University Vienna, where the research was conducted, was informed about these findings and came to the conclusion that the data in this and another, related paper by the same group were fabricated, and that both papers should be retracted. | Applications (stat.AP) | This paper has been withdrawn by the authors due to concerns with referenced data sets. No further revisions. | factual/methodological/other critical errors in manuscript | 202 |
0807.2812v2 | Play Ground for Victor's Magic Squares | This article presents a new development of magic squares with a simple set up. | General Mathematics (math.GM) | This paper has been withdrawn by the author due to a crucial sign error in one of the proof of this paper | factual/methodological/other critical errors in manuscript | 203 |
0807.3059v2 | Agent-based model of competition in a social structure | Indirect competition emerged from the complex organization of human societies, and knowledge of the existing network topology may aid in developing effective strategies for success. Here, we propose an agent-based model of competition with systems co-existing in a `small-world' social network. We show that within the range of parameter values obtained from the model and empirical data, the network evolution is highly dependent on $k$, the local parameter describing the density of neighbors in the network. The model applied to language death and competition of telecommunication companies show strong correspondence with empirical data. | General Finance (q-fin.GN) | 7 pages, 3 figures This paper has been withdrawn due to claims that have been proven to be false | factual/methodological/other critical errors in manuscript | 204 |
0807.3152v5 | Super-rigidity and finiteness of embedded $J$-holomorphic curves on Calabi-Yau threefolds | The paper contains a fundamental defect in its framework of
using the gauge action to study the rigidity problem.
As a result, the calculations leading to the main formula
is also incorrect. | Symplectic Geometry (math.SG) | This paper has been withdrawn by the author due to a crucial defect in the framework | factual/methodological/other critical errors in manuscript | 205 |
0807.3369v46 | A new look at Bell's inequalities and Nelson's theorem | In 1985, Edward Nelson, who formulated the theory of stochastic mechanics, made an interesting remark on Bell's theorem. Nelson analysed the latter in the light of classical fields that behave randomly. He found that if a stochastic hidden variable theory fulfils certain conditions, the inequality of Bell can be violated. Moreover, Nelson was able to prove that this may happen without any instantaneous communication between the two spatially separated measurement stations. Since Nelson's article got almost overlooked by physicists, we try to review his comments on Bell's theorem. We argue that a modification of stochastic mechanics published recently by Fritsche and Haugk can be extended to a theory which fulfils the requirements of Nelson's analysis. The article proceeds to derive the quantum mechanical formalism of spinning particles and the Pauli equation from this version of stochastic mechanics. Then, we investigate Bohm's version of the EPR experiment. Additionally, other setups, like entanglement swapping or time and position correlations, are shortly explained from the viewpoint of our local hidden-variable model. Finally, we mention that this theory could perhaps be relativistically extended. | Quantum Physics (quant-ph) | The stochastic model presented in this article was defect. The parts of this work that are correct are now in a separate article on arxiv.org | factual/methodological/other critical errors in manuscript | 207 |
0807.3531v2 | Classical theory of second-harmonic generation from magnetic metamaterials | Strong second-harmonic generation has recently been experimentally observed from metamaterials consisting of periodic arrays of metal split ring resonators with an effective negative magnetic permeability [Science, 313, 502 (2006)]. To explore the underlying physical mechanism, a classical model derived from microscopic theory is employed here. The quasi-free electrons inside the metal are approximated as a classical Coulomb-interacting electron gas, and their motion under the excitation of an external electromagnetic field is described by the cold-plasma wave equations. Through numerical simulations, it is demonstrated that the microscopic theory includes the dominant physical mechanisms bothqualitatively and quantitatively. | Materials Science (cond-mat.mtrl-sci) | sign errors in equations | factual/methodological/other critical errors in manuscript | 208 |
0807.4764v6 | Jet schemes, invariant chiral differential operators, and Howe duality | This paper has been withdrawn due to an error in the proof of Theorem 5.3. | Representation Theory (math.RT) | This paper has been withdrawn due to an error in the proof of Theorem 5.3 | factual/methodological/other critical errors in manuscript | 216 |
0807.4971v3 | The Mixing Matrix for a 3+2 Model | In this work we present the characterization of the mixing matrix when the mass matrix is considered, without seesaw, for 3+2 models like. | High Energy Physics - Phenomenology (hep-ph) | This paper has been withdrawn by the author due to a crucial error | factual/methodological/other critical errors in manuscript | 217 |
0808.1298v2 | Non Commutative Metrics on Quantum Families of Maps | We show that any quantum family of maps from a non commutative space to a compact quantum metric space has a canonical quantum semi metric structure. | Operator Algebras (math.OA) | This paper has been withdrawn by the author due to a mistake about Theorem 11 | factual/methodological/other critical errors in manuscript | 223 |
0808.1852v2 | The Meccano of life | This article is interested in the origin of the genetic code, it puts forward a scenario of a simultaneous selection of the bases and amino acids and setting up of a correlation between them. Each amino acid is associated with a pair of its own kind, called the binding pair and each binding pair is associated with the codon(s) corresponding to the same amino acid. An explanation is also proposed about the origin of the start and stop codons. | Biomolecules (q-bio.BM) | paper withdrawn by the author due to some errors | factual/methodological/other critical errors in manuscript | 225 |
0808.3280v3 | Photon blockade and nonlinear effects for a quantum dot strongly coupled to a semiconductor microcavity | Our model comprehensively simulates modern nanoscale semiconductor microcavities incorporating cavity quantum electrodynamics within both the weak and strong coupling regimes, using on-resonant laser excitation and nonresonant excitation due to a wetting layer. For weak coupling, the most significant effect is photon antibunching with nonresonant emission. We investigate how the antibunching characteristics change as the cavity finesse is increased towards the strong coupling regime. Antibunching can also be observed in a strongly coupled system with resonant excitation, using the photon blockade mechanism which has been demonstrated in atom systems. We calculate what cavity parameters are required to observe this effect. Experimentally these studies are equivalent to nonlinear pump probe measurements, where a strong pump, either resonant or nonresonant, is used to excite the coupled system, and the resulting state is characterized using a weak, resonant probe beam. | Materials Science (cond-mat.mtrl-sci) | 5 pages, 5 figures, OECS conference 2007, Sicily, Italy the paper is withdrawn due to a crucial correction on one of the graphs which has been successfully adjusted before acceptance in Phys. Rev. B | factual/methodological/other critical errors in manuscript | 230 |
0809.1276v6 | Matter Wave Radiation Leading to Matter Teleportation | The concept of matter wave radiation is put forward, and its equation is established for the first time. The formalism solution shows that the probability density is a function of displacement and time. A free particle and a two-level system are reinvestigated considering the effect of matter wave radiation. Three feasible experimental designs, especially a modified Stern-Gerlach setup, are proposed to verify the existence of matter wave radiation. Matter wave radiation effect in relativity has been formulated in only a raw formulae, which offers another explanation of Lamb shift. A possible mechanics of matter teleportation is predicted due to the effect of matter wave radiation. | General Physics (physics.gen-ph) | Like other waves e.g. electromagnetic wave, gravitational wave, de Broglie matter wave would have its wave source, is the source just Born probability density? It looks absurd. Three is no the room of the matter source in modern physics framework | factual/methodological/other critical errors in manuscript | 239 |
0809.2252v3 | Unconditional security of continuous-variable quantum key distribution | The unconditional security of continuous-variable quantum key distribution is established for all schemes based on the estimation of the channel loss and excess noise. It is proved that, in the limit of large keys, Gaussian attacks are asymptotically optimal among the most general (coherent) attacks, where the transmission is tapped using arbitrary ancillas and stored in a quantum memory as a whole. Then, it is shown that the previously derived bounds on the achievable secret key rates against collective attacks remain asymptotically valid for arbitrary coherent attacks. | Quantum Physics (quant-ph) | This paper has been withdrawn by the authors. The approach investigated in this preprint fails for the following reason: for a fixed $n$, the $ε$-smooth min-entropy is a continuous function of $ε$ for a given $n$-mode state but the Lipschitz constant of the function increases with $n$. As a consequence, one cannot interchange the limits $ε$ tending to 0 with $n$ tending to infinity. Note, however, that an unconditional security proof of continuous-variable quantum key distribution was established in Phys. Rev. Lett. 102, 110504 (2009) (preprint arXiv:0809.2243) | factual/methodological/other critical errors in manuscript | 247 |
0809.2523v2 | Growth conditions and uniqueness of the Cauchy problem for the evolutionary infinity Laplacian | We study the Cauchy problem for the parabolic infinity Laplace equation. We prove a new comparison principle and obtain uniqueness of viscosity solutions in the class of functions with a polinomial growth at infinity, improving previous results obtained assuming a linear growth. | Analysis of PDEs (math.AP) | This paper has been withdrawn by the author due to a gap in the proof of Lemma 2.3. In fact, the condition $Φ(x,y,0,0) \leq 0$ does not directly follow from (6) and (7) | factual/methodological/other critical errors in manuscript | 248 |
0809.4699v3 | Deformation of Sasakian metrics | We study the stability properties of Sasakian metrics in deformation theory. Let $\{F^{t}\}_{t \in T}$ be a smooth family of 1-dimensional transversely holomorphic Riemannian foliation on a closed manifold $M$, where $T$ is an open neighborhood of 0 in the L-dimensional Euclidean space and $F^{0}$ has a compatible Sasakian metric $g$. We give a necessary and sufficient condition under which there exist an open neighborhood $U$ of 0 in $T$ and a smooth family of Riemannian metric $\{g^{t}\}_{t \in U}$ on $M$ such that $g^{t}$ is a compatible Sasakian metric with $F^{t}$ for every $t$ in $U$ and $g^{0}=g$ in terms of the basic Euler classes of 1-dimensional isometric Riemannian foliations. As a corollary, we obtain a result on stability of Sasakian metrics of which the basic (0,2) Dolbeault number is zero in a family of 1-dimensional transversely holomorphic Riemannian foliation on $M$. | Differential Geometry (math.DG) | This paper has been withdrawn by the author due to a crucial error in the argument in the last paragraph of the proof of Lemma 6 | factual/methodological/other critical errors in manuscript | 253 |
0810.0558v2 | The Ratio Index for Budgeted Learning, with Applications | In the budgeted learning problem, we are allowed to experiment on a set of alternatives (given a fixed experimentation budget) with the goal of picking a single alternative with the largest possible expected payoff. Approximation algorithms for this problem were developed by Guha and Munagala by rounding a linear program that couples the various alternatives together. In this paper we present an index for this problem, which we call the ratio index, which also guarantees a constant factor approximation. Index-based policies have the advantage that a single number (i.e. the index) can be computed for each alternative irrespective of all other alternatives, and the alternative with the highest index is experimented upon. This is analogous to the famous Gittins index for the discounted multi-armed bandit problem. The ratio index has several interesting structural properties. First, we show that it can be computed in strongly polynomial time. Second, we show that with the appropriate discount factor, the Gittins index and our ratio index are constant factor approximations of each other, and hence the Gittins index also gives a constant factor approximation to the budgeted learning problem. Finally, we show that the ratio index can be used to create an index-based policy that achieves an O(1)-approximation for the finite horizon version of the multi-armed bandit problem. Moreover, the policy does not require any knowledge of the horizon (whereas we compare its performance against an optimal strategy that is aware of the horizon). This yields the following surprising result: there is an index-based policy that achieves an O(1)-approximation for the multi-armed bandit problem, oblivious to the underlying discount factor. | Data Structures and Algorithms (cs.DS) | This paper has a substantial bug that we are trying to fix. Many thanks to [REDACTED-NAME] for pointing this bug out. Please do not cite in the meantime. Please let us know if you would like to understand and/or try to fix the bug | factual/methodological/other critical errors in manuscript | 257 |
0810.0755v3 | DNA Bubble Life Time in Denaturation | We have investigated the denaturation bubble life time for a homogeneous as well as for a heterogeneous DNA within a Poland-Scheraga model. It is shown that at criticality the bubble life time for a homogeneous DNA is finite provided that the loop entropic exponent c>2 and has a scaling dependence on DNA length for c<2. Heterogeneity in the thermodynamical limit makes the bubble life time infinite for any entropic exponent. | Soft Condensed Matter (cond-mat.soft) | This paper has been withdrawn by the author due to mistakes | factual/methodological/other critical errors in manuscript | 258 |
0810.5610v2 | The BCS Gap Equation on a Banach Space Consisting of Functions both of the Temperature and of the Wave Vector | In previous mathematical studies of the BCS gap equation of superconductivity, the gap function was regarded as an element of a space consisting of functions of the wave vector only. But we regard it as an element of a Banach space consisting of functions both of the temperature and of the wave vector. On the basis of the implicit function theorem we first show that there is a unique solution of class $C^2$ with respect to the temperature, to the simplified gap equation obtained from the BCS gap equation. We then regard the BCS gap equation as a nonlinear integral equation on the Banach space above, and show that there is a unique solution to the BCS gap equation on the basis of the Schauder fixed-point theorem. We find that the solution to the BCS gap equation is continuous with respect to both the temperature and the wave vector, and that the solution is approximated by a function of class $C^2$ with respect to both the temperature and the wave vector. Moreover, the solution to the BCS gap equation is shown to reduce to the solution to the simplified gap equation under a certain condition. | Mathematical Physics (math-ph) | This paper has been withdrawn by the author due to an error in Lemma 4.5 | factual/methodological/other critical errors in manuscript | 276 |
0811.0505v2 | Sharp ill-posedness result for the periodic Benjamin-Ono equation | We prove the discontinuity for the weak $ L^2(\T) $-topology of the flow-map associated with the periodic Benjamin-Ono equation. This ensures that this equation is ill-posed in $ H^s(\T) $ as soon as $ s<0 $ and thus completes exactly the well-posedness result obtained by the author. | Analysis of PDEs (math.AP) | This paper has been withdrawn by the author since there were errors in the calculus of the defect coefficient in Page 11. The corrected calculus gives actually zero which do not lead to a contradiction on the continuity of the flow-map of the Benjamin-Ono equation. The author warmly thank [REDACTED-NAME] Gérard for having pointing out this error to him | factual/methodological/other critical errors in manuscript | 281 |
0811.0935v5 | A New Training Protocol for Channel State Estimation in Wireless Relay Networks | The accuracy of channel state information (CSI) is critical for improving the capacity of wireless networks. In this paper, we introduce a training protocol for wireless relay networks that uses channel estimation and feedforwarding methods. The feedforwarding method is the distinctive feature of the proposed protocol. As we show, each relay feedforwards the imperfect CSI to the destination in a way that provides a higher network capacity and a faster transfer of the CSI than the existing protocols. In addition, we show the importance of the effective CSI accuracy on the wireless relay network capacity by comparing networks with the perfect effective CSI, imperfect effective CSI, and noisy imperfect effective CSI available at the destination. | Information Theory (cs.IT) | This paper has been withdrawn by the author due to technical flaws in SISO section | factual/methodological/other critical errors in manuscript | 283 |
0811.2430v4 | What particles that never met "know" of one another? | An experiment proposed by Yurke and Stoler, and similar to that realized experimentally by Sciarrino et al., is analyzed. In Sciarrino's realization, identical photons from a degenerated down-conversion pair are used, i.e. the photons met in the past. In the experiment analyzed here the particles are also identical, but from different sources. As long as one can tell from which source came each particle, the joint wave function remains factorizable. However, a configuration is created in which one cannot tell anymore which particle came from which source. As a result, the wave function becomes non-factorizable, symmetrical (for bosons) or antisymmetrical (for fermions). In part of the cases the situation is even more surprising: the particles never meet, s.t. the symmetry (antisymmetry) is produced at-a-distance without the particles having had the possibility to interact in any way. | Quantum Physics (quant-ph) | The author revised the article and considers that the proof is not rigorous. The main counter-argument is that one should not draw conclusions from a truncated wave-function | factual/methodological/other critical errors in manuscript | 287 |
0812.0877v2 | Two-Parameter Heavy-Traffic Limits for Infinite-Server Queues | In order to obtain Markov heavy-traffic approximations for infinite-server queues with general non-exponential service-time distributions and general arrival processes, possibly with time-varying arrival rates, we establish heavy-traffic limits for two-parameter stochastic processes. We consider the random variables $Q^e(t,y)$ and $Q^r(t,y)$ representing the number of customers in the system at time $t$ that have elapsed service times less than or equal to time $y$, or residual service times strictly greater than $y$. We also consider $W^r(t,y)$ representing the total amount of work in service time remaining to be done at time $t+y$ for customers in the system at time $t$. The two-parameter stochastic-process limits in the space $D([0,\infty),D)$ of $D$-valued functions in $D$ draw on, and extend, previous heavy-traffic limits by Glynn and Whitt (1991), where the case of discrete service-time distributions was treated, and Krichagina and Puhalskii (1997), where it was shown that the variability of service times is captured by the Kiefer process with second argument set equal to the service-time c.d.f. | Probability (math.PR) | We want to withdraw this article because of a mistake in the proof and replace it with a new version | factual/methodological/other critical errors in manuscript | 297 |
0812.0967v2 | Secret Broadcasting of GHZ type state | Here we described a protocol by which one can broadcast GHZ-type states secretly. We have done this with the help of a cloning machine followed by subsequent measurements. We also made a comparative study of the amount of residual tangle present in these entangled states, obtained as outputs of the measurements. | Quantum Physics (quant-ph) | This paper is withdrawn, as because the results are incorrect | factual/methodological/other critical errors in manuscript | 299 |
0812.1454v3 | Solymosi's multiplicative energy bound for complex numbers | We extend the recent Solymosi's sum-product estimate for reals to the complex case. | Combinatorics (math.CO) | This paper has been withdrawn by the authors. This paper has a fatal error. Many thanks to L. Li who pointed it out | factual/methodological/other critical errors in manuscript | 300 |
0812.1659v3 | Transport diffusion coefficient for a Knudsen gas in a random tube | We consider transport diffusion in a stochastic billiard in a random tube which is elongated in the direction of the first coordinate (the tube axis). Inside the random tube, which is stationary and ergodic, non-interacting particles move straight with constant speed. Upon hitting the tube walls, they are reflected randomly, according to the cosine law: the density of the outgoing direction is proportional to the cosine of the angle between this direction and the normal vector. Steady state transport is studied by introducing an open tube segment as follows: We cut out a large finite segment of the tube with segment boundaries perpendicular to the tube axis. Particles which leave this piece through the segment boundaries disappear from the system. Through stationary injection of particles at one boundary of the segment a steady state with non-vanishing stationary particle current is maintained. We prove (i) that in the thermodynamic limit of an infinite open piece the coarse-grained density profile inside the segment is linear, and (ii) that the transport diffusion coefficient obtained from the ratio of stationary current and effective boundary density gradient equals the diffusion coefficient of a tagged particle in an infinite tube. Thus we prove Fick's law and equality of transport diffusion and self-diffusion coefficients for quite generic rough (random) tubes. | Probability (math.PR) | This paper will not be published, since it contains a serious flaw in eq.(25). See http://arxiv.org/abs/1004.1206 for a corrected and extended version. | factual/methodological/other critical errors in manuscript | 301 |
0812.3754v3 | Semiring Properties of Heyting Algebras | The relationship between Heyting algebras (HA) and semirings is explored. A new class of HAs called Symmetric Heyting algebras (SHAs) is proposed, and a necessary condition on SHAs to be consider semirings is given. We define a new mathematical family called Heyting structures, which are similar to semirings, but with Heyting-algebra operators in place of the usual arithmetic operators usually seen in semirings. The impact of the zero-sum free property of semirings on Heyting structures is shown as also the condition under which it is possible to extend one Heyting structure to another. It is also shown that the union of two or more sets forming Heyting structures is again a Heyting structure, if the operators on the new structure are suitably derived from those of the component structures. The analysis also provides a sufficient condition such that the larger Heyting structure satisfying a monotony law implies that the ones forming the union do so as well. | 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 | 307 |
0812.4009v20 | Graph Field Automata | The Graph Automata have been the paradigm in the expression of utilizing Graphs as a language. Matrix Graph grammars \cite{Pedro} are an algebratization of graph rewriting systems. Here we present the dual of this formalizm which some extensions which we term Graph Field Automata The advantage to this approach is a framework for expressing machines that can use Matrix Graph Grammars. | Computational Complexity (cs.CC) | 8 pages 1 figure v1 initial submission v2 [REDACTED-NAME] v3 More minor changes v4 still more minor changes v5 Rewritten base assumptions, more english corrections and minor changes v6 Major english corrections v7 Rewritten most of the paper. This paper doesn't make any sense | factual/methodological/other critical errors in manuscript | 308 |
0812.4178v2 | Schanuel's conjecture and the exceptional set of $γ$-th arithmetic zeta functions | In this work, we study the arithmetic nature of the numbers of the form $n^{\g}$, for $n \in \N$ and $\g\in \C$. We also consider a related conjecture and we show that it is a consequence of the unipresent Schanuel's conjecture. | Number Theory (math.NT) | The paper has some mistakes | factual/methodological/other critical errors in manuscript | 309 |
0812.4764v2 | On Osculating Interpolation | The development of high-degree interpolation polynomials which use the values of the function and its subsequent derivatives is reformulated. Also, we present a variant of new formula in barycentric form. | Numerical Analysis (math.NA) | This paper has been withdrawn by the author due to a crucial sign error in main formula | factual/methodological/other critical errors in manuscript | 310 |
0901.0088v12 | Realisation of a purely quantum communication | One of the fundamental challenges of modern physics is the apparent conflict between its two basic pillars: special relativity and non-relativistic quantum theory. The conflict streams from the fundamental incompatibility of quantum theory with relativistic principle of locality and is ultimately related to the notion of instantaneous wavefunction collapse under measurements. Perhaps the very founders of quantum theory were most deeply conscious of a fundamental nature of this conflict so that Erwin Schrodinger even once said Niels Bohr that "... if all this damned quantum jumping were really to stay, I should be sorry I ever got involved with quantum theory". Yet, however, it is generally believed that the conflict can be overcome because no physical systems are known, for which the predictions of quantum theory contradict a more fundamental principle - the principle of relativistic causality - which prohibits any signaling with collapse dynamics. Actually, this belief rests on various no-communication theorems related to a very limited range of quantum systems such as EPR-like systems, quantum cloning etc. but no theorem of a general character is known so far. In this work, we just report on the discovering of a quantum system for which the quantum theory definitely predicts a signaling with collapse dynamics. The distinct feature of the system is the presence of spatially-separated orbit-like electrons' wavefunctions of a macroscopic lengthscale and this feature does allow one to realise a purely quantum communication in full accordance with the quantum theory. This communication does not thus imply a faster-than-light motion of anything but rather demonstrates a peculiar quantum way to overcome space, for which the very paradigm of motion is merely meaningless. | General Physics (physics.gen-ph) | This paper has been withdrawn by the author due to a crucial loophole in the interpretation logic | factual/methodological/other critical errors in manuscript | 311 |
0901.1444v2 | Algebraic gossip on Arbitrary Networks | Consider a network of nodes where each node has a message to communicate to all other nodes. For this communication problem, we analyze a gossip based protocol where coded messages are exchanged. This problem was studied by Aoyama and Shah where a bound to the dissemination time based on the spectral properties of the underlying communication graph is provided. Our contribution is a uniform bound that holds for arbitrary networks. | Information Theory (cs.IT) | Paper has been withdrawn due to an error in the main proof | factual/methodological/other critical errors in manuscript | 316 |
0901.1857v2 | Integer-Sided Triangles with integral medians | In this work, we prove that any triangle whose three sidelengths are integers, cannot have all of its three medians also having integral this http URL is done in Proposition this http URL Section 5, we give precise( this http URL and sufficient)conditions for a nonisosceles, integer-sided triangle to have two integral this http URL Section 3, we offer parametric descriptions of three special families of integer-sided this http URL first family consists of all Pythagorean triangles whose medians to their hypotenuses is integral. The other two medians (to the two legs)of any Pythagorean triangle are irrational, a proof of this fact can be found in reference 4 of this this http URL second family consists of all integer-sided isosceles triangles, whose only integral median is the one contained between the two sides of equal length. Finally, the third family consists of all isosceles integer-sided triangles with the two medians of equal length;having integer length. | General Mathematics (math.GM) | 10 pages, 4 figures The reason for withdrawing this article, is a critical error in the proof of Proposition1 | factual/methodological/other critical errors in manuscript | 318 |
0901.2365v6 | On the principal eigenfunction of positive elliptic differential operators and the prescription of $Q$-curvature on closed Riemannian manifolds | In this note we establish the large time non-negativity of the heat kernel for a class of elliptic differential operators on closed, Riemannian manifolds, and apply this result to a problem from conformal differential geometry. | Analysis of PDEs (math.AP) | This paper has been withdrawn due to an error in a reference. | factual/methodological/other critical errors in manuscript | 320 |
0901.3299v2 | Computing Rooted and Unrooted Maximum Consistent Supertrees | A chief problem in phylogenetics and database theory is the computation of a maximum consistent tree from a set of rooted or unrooted trees. A standard input are triplets, rooted binary trees on three leaves, or quartets, unrooted binary trees on four leaves. We give exact algorithms constructing rooted and unrooted maximum consistent supertrees in time O(2^n n^5 m^2 log(m)) for a set of m triplets (quartets), each one distinctly leaf-labeled by some subset of n labels. The algorithms extend to weighted triplets (quartets). We further present fast exact algorithms for constructing rooted and unrooted maximum consistent trees in polynomial space. Finally, for a set T of m rooted or unrooted trees with maximum degree D and distinctly leaf-labeled by some subset of a set L of n labels, we compute, in O(2^{mD} n^m m^5 n^6 log(m)) time, a tree distinctly leaf-labeled by a maximum-size subset X of L that all trees in T, when restricted to X, are consistent with. | Discrete Mathematics (cs.DM) | This paper has been withdrawn by the authors due to an error | factual/methodological/other critical errors in manuscript | 324 |
0901.3786v3 | Refined Asymptotics for Multigraded Sums of Squares | To prove that a polynomial is nonnegative on R^n one can try to show that it is a sum of squares of polynomials (SOS). The latter problem is now known to be reducible to a semidefinite programming (SDP) computation much faster than classical algebraic methods, thus enabling new speed-ups in algebraic optimization. However, exactly how often nonnegative polynomials are in fact sums of squares of polynomials remains an open problem. Blekherman was recently able to show that for degree k polynomials in n variables -- with k>=4 fixed -- those that are SOS occupy a vanishingly small fraction of those that are nonnegative on R^n, as n tends to infinity. With an eye toward the case of small n, we refine Blekherman's bounds by incorporating the underlying Newton polytope, simultaneously sharpening some of his older bounds along the way. Our refined asymptotics show that certain Newton polytopes may lead to families of polynomials where efficient SDP can still be used for most inputs. | Algebraic Geometry (math.AG) | There is an error invalidating the bounds of our main theorem. We are withdrawing this paper until we can replace it with a correct new version | factual/methodological/other critical errors in manuscript | 329 |
0901.4305v5 | Catalan's Conjecture over Number Fields | Catalan conjecture/Mihailescu theorem is a theorem in number theory that was conjectured by Mathematician Eugene Charles Catalan in 1844 and was proved completely by Preda Mihailescu in 2005. Some form of problem dates back atleast to Gersonides who seems to have proved a special case of the conjecture in 1343. The note stating the problem was not given the due imprtance at the begining and appeared among errata to papers which had appeared in the earlier volume of Crelle journal, however the problem got its due considration after work of Cassles and Ko Chao in 1960s. The Catalan problem asks that the equation $x^m-y^n=1$ has no solution for x,y,m,n in +ve integers other than the trivial solution $ 3^2-2^3=1 $. An important and first ingredient for the proof is Cassles criteria which says that whenever we have a solution of $x^p-y^q=1$ with p,q primes then $q|x$ and $p|y$ . Here we look a generalization of the problem, namely we will consider the equation $x^p-y^q=1$ where x,y takes value in ring of integers ${O}_K$ of a number field K and p,q are rational primes. In this article we supply a possible formulation of Cassles criterion and a proof for that in some particular cases of number fields. After this work one can expect to follow Mihailescu and Characterize solutions of Catalan over number fields. | Number Theory (math.NT) | This paper has been withdrawn due to some error | factual/methodological/other critical errors in manuscript | 331 |
0901.4459v2 | Multiplicity of positive solutions for nonlinear field equations in $\R^{N}$ | In this paper we study the multiplicity of positive solutions for nonlinear elliptic equations on $\R^N$. The number of solutions is greater or equal than the number of disjoint intervals on which the nonlinear term is negative. Applications are given to multiplicity of standing waves for the nonlinear Schrödinger, Klein-Gordon and Klein-Gordon-Maxwell equations. | Analysis of PDEs (math.AP) | This paper has been withdrawn by the author due to a mistake in Lemma 2.5 | factual/methodological/other critical errors in manuscript | 332 |
0902.0762v2 | Correlated Drainage Model | In this article we present an example of a random oriented tree model on d-dimensional lattice, that is a forest in d=3 with positive probability. This is in contrast with the other random tree models in the literature which are a forest only when d strictly greater than 3. | Probability (math.PR) | This paper has been withdrawn by the authors due to a crucial error in the main theorem. | factual/methodological/other critical errors in manuscript | 338 |
0902.1729v3 | On the Dimension of AG Trace Codes | We determine the dimension of certain q-ary algebraic-geometric trace codes, extending previous results of Van Der Vlugt for p-ary algebraic-geometric trace codes. | Number Theory (math.NT) | This paper is begin withdrawn due to an error regarding the nature of the field extensions. It is believe that if the extension is unramified then the claim still holds. A revision is underway | factual/methodological/other critical errors in manuscript | 344 |
0902.2538v2 | Analysis of $B \to PP$ Weak Decays Using Quark Diagram Scheme | We investigate decay modes of B mesons emitting two pseudoscalar (P) mesons in the Quark Diagram Scheme at SU(3) level. Several relations among the decay amplitudes are obtained and various branching ratios are predicted. | High Energy Physics - Phenomenology (hep-ph) | This paper has been withdrawn by the author due to a crucial error in calculation | factual/methodological/other critical errors in manuscript | 348 |
0902.3324v2 | Crossed product C*-algebras by finite group actions with the projection free tracial Rokhlin property | In this paper we introduce an analog of the tracial Rokhlin property, called the {\emph {projection free tracial Rokhlin property}}, for $C^*$-algebras which may not have any nontrivial projections. Using this we show that if $A$ is an infinite dimensional stably finite simple unital $C^*$-algebra with stable rank one, with strict comparison of positive elements, with only finitely many extreme tracial states, and with the property that every 2-quasi-trace is a trace, and if $\alpha$ is an action of a finite group $G$ with the projection free tracial Rokhlin property, then the crossed product $C^*(G, A, \alpha)$ also has stable rank one (Except there is a mistake in Lemma 3.16, so this is no longer proven) | Operator Algebras (math.OA) | 41 pages, 0 figures. This paper has been withdrawn by the author due to an error in Lemma 3.16. Without this lemma, the main theorem is no longer proven. Current work in progress attempts to prove the main theorem using other methods | factual/methodological/other critical errors in manuscript | 353 |
0902.4164v2 | The flavor-changing bottom and anti-strange quark production in the littlest Higgs model with T parity at the ILC | In the littlest Higgs model with T-parity (LHT) the mirror quarks induce the special flavor structures and some new flavor-changing (FC) couplings which could greatly enhance the production rates of the FC processes. We in this paper study some bottom and anti-strange production processes in the LHT model at the International Linear Collider (ILC), i.e., $e^+e^-\to b\bar{s}$ and $\gamma\gamma\to b\bar{s}$. The results show that the production rates of these processes are sizeable for the favorable values of the parameters. Therefore, it is quite possible to test the LHT model or make some constrains on the relevant parameters of the LHT through the detection of these processes at the ILC. | High Energy Physics - Phenomenology (hep-ph) | This paper has been withdrawn by the authors. due to some errors in equations | factual/methodological/other critical errors in manuscript | 360 |
0902.4282v4 | Mean curvature blow up in mean curvature flow | In this note we establish that finite-time singularities of the mean curvature flow of compact Riemannian submanifolds are characterised by the blow up of the mean curvature. | Differential Geometry (math.DG) | This paper has been withdrawn by the author due to an error in the proof of Proposition 3.2, in particular the claim that bounded mean curvature implies uniform-in-time continuity of the metric | factual/methodological/other critical errors in manuscript | 361 |
0902.4748v3 | On Pointed Hopf Algebras with classical Weyl Groups | Many cases of infinite dimensional Nichols algebras of irreducible Yetter-Drinfeld modules over classical Weyl groups are found. It is proved that except a few cases Nichols algebras of reducible Yetter-Drinfeld modules over classical Weyl groups are infinite dimensional. Some finite dimensional Nichols algebras of Yetter-Drinfeld modules over classical Weyl groups are given. | Quantum Algebra (math.QA) | This paper has been withdrawn by the author due to a crucial sign error in equation 1 | factual/methodological/other critical errors in manuscript | 364 |
0903.1811v2 | A Liouville comparison principle for solutions of quasilinear differential inequalities | This work is devoted to the study of a Liouville comparison principle for entire weak solutions of quasilinear differential inequalities of the form $A(u) + |u|^{q-1}u \leq A(v) + |v|^{q-1}v$ on ${\Bbb R}^n$, where $n\geq 1$, $q$ is positive, and the operator $A(w)$ belongs to a class of the so-called $\alpha$-monotone operators. Typical examples of such operators are the $p$-Laplacian and its well-known modifications. The results improve and supplement those in [1]. | Analysis of PDEs (math.AP) | This paper has been withdrawn by the author due to a crucial sign error in equation 1 This paper has been withdrawn by the author | factual/methodological/other critical errors in manuscript | 373 |
0903.1907v2 | Ferrimagnetic-like surface resonance from hybrid metamaterial slab | We show that a hybrid metamaterial slab comprising of an one-dimensional array of two different types of cavities exhibits ferrimagnetic-like surface resonances which can be used to realize interesting phenomena such as directive emission as a consequence of strong angle-dependent reflection phase and the selective coupling of a Gaussian incident beam into a higher order diffractive channel, giving rise to the phenomenon of negative reflection and retro-directive backtracking. The findings are verified by experiments in the microwave regime. | Optics (physics.optics) | This paper has been withdrawn by the author due to some errors | factual/methodological/other critical errors in manuscript | 374 |
0903.2243v2 | A Generalization of the Shannon-McMillan-Breiman Theorem and the Kelly Criterion Leading to a Definition of Pragmatic Information | After reviewing the strengthened hypotheses of the Shannon-MacMillan-Breiman Theorem, versus the standard statement of the Noiseless Coding Theorem, we state and prove a similar result for relative information, otherwise known as information gain. If the gain results from receiving a side message, this gain, when averaged over the ensemble of possible side messages, is precisely the pragmatic information defined in Weinberger (2002). The relative information result proven herein can be used to extend the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, an analysis of securities market trading strategies presented in Cover and Thomas (1992). We show, in particular, that their results for statistically independent horse races also apply to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some ergodic process, including, but not limited to the history of previous races. Also, if the bettor is receiving messages (side information) about the probability distribution of winners, the doubling rate of the bettor's winnings can be interpreted as the pragmatic information of the messages. Both the theorem proven herein and the application to trading make a compelling case for Weinberger's definition of pragmatic information. | Information Theory (cs.IT) | This paper has been withdrawn by the author, as counterexamples have been found for the paper's main "theorem", the purported equivalent to the Shannon-MacMillan-[REDACTED-NAME] for relative information. The author apologizes for any confusion that this may have caused. The author is also in the midst of preparing a revised version, and thus, perhaps, more confusion | factual/methodological/other critical errors in manuscript | 375 |
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