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0704.0213v2

Geometric Complexity Theory V: On deciding nonvanishing of a generalized Littlewood-Richardson coefficient

This article has been withdrawn because it has been merged with the earlier article GCT3 (arXiv: CS/0501076 [cs.CC]) in the series. The merged article is now available as: Geometric Complexity Theory III: on deciding nonvanishing of a Littlewood-Richardson Coefficient, Journal of Algebraic Combinatorics, vol. 36, issue 1, 2012, pp. 103-110. (Authors: Ketan Mulmuley, Hari Narayanan and Milind Sohoni) The new article in this GCT5 slot in the series is: Geometric Complexity Theory V: Equivalence between blackbox derandomization of polynomial identity testing and derandomization of Noether's Normalization Lemma, in the Proceedings of FOCS 2012 (abstract), arXiv:1209.5993 [cs.CC] (full version) (Author: Ketan Mulmuley)

Computational Complexity (cs.CC)

This article has been withdrawn because it has been merged with the earlier article (GCT3) in the series, and a new article appears in this GCT5 slot now as shown in the abstract

subsumed by another publication

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This paper has been withdrawn by the author(s) due to some mistakes in this paper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

0704.1080v3

The solutions of the N-identical quantum harmonic oscillators interacting with each other through the harmonic potential

This paper has been withdrawn by the author due to some mistakes

Quantum Physics (quant-ph)

This paper has been withdrawn

reason not specified

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

0704.1409v3

Preconditioned Temporal Difference Learning

This paper has been withdrawn by the author. This draft is withdrawn for its poor quality in english, unfortunately produced by the author when he was just starting his science route. Look at the ICML version instead: this http URL

Machine Learning (cs.LG)

This paper has been withdrawn by the author. Look at the ICML version instead: this http URL

subsumed by another publication

0704.1418v3

On the injectivity and asymptotic stability at infinity

This paper has been withdrawn.

Dynamical Systems (math.DS)

This paper has been withdrawn

reason not specified

0704.1599v4

Critical points for surface maps and the Benedicks-Carleson theorem

We give an alternative proof of the Benedicks-Carleson theorem on the existence of strange attractors in Hénon-like families in the plane. To bypass a huge inductive argument, we introduce an induction-free explicit definition of dynamically critical points. The argument is sufficiently general and in particular applies to the case of non-invertible maps as well. It naturally raises the question of an intrinsic characterization of dynamically critical points for dissipative surface maps.

Dynamical Systems (math.DS)

This paper has been withdrawn by the author. 65 pages, no figure, a new section is added which deals with a model problem

reason not specified

0704.2266v2

Dynamical traps and chaotic advection in a meandering jet flow

We continue our study of chaotic mixing and transport of passive particles in a simple model of a meandering jet flow [Prants, et al, Chaos {\bf 16}, 033117 (2006)]. In the present paper we study and explain phenomenologically a connection between dynamical, topological, and statistical properties of chaotic mixing and transport in the model flow in terms of dynamical traps, singular zones in the phase space where particles may spend arbitrary long but finite time [Zaslavsky, Phys. D {\bf 168--169}, 292 (2002)]. The transport of passive particles is described in terms of lengths and durations of zonal flights which are events between two successive changes of sign of zonal velocity. Some peculiarities of the respective probability density functions for short flights are proven to be caused by the so-called rotational-islands traps connected with the boundaries of resonant islands (including those of the vortex cores) filled with the particles moving in the same frame. Whereas, the statistics of long flights can be explained by the influence of the so-called ballistic-islands traps filled with the particles moving from a frame to frame.

Chaotic Dynamics (nlin.CD)

Double of arXiv:1112.4556

subsumed by another publication

0704.2858v6

Studies on the Calogero-Moser system of type $A_1$

We study the Calogero-Moser system of type $A_1$.

Algebraic Geometry (math.AG)

This paper has been withdrawn by the author. 5 pages

reason not specified

0704.3450v3

The center of the generic algebra of degree p

Let $F$ be an algebraically closed field of characteristic zero, and let $p$ be an odd prime. We show that the center of the generic division algebra of degree $p$ is stably rational over $F$. Equivalently, if we let $V=M_p(F) \oplus M_p(F)$ and $PGL_p$ act on $V$ by simultaneous conjugation, then we show that the function field of the quotient variety $V/PGL_p$ is stably rational over $F$.

Rings and Algebras (math.RA)

I am withdrawing this article

reason not specified

0704.3686v2

Improving Estimates of Monotone Functions by Rearrangement

Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates. We show that these estimates can always be improved with no harm using rearrangement techniques: The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate, and the resulting estimate is closer to the true curve in common metrics than the original estimate. We illustrate the results with a computational example and an empirical example dealing with age-height growth charts.

Methodology (stat.ME)

31 pages, 8 figures, low resolution figures. This paper has been withdraw by the authors because it has been replaced by "[REDACTED-NAME] and [REDACTED-NAME] of [REDACTED-NAME] by Rearrangement," arXiv:0806.4730

subsumed by another publication

0704.3696v3

A weighted graph problem from commutative algebra

We give an especially simple proof of a theorem in graph theory that forms the key part of the solution to a problem in commutative algebra, on how to characterize the integral closure of a polynomial ring generated by quadratic monomials.

Commutative Algebra (math.AC)

Withdrawn, since my later 0805.4449 contains this and much more

subsumed by another publication

0704.3804v2

Superconducting antenna for detection of gravitational waves

Combining the principle of magnetic flux quantization inside a superconducting loop and existence of rigid platforms (i.e., solids, non-deformable under the action of gravitational waves) a design for gravitational wave antenna is suggested. This design could yield a non-resonant detector, with modest sizes and capability to generate detectable signals for gravitational waves from astrophysical sources.

Superconductivity (cond-mat.supr-con)

This paper has been withdrawn because much more advanced concept has been developed by the author with colleagues in 2011

subsumed by another publication

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

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

0705.0736v2

On monoidal equivalences and Ann-equivalences

In this paper, we show another proof of the problem by constructing a strict monoidal category M(C) consisting of M-functors and M-morphisms of a category C and we prove C is equivalent to it. The proof is based on a basic character of monoidal equivalences. Ideas and techniques of these proofs can been used to prove the equivalence between an Ann-category and an almost strict Ann-category.

Category Theory (math.CT)

14 pages

reason not specified

0705.2067v2

Drinfeld-Hecke algebras over cocommutative algebras

If A is a cocommutative algebra with coproduct, then so is the smash product algebra of a symmetric algebra Sym(V) with A, where V is an A-module. Such smash product algebras, with A a group ring or a Lie algebra, have families of deformations that have been studied widely in the literature; examples include symplectic reflection algebras and infinitesimal Hecke algebras. We introduce a family of deformations of these smash product algebras for general A, and characterize the PBW property. We then characterize the Jacobi identity for "grouplike" algebras (that include group rings and the nilCoxeter algebra), and precisely identify the PBW deformations in the example where A is the nilCoxeter algebra. We end with the more prominent case - where A is a Hopf algebra. We show the equivalence of several versions of the "deformed" relations in the smash product, and identify the PBW deformations which are Hopf algebras as well.

Rings and Algebras (math.RA)

This paper has been withdrawn, and replaced by arXiv:1601.04775, which supersedes and strengthens this paper

subsumed by another publication

0705.2362v3

Geometric control theory I: mathematical foundations

A geometric setup for control theory is presented. The argument is developed through the study of the extremals of action functionals defined on piecewise differentiable curves, in the presence of differentiable non-holonomic constraints. Special emphasis is put on the tensorial aspects of the theory. To start with, the kinematical foundations, culminating in the so called variational equation, are put on geometrical grounds, via the introduction of the concept of infinitesimal control . On the same basis, the usual classification of the extremals of a variational problem into normal and abnormal ones is also rationalized, showing the existence of a purely kinematical algorithm assigning to each admissible curve a corresponding abnormality index, defined in terms of a suitable linear map. The whole machinery is then applied to constrained variational calculus. The argument provides an interesting revisitation of Pontryagin maximum principle and of the Erdmann-Weierstrass corner conditions, as well as a proof of the classical Lagrange multipliers method and a local interpretation of Pontryagin's equations as dynamical equations for a free (singular) Hamiltonian system. As a final, highly non-trivial topic, a sufficient condition for the existence of finite deformations with fixed endpoints is explicitly stated and proved.

Optimization and Control (math.OC)

replaced by the more recent article arXiv:1503.08808

subsumed by another publication

0705.2558v3

Invariance Mechanics - A new direction for quantum gravity

This paper has been withdrawn by the author.

General Physics (physics.gen-ph)

This paper has been withdrawn by the author

reason not specified

0705.2676v2

Observe the open universe in the sky?

We first review the related works on the observable consequence of landscape and the regulation of e-foldings during inflation. We focus on a branch of observable consequence of landscape which predicts an open universe with negative curvature if e-foldings $N>62$. After discussing the observable regulation from the aspect by Kaloper, Kleban and Sorbo, we make an argument that in the non-flat background the observable $N$ is suppressed by a factor $k/\rho_{0}$. We point out that this seems to detect the information where e-foldings $N>62$ possibly. Finally, we discuss our outcomes with the recent work by Arkani-Hamed et al.

High Energy Physics - Theory (hep-th)

This paper has been withdrawn

reason not specified

0705.3275v2

Quantum doubles of certain rank two pointed Hopf algebras

A certain class of rank two pointed Hopf algebras is considered. The simple modules of their Drinfel'd double is described using Radford's method \cite{rad}. The socle of the tensor product of two such modules is computed and a formula similar to the one in \cite{one} is obtained in some conditions. Cases when such a tensor product is completely irreducible are also given in the last section.

Rings and Algebras (math.RA)

This paper has been withdrawn by the author. withdrawn to be reviewed

reason not specified

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

0705.4268v3

Higher exponential maps and explicit reciprocity laws I

We generalize the construction of the Bloch-Kato exponential map to p-adically complete higher-dimensional local fields of mixed characteristic (0,p). As an application, we prove an explicit reciprocity law, generalizing work of Cherbonnier and Colmez in the classical case. This result relies on the calculation of the Galois cohomology of a p-adic representation in terms of its (phi,G)-module.

Number Theory (math.NT)

Withdrawn as it is superseded by arXiv:0705.4268, which is a more recent version of the same paper

subsumed by another publication

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

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

0706.0817v2

Measure-valued stochastic recurrences and the stability of queues

In this paper we present a stability criterion for finite measure-valued stochastic recursions, generalizing Loynes's Theorem to spaces of measures. This result provides conditions for the reach of a "total stationary state" for the queue with an infinity of servers and the single-server SRPT queue. Indeed, we give in both cases a condition of existence of a stationary measure-valued recursive sequence characterizing the queueing system exhaustively.

Probability (math.PR)

This paper has been withdrawn by the author. This paper has been published in a newer version, arXiv:0803.2459

subsumed by another publication

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

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

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

0706.1956v4

Spherical Continuous Wavelet Transforms arising from sections of the Lorentz group

We consider the conformal group of the unit sphere $S^{n-1},$ the so-called proper Lorentz group Spin$^+(1,n),$ for the study of spherical continuous wavelet transforms (CWT). Our approach is based on the method for construction of general coherent states associated to square integrable group representations over homogeneous spaces. The underlying homogeneous space is an extension to the whole of the group Spin$^+(1,n)$ of the factorization of the gyrogroup of the unit ball by an appropriate gyro-subgroup. Sections on this homogeneous space are constituted by rotations of the subgroup Spin$(n)$ and Möbius transformations of the type $\phi_a(x)=(x-a)(1+ax)^{-1},$ where $a$ belongs to a given section on a homogeneous space of the unit ball. This extends in a natural way the work of Antoine and Vandergheynst to anisotropic conformal dilations.

Representation Theory (math.RT)

30 pages, 1 figure This paper has been withdrawn by the author since it differs from its final version

subsumed by another publication

0706.2239v2

Infinitesimal Castelnuovo Theory in Abelian Varieties

The purpose of this article is to show that the Castelnuovo theory for abelian varieties, developed by G. Pareschi and M. Popa, can be infinitesimalized. More precisely, we prove that an irreducible principally polarized abelian variety has a finite scheme in extremal position, in the sense of Castelnuovo theory for abelian varieties, if, and only if, it is a Jacobian and the scheme is contained in a unique Abel-Jacobi curve.

Algebraic Geometry (math.AG)

The proofs and the results were corrected and improved in arXiv:1410.4813

subsumed by another publication

0706.2412v6

Generalized gauge-invariance for gravitational waves

The aim of this paper is to show the gauge-invariance on the response of interferometers to gravitational waves (GWs). In this process, after a review of results on the Tranverse-Traceless (TT) gauge, where, in general, the theoretical computations on GWs are performed, which is due for completness, we analyse the gauge of the local observer, which represents the gauge of a laboratory environment on Earth. The gauge-invariance between the two gauges is shown in its full angular and frequency dependences. In previous works in the literature this gauge-invariance was shown only in the low frequencies approximation or in the simplest geometry of the interferometer in respect to the propagating GW (i.e. both of the arms of the interferometer are perpendicular to the propagating GW). As far as the computation of the response functions in the gauge of the local observer is concerned, a common misconception about interferometers is also clarifed.

General Relativity and Quantum Cosmology (gr-qc)

This paper has been withdrawn by the author because an improved and updated version has been put in the archive

subsumed by another publication

0706.2537v2

One-Range Addition Theorems in Terms of -ETOs for STOs and Coulomb-Yukawa Like Correlated Interaction Potentials of Integer and Noninteger Indices

In this study, the one-center expansion formulas in terms of complete orthonormal sets of -exponential type orbitals (-ETOs,) are established for the Slater type orbitals (STOs) and Coulomb-Yukawa like correlated interaction potentials (CIPs) of integer and noninteger indices. These relations are used in obtaining the unsymmetrical and symmetrical one-range addition theorems for STOs and Coulomb-Yukawa like CIPs. The final results are especially useful in the calculations of multicenter multielectron integrals of STOs and CIPs occurring when Hartree-Fock-Roothaan (HFR) and explicitly correlated method are employed.

Chemical Physics (physics.chem-ph)

This paper has been published in Journal of this http URL

subsumed by another publication

0706.3661v3

Thermodynamic properties of magneto-anisotropic nanoparticles

The purpose of this paper is to study the thermodynamic equilibrium properties of a collection of non-interacting three-dimensional (3D) magnetically anisotropic nanoparticles in the light of classical statistical physics. Pertaining to the angular dependence ($\alpha$) of the magnetic field with the anisotropy axis, energy landscape plots are obtained which reveal a continuous transition from a double well to a single well for $\alpha=\frac{\pi}{2}$ and show asymmetric bistable shape for other values of $\alpha$. The present analysis is related with the interpretation of equilibrium magnetization and static susceptibility of nanomagnetic system as a function of external magnetic field, $B$, and temperature, $T$. The magnetization and susceptibility confirms the non Langevin behaviour of magneto-anisotropic monodomain particles. The susceptibility analysis establishes the ferromagnetic, antiferromagnetic and paramagnetic like coupling for various $\alpha$. This study reveals the essential role of magneto anisotropic energy in the interpretation of the magnetic behaviour of a collection of noninteracting single domain nanoparticles.

Statistical Mechanics (cond-mat.stat-mech)

This paper is withdrawn, because it is a older version and the newer version can be found in J. Phys.: Condens. Matter 21, 23600 (2009)

subsumed by another publication

0706.4205v2

The extended Burnside ring and module categories

In this note an `extended Burnside ring' is defined, generated by classes of semisimple module categories over Rep(G) with quasifibre functors. Here G is a finite group and representations are taken over an algebraically closed field of characteristic 0. It is shown that this is equivalent to a ring generated by centrally extended G-sets and hence the name. Ring homomorphisms into the multiplicative group of the field are computed with an explicit formula and tables of these homomorphisms are given for the groups S_4 and S_5 which are of particular interest in the context of reductive algebraic groups. ----- L'anneau de Burnside étendu et catégories de modules. Dans cette note un `Anneau de Burnside étendu' est défini, generé par des classes de catégories de modules semisimples sur Rep(G) avec des foncteurs quasifibres. Ici G est un groupe fini, et des représentations sont prises sur un corps algébriquement clos de caractéristique nulle. Il est demontré que ceci équivaut à un anneau generé par des G-ensembles centralement étendus, d'où le nom. Des homomorphismes d'anneau dans le groupe multiplicatif du corps sont computées avec une formule explicite et des tableaux de ces homomorphismes sont fournis pour les groupes S_4 et S_5 qui sont d'un intérêt particulier dans le contexte de groupes algébriques réductifs.

Representation Theory (math.RT)

This paper has been superceded by 1110.4722

subsumed by another publication

0707.0145v2

Laser Pulse Amplification with Bose-Einstein Condensates

This paper has been withdrawn by the author.

Other Condensed Matter (cond-mat.other)

This paper has been withdrawn by the author due to incompleteness investigation of feasibility of using BECs for laser pulse amplification.

incomplete exposition or more work in progress

0707.0348v2

Self-Organized Characteristics of the International System

Various self-organized characteristics of the international system can be identified with the help of a complexity science perspective. The perspective discussed in this article is based on various complexity science concepts and theories, and concepts related to ecology and ecosystems. It can be argued that the Great Power war dynamics of the international system in Europe during the period 1480-1945, showed self-organized critical (SOC) characteristics, resulting in a punctuated equilibrium dynamic. It seems that the SOC-characteristics of the international system and the punctuated equilibrium dynamic were - in combination with chaotic war dynamics - functional in a process of social expansion in Europe. According to a model presented in this article, population growth was a component of the driving force of the international system during this time frame. The findings of this exploratory research project contradict with generally held opinions in International Relations theory.

Adaptation and Self-Organizing Systems (nlin.AO)

Withdrawn. New framework developed in "War: Origins and Effects" arXiv:1409.6163

subsumed by another publication

0707.0595v2

High resolution spectroscopy of the high velocity hot post-AGB star LS III +52 24 (IRAS 22023+5249)

Aims: To investigate the first high resolution optical spectrum of the B-type star, LS III +52 24, identified as the optical counterpart of the hot post-AGB candidate IRAS 22023+5249 (I22023). Methods: We carried out detailed identifications of the observed absorption and emission features in the high resolution spectrum (4290 - 9015 A) of I22023 obtained with the Utrecht Echelle Spectrograph on the 4.2m William Herschel Telescope. Using Kurucz's WIDTH9 program and the spectrum synthesis code, SYNSPEC, we determined the atmospheric parameters and abundances. The photospheric abundances were derived under the LTE approximation. The NEBULAR package under IRAF was used to estimate the electron temperature (T_e) and the electron density (N_e) from the [N II] and [S II] lines. Results: We estimated T_eff=24000 K, log g=3.0, xi_t=7 kms^{-1}. The derived CNO abundances suggest an evolved star with C/O < 1. P-Cygni profiles of hydrogen and helium indicate ongoing post-AGB mass loss. The presence of [N II] and [S II] lines and the non-detection of [O III] indicate that photoionisation has just started. The derived nebular parameters T_e=7000 K, N_e=1.2X10^{4} cm^{-3} are comparable to those measured in young, compact planetary nebulae (PNe). The nebular expansion velocity was estimated to be 17.5 kms^{-1}. Conclusions: The observed spectral features, large heliocentric radial velocity (-148.31 +/- 0.60 kms^{-1}), atmospheric parameters and chemical composition indicate that I22023, at a distance of 1.95 kpc, is an evolved post-AGB star belonging to the old disk population. The nebular parameters suggest that the central star may be evolving into a compact, young PN, similar to Hen3-1357.

Astrophysics (astro-ph)

This article is superseded by arXiv:1112.1326 to appear in MNRAS

subsumed by another publication

0707.1379v3

Streamwise evolution of the entrainment in a steady two-dimensional bluff-body wake

This paper has been withdrawn by the authors, as it has been rejected in October 2007.

Fluid Dynamics (physics.flu-dyn)

This paper has been withdrawn by the authors, as it has been rejected in October 2007.

reason not specified

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

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

0707.3881v2

Some tensor products

We define the tensor product of 1-motives with motives of weight 0 and we construct explicitely the 1-motive underlying the quotient M_1 \otimes M_2 / W_{-3}(M_1 \otimes M_2).

Algebraic Geometry (math.AG)

This paper has been withdrawn by the author because it is a section of the paper "Multilinear morphisms between 1-motives"

subsumed by another publication

0707.4175v3

On Hadamard matrices at roots of unity

This paper has been withdrawn by the authors, the main result being known since Lam and Leung, J. Algebra 2000.

Combinatorics (math.CO)

This paper has been withdrawn by the authors, the main result being known since Lam and Leung, J. Algebra 2000

subsumed by another publication

0707.4396v4

La $\mathrm{Z}_l$-cohomologie du modèle de Deligne-Carayol est sans torsion

This article is the $\mathrm{Z}_l$-version of my paper "Monodromie du faisceau pervers des cycles évanescents de quelques variétés de Shimura simples" in Invent. Math. 2009 vol 177 pp. 239-280, where we study the vanishing cycles of some unitary Shimura variety. The aim is to prove that the cohomology sheaves of this complexe are free so that, thanks to the main theorem of Berkovich on vanishing cycles, we can deduce that the $\mathrm{Z}_l$-cohomology of the model of Deligne-Carayol is free. There will be a second article which will be the $\mathrm{Z}_l$ version of my paper "Conjecture de monodromie-poids pour quelques varités de Shimura unitaires" in Compositio vol 146 part 2, pp. 367-403. The aim of this second article will be to study the torsion of the cohomology groups of these Shimura varieties.

Algebraic Geometry (math.AG)

the new version is now arXiv:1309.1946

subsumed by another publication

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

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

0708.0510v3

Transient and asymptotic behaviour of small three-dimensional perturbations applied to a growing wake

This paper has been withdrawn by the authors, as it has been rejected in November 2007.

Fluid Dynamics (physics.flu-dyn)

This paper has been withdrawn by the authors, as it has been rejected in November 2007.

administrative or legal issues

0708.0898v2

Optimisation of the 3-body dynamics applied to extra-solar planetary systems

The body of work presented here revolves around the investigation of the existence and nature of extra-solar planetary systems. The fitting of stellar radial velocity time series data is attempted by constructing a model to quantify the orbital properties of a star-planetary system. This is achieved with the Planetary Orbit Fitting Process (POFP). Though specific to the investigated problem, the POFP is founded on two separate, more general ideas. One is a Solver producing the gravitational dynamics of a Three-Body system by integrating its Newtonian equations of motion. The other is an independent optimisation scheme. Both have been devised using MATLAB. Applying the optimisation to the Solver results in a realistic Three-Body dynamics that best describes the radial velocity data under the model-specific orbital-observational constraints. Combining these aspects also allows for the study of dynamical instability derived from interaction, which is reaffirmed as a necessary criterion for evaluating the fit. The validity of POFP solutions with respect to the observations and other models is discussed in this context. The underlying generality and fundamental principles demonstrate a larger frame of operation where problems in Physics and Mathematics can be solved with a multitude of techniques.

Astrophysics (astro-ph)

(in .ps, MNRAS template), 14 pages, 5 figures OUTDATED AND CONTAINS NO MEANINGFUL DEVELOPMENT FOR THE FIELD. CONTINUED WORK CITED/EXPLAINED IN OTHER PUBLICATIONS. PLEASE SCRAP

subsumed by another publication

0708.1068v4

Capability of multi-detector analyses on supernova neutrinos

This paper has been withdrawn by the author, due to errors in the figures.

High Energy Physics - Phenomenology (hep-ph)

This paper has been withdrawn

reason not specified

0708.1993v2

Dynamics of glucose-lactose diauxic growth in E. coli

We present a mathematical model of glucose-lactose diauxic growth in Escherichia coli including both the postive and negative regulation mechanisms of the lactose operon as well as the inducer exclusion. To validate this model, we first calculated the time evolution of beta-galactosidase for only the lactose nutrient and compared the numerical results with experimental data. Second, we compared the calculated cell biomass of the glucose-lactose diauxic growth with the experimental optical density of the diauxic growth for a particular E. coli MG 1655. For both cases, the numerical calculations from this model are in good agreement with these two experiments' data. The diauxic growth pattern of a wild type E. coli was also investigated.

Other Quantitative Biology (q-bio.OT)

This paper has been withdrawn by the author because it was a part of the author's thesis

subsumed by another publication

0708.2611v2

Boundedness and Compactness of Toeplitz operators with L^1 symbols on the Bergman space

We characterise the boundedness of a Toeplitz operator on the Bergman space with an L^1 this http URL also prove that the compactness of a Toeplitz operator on the Bergman space with an L^1 symbol is completely determined by the boundary behaviour of itss Berezin transform. This result extends known results in the cases when the symbol is either a positive L^1 function, an L^\infty function or a general BMO^1 function.

Complex Variables (math.CV)

This paper has been withdrawn

reason not specified

0708.2635v2

Boundedness and Compactness of products of Toeplitz operators on the Bergman Space

In a celebrated conjecture this http URL stated a necessary and sufficient condition on the symbols f, g in the Bergman space, L^2_a(\Delta) of the unit disk, \Delta, for the products T_{f}T_{\bar g} of associated Toeplitz operators to be bounded (respectively compact) on L^2_a(\Delta) . K. Stroethoff and D. Zheng proved that these conditions are necessary. We prove the sufficiency of these conditions, thus solvind Sarason's conjecture.

Complex Variables (math.CV)

The paper has been withdrawn

reason not specified

0708.3309v2

A combinatorial realization of the Heisenberg action on the space of conformal blocks

This paper has been withdrawn by the author. Improved versions ( arXiv:1109.5548 and arXiv:0708.4190 ) are accepted.

Geometric Topology (math.GT)

21 pages, 15 figures ; This paper has been withdrawn by the author. Improved versions (arXiv:1109.5548 and arXiv:0708.4190) are accepted

subsumed by another publication

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

0709.1499v7

Markoff Equation and Nilpotent Matrices

A triple (a,b,c) of positive integers is called a Markoff triple iff it satisfies the diophantine equation a2 + b2 + c2 = abc . Recasting the Markoff tree, whose vertices are Markoff triples, in the framework of intergral upper triangular 3x3 matrices, it will be shown that the largest member of such a triple determines the other two uniquely. This answers a question which has been open for almost 100 years.

Number Theory (math.NT)

Most of the (correct) portion of this paper has been incorporated into the paper "On the Markoff equation" (arXiv:1208.4032)

subsumed by another publication

0709.3334v2

Mistake Analyses on Proof about Perfect Secrecy of One-time-pad

This paper has been withdrawn

Cryptography and Security (cs.CR)

This paper has been withdrawn

reason not specified

0710.2270v3

On the low-energy density of states in disordered d-wave superconductor

We study the low-energy density of states of Dirac fermions in disordered d-wave superconductor. At zero energy, a finite density of states is obtained via the mechanism of dynamical mass generation in an effective (1+1)-dimensional relativistic field theory.

Superconductivity (cond-mat.supr-con)

This paper has been withdrawn by the author due to the absence of new result

not novel

0708.2994v3

Surface electric potential dynamic on graphite

We observe variations on the surface potential of graphite samples that we attribute to the adsorption physisorption of tetracene isomers.

Materials Science (cond-mat.mtrl-sci)

The paper is now submitted to Carbon journal. A fully revised version of the manuscript will replace the previous one

subsumed by another publication

0709.1616v3

Bandwidth Selection for Weighted Kernel Density Estimation

In the this paper, the authors propose to estimate the density of a targeted population with a weighted kernel density estimator (wKDE) based on a weighted sample. Bandwidth selection for wKDE is discussed. Three mean integrated squared error based bandwidth estimators are introduced and their performance is illustrated via Monte Carlo simulation. The least-squares cross-validation method and the adaptive weight kernel density estimator are also studied. The authors also consider the boundary problem for interval bounded data and apply the new method to a real data set subject to informative censoring.

Methodology (stat.ME)

Will be rewritten for resubmission

incomplete exposition or more work in progress

0709.2201v9

A complete proof of The Graceful Tree Conjecture using the concept of Edge Degree

We show the Graceful Tree Conjecture holds.

Discrete Mathematics (cs.DM)

This paper has been withdrawn by the author

reason not specified

0709.2525v5

H-Decompositions

We show that for all graphs H of size n, the complete graph $K_{2n+1}$ has an $H$-decomposition.

Discrete Mathematics (cs.DM)

This paper has been withdrawn by the author

reason not specified

0709.2972v4

Double Fell bundles over discrete double groupoids with folding

In this paper we construct the notions of double Fell bundle and double C*-category for possible future use as tools to describe noncommutative spaces, in particular in finite dimensions. We identify the algebra of sections of a double Fell line bundle over a discrete double groupoid with folding with the convolution algebra of the latter. This turns out to be what one might call a double C*-algebra. We generalise the Gelfand-Naimark-Segal construction to double C*-categories and we form the dual category for a saturated double Fell bundle using the Tomita-Takesaki involution.

Mathematical Physics (math-ph)

Withdrawn to allow for a complete new submission thanks to the addition of other authors. In preparation: "Involutive double categories" with Bertozzini, Conti and Resende

incomplete exposition or more work in progress

0709.3012v2

Construction of a stationary queue with impatient customers

In this paper, we study the stability of queues with impatient customers. Under general stationary ergodic assumptions, we first provide some conditions for such a queue to be regenerative (i.e. to empty a.s. an infinite number of times). In the particular case of a single server operating in First in, First out, we prove the existence (in some cases, on an enlarged probability space) of a stationary workload. This is done by studying a non-monotonic stochastic recursion under the Palm settings, and by stochastic comparison of stochastic recursions.

Probability (math.PR)

This paper has been withdrawn by the author. This paper has been published in a newer version, arXiv:0802.2495

subsumed by another publication

0709.3590v5

An extension of a result concerning convex geometric graphs

We show a general result known as the Erdos_Sos Conjecture: if $E(G)>{1/2}(k-1)n$ where $G$ has order $n$ then $G$ contains every tree of order $k+1$ as a subgraph.

Discrete Mathematics (cs.DM)

This paper has been withdrawn by the author. This paper was presented at [REDACTED-NAME] Days in [REDACTED-NAME] Colorado

subsumed by another publication

0709.4303v2

Security Analyses of One-time System

This paper has been withdrawn

Cryptography and Security (cs.CR)

any comment is welcome, my email [REDACTED-EMAIL]

reason not specified

0709.4367v4

Are biological neurons that vicious ? Or only their models ?

This paper has been withdrawn. Its main conclusions have been published in "On dynamics of integrate-and-fi re neural networks with conductance based synapses", arXiv:0709.4370 and this http URL

Biological Physics (physics.bio-ph)

This paper has been withdrawn

reason not specified

0709.4420v2

Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad

This paper has been withdrawn

Cryptography and Security (cs.CR)

This paper has been withdrawn

reason not specified

0710.0122v2

A canonical bundle formular of projective Lagrangian fibrations

We classify singular fibres of a projective Lagrangian fibration over codimension one points. As an application, we obtain a canonical bundle formula for a projective Lagrangian fibration over a smooth manifold.

Algebraic Geometry (math.AG)

This paper has been withdrawn by the author due to a crucial gap of arguments of the proof

incomplete exposition or more work in progress

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

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

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

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

0710.2762v2

Valence and spin states in perovskites LaCo0.95M0.05O3 (M = Mg, Ga, Ti)

The samples LaCoO3 with dilute substitutions on cobalt sites have been studied using the resistivity, thermopower and magnetic susceptibility measurements over the temperature range up to ~900 K. The Co-site substitution does not affect the magnetic transition at ~100 K and the onset of massive population of hole carriers at ~500 K, characteristic for undoped LaCoO3. On the other hand, the low-temperature transport and magnetism is markedly distinct for samples with extra charge on cobalt ions introduced by the heterovalent dopants (Mg2+, Ti4+) compared to samples with minor non-stoichiometry (LaCoO3, Ga3+ doped sample). Magnetic properties suggest that these extra charges create thermally stable magnetic polarons of total S ~ 2-3. Common features of Co-site doped and La-site doped samples (La1-xSrxCoO3) are discussed

Materials Science (cond-mat.mtrl-sci)

This paper has been withdrawn by the authors. J. Magn. Magn. Mater. 320, e92 (2008)

reason not specified

0710.3446v4

Conformal Invariance for Certain Models of the Bond-Triangular Type

Following the approach outlined in [18], convergence to SLE6 of the Exploration Processes for the correlated bond-triangular type models studied in [7] is established. This puts the said models in the same universality class as the standard site percolation model on the triangular lattice [19]. The result is proven for all domains with boundary (upper) Minkowski dimension less than two. Moreover, the proof of convergence applies in the general context of critical 2D percolation models, under the stipulation that Cardy's Formula can be established.

Mathematical Physics (math-ph)

This paper has been withdrawn as its contents - with the exception of the Appendix on uniform continuity of crossing probabilities - will be replaced by upcoming submissions "[REDACTED-NAME] to SLE_6 I: [REDACTED-NAME] for [REDACTED-NAME] of the Bond-[REDACTED-NAME]" and "Convergence to SLE_6 II: [REDACTED-NAME] and Extraction of Cardy's Formula for [REDACTED-NAME]". The purposed served by the Appendix in proving convergence to SLE_6 in this withdrawn version will be served by the second paper, which instead establishes a sufficiently robust convergence to Cardy's Formula.

subsumed by another publication

0710.3473v2

Modelling the effects of air pollution on health using Bayesian Dynamic Generalised Linear Models

The relationship between short-term exposure to air pollution and mortality or morbidity has been the subject of much recent research, in which the standard method of analysis uses Poisson linear or additive models. In this paper we use a Bayesian dynamic generalised linear model (DGLM) to estimate this relationship, which allows the standard linear or additive model to be extended in two ways: (i) the long-term trend and temporal correlation present in the health data can be modelled by an autoregressive process rather than a smooth function of calendar time; (ii) the effects of air pollution are allowed to evolve over time. The efficacy of these two extensions are investigated by applying a series of dynamic and non-dynamic models to air pollution and mortality data from Greater London. A Bayesian approach is taken throughout, and a Markov chain monte carlo simulation algorithm is presented for inference. An alternative likelihood based analysis is also presented, in order to allow a direct comparison with the only previous analysis of air pollution and health data using a DGLM.

Applications (stat.AP)

Accepted for publication in Environmetrics, October 2nd 2007

subsumed by another publication

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

0710.3633v3

Dynamics in Thompson's Group F

We describe an explicit relationship between strand diagrams and piecewise-linear functions for elements of Thompson's group F. Using this correspondence, we investigate the dynamics of elements of F, and we show that conjugacy of one-bump functions can be described by a Mather-type invariant.

Group Theory (math.GR)

This paper has been merged with the preprint http://arxiv.org/abs/0708.4250 which underwent a major revision and is now called "Conjugacy and Dynamics in Thompson's groups"

subsumed by another publication

0710.4155v2

Hook-content formulae for symplectic and orthogonal tableaux

By considering the specialisation $s_{\lambda}(1,q,q^2,...,q^{n-1})$ of the Schur function, Stanley was able to describe a formula for the number of semistandard Young tableaux of shape $\lambda$ in terms of two properties of the boxes in the diagram for $\lambda$. Using specialisations of symplectic and orthogonal Schur functions, we derive corresponding formulae, first given by El Samra and King, for the number of semistandard symplectic and orthogonal $\lambda$-tableaux.

Combinatorics (math.CO)

Withdrawn; paper is outdated

not novel

0710.4233v8

Hamiltonian stationary Lagrangian tori contained in a hypersphere

The Clifford torus is a torus in a three-dimensional sphere. Homogeneous tori are simple generalization of the Clifford torus which still in a three-dimensional sphere. There is a way to construct tori in a three-dimensional sphere using the Hopf fibration. In this paper, all Hamiltonian stationary Lagrangian tori which is contained in a hypersphere in the complex Euclidean plane are constructed explicitly. Then it is shown that they are homogeneous tori. For the construction, flat quaternionic connections of Hamiltonian stationary Lagrangian tori are considered and a spectral curve of an associated family of them is used.

Differential Geometry (math.DG)

This paper has been withdrawn by the author because the result is trivial

not novel

0710.4631v2

The nature of light in an expanding universe

In this paper, we prove the existence of two degrees of freedom that govern the movement of light in an expanding universe. The use of the fractal manifold model leads to reciprocal causality between variation of geometry and gravity, which both play a complementary role in the universe architecture. This study unravels new facts about the distribution of matter in the universe, and provides a new interpretation of Dark Matter and Dark Energy.

General Physics (physics.gen-ph)

This is an old version not published. The updated version of it was published in [REDACTED-NAME] of [REDACTED-NAME] in [REDACTED-NAME] and corresponds to arXiv:1302.1490, Infinity of Geodesics in an Homogeneous and [REDACTED-NAME] Space-Time

subsumed by another publication

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

0710.5684v2

Why Does the Rouse Model Works at Least Satisfactorily at Polymer Molecular Masses M<M_c ?

Generalization of the Rouse model without any use of the postulates concerning the Gaussian distribution of the vector connecting the ends of segments is advanced. In the initial (in general, nonlinear) Langevin equations, self-averaging over continuous fragments of a macromolecule naturally defines a linear term for the tagged chain, and this term differs from the entropy term of the classical Rouse model only by the numerical coefficient. According to the inertia-free approximation, the initial decay rates of correlation functions for the normal modes are described by the Rouse model independently of the character of fluctuations of the vector connecting the ends of the Kuhn segment. This statement is valid for any moment if the initial Langevin equations are treated in terms of the approximation of dynamic self-consistency. Simulation of the Fraenkel chains by the method of Brownian dynamics shows that decay of autocorrelation functions of shortwave normal modes is fairly described by the linearized equations for a given model of a chain and that the Rouse equation can be used for the longwave modes. The results of this study make it possible to explain a marked difference between the lengths of the Kuhn and Rouse segments that is estimated from static and dynamic experiments.

Soft Condensed Matter (cond-mat.soft)

This paper has been withdrawn by the author, an extended and improved version is: this http URL, this http URL, this http URL, [REDACTED-NAME] the [REDACTED-NAME] [REDACTED-NAME] the [REDACTED-NAME] of [REDACTED-NAME] at [REDACTED-NAME] below [REDACTED-NAME]? [REDACTED-NAME], Ser. A, 2010, V.52, No. 1, pp. 72-81

subsumed by another publication

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

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

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

0711.1605v2

Asymptotic Capacity of Wireless Ad Hoc Networks with Realistic Links under a Honey Comb Topology

We consider the effects of Rayleigh fading and lognormal shadowing in the physical interference model for all the successful transmissions of traffic across the network. New bounds are derived for the capacity of a given random ad hoc wireless network that reflect packet drop or capture probability of the transmission links. These bounds are based on a simplified network topology termed as honey-comb topology under a given routing and scheduling scheme.

Information Theory (cs.IT)

This paper has been withdrawn by the authors. 3 pages, 1 figure, Submitted to IEEE [REDACTED-NAME]

reason not specified

0711.2241v10

Bounds on the cardinality of partition

If A is infinite and well-ordered, then |2^A|<=|Part(A)|<=|A^A|.

General Mathematics (math.GM)

I'm no longer satisfied with my treatment of this topic

incomplete exposition or more work in progress

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

0711.4050v2

Space and time as containers, Space divisibility, and Unrepeatability of events

Our main purpose here is to study some qualitative aspects of space and time. These include the notion of space and time regarded as the containers of respectively bodies and events, the divisibility of space, and the unrepeatability of events. We thereof argue that the ideas of an empty space, portions of empty space and a homogenous space are misleading when they are applied to realized space, and that they are therefore not suitable for space as a condition of corporeal world (as it is often assumed). We also show that smallest (indivisible) and "final" ("ultimate") parts of space and bodies have, at most, a conventional character, and not a "fundamental" one (as it is usually claimed). With respect to time and events, analogous conclusions follow. However, we claim that between space and time there exist rather big qualitative differences, which make time's nature much more difficult to grasp than that of space. In this sense, we discuss the impossibility of repetition of events and some of its applications in modern science, notably, probabilistic and statistical science. Some other implications of this study in conceptual ("philosophical") aspects of modern physics are briefly discussed, such as the "timeless" interpretation of general relativity, the notion of space-time, among others. Finally, some considerations about the usual conception and the scope of modern science in general, and modern physics in particular, are addressed throughout the article.

History and Philosophy of Physics (physics.hist-ph)

This paper has been withdrawn by the author because the paper has been considerable enriched, giving rise to a new title "Space and Time as Containers of the '[REDACTED-NAME] World' with some Conceptual and [REDACTED-NAME] in [REDACTED-NAME]" (available also in arXiv)

incomplete exposition or more work in progress

0711.4409v6

Spherical functors

This paper has been withdrawn and replaced by arXiv:1309.5035 . In this paper we describe some examples of so called spherical functors between triangulated categories, which generalize the notion of a spherical object. We also give sufficient conditions for a collection of spherical functors to yield a weak representation of the category of tangles, and prove a structure theorem for such representations under certain restrictions.

Category Theory (math.CT)

This paper has been withdrawn and replaced by arXiv:1309.5035

subsumed by another publication

0711.4897v5

Deformed special relativity with an invariant minimum speed and its cosmological implications

The paper aims to introduce a new symmetry principle in the space-time geometry through the elimination of the classical idea of rest and by including a universal minimum limit of speed in the subatomic world. Such a limit, unattainable by particles, represents a preferred reference frame associated with a universal background field that breaks Lorentz symmetry. Thus the structure of space-time is extended due to the presence of a vacuum energy density, which leads to a negative pressure at cosmological scales. The tiny values of the cosmological constant and the vacuum energy density shall be successfully obtained, being in good agreement with current observational results.

General Relativity and Quantum Cosmology (gr-qc)

7 pages and 3 figures

incomplete exposition or more work in progress

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

0712.2310v3

From Boltzmann-Gibbs ensemble to generalized ensembles

We reconsider the Boltzmann-Gibbs statistical ensemble in thermodynamics using the multinomial coefficient approach. We show that an ensemble is defined by the determination of four statistical quantities, the element probabilities $p_i$, the configuration probabilities $P_j$, the entropy $S$ and the extremum constraints (EC). This distinction is of central importance for the understanding of the conditions under which a microcanonical, canonical and macrocanonical ensemble is defined. These three ensembles are characterized by the conservation of their sizes. A variation of the ensemble size creates difficulties in the definitions of the quadruplet $\{p_i, P_j, S, \mt{EC}\}$, giving rise for a generalization of the Boltzmann-Gibbs formalism, such one as introduced by Tsallis. We demonstrate that generalized thermodynamics represent a transformation of ordinary thermodynamics in such a way that the energy of the system remains conserved. From our results it becomes evident that Tsallis's formalism is a very specific generalization, however, not the only one. We also revisit the Jaynes's Maximum Entropy Principle, showing that in general it can lead to incorrect results and consider the appropriate corrections.

Statistical Mechanics (cond-mat.stat-mech)

This paper has been withdrawn by the author

reason not specified

0712.3744v4

Convergence properties of the expected improvement algorithm

This paper has been withdrawn from the arXiv. It is now published by Elsevier in the Journal of Statistical Planning and Inference, under the modified title "Convergence properties of the expected improvement algorithm with fixed mean and covariance functions". See this http URL An author-generated post-print version is available from the HAL repository of SUPELEC at this http URL Abstract : "This paper deals with the convergence of the expected improvement algorithm, a popular global optimization algorithm based on a Gaussian process model of the function to be optimized. The first result is that under some mild hypotheses on the covariance function k of the Gaussian process, the expected improvement algorithm produces a dense sequence of evaluation points in the search domain, when the function to be optimized is in the reproducing kernel Hilbert space generated by k. The second result states that the density property also holds for P-almost all continuous functions, where P is the (prior) probability distribution induced by the Gaussian process."

Computation (stat.CO)

This paper has been withdrawn

reason not specified

0712.4159v4

Creating a Digital Ecosystem: Service-Oriented Architectures with Distributed Evolutionary Computing

We start with a discussion of the relevant literature, including Nature Inspired Computing as a framework in which to understand this work, and the process of biomimicry to be used in mimicking the necessary biological processes to create Digital Ecosystems. We then consider the relevant theoretical ecology in creating the digital counterpart of a biological ecosystem, including the topological structure of ecosystems, and evolutionary processes within distributed environments. This leads to a discussion of the relevant fields from computer science for the creation of Digital Ecosystems, including evolutionary computing, Multi-Agent Systems, and Service-Oriented Architectures. We then define Ecosystem-Oriented Architectures for the creation of Digital Ecosystems, imbibed with the properties of self-organisation and scalability from biological ecosystems, including a novel form of distributed evolutionary computing.

Neural and Evolutionary Computing (cs.NE)

I was novice researcher when this was submitted, and I did not at the time understand that my notes for a presentation should not be considered a paper

incomplete exposition or more work in progress

0712.4305v2

One way cuts in oriented graphs

This paper has been withdrawn by the author.

Combinatorics (math.CO)

This paper has been withdrawn by the author. now included in "Subgraphs of weakly quasi-random oriented graphs"

subsumed by another publication

0801.0148v2

An Integral Inequality and the Riccati-Bernoulli Differential Equation

We apply an integral inequality to obtain a rigorous apriori estimate of the accuracy of the partial sum to the power series solution of the celebrated Riccati-Bernoulli differential equation

Classical Analysis and ODEs (math.CA)

12 pages. This paper has been withdrawn. The proof was too long

incomplete exposition or more work in progress

0801.0195v2

An optimal life insurance policy in the investment-consumption problem in an incomplete market

This paper considers an optimal life insurance for a householder subject to mortality risk. The household receives a wage income continuously, which is terminated by unexpected (premature) loss of earning power or (planned and intended) retirement, whichever happens first. In order to hedge the risk of losing income stream by householder's unpredictable event, the household enters a life insurance contract by paying a premium to an insurance company. The household may also invest their wealth into a financial market. The problem is to determine an optimal insurance/investment/consumption strategy in order to maximize the expected total, discounted utility from consumption and terminal wealth. To reflect a real-life situation better, we consider an incomplete market where the householder cannot trade insurance contracts continuously. To our best knowledge, such a model is new in the insurance and finance literature. The case of exponential utilities is considered in detail to derive an explicit solution. We also provide numerical experiments for that particular case to illustrate our results.

Portfolio Management (q-fin.PM)

This paper has been withdrawn by the authors

reason not specified

0801.0208v2

On the capacity of Lagrangians in the cotangent disc bundle of the torus

The paper is wihdrawn due to a critical error in the argument using the spectral sequence

Symplectic Geometry (math.SG)

This paper has been withdrawn by the author. 18 pages

reason not specified

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