August 2005 arXiv papers

chungwei Lin, Andrew. J. Millis

The single-site dynamical mean field theory approximation to the double exchange model is found to exhibit a previously unnoticed instability, in which a well-defined ground state which is stable against small perturbations is found to be unstable to large-amplitude but purely local fluctuations. The instability is shown to arise either from phase separation

Anastasios Psinas

An unstable $D3$-brane universe governed by the DBI action of the tachyon field minimally coupled to a U(1) gauge boson is examined. The cosmological evolution of this coupled system, is further analyzed, in terms of the expansion rate of the inflating brane, which is highly affected by the presence of the tachyonic and gauge field charges. We show, that the

Mariano Anabitarte, Mauricio Bellini

We study a model of power-law inflationary inflation using the Space-Time-Matter (STM) theory of gravity for a five dimensional (5D) canonical metric that describes an apparent vacuum. In this approach the expansion is governed by a single scalar (neutral) quantum field. In particular, we study the case where the power of expansion of the universe is $p \gg

Jack Morava

This very speculative sketch suggests that a theory of fundamental groupoids for tensor triangulated categories could be used to describe the ring of integers as the singular fiber in a family of ring-spectra parametrized by a structure space for the stable homotopy category, and that Bousfield localization might be part of a theory of `nearby' cycles fo

Marcelo Salgado

The 3+1 formulation of scalar-tensor theories of gravity (STT) is obtained in the physical (Jordan) frame departing from the 4+0 covariant field equations. Contrary to the common belief (folklore), the new system of ADM-like equations shows that the Cauchy problem of STT is well formulated (in the sense that the whole system of evolution equations is of firs

Matthias Jamin

The hadronic decay rate of the tau lepton serves as one of the most precise determinations of the QCD coupling alpha_s. The dominant theoretical source of uncertainty at present resides in the seeming disparity of two approaches to improving the perturbative expansion with the help of the renormalisation group, namely fixed-order and contour-improved perturb

Lenhard Ng

We establish an upper bound for the Thurston-Bennequin number of a Legendrian link using the Khovanov homology of the underlying topological link. This bound is sharp in particular for all alternating links, and knots with nine or fewer crossings.

J. Dietel, H. Kleinert

We set up a harmonic lattice model for 2D defect melting which, in contrast to earlier simple-cubic models, lives on a triangular lattice. Integer-valued plastic defect gauge fields allow for the thermal generation of dislocations and disclinations. The model produces universal formulas for the melting temperature expressed in terms of the elastic constants,

Felix A. Aharonian, Luis A. Anchordoqui, Dmitry Khangulyan, Teresa Montaruli

The recent detection of TeV gamma-rays from the microquasar LS 5039 by HESS is one of the most exciting discoveries of observational gamma-ray astronomy in the very high energy regime. This result clearly demonstrates that X-ray binaries with relativistic jets (microquasars) are sites of effective acceleration of particles (electrons and/or protons) to multi

Gerhard Mack, Thorsten Prustel

In gauge theories parallel transporters (PTs) U(C) along paths C play an important role. Traditionally they are unitary or pseudoorthogonal maps between vector spaces. We propose to abandon unitarity of parallel transporters and with it the a priori assumption of metricity in general relativity. A *-operation on parallel transporters serves as a substitute f

Jacob Lund Fisker, Dinshaw S. Balsara

We describe the results of numerical simulations of the dynamics of the boundary layer (BL) between the accretion disk and the surface of a non-magnetic white dwarf (WD) for different viscosities which corresponds to different stages for dwarf novae burst cycles. The simulations cover the inner part of the accretion disk, the BL, and the upper atmosphere of

B. C. Sanctuary

Entangled EPR spin pairs can be treated using the statistical ensemble interpretation of quantum mechanics. As such the singlet state results from an ensemble of spin pairs each with its own specific axis of quantization. This axis acts like a quantum mechanical hidden variable. If the spins lose coherence they disentangle into a mixed state that contains cl

Boaz Tsaban

We show that every function f implemented as a lookup table can be implemented such that the computational complexity of evaluating f^m(x) is small, independently of m and x. The implementation only increases the storage space by a small_constant_ factor.

A. S. Alexandrov

High-temperature superconductivity (HTS) of cuprates represents a challenge to the conventional theory. Here I review a multi-polaron approach to the problem based on our extension of the BCS theory to the strong-coupling regime. Since there is almost no retardation (i.e. no Tolmachev-Morel-Anderson logarithm) reducing the Coulomb repulsion, e-ph interaction

Schuyler D. Van Dyk, Weidong Li, Alexei V. Filippenko

We confirm the discovery of a light echo around the Type II-plateau Supernova 2003gd in Messier 74 (NGC 628), seen in images obtained with the High Resolution Channel of the Advanced Camera for Surveys on-board the Hubble Space Telescope (HST), as part of a larger Snapshot program on the late-time emission from supernovae. The analysis of the echo we present

F. Cianfrani, A. Marrocco, G. Montani

We present a geometrical unification theory in a Kaluza-Klein approach that achieve the geometrization of a generic gauge theory bosonic component. We show how it is possible to derive the gauge charge conservation from the invariance of the model under extra-dimensional translations and to geometrize gauge connections for spinors, thus we can introduce the

J. Meijer, T. Vogel, B. Burchard, I. Rangelow

We propose a method for deterministic implantation of single atoms into solids which relies on a linear ion trap as an ion source. Our approach allows a deterministic control of the number of implanted atoms and a spatial resolution of less than 1 nm. Furthermore, the method is expected to work for almost all hemical elements. The deterministic implantation

Carlo Morosi, Livio Pizzocchero

We consider a perturbed integrable system with one frequency, and the approximate dynamics for the actions given by averaging over the angle. The classical theory grants that, for a perturbation of order epsilon, the error of this approximation is O(epsilon) on a time scale O(1/epsilon), for epsilon -> 0. We replace this qualitative statement with a fully qu

Marco Frasca

Strong coupling expansion is computed for the Einstein equations in vacuum in the Arnowitt-Deser-Misner (ADM) formalism. The series is given by the duality principle in perturbation theory as presented in [M.Frasca, Phys. Rev. A 58, 3439 (1998)]. An example of application is also given for a two-dimensional model of gravity expressed through the Liouville eq

M. Bal, Jonathan R. Friedman, E. M. Rumberger, S. Shah

Microwave radiation applied to single-molecule magnets can induce large magnetization changes when the radiation is resonant with transitions between spin levels. These changes are interpreted as due to resonant heating of the sample by the microwaves. Pulsed-radiation studies show that the magnetization continues to decrease after the radiation has been tur

Zhi Lü

Let $\mathcal{A}_n^k$ denote all nonbounding effective smooth $({\Bbb Z}_2)^k$-actions on $n$-dimensional smooth closed connected manifolds, each of which is cobordant to one with finite fixed set. Motivated by GKM theory, one can associate to each action of $\mathcal{A}_n^k$ a $({\Bbb Z}_2)^k$-colored regular graph of valence $n$. Together with the combinat

Alakabha Datta, Patrick J. O'Donnell

The observed pattern of neutrino mixing may be the result of a 2-3($ μ- τ$) symmetry in the leptonic sector. We consider a two Higgs doublet model with a 2-3 symmetry in the down type quark and the charged lepton sector. The breaking of the 2-3 symmetry by the strange quark mass and the muon mass leads to FCNC in the quark sector and the charged lepton secto

R. Lambiotte, M. Ausloos

We focus on the dynamics of a Brownian particle whose mass fluctuates. First we show that the behaviour is similar to that of a Brownian particle moving in a fluctuating medium, as studied by Beck [Phys. Rev. Lett. 87 (2001) 180601]. By performing numerical simulations of the Langevin equation, we check the theoretical predictions derived in the adiabatic li

Anton Deitmar

The connection between Lefschetz formulae and zeta function is explained. As a particular example the theory of the generalized Selberg zeta function is presented. Applications are given to the theory of Anosov flows and prime geodesic theorems.

Andreas Gustavsson

We introduce a notion of a non-Abelian loop gauge field defined on points in loop space. For this purpose we first find an infinite-dimensional tensor product representation of the Lie algebra which is particularly suited for fields on loop space. We define the non-Abelian Wilson surface as a `time' ordered exponential in terms of this loop gauge field a

R. Lambiotte, L. Brenig

We study non-equipartition of energy in granular fluids composed by an arbitrarily large number of components. We focus on a simple mean field model, based upon a Maxwell collision operator kernel, and predict the temperature ratios for the species. Moreover, we perform Direct Monte Carlo simulations in order to verify the predictions.

Yuri N. Kosovtsov

It is known, due to Mordukhai-Boltovski, Ritt, Prelle, Singer, Christopher and others, that if a given rational ODE has a Liouvillian first integral then the corresponding integrating factor of the ODE must be of a very special form of a product of powers and exponents of irreducible polynomials. These results lead to a partial algorithm for finding Liouvill

R. Lambiotte, M. Ausloos

In this paper, we analyze web-downloaded data on people sharing their music library, that we use as their individual musical signatures (IMS). The system is represented by a bipartite network, nodes being the music groups and the listeners. Music groups audience size behaves like a power law, but the individual music library size is an exponential with devia

Minoru Eto, Youichi Isozumi, Muneto Nitta, Keisuke Ohashi

Domain wall junctions are studied in N=2 supersymmetric U(Nc) gauge theory with Nf(>Nc) flavors. We find that all three possibilities are realized for positive, negative and zero junction charges. The positive junction charge is found to be carried by a topological charge in the Hitchin system of an SU(2) gauge subgroup. We establish rules of the constructio

Luis Anchordoqui, Tao Han, Dan Hooper, Subir Sarkar

The Pierre Auger Observatory for cosmic rays provides a laboratory for studying fundamental interactions at energies well beyond those available at colliders. In addition to hadrons or photons, Auger is sensitive to ultra-high energy neutrinos in the cosmic radiation and models for new physics can be explored by observing neutrino interactions at center-of-m

Andrés Navas

We prove two theorems of reduction of cocycles taking values in the group of diffeomorphisms of the circle. They generalise previous results obtained by the author concerning rigidity for smooth actions on the circle of Kazhdan's groups and higher rank lattices.

M. I. Katsnelson

A comment about importance of Anderson's orthogonality catastrophe for projective Quantum Monte Carlo methods.

Alessio Serafini

A hierarchy of multimode uncertainty relations on the second moments of n pairs of canonical operators is derived in terms of quantities invariant under linear canonical (i.e. symplectic) transformations. Conditions for the separability of multimode continuous variable states are derived from the uncertainty relations, generalizing the inequalities obtained

Yiping Chen, Eduardo López, Shlomo Havlin, H. Eugene Stanley

We study the statistics of the optimal path in both random and scale free networks, where weights $w$ are taken from a general distribution $P(w)$. We find that different types of disorder lead to the same universal behavior. Specifically, we find that a single parameter ($S \equiv AL^{-1/ν}$ for $d$-dimensional lattices, and $S\equiv AN^{-1/3}$ for random n

Masamichi Ishihara

We investigate the amplification of the field induced by white noise. In the present study, we study a stochastic equation which has two parameters, the energy $ω(\vec{k})$ of a free particle and the coupling strength $D$ between the field and white noise, where the quantity $\vec{k}$ represents the momentum of a free particle. This equation is reduced to th

A. Dougall, C. M. Maynard, C. McNeile

We compute the mass of the charm quark using both quenched and dynamical lattice QCD calculations. We examine the effects of mass dependent lattice artifacts by comparing two different formalisms for the heavy quarks. We take the continuum limit of the charm mass in quenched QCD by extrapolating from three different lattice spacings. At a fixed lattice spaci

A. Mandilara, V. M. Akulin, A. V. Smilga, L. Viola

We propose a general method for introducing extensive characteristics of quantum entanglement. The method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference vacuum state. By introducing the notion of tanglemeter, the logarithm of the state vector represented in a special canonical form and expressed via po

Zachary Mesyan

Let R be a ring, M a nonzero left R-module, X an infinite set, and E the endomorphism ring of the direct sum of copies of M indexed by X. Given two subrings S and S' of E, we will say that S is equivalent to S' if there exists a finite subset U of E such that the subring generated by S and U is equal to the subring generated by S' and U. We show

Ewa L. Lokas, Gary A. Mamon, Francisco Prada

We present interpretations of the line-of-sight velocity distribution of stars in the Draco dwarf spheroidal galaxy in terms of CDM and MOND assuming constant mass-to-light ratio and anisotropy. We estimate the two parameters by fitting the line-of-sight velocity dispersion and kurtosis profiles for stellar samples differing by a number of stars rejected as

Yoon Pyo Hong, Indrajit Mitra

We investigate the classical stability of non-supersymmetric Freund-Rubin compactifications of Type IIB string theory on a product of three-dimensional Einstein spaces A_3 x B_3 with both NS-NS and R-R three-form fluxes turned on through A_3 and B_3, and a zero axion. This results in a three parameter family of AdS_4 vacua, with localized sources such as ant

Siew-Ann Cheong, Christopher L. Henley

The reduced density matrix of an interacting system can be used as the basis for a truncation scheme, or in an unbiased method to discover the strongest kind of correlation in the ground state. In this paper, we investigate the structure of the many-body fermion density matrix of a small cluster in a square lattice. The cluster density matrix is evaluated nu

Michael J. Lawler, Victoria Fernandez, Daniel G. Barci, Eduardo Fradkin

We discuss shape (Pomeranchuk) instabilities of the Fermi surface of a two-dimensional Fermi system using bosonization. We consider in detail the quantum critical behavior of the transition of a two dimensional Fermi fluid to a nematic state which breaks spontaneously the rotational invariance of the Fermi liquid. We show that higher dimensional bosonization

D. V. Makarov, M. Yu. Uleysky, M. Yu. Martynov

We investigate sound ray propagation in a range-dependent underwater acoustic waveguide. Our attention is focused on sensitivity of ray dynamics to the vertical structure of a sound-speed perturbation induced by ocean internal waves. Two models of longitudinal sound-speed variations are considered: a periodic inhomogeneity and a stochastic one. It is found t

CP-PACS, JLQCD Collaborations, :, S. Aoki

We perform a nonperturbative determination of the $O(a)$-improvement coefficient $c_{\rm SW}$ and the critical hopping parameter $κ_c$ for $N_f$=3, 2, 0 flavor QCD with the RG-improved gauge action using the Schrödinger functional method. In order to interpolate $c_{\rm SW}$ and $κ_c$ as a function of the bare coupling, a wide range of $β$ from the weak coup

Stefan Wolf, Juerg Wullschleger

So-called non-local boxes, which have been introduced as an idealization-in different respects-of the behavior of entangled quantum states, have been known to allow for unconditional bit commitment between the two involved parties. We show that, actually, any possible non-local correlation which produces random bits on both sides can be used to implement bit

Mohan Sarovar, Hsi-Sheng Goan, T. P. Spiller, G. J. Milburn

Circuit QED is a promising solid-state quantum computing architecture. It also has excellent potential as a platform for quantum control -- especially quantum feedback control -- experiments. However, the current scheme for measurement in circuit QED is low efficiency and has low signal-to-noise ratio for single shot measurements. The low quality of this mea

Wei Liu, Jeremy Goodman, Hantao Ji

In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we present non-ideal two-dimensional magnetohydrodynamic simulations of the nonlinear evolution of MRI in the experimental geometry. The simulations adopt initially uniform vertical magnetic fields, conducting radial boundaries, and periodic vertical boundary con

P. Mateus, Y. Omar

We propose a quantum algorithm for closest pattern matching which allows us to search for as many distinct patterns as we wish in a given string (database), requiring a query function per symbol of the pattern alphabet. This represents a significant practical advantage when compared to Grover's search algorithm as well as to other quantum pattern matchin

Simon Samuelsson, Gunnar Björk

We comment on the recent suggestion to use a family of local uncertainty relations as a standard way of quantifying entanglement in two-qubit systems. Some statements made on the applicability of the proposed "measures" are overly optimistic. We exemplify how these specific "measures" fall short, and present a minor modification of the genera

Runyao Duan, Yuan feng, Mingsheng Ying

We show that two ways of manipulation of quantum entanglement, namely, entanglement-assisted local transformation [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. {\bf 83}, 3566 (1999)] and multiple-copy transformation [S. Bandyopadhyay, V. Roychowdhury, and U. Sen, Phys. Rev. A {\bf 65}, 052315 (2002)], are equivalent in the sense that they can asymptoticall

Eric J. Deeds, Orr Ashenberg, Eugene I. Shakhnovich

It has recently been demonstrated that many biological networks exhibit a scale-free topology where the probability of observing a node with a certain number of edges (k) follows a power law: i.e. p(k) ~ k^-g. This observation has been reproduced by evolutionary models. Here we consider the network of protein-protein interactions and demonstrate that two pub

Jonathan Phillips, Chun-Ku Chen, Kamran Akhtar, Bala Dhandapani

In this paper the selective broadening of the atomic hydrogen lines in pure H2 and Ar/H2 mixtures in a large 'GEC' cell (36 cm length_ 14 cm ID) was mapped as a function of position, H2/Ar ratio, time, power, and pressure. Several observations regarding the selective line broadening were particularly notable as they are unanticipated on the basis of

J. Hübner, J. S. Aitchison, H. M. van Driel

We demonstrate ultrafast all-optical deflection of spatial solitons in an AlGaAs slab waveguide using 190 fs, 1550 nm pulses which are used to generate and deflect the spatial soliton. The steering beam is focused onto the top of the waveguide near the soliton pathway and the soliton is steered due to refractive index changes induced by optical Kerr, or free

Stefan Boettcher, Martin Frank

Using a simple, annealed model, some of the key features of the recently introduced extremal optimization heuristic are demonstrated. In particular, it is shown that the dynamics of local search possesses a generic critical point under the variation of its sole parameter, separating phases of too greedy (non-ergodic, jammed) and too random (ergodic) explorat

Manuel Cardona

Einstein is usually revered as the father of special and general relativity. In this article I demonstrate that he is also the father of Solid State Physics, or even his broader version known as Condensed Matter Physics (including liquids). His 1907 article on the specific heat of solids introduces, for the first time, the effect of lattice vibrations on the

A. Kwang-Hua Chu

A numerical investigation for the stability of the incompressible slip flow of normal quantum fluids (above the critical phase transition temperature) inside a microslab where surface acoustic waves propagate along the walls is presented. Governing equations and associated slip velocity and wavy interface boundary conditions for the flow of normal fluids con

Ricardo A. Depine, Marina E. Inchaussandague, Akhlesh Lakhtakia

The geometric representation at a fixed frequency of the wavevector (or dispersion) surface $ω(\vec k)$ for lossless, homogeneous dielectric--magnetic uniaxial materials is explored, when the elements of the relative permittivity and permeability tensors of the material can have any sign. Electromagnetic plane waves propagating inside the material can exhibi

R. Lambiotte, M. Ausloos

In this paper, we study empirically co-authorship networks of neighbouring scientific disciplines, and describe the system by two coupled networks. By considering a large time window, we focus on the properties of the interface between the disciplines. We also focus on the time evolution of the co-authorship network, and highlight a rich phenomenology includ

A. I. Milstein, I. S. Terekhov, U. D. Jentschura, C. H. Keitel

We investigate quantum electrodynamic effects under the influence of an external, time-dependent electromagnetic field, which mediates dynamic modifications of the radiative corrections. Specifically, we consider the quantum electrodynamic vacuum-polarization tensor under the influence of two external background fields: a strong laser field and a nuclear Cou

Bernard Jancewicz

Plane electromagnetic wave propagating in perfect electromagnetic conductor (PEMC) is considered. Its wave number has no connection with the frequency. An interface is introduced between an ordinary isotropic medium and PEMC. The wave in PEMC is matched to plane electromagnetic wave incident normally on the interface from the ordinary medium and reflected fr

Ali Dabirian, Mahmood Akbari, Niels Asger Mortensen

We describe a semi-analytical approach for three-dimensional analysis of photonic crystal fibre devices. The approach relies on modal transmission-line theory. We offer two examples illustrating the utilization of this approach in photonic crystal fibres: the verification of the coupling action in a photonic crystal fibre coupler and the modal reflectivity i

Tiberiu Teşileanu, Hildegard Meyer-Ortmanns

We consider the spreading and competition of languages that are spoken by a population of individuals. The individuals can change their mother tongue during their lifespan, pass on their language to their offspring and finally die. The languages are described by bitstrings, their mutual difference is expressed in terms of their Hamming distance. Language evo

Timothy C. Jarrett, Douglas J. Ashton, Mark Fricker, Neil F. Johnson

We show analytically that abrupt structural transitions can arise in functionally optimal networks, driven by small changes in the level of transport congestion. Our findings are based on an exactly solvable model system which mimics a variety of biological and social networks. Our results offer an explanation as to why such diverse sets of network structure

M. Yan

This article recounts definition, classification, history, and applications of microstructured optical fibers.

Jonathan Phillips, Chun Ku Chen, Randell Mills

Selective H-atom line broadening was found to be present throughout the volume (13.5 cm ID x 38 cm length) of RF generated H2O plasmas in a GEC cell. Notably, at low pressures (ca. <0.08 Torr), a significant fraction (ca. 20%) of the atomic hydrogen was &#39;hot&#39; with energies greater than 40 eV with a pressure dependence, but only a weak power dependenc

Wojciech Satula

Simple generic aspects of nuclear pairing in homogeneous medium as well as in finite nuclei are discussed. It is argued that low-energy nuclear structure is not sensitive enough to resolve fine details of nuclear nucleon-nucleon (NN) interaction in general and pairing NN interaction in particular what allows for regularization of the ultraviolet (high-moment

S. Flach, M. V. Ivanchenko, O. I. Kanakov

The Fermi-Pasta-Ulam (FPU) problem consists of the nonequipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number q. We continue normal modes from the harmonic limit into the FPU parameter regime and obtain p

Moty Schultz, Lior Klein, J. W. Reiner, M. R. Beasley

${\rm CaRuO_3}$ is a paramagnetic metal and since its low temperature resistivity is described by $ρ=ρ_0+AT^γ$ with $γ\sim 1.5$, it is also considered a non-Fermi liquid (NFL) metal. We have performed extensive magnetoresistance and Hall effect measurements of untwinned epitaxial films of ${\rm CaRuO_3}$. These measurements reveal that ${\rm CaRuO_3}$ exhibi

M. -P. Grosset, A. P. Veselov

A generalisation of the Faulhaber polynomials and Bernoulli numbers related to elliptic curves is introduced and investigated. This is applied to compute the density of states for the classical Lamé operators.

T. Claeys, A. B. J. Kuijlaars, M. Vanlessen

We study unitary random matrix ensembles of the form $Z_{n,N}^{-1} |\det M|^{2α} e^{-N \Tr V(M)}dM$, where $α>-1/2$ and $V$ is such that the limiting mean eigenvalue density for $n,N\to\infty$ and $n/N\to 1$ vanishes quadratically at the origin. In order to compute the double scaling limits of the eigenvalue correlation kernel near the origin, we use the Dei

Pavel Exner

We discuss a pair of isoperimetric problems which at a glance seem to be unrelated. The first one is classical: one places $N$ identical point charges at a closed curve $Γ$ at the same arc-length distances and asks about the energy minimum, i.e. which shape does the loop take if left by itself. The second problem comes from quantum mechanics: we take a Schrö

Pavel Exner, Evans M. Harrell, Michael Loss

We consider a pair of isoperimetric problems arising in physics. The first concerns a Schrödinger operator in $L^2(\mathbb{R}^2)$ with an attractive interaction supported on a closed curve $Γ$, formally given by $-Δ-αδ(x-Γ)$; we ask which curve of a given length maximizes the ground state energy. In the second problem we have a loop-shaped thread $Γ$ in $\ma

Karmadeva Maharana

We use group theoretic methods to obtain the extended Lie point symmetries of the equations of motion for a charged particle in the field of a monopole. Cases with certain model magnetic fields and potentials are also studied. Our analysis gives the generators and Lie algebras generating the inherent symmetries. The equations of motion of a scalar particle p

Wolfgang Lueck, Holger Reich

We discuss which part of the rationalized algebraic K-theory of a group ring is detected via trace maps to Hochschild homology, cyclic homology, periodic cyclic or negative cyclic homology.

S. J. Dilworth, E. Odell, B. Sari

We consider problems concerning the partial order structure of the set of spreading models of Banach spaces. We construct examples of spaces showing that the possible structure of these sets include certain classes of finite semi-lattices and countable lattices, and all finite lattices.

Henry Glover, Dragan Marusic

Following a problem posed by Lovász in 1969, it is believed that every connected vertex-transitive graph has a Hamilton path. This is shown here to be true for cubic Cayley graphs arising from groups having a $(2,s,3)$-presentation, that is, for groups $G=\la a,b| a^2=1, b^s=1, (ab)^3=1, etc. \ra$ generated by an involution $a$ and an element $b$ of order $s

Noam D. Elkies

Normally a chess problem must have a unique solution, and is deemed unsound even if there are alternatives that differ only in the order in which the same moves are played. In an enumerative chess problem, the set of moves in the solution is (usually) unique but the order is not, and the task is to count the feasible permutations via an isomorphic problem in

Massimo Cicognani, Daniele Del Santo, Michael Reissig

We use the Littlewood-Paley decomposition technique to obtain a $C^\infty$-well-posedness result for a weakly hyperbolic equation with a finite order of degeneration

Niko Naumann

A. Moriwaki proved the following arithmetic analogue of the Bogomolov unstability theorem. If a torsion-free hermitian coherent sheaf on an arithmetic surface has negative discriminant then it admits an arithmetically destabilising subsheaf. In the geometric situation it is known that such a subsheaf can be found subject to an additional numerical constraint

H. Gopalkrishna Gadiyar, R. Padma

A prime p is called Sophie Germain prime if 2p+1 is also prime. A formula for the density of such primes is given in a more general setting using a new approach. This method uses the Ramanujan-Fourier series for a modified von Mangoldt function. The proof remains heuristic as interchange of certain limits has not been justified. Experimental evidence using c

Florin Panaite, Freddy Van Oystaeyen

We prove that a certain bialgebroid introduced recently by Kadison is isomorphic to a bialgebroid introduced earlier by Connes and Moscovici. At the level of total algebras, the isomorphism is a consequence of the general fact that an L-R-smash product over a Hopf algebra is isomorphic to a diagonal crossed product.

Juan-Pablo Ortega, Tudor S. Ratiu

This encyclopedia article briefly reviews without proofs some of the main results in cotangent bundle reduction. The article recalls most the necessary prerequisites to understand the main results.

Juan-Pablo Ortega, Tudor S. Ratiu

This encyclopedia article briefly reviews without proofs some of the main results in Poisson reduction. The article recalls most the necessary prerequisites to understand the main results.

Juan-Pablo Ortega, Tudor S. Ratiu

This encyclopedia article briefly reviews without proofs some of the main results in symplectic reduction. The article recalls most the necessary prerequisites to understand the main results, namely, group actions, momentum maps, and coadjoint orbits, among others.

V. M. Gichev, O. S. Morozov

We describe up to finite coverings causal flat affine complete Lorentzian manifolds such that the past and the future of any point are closed near this point. We say that these manifolds are strictly causal. In particular, we prove that their fundamental groups are virtually abelian. In dimension 4, there is only one, up to a scaling factor, strictly causal

Alexandru Ionescu, Carlos Kenig

We prove that the Benjamin-Ono initial value problem is globally well-posed in the Sobolev spaces $H^σ_r$, $σ\geq 0$.

Kurt Herzinger, Stephen Wilson, Nándor Sieben, Jeff Rushall

This paper considers numerical semigroups $S$ that have a non-principal relative ideal $I$ such that $μ_S(I)μ_S(S-I)=μ_S(I+(S-I)) $. We show the existence of an infinite family of such which $I+(S-I)=S\backslash\{0\}$. We also show examples of such pairs that are not members of this family. We discuss the computational process used to find these examples and

John H. Conway, Noam D. Elkies, Jeremy L. Martin

We study a construction of the Mathieu group $M_{12}$ using a game reminiscent of Loyd&#39;s ``15-puzzle&#39;&#39;. The elements of $M_{12}$ are realized as permutations on~12 of the~13 points of the finite projective plane of order~3. There is a natural extension to a ``pseudogroup&#39;&#39; $M_{13}$ acting on all~13 points, which exhibits a limited form of

Tristram Bogart, Anders N. Jensen, Rekha R. Thomas

The circuit ideal, $\ica$, of a configuration $\A = \{\a_1, ..., \a_n\} \subset \Z^d$ is the ideal generated by the binomials ${\x}^{\cc^+} - {\x}^{\cc^-} \in \k[x_1, ..., x_n]$ as $\cc = \cc^+ - \cc^- \in \Z^n$ varies over the circuits of $\A$. This ideal is contained in the toric ideal, $\ia$, of $\A$ which has numerous applications and is nontrivial to co

Peter Howard, Mohammadreza Raoofi, Kevin Zumbrun

Refining previous work in \cite{Z.3, MaZ.3, Ra, HZ, HR}, we derive sharp pointwise bounds on behavior of perturbed viscous shock profiles for large-amplitude Lax or overcompressive type shocks and physical viscosity. These extend well-known results of Liu \cite{Liu97} obtained by somewhat different techniques for small-amplitude Lax type shocks and artificia

Genevra Neumann

A sufficient condition for a cluster point of a planar harmonic function to be an asymptotic value is given, based on a partitioning into regions of constant valence. A sufficient condition for the cluster set of a planar harmonic function to have non-empty interior is given. An example is given of a planar harmonic function where the image of the critical s

Yukinobu Toda

The results of this paper were already known.

Hao Pan

We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers.

Jaroslav Nesetril, Patrice Ossona De Mendez

Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r, &#8711;r(G). These classes are also characterized by the existence of several partition results such as the existence of low tree

Morihiko Saito

We show that the direct image of the filtered logarithmic de Rham complex is a direct sum of filtered logarithmic complexes with coefficients in variations of Hodge structures, using a generalization of the decomposition theorem of Beilinson, Bernstein and Deligne to the case of filtered $D$-modules. The advantage of using the logarithmic complexes is that w

Andrew S. Toms, Wilhelm Winter

Say that a separable, unital C*-algebra D is strongly self-absorbing if there exists an isomorphism $ϕ: D \to D \otimes D$ such that $ϕ$ and $id_D \otimes 1_D$ are approximately unitarily equivalent $*$-homomorphisms. We study this class of algebras, which includes the Cuntz algebras $\mathcal{O}_2$, $\mathcal{O}_{\infty}$, the UHF algebras of infinite type,

Peter Cholak, Leo Harrington

We prove an algebraic extension theorem for the computably enumerable sets, $\mathcal{E}$. Using this extension theorem and other work we then show if $A$ and $\hat{A}$ are automorphic via $Ψ$ then they are automorphic via $Λ$ where $Λ\restriction Ł^*(A) = Ψ$ and $Λ\restriction \E^*(A)$ is $Δ^0_3$. We give an algebraic description of when an arbitrary set $\

Tomomi Muto

We study D-branes transverse to an abelian orbifold C^3/Z_n Z_n. The moduli space of the gauge theory on the D-branes is analyzed by combinatorial calculation based on toric geometry. It is shown that the calculation is related to a problemto count the number of ground states of an antiferromagnetic Ising model. The lattice on which the Ising model is define

Yves Brihaye, Betti Hartmann, Eugen Radu

We consider solutions of the Yang-Mills-Higgs system coupled to gravity in asymptotically de Sitter spacetime. The basic features of two classes of solutions are discussed, one of them corresponding to magnetic monopoles, the other one to sphalerons. We find that although the total mass within the cosmological horizon of these configurations is finite, their

Goran S. Djordjevic, Ljubisa Nesic

A simplified model of tachyon matter in classical and quantum mechanics is constructed. p-Adic path integral quantization of the model is considered. Recent results in using p-adic analysis, as well as perspectives of an adelic generalization, in the investigation of tachyons are briefly discussed. In particular, the perturbative approach in path integral qu