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We examine the problem of using local operations and classical communication (LOCC) to distinguish a known pure state from an unknown (possibly mixed) state, bounding the error probability from above and below. We study the asymptotic rate of detecting multiple copies of the pure state and show that, if the overlap of the two states is great enough, then they can be distinguished asymptotically as well with LOCC as with global measurements; otherwise, the maximal Schmidt coefficient of the pure state is sufficient to determine the asymptotic error rate. [ABSTRACT FROM AUTHOR]

For the three-state ergodic Markov process, the condition of all the fluctuation spectra (i.e., power spectra) with respect to real observables being monotonic over [0,+∞) [Y. Chen, Fluct. Noise Lett. 7, L181 (2007) (Theorem 2.6)] is deduced from Theorem 1 of Qian and Xie [J. Math. Phys. 50, 063301 (2009)]. In addition, we present two examples using Theorem 3 of Qian and Xie [J. Math. Phys. 50, 063301 (2009)]. [ABSTRACT FROM AUTHOR]

We investigate the integrable (2+1)-dimensional Manakov–Santini equation from the Lax–Sato form. Several particular two- and three-component reductions are considered so that the Manakov–Santini equation can be reduced to systems of hydrodynamic type. Then one can construct infinitely many exact solutions of the equation by the hodograph method. [ABSTRACT FROM AUTHOR]

The geometric property of soliton solutions of the three completely integrable sixth-order nonlinear equations (KdV6) is studied by using the method of dynamical systems and the work of Wazwaz [Appl. Math. Comput. 204, 963 (2008)]. This paper proved that a solitary wave solution corresponds to a homoclinic orbit of a four-dimensional dynamical system to a equilibrium point. The orbit lies on the intersection curve of two level set passing through the same equilibrium point. [ABSTRACT FROM AUTHOR]

Linear differential equations with constant coefficients involving a para-Grassmann variable have been considered recently in the work of Mansour and Schork [Symmetry, Integr. Geom.: Methods Appl. 5, 73 (2009)]. In the present paper, this treatment is extended to linear differential equations with variable coefficients. For the equation of first order, an explicit formula for the solution is given. For the equations of higher order, it is shown how the solutions may be determined in terms of the solutions of “ordinary” differential equations (i.e., involving only “bosonic” variables). Some examples of these differential equations are discussed and analogs for the trigonometric functions are introduced. [ABSTRACT FROM AUTHOR]

Galilean conformal algebra (GCA) is an Inönü–Wigner (IW) contraction of a conformal algebra, while Newton–Hooke string algebra is an IW contraction of an Anti-de Sitter (AdS) algebra, which is the isometry of an AdS space. It is shown that the GCA is a boundary realization of the Newton–Hooke string algebra in the bulk AdS. The string lies along the direction transverse to the boundary, and the worldsheet is AdS2. The one-dimensional conformal symmetry so(2,1) and rotational symmetry so(d) contained in the GCA are realized as the symmetry on the AdS2 string worldsheet and rotational symmetry in the space transverse to the AdS2 in AdSd+2, respectively. It follows from this correspondence that 32 supersymmetric GCAs can be derived as IW contractions of superconformal algebras, psu(2,2|4), osp(8|4), and osp(8*|4). We also derive less supersymmetric GCAs from su(2,2|2), osp(4|4), osp(2|4), and osp(8*|2). [ABSTRACT FROM AUTHOR]

This paper deals with the following equation mt=(1/2)(1/mk)xxx-(1/2)(1/mk)x, which is proposed by Z. J. Qiao [J. Math. Phys. 48, 082701 (2007)] and Qiao and Liu [Chaos, Solitons Fractals 41, 587 (2009)]. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the cases of k=-2,-12,12,2, and parametric representations of all possible bounded traveling wave solutions are given in the different (c,g)-parameter regions. [ABSTRACT FROM AUTHOR]

The need to consider n-ary algebraic structures, generalizing Lie and Poisson algebras, has become increasingly important in physics, and it should therefore be of interest to study the mathematical concepts related to n-ary algebras. The purpose of this paper is to investigate ternary multiplications (as deformations of n-Lie structures) constructed from the binary multiplication of a Hom–Lie algebra, a linear twisting map, and a trace function satisfying certain compatibility conditions. We show that the relation between the kernels of the twisting maps and the trace function plays an important role in this context and provide examples of Hom–Nambu–Lie algebras obtained using this construction. [ABSTRACT FROM AUTHOR]

We consider integrable open spin chains related to the quantum affine algebras Uq(o(3)) and Uq(A2(2)). We discuss the symmetry algebras of these chains with the local C3 space related to the Birman–Wenzl–Murakami algebra. The symmetry algebra and the Birman–Wenzl–Murakami algebra centralize each other in the representation space H=x1NC3 of the system, and this determines the structure of the spin system spectra. Consequently, the corresponding multiplet structure of the energy spectra is obtained. [ABSTRACT FROM AUTHOR]

We analyze the optimal unambiguous discrimination of two arbitrary mixed quantum states. We show that the optimal measurement is unique and we present this optimal measurement for the case where the rank of the density operator of one of the states is at most 2 (“solution in four dimensions”). The solution is illustrated by some examples. The optimality conditions proven by Eldar et al. [Phys. Rev. A 69, 062318 (2004)] are simplified to an operational form. As an application we present optimality conditions for the measurement, when only one of the two states is detected. The current status of optimal unambiguous state discrimination is summarized via a general strategy. [ABSTRACT FROM AUTHOR]

We present an exact solution of the three-dimensional Duffin–Kemmer–Petiau oscillator for spins 1 and 0 in the momentum space with the presence of minimal length uncertainty by the technique of vector spherical harmonics. The eigenfunctions are determined for both cases and the energy eigenvalues equation are obtained. The limiting case is then deduced for a small parameter of deformation. [ABSTRACT FROM AUTHOR]

In this paper we study the well posedness of solution to a certain system of nonlinear Klein–Gordon–Schrödinger equations in three space dimensions. Basing on the Strichartz estimates, we obtain the global existence, uniqueness of the solutions, and continuous dependence with respect to initial data in the Sobolev spaces of low regularities by setting appropriate contraction and taking difference estimates. [ABSTRACT FROM AUTHOR]

Recently, the first author [Adachi, “Asymptotic completeness for N-body quantum systems with long-range interactions in a time-periodic electric field,” Commun. Math. Phys. 275, 443 (2007)] proved the asymptotic completeness for N-body quantum systems with long-range interactions in a time-periodic electric field whose mean in time is nonzero by obtaining propagation estimates for the physical propagator. However, in his work, it is needed that potentials under consideration are sufficiently smooth. In this paper, when N=2, we prove the asymptotic completeness of (modified) wave operators under the assumption that the potential has the local singularity of type |x|-1+ε when d≥3 and 0<ε<1, where d is the space dimension. We also discuss the modifiers in the position representation, which are used in the definition of the modified wave operators in the long-range case. [ABSTRACT FROM AUTHOR]

Polar coordinates are used for the complex scalar free field in D=4 dimensions. The resulting nonrenormalizable theory is healed by using a recently proposed symmetric subtraction procedure. The existence of the coordinate transformation is proved by construction. [ABSTRACT FROM AUTHOR]

The recently developed theory of quasi-Lie schemes is studied and applied to investigate several equations of Emden type and a scheme to deal with them and some of their generalizations is given. As a first result we obtain t-dependent constants of the motion for particular instances of Emden equations by means of some of their particular solutions. Previously known results are recovered from this new perspective. Some t-dependent constants of the motion for equations of Emden type satisfying certain conditions are recovered. Finally new exact particular solutions are given for certain cases of Emden equations. [ABSTRACT FROM AUTHOR]

We show that appropriate superpositions of motional states are a reference frame resource that enables breaking of time-reversal superselection so that two parties lacking knowledge about the other’s direction of time can still communicate. We identify the time-reversal reference frame resource states and determine the corresponding frameness monotone, which connects time-reversal frameness to entanglement. In contradistinction to other studies of reference frame quantum resources, this is the first analysis that involves an antiunitary rather than unitary representation. [ABSTRACT FROM AUTHOR]

This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables. [ABSTRACT FROM AUTHOR]

We consider a superintegrable quantum potential in two-dimensional Euclidean space with a second and a third order integral of motion. The potential is written in terms of the fourth Painlevé transcendent. We construct for this system a cubic algebra of integrals of motion. The algebra is realized in terms of parafermionic operators and we present Fock-type representations which yield the corresponding energy spectra. We also discuss this potential from the point of view of higher order supersymmetric quantum mechanics and obtain ground state wave functions. [ABSTRACT FROM AUTHOR]

The subject of limit curve theorems in Lorentzian geometry is reviewed. A general limit curve theorem is formulated, which includes the case of converging curves with endpoints and the case in which the limit points assigned since the beginning are one, two, or at most denumerable. Some applications are considered. It is proved that in chronological spacetimes, strong causality is either everywhere verified or everywhere violated on maximizing lightlike segments with open domain. As a consequence, if in a chronological spacetime two distinct lightlike lines intersect each other then strong causality holds at their points. Finally, it is proved that two distinct components of the chronology violating set have disjoint closures or there is a lightlike line passing through each point of the intersection of the corresponding boundaries. [ABSTRACT FROM AUTHOR]

In 1940, Ulam proposed the famous Ulam stability problem. In this paper we introduce a general Cauchy–Jensen functional equation and prove the generalized Ulam stability of C*-ternary homomorphisms and C*-ternary derivations in C*-ternary algebras for the general Cauchy–Jensen equation. [ABSTRACT FROM AUTHOR]

We introduce an extension of the character expansion method to the case of supergroups. This method allows us to calculate a superversion of the Leutwyler–Smilga integral which, to the best of our knowledge, has not been calculated before. We also use the method to generalize a previously calculated superversion of the Berezin–Karpelevich integral. Our character expansion method should also allow for the calculation of other supergroup integrals. [ABSTRACT FROM AUTHOR]

In a recently published paper in this journal [A. Cheaghlou and O. Faizy, J. Math. Phys. 49, 022104 (2008)], the authors introduce the Gazeau–Klauder coherent states for the trigonometric Rosen–Morse potential as an infinite superposition of the wavefunctions. It is shown that their proposed measure to realize the resolution of the identity condition is not positive definite. Consequently, the claimed coherencies for the trigonometric Rosen–Morse wavefunctions cannot actually exist. [ABSTRACT FROM AUTHOR]

We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated with a matrix, the representation theory can be understood in terms of “loop” and “string” representations, which are closely related to the dynamics of an iterated map in the plane. As a particular class of algebras, we introduce the “Hénon algebras,” for which the dynamical map is a generalized Hénon map, and give an example where irreducible representations of all dimensions exist. [ABSTRACT FROM AUTHOR]

The Dirac equation written on the boundary of the Nutku helicoid space consists of a system of ordinary differential equations. We tried to analyze this system and we found that it has a higher singularity than those of the Heun equations which give the solutions of the Dirac equation in the bulk. We also lose an independent integral of motion on the boundary. This facts explain why we could not find the solution of the system on the boundary in terms of known functions. We make the stability analysis of the helicoid and catenoid cases and end up with an Appendix which gives a new example wherein one encounters a form of the Heun equation. [ABSTRACT FROM AUTHOR]

This paper is the first in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. In this paper, we discuss two different types of language that can be attached to a system S. The first is a propositional language PL(S); the second is a higher-order, typed language L(S). Both languages provide deductive systems with an intuitionistic logic. The reason for introducing PL(S) is that, as shown in Paper II of the series, it is the easiest way of understanding, and expanding on, the earlier work on topos theory and quantum physics. However, the main thrust of our program utilizes the more powerful language L(S) and its representation in an appropriate topos. [ABSTRACT FROM AUTHOR]

This paper is the third in a series whose goal is to develop a fundamentally new way of viewing theories of physics. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. In Paper II, we studied the topos representations of the propositional language PL(S) for the case of quantum theory, and in the present paper we do the same thing for the, more extensive, local language L(S). One of the main achievements is to find a topos representation for self-adjoint operators. This involves showing that, for any physical quantity A, there is an arrow δo(A):Σ_→R≽_, where R≽_ is the quantity-value object for this theory. The construction of δo(A⁁) is an extension of the daseinisation of projection operators that was discussed in Paper II. The object R≽_ is a monoid object only in the topos, τ[lowercase_phi_synonym]=SetsV(H)op, of the theory, and to enhance the applicability of the formalism, we apply to R≽_ a topos analog of the Grothendieck extension of a monoid to a group. The resulting object, k(R≽_), is an abelian group object in τ[lowercase_phi_synonym]. We also discuss another candidate, R↔_, for the quantity-value object. In this presheaf, both inner and outer daseinisations are used in a symmetric way. Finally, there is a brief discussion of the role of unitary operators in the quantum topos scheme. [ABSTRACT FROM AUTHOR]

This paper is the second in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. In this paper, we study in depth the topos representation of the propositional language, PL(S), for the case of quantum theory. In doing so, we make a direct link with, and clarify, the earlier work on applying topos theory to quantum physics. The key step is a process we term “daseinisation” by which a projection operator is mapped to a subobject of the spectral presheaf—the topos quantum analog of a classical state space. In the second part of the paper, we change gear with the introduction of the more sophisticated local language L(S). From this point forward, throughout the rest of the series of papers, our attention will be devoted almost entirely to this language. In the present paper, we use L(S) to study “truth objects” in the topos. These are objects in the topos that play the role of states: a necessary development as the spectral presheaf has no global elements, and hence, there are no micro-states in the sense of classical physics. Truth objects therefore play a crucial role in our formalism. [ABSTRACT FROM AUTHOR]

This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. The previous papers in this series are concerned with implementing this program for a single system. In the present paper, we turn to considering a collection of systems; in particular, we are interested in the relation between the topos representation for a composite system and the representations for its constituents. We also study this problem for the disjoint sum of two systems. Our approach to these matters is to construct a category of systems and to find a topos representation of the entire category. [ABSTRACT FROM AUTHOR]

A new class of dynamical systems are presented, together with their solutions. Some of these models are isochronous, namely, their generic solutions are all completely periodic with the same period; others are characterized by friction, all solutions vanishing in the remote future; and still others are “asymptotically isochronous,” approaching an isochronous behavior in the remote future. [ABSTRACT FROM AUTHOR]

We consider entanglement distillation from a single copy of multipartite quantum states, and instead of rates we analyze the “quality” of the distilled entanglement. This quality is quantified by the fidelity with the gigahertz state. We show that each not fully separable state σ can increase the quality of the entanglement distilled from other states, no matter how weakly entangled is σ. We also generalize this to the case where the goal is distilling states different from the gigahertz. These results provide new insights on the geometry of the set of separable states and its dual (the set of entanglement witnesses). [ABSTRACT FROM AUTHOR]

The presented paper develops a new method for solving Einstein equations explicitly. Not only the solutions are new but also the mathematical framework of their construction which is given by a nonstandard function theory built over nonstandard algebras (in the following denoted as GAPs) and will be called here as “GAP Theory.” It is shown that the GAP theory succeeds in regions, where group theory fails: the group structure is too small to solve Einstein equations explicitly. [ABSTRACT FROM AUTHOR]

We find sets of solutions to the generalized spheroidal wave equation (GSWE) or, equivalently, to the confluent Heun equation. Each set is constituted by three solutions, one given by a series of ascending powers of the independent variable, and the others by series of regular and irregular confluent hypergeometric functions. For a fixed set, the solutions converge over different regions of the complex plane but present series coefficients proportional to each other. These solutions for the GSWE afford solutions to a double-confluent Heun equation by a taking-limit process due to Leaver. [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)]. Another procedure, called Whittaker-Ince limit [B. D. Figueiredo, J. Math. Phys. 46, 113503 (2005)], provides solutions in series of powers and Bessel functions for two other equations with a different type of singularity at infinity. In addition, new solutions are obtained for the Whittaker-Hill and Mathieu equations [F. M. Arscott, Proc. R. Soc. Edinburg A67, 265 (1967)] by considering these as special cases of both the confluent and double-confluent Heun equations. In particular, we find that each of the Lindemann-Stieltjes solutions for the Mathieu equation [E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press (1945)] is associated with two expansions in series of Bessel functions. We also discuss a set of solutions in series of hypergeometric and confluent hypergeometric functions for the GSWE and use their Leaver limits to obtain infinite-series solutions for the Schrödinger equation with an asymmetric double-Morse potential. Finally, the possibility of extending the solutions of the GSWE to the general Heun equation is briefly discussed. [ABSTRACT FROM AUTHOR]

We study the (λ/4!)φ4 massless scalar field theory in a four-dimensional Euclidean space, where all but one of the coordinates are unbounded. We are considering Dirichlet boundary conditions in two hyperplanes, breaking the translation invariance of the system. We show how to implement the perturbative renormalization up to two-loop level of the theory. First, analyzing the full two and four-point functions at the one-loop level, we show that the bulk counterterms are sufficient to render the theory finite. Meanwhile, at the two-loop level, we must also introduce surface counterterms in the bare Lagrangian in order to make finite the full two and also four-point Schwinger functions. [ABSTRACT FROM AUTHOR]

We give sufficient conditions for ergodicity of the Markovian semigroups associated to Dirichlet forms on standard forms of von Neumann algebras constructed by the method proposed by Park. We apply our result to show that the diffusion type Markovian semigroups for quantum spin systems are ergodic in the region of high temperatures where the uniqueness of the KMS state holds. [ABSTRACT FROM AUTHOR]

We investigate the behavior of the Green functions of Schrödinger operators near the diagonal. The only nontrivial cases, where the on-diagonal singularities are nonzero and do not depend on the spectral parameter, are two and three dimensions. In the case of two dimensions we show that the singularity is independent of both the scalar and the gauge potentials. In dimension three, we obtain conditions for preserving the singularity under perturbations by nonregular potentials. Some examples illustrating dependence of the singularity on general scalar and gauge potentials are presented. [ABSTRACT FROM AUTHOR]

We derive recursively the perturbation series for the ground-state energy of the D-dimensional anharmonic oscillator and resum it using variational perturbation theory (VPT). From the exponentially fast converging approximants, we extract the coefficients of the large-D expansion to higher orders. The calculation effort is much smaller than in the standard field-theoretic approach based on the Hubbard-Stratonovich transformation. [ABSTRACT FROM AUTHOR]

A kinetic model for a granular gas interacting with a given background by binary dissipative collisions is analyzed, with particular reference to the derivation of macroscopic equations for the fundamental observables. Particles are modelled as inelastic hard spheres under the assumption of collision dominated regime (small mean free path). Closure of the relevant moment equations is achieved by resorting to a maximum entropy principle, and two specific entropy functionals have been worked out in detail, in the class of the admissible ones for the relevant linear extended Boltzmann equation. Considered macroscopic fields include density, mass velocity, and granular temperature. In the hydrodynamic limit when the mean free path tends to zero, a single drift-diffusion equation of Navier-Stokes type is recovered for the only hydrodynamic variable of the physical problem. [ABSTRACT FROM AUTHOR]

Integrable systems are usually given in terms of functions of continuous variables (on R), in terms of functions of discrete variables (on Z), and recently in terms of functions of q-variables (on Kq). We formulate the Gel’fand-Dikii (GD) formalism on time scales by using the delta differentiation operator and find more general integrable nonlinear evolutionary equations. In particular they yield integrable equations over integers (difference equations) and over q-numbers (q-difference equations). We formulate the GD formalism also in terms of shift operators for all regular-discrete time scales. We give a method allowing to construct the recursion operators for integrable systems on time scales. Finally, we give a trace formula on time scales and then construct infinitely many conserved quantities (Casimirs) of the integrable systems on time scales. [ABSTRACT FROM AUTHOR]

Eigenfunctions of the equation ∇vector ×Bvector =λBvector are found for finite cylindrical geometry with normal boundary condition Bvector ·n⁁=0 and nonaxisymmetric modes ∼eimθ,m≠0. The vector field Bvector can be represented by a scalar generating function of the Chandrasekhar-Kendall type with radial Bessel functions for the nondegenerate cases. A general set of solutions can also be generated by transformation of variables. A series solution in terms of radial Bessel functions is found which has excellent convergence properties (an∼1/n4) and a robust method of locating eigenvalues is described. [ABSTRACT FROM AUTHOR]

We prove the existence of two-cluster threshold resonances in N-body problems and study their perturbation by intercluster interactions. As application, we construct concrete examples based on Yukawa potentials for which the N-body Efimov effect happens with N>=4. [ABSTRACT FROM AUTHOR]

We reexamine here the issue of consistency of minimal action formulation with the minimal coupling procedure (MCP) in spaces with torsion. In Riemann­Cartan spaces, it is known that a proper use of the MCP requires that the trace of the torsion tensor be a gradient, Τµ= аµθ, and that the modified volume element τθ=еθ√gdχ¹^⋯^χn be used in the action formulation of a physical model. We rederive this result here under considerably weaker assumptions, reinforcing some recent results about the inadequacy of propagating torsion theories of gravity to explain the available observational data. The results presented here also open the door to possible applications of the modified volume element in the geometric theory of crystalline defects. [ABSTRACT FROM AUTHOR]

We prove that the mathematical framework for the de Sitter top system is the de Sitter fiber bundle. In this context, the concept of soldering associated with a fiber bundle plays a central role. We comment on the possibility that our formalism may be of particular interest in different contexts including MacDowell-Mansouri theory, two time physics, and oriented matroid theory. [ABSTRACT FROM AUTHOR]

We construct a new geometric framework based on the concepts of left and right jet-bundles of a classical space-time V in order to analyze the impulsive behavior of a unilateral constraint S. The setup allows deep insights into how one can choose an ideality criterion for the constraint S when the hypothesis of conservation of kinetic energy is assumed. We show that the conservation of kinetic energy alone univocally determines the impulsive reaction when the codimension of S is 1, and that it leaves the impulsive reaction partially undetermined when the codimension of S is greater than 1. If the codimension of S is greater than 1, we prove that an additional minimality requirement determines a physically meaningful constitutive characterization of S. We show that both the Newton-like and the Poisson-like approaches to the description of the reactive impulse are equivalent, in the sense that both give the same results about the ideality criterion. Moreover, we prove that the same results hold using the classical approach based on reflection operators, possible only in case of codimension 1. We present also several physically meaningful examples. [ABSTRACT FROM AUTHOR]

We extend to the K-SAT and p-XOR-SAT optimization problems the results recently achieved, by introducing the concept of random multi-overlap structure, for the Viana-Bray model of diluted mean field spin glass. More precisely we can prove a generalized bound and an extended variational principle for the free energy per site in the thermodynamic limit. Moreover a trial function implementing ultrametric breaking of replica symmetry is exhibited. The ultrametric structure exhibits the same factorization property as the optimal structures for the Viana-Bray model and the Sherrington-Kirkpatrick nondiluted model. [ABSTRACT FROM AUTHOR]

We consider wavelets in L2(Rd) which have generalized multiresolutions. This means that the initial resolution subspace V0 in L2(Rd) is not singly generated. As a result, the representation of the integer lattice Zd restricted to V0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on Rd can be constructed directly from the generalized wavelet filters. [ABSTRACT FROM AUTHOR]

We present an explicit numerical method to obtain the Cartan-Khaneja-Glaser decomposition of a general element G∈SU(2N) in terms of its “Cartan” and “non-Cartan” components. This effectively factors G in terms of group elements that belong in SU(2n) with n

A basis of N2 projectors, each an N2×N2 matrix with constant elements, is implemented to construct a class of braid matrices R⁁(θ), θ being the spectral parameter. Only odd values of N are considered here. Our ansatz for the projectors Pα appearing in the spectral decomposition of R⁁(θ) leads to exponentials exp(mαθ) as the coefficient of Pα. The sums and differences of such exponentials on the diagonal and the antidiagonal, respectively, provide the (2N2-1) nonzero elements of R⁁(θ). One element at the center is normalized to unity. A class of supplementary constraints imposed by the braid equation leaves 1/2(N+3)(N-1) free parameters mα. The diagonalizer of R⁁(θ) is presented for all N. Transfer matrices t(θ) and L(θ) operators corresponding to our R⁁(θ) are studied. Our diagonalizer signals specific combinations of the components of the operators that lead to a quadratic algebra of N2 constant N×N matrices. The θ dependence factors out for such combinations. R⁁(θ) is developed in a power series in θ. The basic difference arising for even dimensions is made explicit. Some special features of our R⁁(θ) are discussed in a concluding section. [ABSTRACT FROM AUTHOR]

We present an extended version of max-plus algebra which includes the inverse operator of “max.” This algebra enables us to ultradiscretize the system including subtractions and obtain new ultradiscrete equations. The known ultradiscrete equations can also be recovered by this construction. [ABSTRACT FROM AUTHOR]

In this paper, local and nonlocal symmetry classifications are considered for four equivalent nonlinear telegraph equations. A complete potential symmetry classification of a scalar nonlinear telegraph equation is given through the point symmetry classification of a related potential system. Six new classes of equations are shown to admit potential symmetries. The relationships between local (including contact) and nonlocal (potential) symmetries of these equations are explored. A physical example is considered for possible applications of the obtained potential symmetries. [ABSTRACT FROM AUTHOR]