a note on the one particle and hilbert schmidt cohomologies of the poincare group in three spacetime dimensions cocycles for p up arrow 2 1 with values in a hilbert space are studied it is found that cocycles for irreducible representations apart from the case of vanishing momentum are trivial further cocycles for the action v v 1 with values in the representation space of v are investigated and found to be trivial some consequences for physics are obtained

decoding algorithm as a moment problem related to the extended lotka volterra system the moment problem related to the extended lotka volterra system sometimes also called the hungry lotka volterra system or the narita itoh bogoyavlensky lattice over finite fields is introduced it turns out the moment problem could be used to design an algorithm for decoding multiple bch goppa codes over the same finite field simultaneously when multiple codes have the same error locations the algorithm requires fewer known syndromes and has lower computational complexity than running the decoding algorithm in nakamura 1996 phys lett a 223 75 81 multiple times

the qr decomposition and the singular value decomposition in the symmetrized max plus algebra revisited this paper is an updated and extended version of the paper the qr decomposition and the singular value decomposition in the symmetrized max plus algebra b de schutter and b de moor siam j matrix anal appl 19 1998 pp 378 406 the max plus algebra which has maximization and addition as its basic operations can be used to describe and analyze certain classes of discrete event systems such as flexible manufacturing systems railway networks and parallel processor systems in contrast to conventional algebra and conventional linear system theory the max plus algebra and the max plus algebraic system theory for discrete event systems are at present far from fully developed and many fundamental problems still have to be solved currently much research is going on to deal with these problems and to further extend the max plus algebra and to develop a complete max plus algebraic system theory for discrete event systems in this paper we address one of the remaining gaps in the max plus algebra by considering matrix decompositions in the symmetrized max plus algebra the symmetrized max plus algebra is an extension of the max plus algebra obtained by introducing a max plus algebraic analogue of the operator we show that we can use well known linear algebra algorithms to prove the existence of max plus algebraic analogues of basic matrix decompositions from linear algebra such as the qr decomposition the singular value decomposition the hessenberg decomposition the lu decomposition and so on these max plus algebraic matrix decompositions could play an important role in the max plus algebraic system theory for discrete event systems

from stochastic partial difference equations to stochastic cellular automata through the ultra discretization we derive stochastic cellular automata with finite range interactions from stochastic partial difference equations through the ultra discrete limit a typical example for stochastic cellular automata is the domany kinzel model which is equivalent to mixed site bond oriented percolation as a special case

dualities for a class of finite range probabilistic cellular automata in one dimension in this paper we study dualities for a class of one dimensional probabilistic cellular automata with finite range interactions by using a sequence of extended cellular automata

quantum operators in classical probability theory iv quasi duality and thinnings of interacting particle systems duality has proved to be a powerful technique in the study of interacting particle systems ips this concept can be enlarged and a quasi duality defined between various pairs of ips previously thought unrelated consequently theorems of a similar style to those involving duality can be deduced the concept of quasi duality follows naturally from our previous studies into the use ofsingle site operators an idea borrowed from quantum physics in paper ii of this series it is shown that a necessary condition for quasi duality is that the eigenvalues of the corresponding two site infinitesimal generators be the same and using this observation a number of quasi dual pairs have been found and studied it is further shown that if two different ips share a common dual then one can be considered as a thinning of the other

from quantum cellular automata to quantum lattice gases a natural architecture for nanoscale quantum computation is that of a quantum cellular automaton motivated by this observation we begin an investigation of exactly unitary cellular automata after proving that there can be no nontrivial homogeneous local unitary scalar cellular automaton in one dimension we weaken the homogeneity condition and show that there are nontrivial exactly unitary partitioning cellular automata we find a one parameter family of evolution rules which are best interpreted as those for a one particle quantum automaton this model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the dirac equation we describe two generalizations of this automaton the second of which to multiple interacting particles is the correct definition of a quantum lattice gas

calculating laplace transforms in terms of the toda molecule a method for calculating a continued fraction expansion of laplace transforms is presented in terms of the tau function of the continuous time toda molecule equation and its integrable discretization the z transform and a discrete analogue of the laplace transform of a set of finite samples are also formulated

fock representations of the lie superalgebra q n 1 for the lie superalgebra q n 1 a description is given in terms of creation and annihilation operators in such a way that the defining relations of q n 1 are determined by quadratic and triple supercommutation relations of these operators fock space representations vp of q n 1 are defined by means of these creation and annihilation operators these new representations are introduced as quotient modules of some induced module of q n 1 the representations vp are not graded but they possess a number of properties that are of importance for physical applications for p a positive integer these representations vp are finite dimensional with a unique highest weight of multiplicity one the hermitian form that is consistent with the natural adjoint operation on q n 1 is shown to be positive definite on vp for q 2 these representations are dispin for the general case of q n 1 many structural properties of vp are derived

schur flow for orthogonal polynomials on the unit circle and its integrable discretization a one parameter deformation of the measure of orthogonality for orthogonal polynomials on the unit circle is considered the corresponding dynamics of the schur parameters of the orthogonal polynomials is shown to be characterized by the complex semi discrete modified kdv equation namely the schur flow a discrete analogue of the miura transformation is found an integrable discretization of the schur flow enables us to compute a pade approximation of the caratheodory functions or equivalently to compute a perron caratheodory continued fraction in a polynomial time

fock representation of the renormalized higher powers of white noise and the centreless virasoro or witt zamolodchikov w lie algebra the identification of the lie algebra of the renormalized higher powers of white noise rhpwn and the analytic continuation of the second quantized centreless virasoro or witt zamolodchikov w lie algebra of conformal field theory and high energy physics was recently established in 5 based on results obtained in 3 and 4 in the present paper we show how the rhpwn fock kernels must be truncated in order to be positive semi definite and we obtain a fock representation of the two algebras we show that the truncated renormalized higher powers of white noise trhpwn fock spaces of order 2 host the continuous binomial and beta processes

structural topology optimization for the design of broadband dielectric resonator antennas using the finite difference time domain technique dielectric resonator antennas dras are a relatively new class of antenna that utilizes the radiation phenomena of dielectric resonators in open space since mainly analytical approaches have been applied to investigate dra designs the current dra forms are limited to simple geometric shapes and high performance dras with complex shapes have not yet been developed topology optimization is capable of yielding high performance structures and has been extensively applied to a variety of structural optimization problems applying it to the task of dra design may be extremely useful for the design of high performance antennas on the other hand the finite difference time domain fdtd method has been used to numerically evaluate general antenna performance since it is numerically robust during time domain analyses and can handle complex models thus the integration of topology optimization with the fdtd method has the potential to enable innovative designs of advanced antennas that offer exceptional performance in this research we propose a new topology optimization method for the design of dras that aim to operate with enhanced bandwidths using the fdtd method first the concept of topology optimization is briefly discussed and a way to integrate topology optimization with the fdtd method is proposed next design requirements are clarified and the corresponding objective functions and the optimization problem are formulated an optimization algorithm is constructed based on these formulations finally several dra design examples are presented to confirm the usefulness of the proposed method

a generalization of the bargmann fock representation to supersymmetry in the bargmann fock representation the coordinates act as bosonic creation operators while the partial derivatives act as annihilation operators on holomorphic 0 forms as states of a d dimensional bosonic oscillator also considering p forms and further geometrical objects as the exterior derivative and lie derivatives on a holomorphic we end up with an analogous representation for the d dimensional supersymmetric oscillator in particular the supersymmetry multiplet structure of the hilbert space corresponds to the cohomology of the exterior derivative in addition a 1 complex parameter group emerges naturally and contains both time evolution and a homotopy related to cohomology the emphasis is on calculus

simultaneous structural topology optimization of electromagnetic sources and ferromagnetic materials abstract for the design of electric machines such as actuators sensors and motors the topology optimization for em sources as well as ferromagnetic materials fms is in great request generally permanent magnets pms and coils serve as electromagnetic em sources in electric machines however most of researches in relation with topology optimization in electric machinery are focused mostly on the design of ferromagnetic materials such as yokes and stators in this paper the topology optimization methodology for the simultaneous design of pms and fms is developed and it is expanded to the design of fms with coils the proposed method makes it possible to obtain a clear topology with little gray density elements in the design domain and shows the stable convergence history the proposed method is applied to the optimization problem of a c core actuator and a magnetostrictive sensor the sensitivity analysis and the update of design variables are accomplished by the adjoint variable method and the sequential linear programming respectively

conserved quantities of the discrete finite toda equation and lower bounds of the minimal singular value of upper bidiagonal matrices some numerical algorithms are known to be related to discrete time integrable systems where it is essential that quantities to be computed for example eigenvalues and singular values of a matrix poles of a continued fraction are conserved quantities in this paper a new application of conserved quantities of integrable systems to numerical algorithms is presented for an n n n 2 real upper bidiagonal matrix b where all the diagonals and the upper subdiagonals are positive conserved quantities tr btb m 1 m 1 2 of the discrete finite toda equation give a sequence of lower bounds of the minimal singular value of b recurrence relations for computing higher order conserved quantities tr btb m 1 are also derived

algorithms associated with arithmetic geometric and harmonic means and integrable systems abstract gauss algorithm for arithmetic geometric mean agm can be regarded as a discrete time integrable dynamical system having an elliptic theta function solution and a conserved quantity in this paper we consider algorithms associated with arithmetic geometric and harmonic means from a viewpoint of integrable systems first a max plus limit and its inverse limit of the agm algorithm are discussed these mean operations are shown to be connected to each other by the max plus limit secondly continous time dynamical systems associated with the arithmetic harmonic mean ahm algorithm are found thirdly it is shown that the ahm algorithm in indefinite case has a chaotic dynamics and is a generator of numbers which obey the cauchy distribution finally an extension of the ahm algorithm to the space of positive definite symmetric matrices is considered

bosonic fock representations of the affine virasoro algebra bosonic fock representations of the virasoro algebra and the affine lie algebras attached to classical lie algebras with non zero centres are explicitly presented based on these fock representations of the affine virasoro algebra are constructed an automorphism of the affine virasoro algebra is also given

involutive automorphisms of the class of affine kac moody algebras bl 1 all the conjugacy classes of involutive automorphisms of the affine kac moody algebras bl 1 for l or 1 are determined using the matrix formulation of automorphisms of an affine kac moody algebra

structural optimization of ferromagnetic materials based on the magnetic reluctivity for magnetic field problems abstract topology optimization of ferromagnetic materials in magnetic fields using the homogenization method and the density method has been attempted from an angle of the interpolation scheme based on the magnetic permeability however optimization results based on such methods may have poor convergence history in comparison with the structural topology optimization of an elastic problem this study intends to verify that the interpolation scheme using the magnetic permeability may cause problems in the sensitivity analysis for the structural optimization in magnetic fields and suggests a novel interpolation scheme based on the magnetic reluctivity numerical examples are focused on magnetic actuators to maximize the magnetic force attracting an armature this study is focused to maximize force itself using the maxwell stress method and the sensitivity analysis by the adjoint variable method whereas previous work to maximize force are based on the magnetic energy computation mostly without considering the actuating direction it is confirmed that optimal models by the proposed method have improved performance and better robust iteration history compared with the previous method

leibniz algebra deformations of a lie algebra in this note we compute leibniz algebra deformations of the three dimensional heisenberg lie algebra n3 and compare it to its lie deformations it turns out that there are three extra leibniz deformations we also describe a versal leibniz deformation of n3 with the versal base

displaced fock representations of the canonical commutation relations defines displaced fock representations of the canonical commutation relations in an algebraic framework then the author considers the problem of unitary implementability of the symmetry group which acts on the one particle space of the theory this action induces an automorphism of the algebra of the ccr and a condition is found to ensure that this automorphism be implemented by a unitary group representation in the space of the displaced fock representation using this condition the author proves the existence of infinitely many displaced fock representations in which the group automorphism is implemented by a unitary action this is done for a specific choice of a subgroup of the poincare group and for all cases of integer value of spin

q graded heisenberg algebras and deformed supersymmetries the notion of q grading on the enveloping algebra generated by products of q deformed heisenberg algebras is introduced for q complex number in the unit disk within this formulation we consider the extension of the notion of supersymmetry in the enveloping algebra we recover the ordinary z2 grading or grassmann parity for associative superalgebra and a modified version of the usual supersymmetry as a specific problem we focus on the interesting limit q 1 for which the arik and coon deformation j math phys 17 524 1976 of the heisenberg algebra allows one to map fermionic modes to bosonic ones in a modified sense different algebraic consequences are discussed

some cohomologically rigid solvable leibniz algebras abstract in this paper we describe solvable leibniz algebras whose quotient algebra by one dimensional ideal is a lie algebra with rank equal to the length of the characteristic sequence of its nilpotent radical we prove that such leibniz algebra is unique and centerless also it is proved that the first and the second cohomology groups of the algebra with coefficients in the adjoint representation is trivial

variational approach by means of adjoint systems to structural optimization and sensitivity analysis i variation of material parameters within fixed domain abstract for a linear elastic structure the first variation of an arbitrary stress strain and displacement functionals corresponding to variation of material parameters within specified domain is derived by using the solution for primary and adjoint systems this variation is of fundamental importance in sensitivity analysis optimal design and identification problems simple examples of optimal stiffness design and identification of stiffness parameters in beams are presented

on tropical eigenvalues of tridiagonal toeplitz matrices abstract in this paper we determine the tropical algebraic eigenvalues of toeplitz matrices it is proved that these matrices have at most two distinct tropical eigenvalues and the explicit formulas for those eigenvalues are given also the asymptotic behavior of eigenvalues of parameterized tridiagonal toeplitz matrices over the classical field of complex numbers is shown

determinantal solutions of solvable chaotic systems it is shown that two solvable chaotic systems the arithmetic harmonic mean ahm algorithm and the ulam von neumann uvn map have determinantal solutions an additional formula for certain determinants and riccati difference equations play a key role in both cases two infinite hierarchies of solvable chaotic systems are presented which have determinantal solutions

topology optimization using a reaction diffusion equation abstract this paper presents a structural topology optimization method based on a reaction diffusion equation in our approach the design sensitivity for the topology optimization is directly employed as the reaction term of the reaction diffusion equation the distribution of material properties in the design domain is interpolated as the density field which is the solution of the reaction diffusion equation so free generation of new holes is allowed without the use of the topological gradient method our proposed method is intuitive and its implementation is simple compared with optimization methods using the level set method or phase field model the evolution of the density field is based on the implicit finite element method as numerical examples compliance minimization problems of cantilever beams and force maximization problems of magnetic actuators are presented to demonstrate the method s effectiveness and utility

whittaker modules for heisenberg algebras and imaginary whittaker modules for affine lie algebras abstract we classify the irreducible whittaker modules for finite and infinite dimensional heisenberg algebras and for the lie algebra obtained by adjoining a degree derivation to an infinite dimensional heisenberg algebra we use these modules to construct a new class of modules for non twisted affine lie algebras which we call imaginary whittaker modules we show that the imaginary whittaker modules of non zero level are irreducible

space time topology optimization for one dimensional wave propagation abstract a space time extension of the topology optimization method is presented the formulation with design variables in both the spatial and temporal domains is used to create structures with an optimized distribution of material properties that can vary in time the method is outlined for one dimensional transient wave propagation in an elastic rod with time dependent young s modulus by two simulation examples it is demonstrated how dynamic structures can display rich dynamic behavior such as wavenumber frequency shifts and lack of energy conservation the optimization method s potential for creating structures with novel dynamic behavior is illustrated by a simple example it is shown that an elastic rod in which the optimized stiffness distribution is allowed to vary in time can be much more efficient in prohibiting wave propagation compared to a static bandgap structure optimized designs in form of spatio temporal laminates and checkerboards are generated and discussed the example lays the foundation for creating designs with more advanced functionalities in future work

an application of the discrete time toda lattice to the progressive algorithm by lanczos and related problems the finite or the semi infinite discrete time toda lattice has many applications to various areas in applied mathematics the purpose of this paper is to review how the toda lattice appears in the lanczos algorithm through the quotient difference algorithm and its progressive form pqd then a multistep progressive algorithm mpa for solving linear systems is presented the extended lanczos parameters can be given not by computing inner products of the extended lanczos vectors but by using the pqd algorithm with highly relative accuracy in a lower cost the asymptotic behavior of the pqd algorithm brings us some applications of mpa related to eigenvectors

topology optimization for stationary fluid structure interaction problems using a new monolithic formulation this paper outlines a new procedure for topology optimization in the steady state fluid structure interaction fsi problem a review of current topology optimization methods highlights the difficulties in alternating between the two distinct sets of governing equations for fluid and structure dynamics hereafter the fluid and structural equations respectively and in imposing coupling boundary conditions between the separated fluid and solid domains to overcome these difficulties we propose an alternative monolithic procedure employing a unified domain rather than separated domains which is not computationally efficient in the proposed analysis procedure the spatial differential operator of the fluid and structural equations for a deformed configuration is transformed into that for an undeformed configuration with the help of the deformation gradient tensor for the coupling boundary conditions the divergence of the pressure and the darcy damping force are inserted into the solid and fluid equations respectively the proposed method is validated in several benchmark analysis problems topology optimization in the fsi problem is then made possible by interpolating young s modulus the fluid pressure of the modified solid equation and the inverse permeability from the damping force with respect to the design variables

peakons strings and the finite toda lattice as is well known the toda lattice flow may be realized as an isospectral flow of a jacobi matrix a bijective map from a discrete string problem with positive weights to jacobi matrices allows the pure peakon flow of the camassa holm equation to be realized as an isospectral jacobi flow as well this gives a unified picture of the toda jacobi and multipeakon flows and leads to explicit solutions of the jacobi flows via stieltjes determination of the continued fraction expansion of a stieltjes transform a simple modification produces a bijection from generalized strings with positive and negative weights to singular jacobi matrices and thus brings peakon antipeakon flows into the same picture c

a homogenization method for shape and topology optimization abstract shape and topology optimization of a linearly elastic structure is discussed using a modification of the homogenization method introduced by bendsoe and kikuchi together with various examples which may justify validity and strength of the present approach for plane structures

leibniz algebras of heisenberg type we introduce and provide a classification theorem for the cl ass of heisenberg fock leibniz algebras this category of algebras is formed by those leibniz algebras l whose corresponding lie algebras are heisenberg algebras hn and whose hn modules i where i denotes the ideal generated by the squares of elements of l are isomorphic to fock modules we also consider the three dimensional heisenberg algebra h3 and study three classes of leibniz algebras with h3 as corresponding lie algebra by taking certain generalizations of the fock module moreover we describe the class of leibniz algebras with hn as corresponding lie algebra and such that the action i hn i gives rise to a minimal faithful representation of hn the classification of this family of leibniz algebras for the case of n 3 is given ams subject classifications 2010 17a32 17b30 17b10

boolean lie algebras and the leibniz rule using internal negations acting on boolean functions the notion of boolean lie algebra is introduced the underlying lie product is the boolean analogue of the poisson bracket the structure of a boolean lie algebra is determined it turns out to be solvable but not nilpotent we prove that the adjoint representation of an element of the boolean lie algebra acts as a derivative operator on the space of boolean functions the adjoint representation is related to the previously known concept of the sensitivity function using the notion of adjoint representation we give the definition of a temporal derivative applicable to iterative dynamics of boolean mappings

quantum operators in classical probability theory ii the concept of duality in interacting particle systems duality has proved to be a powerful tool in the theory of interacting particle systems the approach in this paper is algebraic rather than via harris diagrams a form of duality is found which includes coalescing and annihilating duality as special cases this enables new results for the branching annihilating random walk and the biased annihilating branching process to be derived

some covariant representations of massless fermi fields studies the class of pure quasi free gauge invariant states of the fermion algebra the authors show that the question of g covariance of the corresponding representations i e implementability of some group g of one particle symmetry transformations is related to a cohomology group with values in the hilbert schmidt class in four dimensional space time this cohomology is nontrivial thus leading to g covariant non fock representations when g is taken to be the space time translation group together with rotations or space time translations together with boosts in one direction and rotations about it and the fermion mass is zero in two space time dimensions some new fully poincare covariant representations for free massless fermions are constructed

cramer and cayley hamilton in the max algebra abstract cramer s rule and the cayley hamilton theorem are formulated and provided in the so called max algebra which consists of the set of reals provided with two operations maximization and addition it is surprising to see that these well known theorems carry over to the max algebra almost without any changes provided that the conventional addition and multiplication are replaced by maximization and addition respectively the definitions of determinant and eigenvalue have to be adjusted to this new formulation the role of the determinant is taken over by the permanent and a refinement of this latter concept called the dominant

naturally graded n 3 filiform leibniz algebras naturally graded nilpotent p filiform leibniz algebras are studied for p n 4 where n is the dimension of the algebra using linear algebra methods we describe the naturally graded n 3 filiform leibniz algebras

bosonic and k fermionic coherent states for a class of polynomial weyl heisenberg algebras the aim of this paper is to construct coherent states la perelomov and la barut girardello for a polynomial weyl heisenberg algebra this generalized weyl heisenberg algebra denoted by depends on r real parameters and is an extension of the one parameter algebra daoud and kibler 2010 j phys a math theor 43 115303 which covers the cases of the su 1 1 algebra for 0 the su 2 algebra for 0 and the h4 ordinary weyl heisenberg algebra for 0 for finite dimensional representations of and where is a truncation of order s of in the sense of pegg barnett a connection is established with k fermionic algebras or quon algebras this connection makes it possible to use generalized grassmann variables for constructing certain coherent states coherent states of the perelomov type are derived for infinite dimensional representations of and for finite dimensional representations of and through a fock bargmann analytical approach based on the use of complex or bosonic variables the same approach is applied for deriving coherent states of the barut girardello type in the case of infinite dimensional representations of in contrast the construction of coherent states la barut girardello for finite dimensional representations of and can be achieved solely at the price of replacing complex variables by generalized grassmann or k fermionic variables some of the results are applied to su 2 su 1 1 and the harmonic oscillator in a truncated or not truncated form this article is part of a special issue of journal of physics a mathematical and theoretical devoted to coherent states mathematical and physical aspects

a walk on max plus algebra abstract max plus algebra is a kind of idempotent semiring over r max r with two operations max and in this paper we introduce a new model of a walk on one dimensional lattice on z as an analogue of the quantum walk over the max plus algebra and we call it max plus walk in the conventional quantum walk the summation of the l 2 norm of the states over all the positions is a conserved quantity in contrast the summation of eigenvalues of state decision matrices is a conserved quantity in the max plus walk moreover spectral analysis on the total time evolution operator is also given

fock representations of the superalgebra sl n 1 m its quantum analogue uq sl n 1 m and related quantum statistics fock space representations of the lie superalgebra sl n 1 m and of its quantum analogue uq sl n 1 m are written down the results are based on a description of these superalgebras via creation and annihilation operators the properties of the underlying statistics are briefly discussed

solutions to shape and topology eigenvalue optimization problems using a homogenization method a solution strategy to find the shape and topology of structures that maximize a natural frequency is presented the methodology is based on a homogenization method and the representation of the shape of the structure as a material property the problem is formulated as a reinforcement problem in which a given structure is reinforced using a prescribed amount of material two dimensional plane elasticity problems are considered examples are presented for illustration

continued fractions and integrable systems stieltjes solution of the classical moment problem is the forerunner of inverse spectral theory in the modern theory of completely integrable systems the method of inverse scattering is used to obtain explicit solutions of a class of hamiltonian systems which arise as isospectral deformations of a linear operator in this lecture we explain how stieltjes s formulas are used to obtain explicit solutions to a number of completely integrable systems including discrete reductions of some nonlinear partial differential equations and the isospectral deformations of jacobi matrices a k a toda flows

some covariant representations of massless boson fields considers the c algebra of the canonical commutation relations ccr acted on by a group g of one particle symmetry transformations v a symplectic operator t defines a representation pi t pi f omicron t where pi f is the fock representation the automorphisms of the ccr algebra that are induced by g are shown to be continuously implemented in pi t if and only if a v g av g is a continuous hilbert schmidt 1 cocycle of g here a is related to t by t exp a a being a suitable bounded antilinear self adjoint operator some new examples of fully poincare covariant representations of massless fields in 1 1 dimensions are constructed

special solutions of the toda chain and combinatorial numbers we classify all solutions of the restricted toda chain from the ansatz that all moments are expressed in terms of polynomials of some variable we show that each such solution corresponds to the sheffer class orthogonal polynomials it is shown that corresponding hankel determinants are related to some well known combinatorial numbers

combinatorial expressions of the solutions to initial value problems of the discrete and ultradiscrete toda molecules combinatorial expressions are presented of the solutions to initial value problems of the discrete and ultradiscrete toda molecules for the discrete toda molecule a subtraction free expression of the solution is derived in terms of non intersecting paths for which two results in combinatorics flajolet s interpretation of continued fractions and gessel viennot s lemma on determinants are applied by ultradiscretizing the subtraction free expression the solution to the ultradiscrete toda molecule is obtained it is finally shown that the initial value problem of the ultradiscrete toda molecule is exactly solved in terms of shortest paths on a specific graph the behavior of the solution is also investigated in comparison with the box ball system

the hilbert schmidt cohomology for the poincare group we consider cocycles for the poincart group pi satisfying gk v k v g where v is an irreducible strongly continuous representation of pi and g e b y the hilbert schmidt operators on the representation space 3 of v it is shown that i ii must be of the form g v av a with a e b x the method can be extended to analyse the cocycles of products of arbitrary irreducible representations of pi providing neither representation belongs to the little group of vanishing four momentum

algebraic curves for commuting elements in the q deformed heisenberg algebra in this paper we extend the eliminant construction of burchnall and chaundy for commuting differential operators in the heisenberg algebra to the q deformed heisenberg algebra and show that it again provides annihilating curves for commuting elements provided q satisfies a natural condition as a side result we obtain estimates on the dimensions of the eigenspaces of elements of this algebra in its faithful module of laurent series

max plus singular values in this paper we prove a new characterization of the max plus singular values of a max plus matrix as the max plus eigenvalues of an associated max plus matrix pencil this new characterization allows us to compute max plus singu lar values quickly and accurately as well as capturing the asymptotic behavior of the singular values of classical matrices whose entries are exponentially pa rameterized we show experimentally that max plus singular values give order of magnitude approximations to the classical singular values of parameter inde pendent classical matrices we also discuss hungarian scaling which is a diagonal scaling strategy for preprocessing classical linear systems we show that hungarian scaling can dramatically reduce the 2 norm condition number and that this action can be explained using our new theory for max plus singular values keywords tropical algebra max plus algebra singular values diagonal scaling condition number optimal assignment problem we also discuss hungarian scaling which is a diagonal scaling strategy for preprocessing classical linear systems we show that hungarian scaling can dramatically reduce the d norm condition number and that this action can be explained using our new theory for max plus singular values