on the existence of periodic solutions to p laplacian rayleigh differential equation with a delay abstract in this paper the authors study the existence of periodic solutions to a p laplacian rayleigh differential equation with a delay as follows p y t f y t g y t t e t where p 1 is a constant p r r p u u p 2 u f g e c r r t t t with t 0 t 0 t and e t t e t t 0 is a constant by using mawhin s continuation theorem some new results are obtained

braid structure and raising lowering operator formalism in sutherland model we algebraically construct the fock space of the sutherland model in terms of the eigenstates of the pseudomomenta as basis vectors for this purpose we derive the raising and lowering operators which increase and decrease eigenvalues of pseudomomenta the operators exchanging eigenvalues of two pseudomomenta have been known all the eigenstates are systematically produced by starting from the ground state and multiplying these operators by it

existence and uniqueness of periodic solutions for a p laplacian duffing equation with a deviating argument abstract by means of mawhin s continuation theorem we study a class of p laplacian duffing type differential equations of the form p x t c x t g t x t x t t e t some new results on the existence and uniqueness of periodic solutions for the above equation are obtained it is significant that the growth degree with respect to the variables u v imposed on g t u v is allowed to be greater than p 1 so our results generalize and improve on the corresponding results in related papers

periodic solutions for p laplacian lienard equation with a deviating argument abstract by employing mawhin s continuation theorem the existence of periodic solutions of the p laplacian lienard equation with a deviating argument p x t f x t x t g x t t e t under various assumptions are obtained

harmonic analysis as spectral theory of laplacians by writing the fourier inversion formula on euclidean space in polar coordinates we obtain f x 0 fgl x dx where fgl x 2fgl x which is the spectral theory of the laplacian how do properties of f relate to properties of the family of eigenfunctions fgl answers are provided for the following spaces l2 s s d in odd dimensions analogous results are obtained for harmonic analysis on hyperbolic space constant curvature semi riemannian spaces the heisenberg group and for differential forms on hyperbolic space for f l2 there is a plancherel formula f 22 limt o 1t bt z f x 2dx d where bt z denotes the ball of radius t about an arbitrary point z which is independent of the dimension and the identical formula holds in hyperbolic space if the parametrization of the eigenvalues is shifted for certain semi riemannian symmetric spaces we obtain a paley wiener theorem that explains the role of discrete series in producing functions of compact support and also involve certain non unitary representations that contain the discrete series representations for the heisenberg group the plancherel formula is of a different nature requiring that the eigenfunctions be almost periodic in one variable

periodic solutions for p laplacian rayleigh equations abstract by employing mawhin s continuation theorem the existence of the p laplacian delay rayleigh equation p x t f x t g x t t e t under various assumptions is obtained

a unification of knizhnik zamolodchikov and dunkl operators via affine hecke algebras some generalizations of the lusztig lascoux schutzenberger operators for affine hecke algebras are considered as corollaries we obtain lusztig s isomorphisms from affine hecke algebras to their degenerate versions a natural interpretation of the dunkl operators and a new class of differential difference operators generalizing dunkl s ones and the knizhnik zamolodchikov operators from the two dimensional conformal field theory

existence uniqueness and regularity results on nonlocal balance laws abstract we consider a class of nonlocal balance laws as initial value problems on a finite time horizon and show existence and uniqueness of the corresponding weak solutions the description nonlocal refers to the velocity of the balance law that depends on the weighted integral over an area in space at any given time existence of a weak solution for initial data and right hand side data in l 1 l in l and in special cases in l 1 is shown via the method of characteristics resulting in a fixed point problem in the nonlocal term the uniqueness of a weak solution with relatively weak assumptions on the flux function and the nonlocal term is established so that the uniqueness result does not require the well known kru kov entropy condition as it is typical for local balance laws and was up to now used in the available literature also for nonlocal balance laws

convolution identities for dunkl orthogonal polynomials from the osp 1 2 lie superalgebra new convolution identities for orthogonal polynomials belonging to the q 1 analog of the askey scheme are obtained specialization of the chihara polynomials will play a central role as the eigenfunctions of a special element of the lie superalgebra osp 1 2 in the positive discrete series representation using the clebsch gordan coefficients a convolution identity for the specialized chihara the dual 1 hahn and the big 1 jacobi polynomials are found using the racah coefficients a convolution identity for the big 1 jacobi and the bannai ito polynomials is found finally these results are applied to construct a bilinear generating function for the big 1 jacobi polynomials new convolution identities for orthogonal polynomials belonging to the q 1 analog of the askey scheme are obtained specialization of the chihara polynomials will play a central role as the eigenfunctions of a special element of the lie superalgebra osp 1 2 in the positive discrete series representation using the clebsch gordan coefficients a convolution identity for the specialized chihara the dual 1 hahn and the big 1 jacobi polynomials are found using the racah coefficients a convolution identity for the big 1 jacobi and the bannai ito polynomials is found finally these results are applied to construct a bilinear generating function for the big 1 jacobi polynomials

an algebraic approach to shape invariance with reflections we consider a realization of supersymmetric shape invariant quantum systems where generalized ladder operators are constructed through the association of the supersymmetric partner operators the parameter potential translation operator and the reflection operator the basic algebraic relations as well as the system eigenstates and energy eigenvalues are obtained as an illustration we apply the generalized formalism for two important shape invariant potential systems the scarf hyperbolic and the morse potentials

integrable models from twisted half loop algebras this paper is devoted to the construction of new integrable quantum mechanical models based on certain subalgebras of the half loop algebra of various results about these subalgebras are proven by presenting them in the notation of the st petersburg school these results are then used to demonstrate the integrability and find the symmetries of two types of physical system twisted gaudin magnets and calogero type models of particles on several half lines meeting at a point

an uncertainty inequality for fourier dunkl series an uncertainty inequality for the fourier dunkl series introduced by the authors in o ciaurri j l varona a whittaker shannon kotel nikov sampling theorem related to the dunkl transform proc amer math soc 135 2007 2939 2947 is proved this result is an extension of the classical uncertainty inequality for the fourier series

on the singular local limit for conservation laws with nonlocal fluxes we give an answer to a question posed in amorim et al esaim math model numer anal 49 1 19 37 2015 which can loosely speaking be formulated as follows consider a family of continuity equations where the velocity depends on the solution via the convolution by a regular kernel in the singular limit where the convolution kernel is replaced by a dirac delta one formally recovers a conservation law can we rigorously justify this formal limit we exhibit counterexamples showing that despite numerical evidence suggesting a positive answer one does not in general have convergence of the solutions we also show that the answer is positive if we consider viscous perturbations of the nonlocal equations in this case in the singular local limit the solutions converge to the solution of the viscous conservation law

integrable spin chain with reflecting end a new integrable spin chain of the haldane shastry type is introduced it is interpreted as the inverse square interacting spin chain with a reflecting end the lattice sites of this model consist of the square roots of the zeros of the laguerre polynomial using the exchange operator formalism the integrals of motion for the model are explicitly constructed

uncertainty principles in harmonic analysis abstract let l 2 r n 2 1 generalizing the heisenberg uncertainty principle lower bounds for the variance of the measure x 2 dx are established under assumptions on the fourier transform tf if e is a subset of r n of codimension one which is suitably uniformly distributed and b is a parameter which measures the maximum distance from a point to e then the estimate var x 2 dx cb 2 holds provided e tf 2 d c b 1 for suitable constants c and c examples of sets e are families of parallel hyperspaces or concentric spheres analogous results are established for normalized l 2 functions on the sphere s n here the lower bound is inf y s n s n sin d x y 2 x 2 dx cb 2 and the hypothesis on the spherical harmonic expansion k 0 k is k a k 2 2 c b 1 where a is a set of integers with gaps at most b for both even and odd numbers

mixed norm estimates for the cesaro means associated with dunkl hermite expansions our main goal in this article is to study mixed norm estimates for the cesaro means associated with dunkl hermite expansions on r d these expansions arise when one considers the dunkl hermite operator or dunkl harmonic oscillator h kappa delta kappa vertical bar x vertical bar 2 where delta kappa stands for the dunkl laplacian it is shown that the desired mixed norm estimates are equivalent to vector valued inequalities for a sequence of cesaro means for laguerre expansions with shifted parameter in order to obtain such vector valued inequalities we develop an argument to extend these laguerre operators for complex values of the parameters involved and apply a version of the three lines lemma

existence uniqueness and regularity of multi dimensional nonlocal balance laws with damping abstract in this article we generalize some existence and uniqueness results in 22 for scalar nonlocal balance laws to multi dimensional nonlocal balance laws also in the multi dimensional case it is possible to get rid of the entropy condition which is usually postulated to guarantee a unique weak solution of local balance laws but which we prove to be redundant in the nonlocal case we start with a well known existence theorem for linear balance laws and the explicit formula for a solution to obtain a fixed point problem in the nonlocal term using banach s fixed point theorem we prove existence and uniqueness of a fixed point this existence and uniqueness result is used for constructing and proving a unique solution of the multi dimensional nonlocal balance law on a sufficiently small time horizon while in many publications the nonlocal term will be considered over the entire space domain we present an existence and uniqueness result which allows rather general integration areae for the nonlocal term eventually we obtain a unique weak solution on every finite time horizon existence and uniqueness are complemented by stability results and an exhaustive study on more regular weak solutions in case the data is more regular

global well posedness and scattering for a class of nonlinear dunkl schrodinger equations in this paper we introduce a class of nonlinear schrodinger equations associated with the dunkl operators in this regard we study local and global well posedness and the scattering theory associated with these equations

quantum versus classical integrability in calogero moser systems calogero moser systems are classical and quantum integrable multiparticle dynamics defined for any root system the quantum calogero systems having 1 q2 potential and a confining q2 potential and the sutherland systems with 1 sin2q potentials have integer energy spectra characterized by the root system various quantities of the corresponding classical systems e g minimum energy frequencies of small oscillations the eigenvalues of the classical lax pair matrices etc at the equilibrium point of the potential are investigated analytically as well as numerically for all root systems to our surprise most of these classical data are also integers or they appear to be quantized to be more precise these quantities are polynomials of the coupling constant s with integer coefficients the close relationship between quantum and classical integrability in calogero moser systems deserves fuller analytical treatment which would lead to better understanding of these systems and of integrable systems in general

periodic solutions for lienard type p laplacian equation with a deviating argument in this paper we use the coincidence degree theory to establish new results on the existence of t periodic solutions for the lienard type p laplacian equation with a deviating argument of the form f p x t f x t x t g t x t t t e t

an uncertainty principle for ultraspherical expansions abstract motivated by heisenberg weyl type uncertainty principles for the torustand the spheres2due to breitenberger narowich ward and others we derive an uncertainty relation for radial functions on the spheressn r n 1and more generally for ultraspherical expansions on 0 in this setting the frequency variance of al2 function on 0 is defined by means of the ultraspherical differential operator which plays the role of a laplacian our proof is based on a certain first order differential difference operator on the doubled interval moreover using the densitiesftof gaussian measures on 0 with the timettending to 0 we show that the bound of our uncertainty principle is optimal

nonlinear generalized dunkl wave equations and applications abstract in this paper we introduce a class of nonlinear wave equations associated with the generalized dunkl laplace operator we study local and global well posedness next we establish the linearization of bounded energy solutions in the spirit of gerard 1996 9 the proof uses strichartz type inequalities and the energy estimate

operational rules and a generalized hermite polynomials in this paper we use operational rules associated with three operators corresponding to a generalized hermite polynomials introduced by szego to derive as far as we know new proofs of some known properties as well as new expansions formulae related to these polynomials

weak uncertainty principle for fractals graphs and metric measure spaces we develop a new approach to formulate and prove the weak uncertainty inequality which was recently introduced by okoudjou and strichartz we assume either an appropriate measure growth condition with respect to the effective resistance metric or in the absence of such a metric we assume the poincare inequality and reverse volume doubling property we also consider the weak uncertainty inequality in the context of nash type inequalities our results can be applied to a wide variety of metric measure spaces including graphs fractals and manifolds

a new kind of two parameter deformation of heisenberg and parabose algebras and related deformed derivative we propose a new kind of two parameter p q deformed heisenberg and parabose algebra which reduces to the heisenberg algebra for the p 1 case and to parabose algebra for q 1 case corresponding to the two parameter deformed oscillator we also introduce a new kind of p q deformed derivative which relates to the ordinary derivative and q deformed derivative in an explicit manner we study the structure of fock like space of the new p q deformed oscillators and derive a formal solution for the eigenvalue equation of the hamiltonian

well posedness of a conservation law with non local flux arising in traffic flow modeling we prove the well posedness of entropy weak solutions of a scalar conservation law with non local flux arising in traffic flow modeling the result is obtained providing accurate mathbf l infty l bv and mathbf l 1 l1 estimates for the sequence of approximate solutions constructed by an adapted lax friedrichs scheme

extended trigonometric cherednik algebras and nonstationary schrodinger equations with delta potentials we realize an extended version of the trigonometric cherednik algebra as affine dunkl operators involving heaviside functions we use the quadratic casimir element of the extended trigonometric cherednik algebra to define an explicit nonstationary schrodinger equation with delta potential we use coordinate bethe ansatz methods to construct solutions of the nonstationary schrodinger equation in terms of generalized bethe wave functions it is shown that the generalized bethe wave functions satisfy affine difference knizhnik zamolodchikov equations as functions of the momenta the relation to the vector valued root system analogs of the quantum bose gas on the circle with delta function interactions is indicated

degenerate principal series representations and their holomorphic extensions let x h l be an irreducible real bounded symmetric domain realized as a real form in an hermitian symmetric domain d g k the intersection s of the shilov boundary of d with x defines a distinguished subset of the topological boundary of x and is invariant under h it can be realized as s h p for certain parabolic subgroup p of h we study the spherical representations of h induced from p we find formulas for the spherical functions in terms of the macdonald hypergeometric function this generalizes the earlier result of faraut koranyi for hermitian symmetric spaces d we consider a class of h invariant integral intertwining operators from the representations on l2 s to the holomorphic representations of g restricted to h we construct a new class of complementary series for the groups h so n m su n m with n m 2 and sp n m with n m 1 we realize them as discrete components in the branching rule of the analytic continuation of the holomorphic discrete series of g su n m su n m su n m and su 2n 2m respectively

riesz transform and riesz potentials for dunkl transform analogues of riesz potentials and riesz transforms are defined and studied for the dunkl transform associated with a family of weight functions that are invariant under a reflection group the lp boundedness of these operators is established in certain cases

sufficient conditions for the existence of periodic solutions to some second order differential equations with a deviating argument abstract by means of mawhin s continuation theorem we study some second order differential equations with a deviating argument x t f t x t x t t x t e t some new results on the existence of periodic solutions are obtained the interest is that we allow the degree with respect to the variables x 0 x 1 x 2 of f t x 0 x 1 x 2 to be greater than 1 and also the result theorem 3 2 is related to the deviating argument t meanwhile we give an example to demonstrate our result

coupled fixed points of multivalued operators and first order odes with state dependent deviating arguments abstract we establish a coupled fixed point theorem for a meaningful class of mixed monotone multivalued operators and then we use it to derive some results on the existence of quasisolutions and unique solutions to first order functional differential equations with state dependent deviating arguments our results are very general and can be applied to functional equations featuring discontinuities with respect to all of their arguments but we emphasize that they are new even for differential equations with continuously state dependent delays

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

existence and uniqueness of periodic solutions for a kind of lienard type p laplacian equation abstract by using topological degree theory and some analysis skills we obtain some sufficient conditions for the existence and uniqueness of periodic solutions for lienard type p laplacian differential equations

existence of periodic solutions to a p laplacian lienard differential equation with a deviating argument abstract by means of mawhin s continuation theorem a kind of p laplacian lienard differential equation with a deviating argument as follows p y t f y t y t h y t g y t t e t is studied a new result on the existence of periodic solutions is obtained the interest is that the relation between the existence of periodic solutions and the deviating argument t is investigated meanwhile the approaches used to estimate a priori bounds of periodic solutions are different from the corresponding ones in the known literature

intertwining relations for the matrix calogero like models supersymmetry and shape invariance we investigate the intertwining relations for n particle calogero like models with internal degrees of freedom starting from the well known dunkl polychronakos operators we construct a new type of local without exchange operation differential operator these operators intertwine the matrix hamiltonians corresponding to irreducible representations of the permutation group sn in particular cases this method allows us to construct a new class of exactly solvable dirac like equations and a new class of matrix models with shape invariance we establish a connection with the approach of multi dimensional supersymmetric quantum mechanics

on approximation of local conservation laws by nonlocal conservation laws abstract we show that for monotone initial datum the solution of nonlocal conservation laws converges to the entropy solution of the corresponding local conservation laws when the nonlocal reach tends to zero this particularly covers the principle cases of conservation laws shocks and rarefactions the considered problem is addressed by studying the entropy of the nonlocal conservation laws in the limit and by exploiting the semi explicit solution formula developed in 30

differential difference operators associated to reflection groups there is a theory of spherical harmonics for measures invariant under a finite reflection group the measures are products of powers of linear functions whose zero sets are the mirrors of the reflections in the group times the rotation invariant measure on the unit sphere in rn a commutative set of differential difference operators each homogeneous of degree 1 is the analogue of the set of first order partial derivatives in the ordinary theory of spherical harmonics in the case of r2 and dihedral groups there are analogues of the cauchy riemann equations which apply to gegenbauer and jacobi polynomial expansions the analysis of orthogonality structures for polynomials in several variables is a problem of vast dimensions this paper is part of an ongoing program to establish a workable theory for one particular class the underlying structure is based on finite coxeter groups these are finite groups acting on euclidean space generated by reflections in the zero sets of a collection of linear functions the roots the weight functions for the orthogonality are products of powers of these linear functions restricted to the surface of the unit sphere in addition the weight function is required to be invariant under the action of the group the resulting theory has strong similarities to the theory of spherical harmonics this was established in previous papers of the author 3 4 5 most notably a homogeneous polynomial is orthogonal to all polynomials of lower degree if and only if it is annihilated by a certain second order differential difference operator ordinary partial differentiation acts as an endomorphism on ordinary harmonic functions the use of such operators and their adjoints leads to recurrence formulas and orthogonal decompositions for harmonic polynomials in this paper we construct a commutative set of first order differentialdifference operators associated to the second order operator previously mentioned received by the editors june 1 1987 1980 mathematics subject classification 1985 revision primary 33a45 33a65 20h15 secondary 20c30 42c10 51f15

two step asymptotics of scaled dunkl processes dunkl processes are generalizations of brownian motion obtained by using the differential difference operators known as dunkl operators as a replacement of spatial partial derivatives in the heat equation special cases of these processes include dyson s brownian motion model and the wishart laguerre eigenvalue processes which are well known in random matrix theory it is known that the dynamics of dunkl processes is obtained by transforming the heat kernel using dunkl s intertwining operator it is also known that under an appropriate scaling their distribution function converges to a steady state distribution which depends only on the coupling parameter as the process time t tends to infinity we study scaled dunkl processes starting from an arbitrary initial distribution and we derive expressions for the intertwining operator in order to calculate the asymptotics of the distribution function in two limiting situations in the first one is fixed and t tends to infinity approach to the steady s

riesz transforms and fractional integration for orthogonal expansions on spheres balls and simplices abstract this paper studies the hardy littlewood sobolev hls inequality and the riesz transforms for fractional integration associated to weighted orthogonal polynomial expansions on spheres balls and simplexes with weights being invariant under a general finite reflection group on r d the sharp index for the validity of the hls inequality is determined and the l p boundedness of the riesz transforms is established in particular our results extend a classical inequality of muckenhoupt and stein on conjugate ultraspherical polynomial expansions our idea is based on a new decomposition of the dunkl laplace beltrami operator on the sphere and some sharp asymptotic estimates of the weighted christoffel functions

regularity theory and adjoint based optimality conditions for a nonlinear transport equation with nonlocal velocity in this contribution the optimal boundary control problem for a first order nonlinear nonlocal hyperbolic pde is studied motivated by various applications ranging from re entrant manufacturing systems to particle synthesis processes we establish the regularity of solutions for w 1 p data based on a general l 2 tracking type cost functional the existence uniqueness and regularity of the adjoint system in w 1 p is derived using the special structure induced from the nonlocal flux function of the state equation the assumption of w 1 p and not l p regularity comes thereby due to the fact that the adjoint equation asks for more regularity to be well defined this problem is discussed in detail and we give a solution by defining a special type of cost functional such that the corresponding optimality system is well defined

symplectic reflection algebras calogero moser space and deformed harish chandra homomorphism to any finite group sp v of automorphisms of a symplectic vector space v we associate a new multi parameter deformation h of the algebra v smash product of with the polynomial algebra on v the parameter runs over points of r where r number of conjugacy classes of symplectic reflections in the algebra h called a symplectic reflection algebra is related to the coordinate ring of a poisson deformation of the quotient singularity v this leads to a symplectic analogue of mckay correspondence which is most complete in case of wreath products if is the weyl group of a root system in a vector space and v then the algebras h are certain rational degenerations of the double affine hecke algebra introduced earlier by cherednik

a model of crystal precipitation abstract we study a model of crystal precipitation the mathematical formulation reduces to studying one conservation law in one space variable n x t t n x t g x 0 where g is a nonlinear and non local function of the unknown function n further the behavior of g changes drastically along a curve x x t which depends on n results on global existence uniqueness and asymptotic behavior as t are established

littlewood paley operators associated with the dunkl operator on r we consider a vector version of l p multipliers for the dunkl transform on r and we prove l p inequalities for the littlewood paley operators

some new examples of markov processes which enjoy the time inversion property in this paper we give a sufficient condition on the semi group densities of an homogeneous markov process taking values in n which ensures that it enjoys the time inversion property our condition covers all previously known examples of markov processes satisfying this property as new examples we present a class of markov processes with jumps the dunkl processes and their radial parts

on the existence of periodic solutions for pp laplacian generalized lienard equation by employing mawhin s continuation theorem the existence of periodic solutions of the p laplacian generalized lienard equation with deviating argument p x t f t x t x t t g x t t e t p x t f t x t x t t g x t t e t under various assumptions are obtained

optimally space localized band limited wavelets on s q 1 the localization of a function can be analyzed with respect to different criteria in this paper we focus on the uncertainty relation on spheres introduced by goh and goodman uncertainty principles and asymptotic behavior appl comput harmon anal 16 2004 69 89 where the localization of a function is measured in terms of the product of two variances the variance in space domain and the variance in frequency domain after deriving an explicit formula for the variance in space domain of a function in the space wn qs of spherical polynomials of degree at most n s which are orthogonal to all spherical polynomials of degree at most n we are able to identify up to rotation and multiplication by a constant the polynomial in wn qs with minimal variance in space domain or in other words to determine the optimally space localized polynomial in wn qs

irreducible representations of the rational cherednik algebra associated to the coxeter group h3 abstract this paper describes irreducible representations in category o of the rational cherednik algebra h c h 3 h associated to the exceptional coxeter group h 3 and any complex parameter c we compute the characters of all these representations explicitly as a consequence we classify all the finite dimensional irreducible representations of h c h 3 h

on the existence of periodic solutions for p laplacian generalized lienard equation abstract by employing mawhin s continuation theorem the existence of periodic solutions of the p laplacian generalized lienard equation with deviating argument p x t f t x t x t t g x t t e t under various assumptions are obtained

uncertainty principles for jacobi expansions abstract in this paper an uncertainty principle for jacobi expansions is derived as a generalization of that for ultraspherical expansions by rosler and voit indeed a stronger inequality is proved which is new even for fourier cosine or ultraspherical expansions a complex base of exponential type on the torus z c z 1 related to jacobi polynomials is introduced which are the eigenfunctions both of certain differential difference operators of the first order and the second order an uncertainty principle related to such exponential base is also proved

new results on the existence of periodic solutions to a p laplacian differential equation with a deviating argument by means of mawhin s continuation theorem a kind of p laplacian differential equation with a deviating argument as follows p x t f t x t x t t x t e t is studied some new results on the existence of periodic solutions are obtained the main results theorems 3 2 and 3 3 are all related to the deviating argument t meanwhile the degrees with respect to the variables x0 x1 of f t x0 x1 x2 are allowed to be grater than p 1 which is different from the corresponding conditions of known literature

a continuum model for a re entrant factory high volume multistage continuous production flow through a re entrant factory is modeled through a conservation law for a continuous density variable on a continuous production line augmented by a state equation for the speed of the production along the production line the resulting nonlinear nonlocal hyperbolic conservation law allows fast and accurate simulations little s law is built into the model it is argued that the state equation for a re entrant factory should be nonlinear comparisons of simulations of the partial differential equation pde model and discrete event simulations are presented a general analysis of the model shows that for any nonlinear state equation there exist two steady states of production below a critical start rate a high volume high throughput time state and a low volume low throughput time state the stability of the low volume state is proved output is controlled by adjusting the start rate to a changed demand rate two linear factories and a re entrant factory each one modeled by a hyperbolic conservation law are linked to provide proof of concept for efficient supply chain simulations instantaneous density and flux through the supply chain as well as work in progress wip and output as a function of time are presented extensions to include multiple product flows and preference rules for products and dispatch rules for re entrant choices are discussed

orthogonal polynomials on the sphere with octahedral symmetry for any finite reflection group g acting on rn there is a family of g invariant measures h2 dw where h is a certain product of linear functions whose zero sets are the reflecting hyperplanes for g on the unit sphere and an associated partial differential operator lh f a fh fa h a is the laplacian analogously to spherical harmonics there is an orthogonal with respect to h2 do decomposition of homogeneous polynomials that is if p is of degree n then i n 21 p x j ix12jpn 2 x 0 where lh p 0 and deg p i for each i but with the restriction that p and p must all be g invariant the main topic is the hyperoctahedral group with h x x ix2 i n u x xj i j the special case n 2 leads to jacobi polynomials a detailed study of the case n 3 is made an important result is the construction of a third order differential operator that maps polynomials associated to h with indices a i to those associated with a 2 fi 1 introduction regular figures have long been objects of fascination we study here the interplay between them and the theory of orthogonal polynomials this will also touch on finite groups generated by reflections and their polynomial invariants as well as a generalization of spherical harmonics the underlying situation throughout will consist of spaces of homogeneous polynomials on rn that satisfy a second order differential equation and whose restrictions to the unit sphere have an orthogonality relation with respect to a weight function and of a finite reflection group for which all these objects are invariant the weight measure h2 x dw x on the unit sphere s in r3 where h x xlx2x3 a x 23 3 a 2 dw is surface area and the associated polynomials will be studied most intensely some of the highlights of the theory are as follows define the differential operator lhf f fah received by the editors april 19 1982 and in revised form december 15 1982 1980 mathematics subject classification primary 33a45 33a65 secondary 20h15 this research was partially supported by nsf grant mcs 81 02581 d 984 american mathematical society 0002 9947 84 1 00 25 per page

integrable n particle hamiltonians with yangian or reflection algebra symmetry we use the dunkl operator approach to construct one dimensional integrable models describing n particles with internal degrees of freedom these models are described by a general hamiltonian belonging to the centre of the yangian or the reflection algebra which ensures that they admit the corresponding symmetry in particular the open problem of the symmetry is answered for the bn type sutherland model with spin and for a generalized bn type nonlinear schrodinger hamiltonian

periodic solutions for p laplacian rayleigh equations with a deviating argument abstract by using the generalized borsuk theorem in coincidence degree theory some new criteria for guaranteeing the existence of periodic solutions for p laplacian rayleigh equations with a deviating argument are derived