optimal decay rates for the compressible fluid models of korteweg type abstract we consider the compressible navier stokes korteweg system that models the motions of the compressible isothermal viscous capillary fluids we prove the optimal l 2 and l p p 2 decay rates for the classical solutions and their spatial derivatives in particular the optimal l 2 decay rate of the second order spatial derivatives is obtained the proof is based on the detailed study of the linear decay estimates and nonlinear energy estimates

global solutions to a model of structural phase transitions in shape memory alloys abstract global in time existence and uniqueness of solutions to a nonlinear system of coupled evolution equations is discussed the system represents a model of dynamical structural phase transitions martensitic transformations in shape memory alloys

duality for ext groups and extensions of discrete series for graded hecke algebras in this paper we study extensions of graded affine hecke algebra modules in particular based on an explicit projective resolution on graded affine hecke algebra modules we prove a duality result for ext groups this duality result with an ind res resolution gives an algebraic proof of the fact that all higher ext groups between a tempered module and a discrete series vanish

vanishing capillarity limit of the compressible non isentropic navier stokes korteweg system to navier stokes system abstract in this paper we consider the three dimensional compressible nonisentropic fluid model of korteweg type we mainly present the vanishing capillarity limit of smooth solution to the initial value problem based on the uniform estimates with respect to the capillary coefficient we show the unique smooth solutions of the three dimensional korteweg model converges globally in time to the smooth solution of the three dimensional compressible nonisentropic navier stokes system as tends to zero also we give the convergence rate estimates in h 2 norm with respect to

regular articlethe structure of the young symmetrizers for spin representations of the symmetric group ii the first paper in this series established that the projective analogue of the young symmetrizer recently introduced by nazarov has a naturalpxq structure comparable with thepq form of the classical symmetrizer this second paper develops the theory on this decomposition further a more efficient construction of the projective symmetrizer is presented for certain classes of partitions this approach yields a compact expression for the intermediate factorx in the projective decomposition

baker campbell hausdorff relations for supergroups one parameter subgroups the exponential mapping and canonical coordinates have previously been defined for connected supergroups in this paper a technique for obtaining analytical expressions linking different coordinate schemes for supergroups is presented these are the baker campbell hausdorff relations the method is illustrated in detail with the examples of supergroups based on the supersymmetric quantum mechanical superalgebra sqm 2 and on the inonu wigner contraction isop 1 2 of the simple superalgebra osp 1 2

shifted tableaux and the projective representations of symmetric groups les groupes de representation de s n classes de conjugaison algebres de clifford et la representation spin de base produits induits pour des representations spin une application caracteristique pour des caracteres de spin tableaux decales et q fonctions de schur les caracteres de spin irreductibles de s n et a n une analogue decalee de la regle lr produits tensoriels interieurs

global properties of supermanifolds we construct new examples of supermanifolds and determine the vector bundle structure of the supermanifolds commonly used in physics we show that any supermanifold admits a foliation whose leaves are locally tangent to the soul directions in the coordinate charts and which is one of a nested sequence of foliations we point out that the existence of these foliations implies restrictions on the possible topologies of supermanifolds for example a compact supermanifold with a single even dimension must have vanishing euler characteristic we also show that a globally defined superfield on a nice compact supermanifold must be constant along the leaves of the foliations by this mechanism the global topology of a supermanifold can be used to impose physically interesting constraints on superfields as an example we exhibit a supermanifold which has the local geometry of flat superspace but is such that all globally defined superfields are chiral

relations between young s natural and the kazhdan lusztig representations of sn abstract our main result here is that under a suitable order of standard tableaux the classical representation of sn introduced by young in the collected papers of alfred young 1873 1940 univ of toronto press toronto qsa iv and usually referred as the natural representattion the the more recently discovered invent math 53 1979 165 184 kazhdan lusztig k l representation are related by an upper triangular integral matrix with unit diagonal elements we have been led to this discovery by a numerical exploration we noted it in each of the irreducible representations of sn up to n 6 the calculations in these cases were carried out by constructing the corresponding kazhdan lusztig graphs from tables m goresky tables of kazhdan lusztig polynomials unpublished of k l polynomials to extend the calculations to n 7 we have used graphs obtained by means of an algorithm given by lascoux and schutzenberger polynomes de kazhdan lusztig pour les grassmanniennes preprint remarkably the same property holds also for these graphs these findings appear to confirm the assertion made by these authors that their algorithm does indeed yield k l graphs for the case of hook shapes we have obtained an explicit construction of the transforming matrices a result which was also suggested by our numerical data for general shapes the transforming matrices are less explicit and our proof is based on certain properties of the kazhdan lusztig representations given in their article invent math 53 1979 165 184 and on a purely combinatorial construction of the natural representation

projective representations of symmetric groups via sergeev duality in this article we determine the irreducible projective representations of the symmetric group sd and the alternating group ad over an algebraically closed field of characteristic p 6 2 these matters are well understood in the case p 0 thanks to the fundamental work of schur 24 in 1911 as well as the much more recent work of nazarov 19 20 sergeev 25 26 and others so the focus here is primarily on the case of positive characteristic where surprisingly little is known as yet in particular we obtain a natural combinatorial labelling of the irreducibles in terms of a certain set rpp d of restricted p strict partitions of d such partitions arose recently in work of kashiwara miwa peterson and yung 11 and leclerc and thibon 14 on the q deformed fock space of the affine kac moody algebra of type a p 1 leclerc and thibon proposed that rpp d should label the irreducible projective representations in some natural way and we show here how this can be done note that for p 3 5 the labelling problem was solved in 1 3 while if p 2 all projective representations of sd and ad are linear so do not need to be considered further here to be more precise recall that is a partition of d if 1 2 is a non increasing sequence of non negative integers summing to d call p strict if in addition

on the maximal lp lq regularity for a compressible fluid model of korteweg type on general domains abstract the aim of this paper is to show the maximal l p l q regularity for a compressible fluid model of korteweg type on general domains of the n dimensional euclidean space for n 2 e g bounded domains exterior domains half spaces layers tubes and their perturbed domains our approach is based on the theory of the r boundedness for a generalized resolvent problem associated with the korteweg type model

nonlinear stability of traveling wave solutions for the compressible fluid models of korteweg type abstract this paper is concerned with the existence and time asymptotic nonlinear stability of traveling wave solutions to the cauchy problem of the one dimensional compressible fluid models of korteweg type which governs the motions of the compressible fluids with internal capillarity the existence of traveling wave solutions is obtained by the phase plane analysis then the traveling wave solution is shown to be asymptotically stable by the elementary l 2 energy method

affine sergeev algebra and q analogues of the young symmetrizers for projective representations of the symmetric group we study a q deformation for the crossed product of the symmetric group s n with the clifford algebra on n anticommuting generators we obtain a q version of the projective analogue for the classical young symmetrizer introduced by the second author our main tool is an analogue of the hecke algebra of complex valued functions on the group mbox gl n over a p adic field relative to the iwahori subgroup

effective velocity in compressible navier stokes equations with third order derivatives abstract a formulation of certain barotropic compressible navier stokes equations with third order derivatives as a viscous euler system is proposed by using an effective velocity variable the equations model for instance viscous korteweg or quantum navier stokes flows the formulation in the new variable allows for the derivation of an entropy identity which is known as the bd bresch desjardins entropy equation as a consequence of this estimate a new global in time existence result for the one dimensional quantum navier stokes equations with strictly positive particle densities is proved

on the theory of one parameter subgroups of supergroups the one parameter subgroups of supergroups are defined and their primary properties are delineated parametrization schemes analogous to those used in lie group theory are investigated in particular exponentiation is introduced and related to the one parameter subgroups canonical coordinates of three kinds are investigated the third of which has no analog in conventional lie theory we illustrate our results with the examples of the supersymmetric quantum mechanical superalgebra sqm 2 and the simple superalgebra osp 1 2

spin hecke algebras of finite and affine types we introduce the spin hecke algebra which is a q deformation of the spin symmetric group algebra and its affine generalization we establish an algebra isomorphism which relates our spin affine hecke algebras to the affine hecke clifford algebras of olshanski and jones nazarov relation between the spin affine hecke algebra and a nonstandard presentation of the usual affine hecke algebra is displayed and the notion of covering affine hecke algebra is introduced to provide a link between these algebras various algebraic structures for the spin affine hecke algebra are established

global classical solutions to the one dimensional compressible fluid models of korteweg type with large initial data abstract this paper is concerned with the global existence of classical solutions with large initial data away from vacuum to the cauchy problem of the one dimensional isothermal compressible fluid models of korteweg type with density dependent viscosity coefficient and capillarity coefficient the case when the viscosity coefficient and the capillarity coefficient for some parameters r is considered under some conditions on we first show the global existence of large solutions around constant states if the far fields of the initial data are the same while if the far fields of the initial data are different we prove the global stability of rarefaction waves with large strength here global stability means the initial perturbation can be arbitrarily large our analysis is based on the elementary energy method and the technique developed by y kanel 29

global solutions of a high dimensional system for korteweg materials the global existence of solutions to a high dimensional system of korteweg materials is established when the initial data are small the complete model was proposed by dunn and serrin and the local existence of the solution was obtained in an earlier paper by the authors

asymptotic stability of strong rarefaction waves for the compressible fluid models of korteweg type abstract this paper is concerned with the time asymptotic behavior toward strong rarefaction waves of solutions to one dimension compressible fluid models of korteweg type which governs the motions of the compressible fluids with internal capillarity assume that the corresponding riemann problem to the compressible euler system can be solved by rarefaction waves v r u r t x if the initial data is a small perturbation of an approximate rarefaction wave for v r u r t x we show that the corresponding cauchy problem admits a unique global smooth solution which tends to v r u r t x time asymptotically since we do not require the strength of the rarefaction waves to be small this result gives the nonlinear stability of strong rarefaction waves for the one dimensional compressible fluid models of korteweg type the analysis is based on the elementary l 2 energy method together with continuation argument

spin nilhecke algebras of classical type abstract we formulate and study the spin nilhecke algebras nh n b and nh n d of type b d which differ from the usual nilhecke algebras by some odd signs the type b spin nilhecke algebra is a nil version of the spin type b hecke algebra introduced earlier by the second author and khongsap but not for the type d one we construct faithful polynomial representations pol n of the nilhecke algebras via odd demazure operators we formulate the spin schubert polynomials and use them to show that the spin nilhecke algebras are matrix algebras with entries in a subalgebra of pol n consisting of spin symmetric polynomials all these results have their counterparts for the usual nilhecke algebras over the rational field our work is a generalization of results of lauda and ellis khovanov lauda in usual spin type a

the projective representations of the hyperoctahedral group the hyperoctahedral group the weyl group of the root system bn has seven distinct nonsplit double covers for n 4 and hence seven families of projective representations we give constructions of all the irreducible representations of these seven double covers in terms of symmetric group representations and determine the associated character tables as a corollary we also obtain the irreducible projective representations and characters of the weyl group of the root system dn

relative entropy in multi phase models of 1d elastodynamics convergence of a non local to a local model abstract in this paper we study a local and a non local regularization of the system of nonlinear elastodynamics with a non convex energy we show that solutions of the non local model converge to those of the local model in a certain regime the arguments are based on the relative entropy framework and provide an example of how local and non local regularizations may compensate for non convexity of the energy and enable the use of the relative entropy stability theory even if the energy is not quasi or poly convex

stabilization for equations of one dimensional viscous compressible heat conducting media with nonmonotone equation of state abstract we consider the navier stokes system describing motions of viscous compressible heat conducting and self gravitating media we use the state function of the form p u p 0 u p 1 u linear with respect to the temperature but we admit rather general nonmonotone functions p 0 and p 1 of u which allows us to treat various physical models of nuclear fluids for which p and u are the pressure and the specific volume or thermoviscoelastic solids for solutions to an associated initial boundary value problem with fixed free boundary conditions and arbitrarily large data we prove a collection of estimates independent of time interval including uniform two sided bounds for u and describe asymptotic behavior as t namely we establish the stabilization pointwisely and in l q for u in l 2 for and in l q for v the velocity for any q 2 for completeness the proof of the corresponding global existence theorem is also included

existence of solutions for a mathematical model related to solid solid phase transitions in shape memory alloys we consider a strongly nonlinear pde system describing solid solid phase transitions in shape memory alloys the system accounts for the evolution of an order parameter related to different symmetries of the crystal lattice in the phase configurations of the stress and the displacement u and of the absolute temperature the resulting equations present several technical difficulties to be tackled in particular we emphasize the presence of nonlinear coupling terms higher order dissipative contributions possibly multivalued operators as for the evolution of temperature a highly nonlinear parabolic equation has to be solved for a right hand side that is controlled only in l 1 we prove the existence of a solution for a regularized version by use of a time discretization technique then we perform suitable a priori estimates which allow us pass to the limit and find a weak global in time solution to the system

yangian of the queer lie superalgebra consider the complex matrix lie superalgebra with the standard generators where define an involutory automorphism of by the twisted polynomial current lie superalgebra has a natural lie co superalgebra structure we quantise the universal enveloping algebra as a co poisson hopf superalgebra for the quantised algebra we give a description of the centre and construct the double in the sense of drinfeld we also construct a wide class of irreducible representations of the quantised algebra

convergence to the superposition of rarefaction waves and contact discontinuity for the 1 d compressible navier stokes korteweg system abstract this paper is concerned with the vanishing capillarity viscosity limit for the one dimensional compressible navier stokes korteweg system to the riemann solution of the euler system that consists of the supposition of two rarefaction waves and a contact discontinuity it is shown that there exists a family of smooth solutions to the compressible navier stokes korteweg system which converge to the riemann solution away from the initial time t 0 and the contact discontinuity located at x 0 as the coefficients of capillarity viscosity and heat conductivity tend to zero moreover a uniform convergence rate in terms of the above physical parameters is also obtained here the strengths of both the rarefaction waves and the contact discontinuity are not required to be small

global solutions to the equations of a ginzburg landau theory for structural phase transitions in shape memory alloys abstract global existence of smooth solutions is proved for the system of partial differential equations governing the dynamics of martensic phase transitions in shape memory alloys the free energy is assumed in ginzburg landau form and nonconvex in the order parameter

a categorification of twisted heisenberg algebras abstract we categorify a quantized twisted heisenberg algebra associated to a finite subgroup of sl 2 c

stability of periodic solutions of conservation laws with viscosity analysis of the evans function nonclassical conservation laws with viscosity arising in multiphase fluid and solid mechanics exhibit a rich variety of traveling wave phenomena including homoclinic pulse type and periodic solutions along with the standard heteroclinic shock or front type solutions here we investigate stability of periodic traveling waves within the abstract evans function framework established by r a gardner our main result is to derive a useful stability index analogous to that developed by gardner and zumbrun in the traveling front or pulse context giving necessary conditions for stability with respect to initial perturbations that are periodic on the same period t as the traveling wave moreover we show that the periodic stability index has an interpretation analogous to that of the traveling front or pulse index in terms of well posedness of an associated riemann problem for an inviscid medium now to be interpreted as allowing a wider class of measure valued solutions or alternatively in terms of existence and nonsingularity of a local mass map from perturbation mass to potential time asymptotic t periodic states a closely related calculation yields also a complementary long wave stability criterion necessary for stability with respect to periodic perturbations of arbitrarily large period nt n we augment these analytical results with numerical investigations analogous to those carried out by brin in the traveling front or pulse case approximating the spectrum of the linearized operator about the wave

clifford algebra as quantum language we suggest clifford algebra as a useful simplifying language for present quantum dynamics clifford algebras arise from representations of the permutation groups as they arise from representations of the rotation groups aggregates using such representations for their permutations obey clifford statistics the vectors supporting the clifford algebras of permutations and rotations are plexors and spinors respectively physical spinors may actually be plexors describing quantum ensembles not simple individuals we use clifford statistics to define quantum fields on a quantum space time and to formulate a quantum dynamics field space time unity that evades the compactification problem the quantum bits of history regarded as a quantum computation seem to obey a clifford statistics

global existence for a second order thermo mechanical model of shape memory alloys abstract a thermo mechanical model of structural phase transitions in solids is considered in this model the free energy depends on temperature macroscopic deformation and also on the proportions of the phases the related initial boundary value problem consists of equilibrium equations for energy and momentum coupled with an evolution variational inequality for the phase proportions fourth order regularizing terms are neglected in the momentum balance equation using an approximation a priori estimates passage to the limit procedure we show the existence of a solution in any dimension of space

the structure of the young symmetrizers for spin representations of the symmetric group i abstract this paper is the first in a series of three papers on the young symmetrizers for the spin representations of the symmetric group in this opening paper it is shown that the projective analogue of the young symmetrizer recently introduced by nazarov has a structure resembling thep q form exhibited by the classical symmetrizer in contrast to the classical case our decomposition of the projective symmetrizer requires an additional intermediate factorx this factor will be studied in greater detail in the later papers

nonconvex model of material growth mathematical theory the model of volumetric material growth is introduced in the framework of finite elasticity the new results obtained for the model are presented with complete proofs the state variables include the deformations temperature and the growth factor matrix function the existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown the mathematical results can be applied to a wide class of growth models in mechanics and biology

cocenters of hecke clifford and spin hecke algebras abstract we determine a basis of the cocenter i e the trace or zeroth hochschild homology of the degenerate affine hecke clifford and spin hecke algebras in classical types

on a system of nonlinear pdes with temperature dependent hysteresis in one dimensional thermoplasticity abstract in this paper we develop a thermodynamically consistent description of the uniaxial behaviour of thermoelastoplastic materials that are characterized by a constitutive law of the form x t p e x t x t where e denote the fields of strain stress and absolute temperature respectively and where p 0denotes a family of rate independent hysteresis operators of prandtl ishlinskii type parametrized by the absolute temperature the system of state equations governing the space time evolution of the material are derived it turns out that the resulting system of two nonlinearly coupled partial differential equations involves partial derivatives of hysteretic nonlinearities at different places it is shown that an initial boundary value problem for this system admits a global weak solution the paper can be regarded as a first step towards a thermodynamic theory of rate independent hysteresis operators depending on temperature

on the existence of global integral forms on supermanifolds it is shown that the berezin approach to integration on supermanifolds can be applied to cases where the supermanifold is a twisted extension of a real manifold this is done by showing that supermanifolds admit a subatlas of coordinate charts with transition functions of a quite restricted kind

maximal attractor for the system of a landau ginzburg theory for structural phase transitions in shape memory alloys abstract in this paper a system of nonlinear partial differential equations modelling the dynamics of martensitic phase transitions in shape memory alloys is further investigated in a previous paper published in siam j math anal the global existence of a unique solution and the asymptotic behaviour of the solution as time goes to infinity have been established in the present paper the existence of a compact maximal attractor is proved

existence of global strong solution for korteweg system with large infinite energy initial data this work is devoted to the study of the initial boundary value problem for a general isothermal model of capillary fluids derived by j e dunn and j serrin 1985 see cite fds which can be used as a phase transition model we will prove the existence of local and global under a condition of smallness on the initial data strong solutions with discontinuous initial density where ln rho 0 belongs to the besov space b n 2 infty r n in passing our result allow to consider initial data with discontinuous interfaces up our knowledge in the literature the results of existence of strong solutions require generally continuous initial density it implies also that we can work with initial data space of infinite energy our result relies on the fact that the density can be written as the sum of the solution rho l associated to linear system and a remainder density bar rho which is more regular than rho l by taking into account the regularizing effects induced on the bilinear convection term the main difficulty concerns the proof of new estimate of maximum principle type for the linear system associated to the korteweg system the proof is based on a characterization of the besov space in terms of the semi group associated to this linear system let also mention that we prove the existence of global strong solution with a smallness hypothesis which is subcritical in terms of the scaling of the equations it allows us to exhibit a family of large energy initial data for the scaling of the equations providing global strong solution in particular for the first time up our knowledge we show the existence of global strong solution for some large energy initial data when n 2 we finish this paper by introducing the notion of quasi solutions for the korteweg s system a tool which has been developed in the framework of the compressible navier stokes equations cite arxiv arxiv1 hal cras1 cras2 which enables us to improve the previous result and by obtaining the existence of global strong solution with large initial velocity in b n 1 2 infty in particular when n 2 it implies the existence of global strong solution with large energy data as a corollary we get global existence and uniqueness for highly compressiblekorteweg system when n geq2 it means that for any large initial data under an irrotational condition on the initial velocity we have the existence of global strong solution provided that the pressure is sufficiently highly compressible

kinetic relations for a lattice model of phase transitions the aim of this article is to analyse travelling waves for a lattice model of phase transitions specifically the fermi pasta ulam chain with piecewise quadratic interaction potential first for fixed sufficiently large subsonic wave speeds we rigorously prove the existence of a family of travelling wave solutions second it is shown that this family of solutions gives rise to a kinetic relation which depends on the jump in the oscillatory energy in the solution tails third our constructive approach provides a very good approximate travelling wave solution

global solution to a fremond model for shape memory alloys with thermal memory the aim of this paper is to establish an existence and uniqueness result for a diffusive austenite martensite phase transition problem related to shape memory alloys with thermal memory we deal with a fremond model in the framework of a linearized energy balance equation and of a dissipative variational inequality for the phase variables with diffusion terms in addition the heat flux is supposed to satisfy the cattaneo maxwell law as a particular case of gurtin and pipkin s theory an initial boundary value problem is considered and existence and uniqueness of solutions as well continuous dependence on the data are proved

degenerate affine hecke algebras and centralizer construction for the symmetric groups in our recent papers the centralizer construction was applied to the series of classical lie algebras to produce the quantum algebras called twisted yangians here we extend this construction to the series of the symmetric groups s n we study the stable properties of the centralizers of s n m in the group algebra c s n as n with m fixed we construct a limit centralizer algebra a and describe its algebraic structure the algebra a turns out to be closely related with the degenerate affine hecke algebras we also show that the so called tame representations of s yield a class of natural a modules

cohomology of supermanifolds the aim of this chapter is to unfold a basic cohomological theory for supermanifolds which will be exploited in the next chapter to study the structure of superbundles in particular to build a theory of characteristic classes this cohomology theory does not embody only trivial extensions of results valid for differentiable manifolds for instance the natural analogue of the de rham theorem does not hold in general and similarly in the case of complex supermanifolds there is generally speaking no analogue of the dolbeault theorem these features are consequences of the fact that the structure sheaf of a supermanifold does not need to be cohomologically trivial related to this is also the fact that the cohomology of the complex of global graded differential forms on a g supermanifold m a i e the super de rham cohomology of m a depends on the g supermanifold structure of m a so that homeomorphic and even smoothly diffeomorphic g supermanifolds may have a different super de rham cohomology that is super de rham cohomology is a fine invariant of the supermanifold structure

type a blocks of super category o we show that every block of category oo for the general linear lie superalgebra glm n k glm n k is equivalent to some corresponding block of category oo for the queer lie superalgebra qm n k qm n k this implies the truth of the kazhdan lusztig conjecture for the so called type a blocks of category oo for the queer lie superalgebra as formulated by cheng kwon and wang

supergroups factorizations through matrix realization using a matrix realization generic elements of the supergroups u m n and osp m 2n are obtained through the exponentiation of the corresponding super lie algebra elements the emphasis is put on the contribution of the odd part the application to the factorization problem is given and the relationship with nonlinear differential superequations is clarified

global attractor for the ginzburg landau thermoviscoelastic systems with hinged boundary conditions this paper is concerned with the following one dimensional nonlinear system of equations 0 1 utt p e x uxxt ruxxxx f 0 2 cv t xx p et et2 g where both and r are positive constants the corresponding free energy density is assumed to be in ginzburg landau form and nonconvex as a function of the order parameter results concerning the existence and uniqueness of the global solution the asymptotic behavior of the solution as time tends to infinity and the compactness of the orbit are obtained furthermore we investigate dynamics of the system and prove the existence of global attractor

some examples of compact supermanifolds with non abelian fundamental group a detailed construction is given of a supermanifold which is compact and has far from trivial topology higher dimensional examples are also described the grassmann algebra from which the supermanifolds are constructed may have finite or infinite dimension

convergent numerical approximations of the thermomechanical phase transitions in shape memory alloys discrete approximations are constructed to a nonlinear evolutionary system of partial differential equations arising from modelling the dynamics of solid state phase transitions of thermomechenical nature in the case of one space dimension the class of problems considered includes the so called shape memory alloys in particular it is shown that the obtained discrete solutions converge to the solution of the original problem and numerical simulations for the shape memory alloy au23cu30zn47 demonstrate the quality of the discrete model

large time behavior of smooth solutions to the isothermal compressible fluid models of korteweg type with large initial data abstract this paper is concerned with the large time behavior of smooth non vacuum solutions with large initial data to the cauchy problem of the one dimensional isothermal compressible fluid models of korteweg type with the viscosity coefficient and the capillarity coefficient here r and r are some parameters depending on whether the far fields of the initial data are the same or not we prove that the corresponding cauchy problem admits a unique global smooth solution which tends to constant states or rarefaction waves respectively as time goes to infinity provided that and satisfy some conditions note that the initial perturbation can be arbitrarily large the proofs are given by the elementary energy method and kanel s technique kanel 1968 compared with former results in this direction obtained by germain and lefloch 2016 and chen et al 2015 the main novelties of this paper lie in the following first we obtain the global existence of smooth solutions with large data for some new varieties of parameters and second the large time behavior of smooth large solutions around constant states is established

global existence and optimal decay rate of the compressible navier stokes korteweg equations with external force abstract in this paper we consider the three dimensional compressible fluid models of korteweg type the equation takes the form of the compressible navier stokes equation with the cauchy stress tensor in the momentum equations under the smallness assumption of the external force in some sobolev space we first show the existence of stationary solution by standard iterative arguments next we present that the global in time solution of the initial value problem for the three dimensional compressible navier stokes korteweg equations exists uniquely and approaches the stationary solution as t provided the prescribed initial data and the external force are sufficiently small finally based on the elaborate energy estimates of the solution for the nonlinear system and l 2 decay estimates of semigroup generated by the corresponding linearized equation we show the optimal l 2 convergence rates of the solution towards the stationary solution as far as we know this is the first result about the global existence and l 2 decay rate of smooth solutions for the compressible navier stokes korteweg equations with the external force

a note on the meaning of covariant derivatives in supersymmetry we analyze in this paper the group theoretical meaning of the covariant derivatives and show that they are horizontal left invariant vector fields on superspace obtained from a super lie group which at the same time exhibits the structure of a principal bundle with a canonical connection the geometrical construction is general and not restricted to the super poincare group

global existence and asymptotic behavior in nonlinear thermoviscoelasticity abstract we study global existence uniqueness and asymptotic behavior as time tends to infinity of weak solutions to the system of nonlinear thermoviscoelasticity various boundary conditions are considered it is shown that for any initial data u 0 v 0 0 l w 1 h 1 there is a unique global solution u v deformation gradient velocity temperature such that u c 0 l v c 0 w 1 l 0 w 1 c 0 h 1 the constitutive assumptions for the helmholtz free energy include the models for the study of phase transition problems in shape memory alloys

lattices supersymmetry and kahler fermions it is shown that a graded extension of the space group of a generalised simple cubic lattice exists in any space dimension d the fermionic variables which arise admit a kahlerian interpretation each graded space group is a subgroup of a graded extension of the appropriate euclidean group e d the relevance of this to the construction of lattice theories is discussed

equivariant k theory generalized symmetric products and twisted heisenberg algebra for a space x acted on by a finite group the product space xn affords a natural action of the wreath product n n sn the direct sum of equivariant k groups were shown earlier by the author to carry several interesting algebraic structures in this paper we study the k groups of n equivariant clifford supermodules on xn we show that is a hopf algebra and it is isomorphic to the fock space of a twisted heisenberg algebra twisted vertex operators make a natural appearance the algebraic structures on x when is trivial and x is a point specialize to those on a ring of symmetric functions with the schur q functions as a linear basis as a by product we present a novel construction of k theory operations using the spin representations of the hyperoctahedral groups

baker campbell hausdorff relations for the super poincare group baker campbell hausdorff relations are obtained for the connected supergroup associated with the super poincare algebra iosp 1 4

identifiability of the landau ginzburg potential in a mathematical model of shape memory alloys abstract the nonlinear partial differential equations considered here arise from the conservation laws of linear momentum and energy and describe structural phase transitions in one dimensional shape memory solids with non convex landau ginzburg free energy potentials in this article the theories of analytic semigroups and real interpolation spaces for maximal accretive operators are used to show that the solutions of the model depend continuously on the admissible parameters also we show that the non physical parameters that define the free energy are identifiable from the model

supersymmetry and supercoherent states of a nonrelativistic free particle coordinate atypical representation of the orthosymplectic superalgebra osp 2 2 in a hilbert superspace of square integrable functions constructed in a special way is given the quantum nonrelativistic free particle hamiltonian is an element of this superalgebra which turns out to be a dynamical superalgebra for this system the supercoherent states defined by means of a supergroup displacement operator are explicitly constructed these are the coordinate representation of the known atypical abstract super group osp 2 2 coherent states we interpret obtained results from the classical mechanics viewpoint as a model of classical particle which is immovable in the even sector of the phase superspace and is in rectilinear movement in the appropriate coordinate system in its odd sector

hecke clifford algebras and spin hecke algebras iii the trigonometric type abstract the notions of trigonometric spin double affine hecke algebras tsdaha and trigonometric double affine hecke clifford algebras tdahca associated to classical weyl groups are introduced the pbw basis property is established an algebra isomorphism relating tdahca to tsdaha is obtained