navier stokes equations for stochastic particle systems on the lattice we introduce a class of stochastic models of particles on the cubic lattice d with velocities and study the hydrodynamical limit on the diffusive spacetime scale assuming special initial conditions corresponding to the incompressible regime we prove that in dimensiond 3 there is a law of large numbers for the empirical density and the rescaled empirical velocity field moreover the limit fields satisfy the corresponding incompressible navier stokes equations with viscosity matrices characterized by a variational formula formally equivalent to the green kubo formula

variational approach and exact solutions for a generalized coupled zakharov kuznetsov system abstract in the present paper we obtain a variational principle for a generalized coupled zakharov kuznetsov system which does not admit any lagrangian formulation in its present form the eminent noether s theorem will then be employed to compensate for this approach in addition exact solutions will be constructed for the generalized coupled zakharov kuznetsov system using the kudryashov method and the jacobi elliptic function method

stationary states and hydrodynamics of fhp cellular automata the large scale behavior of fhp type cellular automata is investigated in the presence of some additional random effects it is shown that every translationinvariant stationary state of the modified model is a superposition of product measures by means of the entropy argument of yau and of olla varadhan and yau the macroscopic euler type equations governing the hydrodynamic behavior of fhp automata are also derived

exact solutions of the generalized lane emden equation a generalized lane emden equation with indices n is discussed which reduces to the lane emden equation proper for 2 1 1 general properties of the set of solutions of this equation are derived and exact solutions are given these include a singular solution without free integration constant for arbitrary n and for particular relations between n and among the two parameter solutions nonequivalent families of solutions of the same equation are obtained

divergence symmetries of semilinear polyharmonic equations involving critical nonlinearities abstract it is shown that a lie point symmetry of the semilinear polyharmonic equations involving nonlinearities of power or exponential type is a variational divergence symmetry if and only if the equation parameters assume critical values the corresponding conservation laws for critical polyharmonic semilinear equations are established

lie point symmetries of the lane emden systems abstract it is shown that a lie point symmetry of the lane emden system is a noether symmetry if and only if its parameters belong to the critical hyperbola

elliptic equations with nearly critical growth n f 2 n 2 it has no solution for any star shaped domain 13 recently considerable interest has grown around problems like i in which the right hand side up is replaced by a perturbation f u of the pure power such as f u au up where 1 e iw and 0

instability of invariant boundary conditions of a generalized lane emden equation of the second kind abstract a generator of lie point symmetries admitted by a lane emden equation of the second kind for arbitrary shape factor k is used to determine invariant boundary conditions admitted by the equation the generator of lie point symmetries is then used to reduce the order of the lane emden equation a phase plane analysis of the reduced equation indicates that the stability of the invariant boundary condition y 0 on the line x 0 changes with changing shape factor k we show that for values of the shape factor k 1 the boundary condition y 0 is stable on the line x 0 while it is unstable for k 1

equilibrium fluctuations for a system of harmonic oscillators with conservative noise we investigate the harmonic chain forced by a multiplicative noise the evolution is given by an infinite system of stochastic differential equations total energy and deformation are preserved the conservation of momentum is destroyed by the noise gaussian product measures are the extremal stationary states of this model equilibrium fluctuations of the conserved fields at a diffusive scaling are described by a couple of generalized ornstein uhlenbeck processes

hydrodynamical limit for spatially heterogeneous simple exclusion processes we prove hydrodynamical limit for spatially heterogeneous asymmetric simple exclusion processes on z d the jump rate of particles depends on the macroscopic position x through some nonnegative smooth velocity profile x hydrodynamics are described by the entropy solution to a spatially heterogeneous conservation law of the form

a class of pseudonoise sequences over gf p with low correlation zone a new class of pseudonoise sequences over gf p based on gordon mills welch 1962 sequences is constructed the sequences have the property that in a specified zone the out of phase autocorrelation and cross correlation values are all equal to 1 such sequences with low correlation zone lcz are suitable for approximately synchronized code division multiple access cdma system

stochastic mode reduction for the immersed boundary method we apply the formulation of a stochastic mode reduction method developed in a recent paper of majda timofeyev and vanden eijnden comm pure appl math 54 2001 pp 891 974 mtv to obtain simplified equations for the dynamics of structures immersed in a thermally fluctuating fluid at low reynolds or kubo number as simulated by a recent extension of the immersed boundary ib method by kramer and peskin proceedings of the second mit conference on computational fluid and solid mechanics elsevier science oxford uk 2003 pp 1755 1758 the effective dynamics of the immersed structures are not obvious in the primitive equations which involve both fluid and structure dynamics but the procedure of mtv allows the rigorous derivation of a reduced stochastic system for the immersed structures alone we find in the limit of small reynolds or kubo number that the lagrangian particle constituents of the immersed structures undergo a drift diffusive motion with several physically correct featur

lie point symmetries and exact solutions of quasilinear differential equations with critical exponents abstract we consider a general class of quasilinear ordinary differential equations which contains in particular the lane emden equation the liouville equation the poisson boltzmann equation equations involving the radial forms of the laplace p laplace and the k hessian operators the lie point symmetry group of these equations is calculated then the corresponding noether symmetries are found and used to obtain first integrals and exact solutions of the equations with critical exponents

on nontrivial solutions of critical polyharmonic elliptic systems abstract in the present work we consider elliptic systems involving polyharmonic operators and critical exponents we discuss the existence and nonexistence of nontrivial solutions to these systems our theorems improve and or extend the ones established by bartsch and guo t bartsch y guo existence and nonexistence results for critical growth polyharmonic elliptic systems j differential equations 220 2006 531 543 in both aspects of spectral interaction and regularity of lower order perturbations

hydrodynamical limit for a hamiltonian system with weak noise starting from a general hamiltonian system with superstable pairwise potential we construct a stochastic dynamics by adding a noise term which exchanges the momenta of nearby particles we prolve that in the scaling limit the time conserved quantities energy momenta and density satisfy the euler equation of conservation laws up to a fixed timet provided that the euler equation has a smooth solution with a given initial data up to timet the strength of the noise term is chosen to be very small but nonvanishing so that it disappears in the scaling limit

a new family of p ary sequences of period p n 1 2 with low correlation for an odd prime p congruent to 3 modulo 4 and an odd integer n a new family of p ary sequences of period n pn 1 2 with low correlation is proposed the family is constructed by shifts and additions of two decimated m sequences with the decimation factors 2 and 2d d n pn 1 the upper bound for the maximum magnitude of nontrivial correlations of this family is derived using well known kloosterman sums the upper bound is shown to be 2 n 1 2 2pn which is twice the welch s lower bound and approximately 1 5 times the sidelnikov s lower bound the size of the family is 2 pn 1 which is four times the period of sequences

derivation of the leroux system as the hydrodynamic limit of a two component lattice gas the long time behavior of a couple of interacting asymmetric exclusion pro cesses of opposite velocities is investigated in one space dimension we do not allow two particles at the same site and a collision effect exchange takes place when particles of opposite velocities meet at neighboring sites there are two conserved quantities and the model admits hyperbolic euler scaling the hydrodynamic limit results in the classical leroux system of conservation laws even beyond the appearance of shocks actually we prove convergence to the set of entropy solutions the question of unique ness is left open to control rapid oscillations of lax entropies via logarithmic sobolev inequality estimates the symmetric part of the process is speeded up in a suitable way thus a slowly vanishing viscosity is obtained at the macroscopic level following 4 5 the stochastic version of tartar murat theory of compensated compactness is extended to two component stochastic models

positivity for equations involving polyharmonic operators with dirichlet boundary conditions cranston fabes and zhao 26 5 established the uniform bound sup x y 2 x 6 y r g1 n x z g1 n z y dz g1 n x y m 1 1 where g1 n x y is the green function for the laplacian with dirichlet boundary conditions on a lipschitz domain rn with n 3 see 27 for n 2 this estimate was used in 23 and 18 to obtain positivity uniformly with respect to f 0 for noncooperative elliptic systems as

on entropy minimization and convergence we examine the minimization of information entropy for measures on the phase space of bounded domains subject to constraints that are averages of grand canonical distributions we describe the set of all such constraints and show that it equals the set of averages of all probability measures absolutely continuous with respect to the standard measure on the phase space with the exception of the measure concentrated on the empty configuration we also investigate how the set of constrains relates to the domain of the microcanonical thermodynamic limit entropy we then show that for fixed constraints the parameters of the corresponding grand canonical distribution converge as volume increases to the corresponding parameters derivatives when they exist of the thermodynamic limit entropy the results hold when the energy is the sum of any stable tempered interaction potential that satisfies the gibbs variational principle e g lennard jones and the kinetic energy the same tools and the strict convexity of the thermodynamic limit pressure for continuous systems valid whenever the gibbs variational principle holds give solid foundation to the folklore local homeomorphism between thermodynamic and macroscopic quantities

toward the fourier law for a weakly interacting anharmonic crystal for a system of weakly interacting anharmonic oscillators perturbed by an energy preserving stochastic dynamics we prove an autonomous stochastic evolution for the energies at large time scale with respect to the coupling parameter it turn out that this macroscopic evolution is given by the so called conservative non gradient ginzburg landau system of stochastic differential equations the proof exploits hypocoercivity and hypoellipticity properties of the uncoupled dynamics

ergodicity in infinite hamiltonian systems with conservative noise we study the stationary measures of an infinite hamiltonian system of interacting particles in 3 subject to a stochastic local perturbation conserving energy and momentum we prove that the translation invariant measures that are stationary for the deterministic hamiltonian dynamics reversible for the stochastic dynamics and with finite entropy density are convex combination of gibbs states this result implies hydrodynamic behavior for the systems under consideration

sharp sobolev inequalities on the sphere and the moser trudinger inequality where de denotes normalized surface measure v is the conformal gradient and q 2n n 2 a modern folklore theorem is that by taking the infinitedimensional limit of this inequality one obtains the gross logarithmic sobolev inequality for gaussian measure which determines nelson s hypercontractive estimates for the hermite semigroup see 8 one observes using conformal invariance that the above inequality is equivalent to the sharp sobolev inequality on rn for which boundedness and extremal functions can be easily calculated using dilation invariance and geometric symmetrization the roots here go back to hardy and littlewood the advantage of casting the problem on the sphere is that the role of the constants is evident and one is led immediately to the conjecture that this inequality should hold whenever possible for example 2 q 0o if n 2 this is in fact true and will be demonstrated in section 2 a clear question at this point is what is the situation in dimension 2 two important arguments 25 26 27 dealt with this issue both motivated by geometric variational problems because q goes to infinity for dimension 2 the appropriate function space is the exponential class responding in part

the brownian motion as the limit of a deterministic system of hard spheres we provide a rigorous derivation of the brownian motion as the limit of a deterministic system of hard spheres as the number of particles n goes to infinity and their diameter varepsilon simultaneously goes to 0 in the fast relaxation limit alpha n varepsilon d 1 rightarrow infty with a suitable diffusive scaling of the observation time as suggested by hilbert in his sixth problem we rely on a kinetic formulation as an intermediate level of description between the microscopic and the fluid descriptions we use indeed the linear boltzmann equation to describe one tagged particle in a gas close to global equilibrium our proof is based on the fundamental ideas of lanford the main novelty here is the detailed study of the branching process leading to explicit estimates on pathological collision trees

one dimensional hard rod caricature of hydrodynamics navier stokes correction for local equilibrium initial states a one dimensional system consisting of identical hard rod particles of length a is studied in the hydrodynamical limit a navier stokes correction to the euler equation is found for an initial local equilibrium family of states of constant density the correction is given at by a non linear second order differential operator acting on f q v the hydrodynamical density at a point of the species of fluid with velocity

new families of m ary sequences with low correlation constructed from sidel nikov sequences in this correspondence for a positive integer m and a prime p such that m pn 1 three families of m ary sequences using the m ary sidel nikov sequences with period pn 1 are constructed two small families contain pn 1 2 m 2 or pn m 3 m ary sequences and both of their maximum magnitudes of correlation values are upper bounded by 2 radic pn 6 the largest family has its maximum magnitude of correlation values upper bounded by 3 radic pn 5 and the family size is m 1 2 2n 1 1 m 1 for p 2 or m 1 2 pn 3 2 m m 1 2 for an odd prime p

infinitely many nonradial solutions of a euclidean scalar field equation abstract we study the equation u b x u x u x r n u h 1 r n the existence of a nonradial solution has been an open problem for some time even in the autonomous case under suitable hypotheses mainly on we find an unbounded sequence of nonradial solutions if n 4 or n 6 we also obtain infinitely many solutions if b and are not rotationally symmetric with respect to x but satisfy only a weaker symmetry

first integrals and bifurcations of a lane emden equation of the second kind first integrals admitted by an approximate lane emden equation modelling a thermal explosion in a rectangular slab and cylindrical vessel are investigated by imposing the boundary conditions on the first integrals we obtain a nonlinear relationship between the temperature at the center of the vessel and the temperature gradient at the wall of the vessel for a rectangular slab the presence of a bifurcation indicates multivalued solutions for the temperature at the center of the vessel when the temperature gradient at the wall is fixed for a cylindrical vessel we find a bifurcation indicating multivalued solutions for the temperature gradient at the walls of the vessel when the temperature at the center of the vessel is fixed

solutions of singular ivps of lane emden type by the variational iteration method abstract in this paper approximate exact solutions of a class of lane emden type singular ivps problems by the variational iteration method are presented the variational iteration method yields solutions in the forms of convergent series with easily calculable terms the scheme is shown to be highly accurate and in some cases yields exact solutions in few iterations

hydrodynamic limit for particle systems with nonconstant speed parameter we establish the hydrodynamic limit for a class of particle systems on d with nonconstant speed parameter assuming that the speed parameter is continuously differentiable in the spatial variable if the particle system is on the one dimensional lattice and totally asymmetric we derive the hydrodynamic equation for continuous speed parameters we obtain nontrivial upper and lower bounds when either the speed parameter is discontinuous or there is a blockage at a fixed site

symmetry analysis of the bidimensional lane emden systems abstract we carry out a complete group classification of the nonlinear lane emden systems in dimension two the noether symmetries are found and their corresponding conservation laws are established

scaling limit for interacting ornstein uhlenbeck processes the problem of describing the bulk behavior of an interacting system consisting of a large number of particles comes up in different contexts see for example 1 for a recent exposition in 4 one of the authors considered the case of interacting diffusions on a circle and proved that the density of particles evolves according to a nonlinear diffusion equation the interacting particles evolved according to a generator that was symmetric in equilibrium in this article we consider interacting ornstein uhlenbeck processes here the diffusion generator is not symmetric relative to the equilibrium and the earlier methods have to be modified considerably we use some ideas that were employed in 3 to extend the central limit theorem from the symmetric to nonsymmetric cases

a construction of a new family of m ary sequences with low correlation from sidel nikov sequences in this paper a new family of m ary sequences of period pn 1 is proposed the proposed family is constructed by the addition of cyclic shifts of an m ary sidel nikov sequence and its reverse sequence the number of sequences contained in this family is about m 1 2 times of their period and the maximum magnitude of their correlation values is upper bounded by 4 pn 5

motion by mean curvature from the ginzburg landau interface model we consider the scalar field t with a reversible stochastic dynamics which is defined by the standard dirichlet form relative to the gibbs measure with formal energy the potential v is even and strictly convex we prove that under a suitable large scale limit the t field becomes deterministic such that locally its normal velocity is proportional to its mean curvature except for some anisotropy effects as an essential input we prove that for every tilt there is a unique shift invariant ergodic gibbs measure for the field

large deviations and the maximum entropy principle for marked point random fields we establish large deviation principles for the stationary and the individual empirical fields of poisson and certain interacting random fields of marked point particles in d the underlying topologies are induced by a class of not necessarily bounded local functions and thus finer than the usual weak topologies our methods yield further that the limiting behaviour of conditional poisson distributions as well as certain distributions of gibbsian type is governed by the maximum entropy principle we also discuss various applications and examples

large deviations for gibbs random fields a large deviation principle for gibbs random fields on zd is proven and a corresponding large deviations proof of the gibbs variational formula is given a generalization of the lanford theory of large deviations is also obtained

derivation of the euler equations from quantum dynamics we derive the euler equations from quantum dynamics for a class of fermionic many body systems we make two types of assumptions the first type are physical assumptions on the solution of the euler equations for the given initial data the second type are a number of reasonable conjectures on the statistical mechanics and dynamics of the fermion hamiltonian

large deviations and the equivalence of ensembles for gibbsian particle systems with superstable interaction for gibbsian systems of particles inr d we investigate large deviations of the translation invariant empirical fields in increasing boxes the particle interaction is given by a superstable regular pair potential the large deviation principle is established for systems with free or periodic boundary conditions and under a stronger stability hypothesis on the potential for systems with tempered boundary conditions and for tempered infinite volume gibbs measures as a by product we obtain the gibbs variational formula for the pressure we also prove the asymptotic equivalence of microcanonical and grand canonical gibbs distributions and establish a variational expression for the thermodynamic entropy density

uniqueness results for semilinear polyharmonic boundary value problems on conformally contractible domains i abstract we study polyharmonic boundary value problems mu f u m n with dirichlet boundary conditions on bounded and unbounded conformally contractible domains in r n such domains can be contracted to a point bounded case or to infinity unbounded case by one parameter groups of conformal maps the class of star shaped domain is a subclass the problem has variational structure this allows us to derive a sufficient condition for uniqueness by studying the interaction of one parameter transformation groups with the underlying functional l if the transformation group strictly reduces the values of l then uniqueness of the critical point of l follows the proof is inspired by e noether s theorem on symmetries and conservation laws applications of the uniqueness principle are given in part ii of this paper

attractor properties for irreversible and reversible interacting particle systems we consider translation invariant interacting particle systems on the lattice with finite local state space admitting at least one gibbs measure as a time stationary measure the dynamics can be irreversible but should satisfy some mild non degeneracy conditions we prove that weak limit points of any trajectory of translation invariant measures satisfying a non nullness condition are gibbs states for the same specification as the time stationary measure this is done under the additional assumption that zero entropy loss of the limiting measure w r t the time stationary measure implies that they are gibbs measures for the same specification we show how to prove the non nullness for a large number of cases and also give an alternate version of the last condition such that the non nullness requirement can be dropped as an application we obtain the attractor property if there is a reversible gibbs measure our method generalizes convergence results using relative entropy techniques to a large class of dynamics including irreversible and non ergodic ones

group classification of semilinear kohn laplace equations abstract we study the lie point symmetries of semilinear kohn laplace equations on the heisenberg group h 1 and obtain a complete group classification of these equations

a new family of p ary sequences with low correlation constructed from decimated sequences in this paper for an odd prime p and an integer n geq 3 a new family of p ary sequences of period p n 1 over 2 with low correlation is constructed the new family is constructed by shifts and additions of two decimated sequences of a p ary m sequence and its family size is 2 p n 1 the complete correlation distribution of this new family is derived it is also shown that the family is optimal with respect to the parameter theta rm rms which denotes the root mean square of all nontrivial correlations compared with the known sequence families our sequence family is new and has a larger family size which is four times of its period

hydrodynamic limit for a system with finite range interactions we study a system of interacting diffusions the variables present the amount of charge at various sites of a periodic multidimensional lattice the equilibrium states of the diffusion are canonical gibbs measures of a given finite range interaction under an appropriate scaling of lattice spacing and time we derive the hydrodynamic limit for the evolution of the macroscopic charge density

an invitation to modern group analysis of differential equations abstract the purpose of this review paper is two fold first we point out one more time the importance and usefulness of the s lie theory of symmetries of differential equations in particular some illustrative examples are presented then we discuss the noetherian approach to rellich pohozaev type identities

nonbinary kasami sequences over gf p the correlation values and the distribution of these correlation values for the small set of nonbinary kasami sequences over gf p p prime are presented the correlation results are an extension of the binary results and have p 2 correlation levels this nonbinary kasami set is asymptotically optimum with respect to its correlation properties these sequences are obtained as in the binary case from a large primitive polynomial of degree n 2 m and a small primitive polynomial of degree m that yields a sequence length of p sup n 1 and maximum nontrivial correlation value of 1 p sup m nonbinary kasami sequences are directly implemented using shift registers and are applicable for code division multiple access systems

the liouville bratu gelfand problem for radial operators abstract we determine precise existence and multiplicity results for radial solutions of the liouville bratu gelfand problem associated with a class of quasilinear radial operators which includes perturbations of k hessian and p laplace operators

existence and multiplicity of nodal solutions for nonlinear elliptic equations with critical sobolev growth abstract let be a smooth bounded domain of r n n 3 and let a x and f x be two smooth functions defined on a neighbourhood of first we study the existence of nodal solutions for the equation u a x u f x u 4 n 2 u on u 0 on in particular when is a solid torus of r 3 we describe three infinity of pairs of solutions of the equation u u 4 n 2 u on u 0 on afterwards we study the equation when the zero dirichlet condition on the boundary is replaced by a non zero dirichlet condition

a class of binomial bent functions over the finite fields of odd characteristic this paper studies a class of binomial functions over the finite fields of odd characteristic and characterizes their bentness in terms of the kloosterman sums numerical results show that the proposed class contains bent functions that are affinely inequivalent to all known monomial and binomial ones

onsager relations and eulerian hydrodynamic limit for systems with several conservation laws we present the derivation of the hydrodynamic limit under eulerian scaling for a general class of one dimensional interacting particle systems with two or more conservation laws following yau s relative entropy method it turns out that in case of more than one conservation laws in order that the system exhibit hydrodynamic behaviour some particular identities reminiscent of onsager s reciprocity relations must hold we check validity of these identities whenever a stationary measure with product structure exists it also follows that as a general rule the equilibrium thermodynamic entropy as function of the densities of the conserved variables is a globally convex lax entropy of the hyperbolic systems of conservation laws arising as hydrodynamic limit as concrete examples we also present a number of models modeling deposition or domain growth phenomena the onsager relations arising in the context of hydrodynamic limits under hyperbolic scaling seem to be novel the fact that equilibrium thermodynamic entropy is lax entropy for the arising euler equations was noticed earlier in the context of hamiltonian systems with weak noise see ref 7

nonlinear diffusion limit for a system with nearest neighbor interactions we consider a system of interacting diffusions the variables are to be thought of as charges at sites indexed by a periodic one dimensional lattice the diffusion preserves the total charge and the interaction is of nearest neighbor type with the appropriate scaling of lattice spacing and time a nonlinear diffusion equation is derived for the time evolution of the macroscopic charge density

prime phase sequences with periodic correlation properties better than binary sequences for the case where p is an odd prime n or 2 is an integer and omega is a complex primitive pth root of unity a construction is presented for a family of p sup n p phase sequences symbols of the form omega sup i where each sequence has length p sup n 1 and where the maximum nontrivial correlation value c sub max does not exceed 1 square root p sup n a complete distribution of correlation values is provided as a special case of this construction a previous construction due to sidelnikov 1971 is obtained the family of sequences is asymptotically optimum with respect to its correlation properties and in comparison with many previous nonbinary designs the present design has the additional advantage of not requiring an alphabet of size larger than three the new sequences are suitable for achieving code division multiple access and are easily implemented using shift registers they wee discovered through an application of deligne s bound 1974 on exponential sums of the weil type in several variables the sequences are also shown to have strong identification with certain bent functions

special conformal groups of a riemannian manifold and lie point symmetries of the nonlinear poisson equation abstract we obtain a complete group classification of the lie point symmetries of nonlinear poisson equations on generic pseudo riemannian manifolds m using this result we study their noether symmetries and establish the respective conservation laws it is shown that the projection of the lie point symmetries on m are special subgroups of the conformal group of m in particular if the scalar curvature of m vanishes the projection on m of the lie point symmetry group of the poisson equation with critical nonlinearity is the conformal group of the manifold we illustrate our results by applying them to the thurston geometries

on kac s chaos and related problems this paper is devoted to establish quantitative and qualitative estimates related to the notion of chaos as firstly formulated by m kac cite kac1956 in his study of mean field limit for systems of n undistinguishable particles as n to infty first we quantitatively liken three usual measures of it kac s chaos some involving the all n variables other involving a finite fixed number of variables the cornerstone of the proof is a new representation of the monge kantorovich wasserstein mkw distance for symmetric n particle probability measures in terms of the distance between the law of the associated empirical measures on the one hand and a new estimate on some mkw distance on probability measures spaces endowed with a suitable hilbert norm taking advantage of the associated good algebraic structure next we define the notion of it entropy chaos and it fisher information chaos in a similar way as defined by carlen et al cite ccllv we show that it fisher information chaos is stronger than it entropy chaos which in turn is stronger than it kac s chaos more importantly with the help of the hwi inequality of otto villani we establish a quantitative estimate between these quantities which in particular asserts that it kac s chaos plus it fisher information bound implies it entropy chaos we then extend the above quantitative and qualitative results about chaos in the framework of probability measures with support on the it kac s spheres revisiting cite ccllv and giving a possible answer to cite open problem 11 ccllv additionally to the above mentioned tool we use and prove an optimal rate local clt in l infty norm for distributions with finite 6 th moment and finite l p norm for some p 1 last we investigate how our techniques can be used without assuming chaos in the context of probability measures mixtures introduced by de finetti hewitt and savage in particular we define the level 3 fisher information for mixtures and prove that it is l s c and affine as that was done in cite rr for the level 3 boltzmann s entropy

lie and noether symmetries for a class of fourth order emden fowler equations a group classification of a fourth order ordinary differential equation is carried out the noether symmetries are considered and some first integrals are established solutions for special lane emden systems are also obtained from the invariant solutions of the investigated equation

group representations arising from lorentz conformal geometry abstract it is shown that there exist conformally covariant differential operators d 2 l k of all even orders 2 l on differential forms of all orders k in the double cover n of the n dimensional compactified minkowski space n these act as intertwining differential operators for natural representations of o 2 n the conformal group of n for even n the resulting decompositions of differential form representations of o 2 n the orthochronous conformal group produce infinite families of unitary representations the most interesting of which are carried by positive mass squared positive frequency quotients for 2l n 2k physically these generalize unitary representations of the conformal group associated with the modified wave operator d 2 0 n 2 2 2 and the maxwell operator on vector potentials d 2 n 2 2 d all the representation spaces produced unitary and nonunitary may be viewed as infinite systems of harmonic oscillators as a by product of the spectral resolution of the d 2 l k one gets some striking wave propagative properties for all of the equations d 2 l k 0 including huygens principle in the curved spacetime n the operators d 2 l k have not been seen before except in the special cases k 0 or n and k n 2 2 l 1 the maxwell operator thus much new information is obtained even in the physical case n 4

group analysis of a hyperbolic lane emden system in this paper we carry out a complete noether and lie group classification of the radial form of a coupled system of hyperbolic equations from the noether symmetries we establish the corresponding conserved vectors we also determine constraints that the nonlinearities should satisfy in order for the scaling symmetries to be noetherian this led us to a critical hyperbola for the systems under consideration an explicit solution is also obtained for a particular choice of the parameters

scaling limits for interacting diffusions we consider a large number of particles diffusing on a circle interacting through a drift resulting from the gradient of a pair potential whose support is of the order of the interparticle distance we derive a nonlinear bulk diffusion equation for the density of the particle distribution on the circle the diffusion coefficient is determined as a function of density in terms of standard thermodynamical objects

multiple solutions of a critical polyharmonic equation we prove that for n 2m the equation mu u 4m n 2mu on rn has a sequence of nodal finite energy solutions which is unbounded in dm 2 rn this generalizes a classical result of weiyue ding for m 1

infinitely many solutions for some nonlinear elliptic problems in symmetrical domains on considere le probleme aux valeurs limites u u u u 2 2 0 u h 0 1 ou r n est un domaine borne n 3 2 2n n 2 est l exposant critique pour le plongement de sobolev et est un parametre positif reel on demontre l existence d une infinite de solutions quand a de bonnes symetries

a new class of balanced near perfect nonlinear mappings and its application to sequence design a mapping from zn to zm can be directly applied for the design of a sequence of period n with alphabet size m where zn denotes the ring of integers modulo n the nonlinearity of such a mapping is closely related to the autocorrelation of the corresponding sequence when m is a divisor of n the sequence corresponding to a perfect nonlinear mapping has perfect autocorrelation but it is not balanced in this paper we study balanced near perfect nonlinear npn mappings applicable for the design of sequence sets with low correlation we first construct a new class of balanced npn mappings from z p2 p to zp for an odd prime p we then present a general method to construct a frequency hopping sequence fhs set from a nonlinear mapping by applying it to the new class we obtain a new optimal fhs set of period p2 p with respect to the peng fan bound whose fhss are balanced and optimal with respect to the lempel greenberger bound moreover we construct a low correlation sequence set with size p period p2 p and maximum correlation magnitude p from the new class of balanced npn mappings which is asymptotically optimal with respect to the welch bound

near optimal partial hadamard codebook construction using binary sequences obtained from quadratic residue mapping in this paper a new class of n k near optimal partial hadamard codebooks is proposed the construction of the proposed codebooks from hadamard matrices is based on binary row selection sequences which are generated by quadratic residue mapping of p ary m sequences the proposed codebooks have parameters n p n and k p 1 2p n sqrt n 1 for an odd prime p and an even positive integer n we prove that the maximum magnitude of inner products between the code vectors of the proposed codebooks asymptotically achieves the welch bound equality for sufficiently large p and derive their inner product distribution

on the derivation of the incompressible mavier stokes equation for hamiltonian particle systems we consider a hamiltonian paticle system interacting by means of a pair potetial we look at the behavior of the system on a space scale of order e 1 times of order e 2 and mean velocities of order e with e a scale parameter assuming that the phase space density of the particles is give by a series in e the analog of the chapman enskog expansion the behavior of the system under this rescaling is described to the lowest order in e by the incompressible navier stokes equations the viscosity is given in terms of microscopic correlations and its expression agrees with the green kubo formula

solitary wave solutions to some classes of nonlinear evolution type equations using inverse variational methods abstract invariants of reduced forms of a p d e are obtainable from a variational principle even though the p d e itself does not admit a lagrangian the reductions carry all the advantages regarding noether symmetries and double reductions via first integrals or conserved quantities the examples we consider are nonlinear evolution type equations like the general form of the fizhugh nagumo and kdv burgers equations some aspects of painleve properties of the reduced equations are also obtained

lattice gases large deviations and the incompressible navier stokes equations we study the incompressible limit for a class of stochastic particle systems on the cubic lattice zd d 3 for initial distributions corresponding to arbitrary macroscopic l2 initial data the distributions of the evolving empirical momentum densities are shown to have a weak limit supported entirely on global weak solutions of the incompressible navier stokes equations furthermore explicit exponential rates for the convergence large deviations are obtained the probability to violate the divergence free condition decays at rate at least exp e d l while the probability to violate the momentum conservation equation decays at rate exp fe d 2 with an explicit rate function given by an hi1 norm

cross correlation of p ary gmw sequences the cross correlation function of p ary p prime gmw sequences is investigated the well known m sequences are incorporated in these sequences gmw sequences also have the two level autocorrelation function but their linear span may be much larger than those of m sequences the calculation of the cross correlation function of gmw sequences is reduced to the cross correlation of the m sequences because many results on this kind of sequence are known in the literature only the cross correlation function of an m sequence with a gmw sequence has been known up to now

radial solutions of a polyharmonic equation with power nonlinearity abstract we classify the regular radial solutions of the equation m u u u p 1 with m a positive integer and p 1 any such solution u is uniquely determined by the center values of u and its iterated laplacians up to order m 1 that is by the center point u 0 u 0 m 1 u 0 most solutions have finite exit radius that is they are unbounded and defined on open balls of finite radius are eventually monotonic with respect to the radial variable and diverge to or the center points of these solutions form two open half spaces in r m separated by an m 1 dimensional manifold m solutions with center points on m are either global or they have finite exit radius and oscillate about 0 with unbounded amplitude our results yield precise information regarding the existence multiplicity and nature of large radial solutions of m u u u p 1 on a ball of given radius

microscopic theory of isothermal elastodynamics this paper examines random perturbations of the anharmonic chain of coupled oscillators the microscopic system has two conservation laws and its hyperbolic scaling limit results in the quasi linear wave equation p system of isothermal isentropic elasticity in the shock regime the compensated compactness method is used lastly results from j w shearer and d serre are applied

entropy large deviations and scaling limits we often model the evolution of a complex system at the lowest or micro level because that is what makes the most physical sense but if the system is large we invariably want answers to questions posed on the larger macro or global scale this then involves the study of equations with a large number of variables and extracting useful information from their solutions the macroscopic quantities of interest may not contain complete information about the microscopic variables that drive their evolution something has to be done to obtain a closed system of equations for quantities of interest different contexts require different approaches we are concerned here with the evolution of large systems of interacting particles or field variables that have some built in noise and outline some of the work done at the institute during the last 25 years 2013 wiley periodicals inc

monomial and quadratic bent functions over the finite fields of odd characteristic considered are p ary bent functions having the form f x tr sub n spl sigma sub i 0 sup s a sub i x sup di a new class of ternary monomial regular bent function with the dillon exponent is discovered the existence of dillon bent functions in the general case is an open problem of deciding whether a certain kloosterman sum can take on the value 1 also described is the general gold like form of a bent function that covers all the previously known monomial quadratic cases the weak regularity of the new as well as of known monomial bent functions is discussed and the first example of a not weakly regular bent function is given finally some criteria for an arbitrary quadratic function to be bent are proven

existence and nonexistence results for critical growth polyharmonic elliptic systems abstract in this work we consider semilinear elliptic systems for the polyharmonic operator having a critical growth nonlinearity we establish conditions for existence and nonexistence of nontrivial solutions to these systems

stationary states of random hamiltonian systems we investigate the ergodic properties of hamiltonian systems subjected to local random energy conserving perturbations we prove for some cases e g anharmonic crystals with random nearest neighbor exchanges or independent random reflections of velocities that all translation invariant stationary states with finite entropy per unit volume are microcanonical gibbs states the results can be utilized in proving hydrodynamic behavior of such systems

nodal solutions for the fractional yamabe problem on heisenberg groups we prove that the fractional yamabe equation rm cal l gamma u vert u vert 4 gamma q 2 gamma u on the heisenberg group n has n 1 2 sequences of nodal sign changing weak solutions whose elements have mutually different nodal properties where rm cal l gamma denotes the cr fractional sub laplacian operator on n q 2n 2 is the homogeneous dimension of n and gamma in bigcup nolimits k 1 n k kq q 1 our argument is variational based on a ding type conformal pulling back transformation of the original problem into a problem on the cr sphere s2n 1 combined with a suitable hebey vaugon type compactness result and group theoretical constructions for special subgroups of the unitary group u n 1

reversibility in infinite hamiltonian systems with conservative noise the set of stationary measures of an infinite hamiltonian system with noise is investigated the model consists of particles moving in r 3 with bounded velocities and subject to a noise that does not violate the classical laws of conservation see ovy following lo we assume that the noise has also a finite radius of interaction and prove that translation invariant stationary states of finite specific entropy are reversible with respect to the stochastic component of the evolution therefore the results of lo imply that such invariant measures are superpositions of gibbs states

stationary nonequilibrium states in boundary driven hamiltonian systems shear flow we investigate stationary nonequilibrium states of systems of particles moving according to hamiltonian dynamics with specified potentials the systems are driven away from equilibrium by maxwell demon reflection rules at the walls these deterministic rules conserve energy but not phase space volume and the resulting global dynamics may or may not be time reversible or even invertible using rules designed to simulate moving walls we can obtain a stationary shear flow assuming that for macroscopic systems this flow satisfies the navier stokes equations we compare the hydrodynamic entropy production with the average rate of phase space volume compression we find that they are equalwhen the velocity distribution of particles incident on the walls is a local maxwellian an argument for a general equality of this kind based on the assumption of local thermodynamic equilibrium is given molecular dynamic simulations of hard disks in a channel produce a steady shear flow with the predicted behavior

one dimensional hard rod caricature of hydrodynamics we give here a rigorous deduction of the hydrodynamic equation which holds in the hydrodynamic limit for a model system of one dimensional identical hard rods interacting through elastic collisions the equation should be considered as the analog of the euler equation of real hydrodynamics owing to the degeneracy of the model it is written in terms of a functiong q v t expressing the density of particles with velocityv at the pointq at timet for this equation we prove an existence and uniqueness theorem in some natural class of functions our main result is the proof that if 0 is a class of initial states which are homogeneous on a scale much less than e 1 and if the corresponding particle densities tend ase 0 in the proper scale to the initial hydrodynamic densitygo q v then under some general assumptions on the states and ong0 the particle densities of the evolved states at timee 1t tend ase 0 to the unique solution of the hydrodynamic equation with initial conditiong0 the proof is completed by exhibiting a large class of initial families 0 which possess the required properties

first integrals for the modified emden equation q α t q qn 0 it is shown that the modified emden equation q t q qn 0 possesses first integrals for functions t other than kt 1 the function t is obtained explicitly in the case n 3 and parametrically for other n 2 the case n 2 is seen to be particularly difficult to solve