distribution of periodic torus orbits and duke s theorem for cubic fields we study periodic torus orbits on spaces of lattices using the action of the group of adelic points of the underlying tori we define a natural equivalence relation on these orbits and show that the equivalence classes become uniformly distributed this is a cubic analogue of duke s theorem about the distribution of closed geodesics on the modular surface suitably interpreted the ideal classes of a cubic totally real field are equidistributed in the modular 5 fold sl3 z sl3 r so3 in particular this proves a stronger form of the folklore conjecture that the collection of maximal compact flats in sl3 z sl3 r so3 of volume infinity

enhancement of stability and accuracy of the moving particle semi implicit method as a lagrangian gridless particle method the mps moving particle semi implicit method has been proven useful in a wide range of engineering applications up to now most of mps applications have been limited to problems with compressive stress states this paper investigates the performance and stability of mps method in simulation of more general hydrodynamic problems including those characterized by tensile stresses or by changes in the stress states it is shown that mps based simulations are prone to become destabilized in presence of attractive interparticle forces this instability appears to be similar to the so called tensile instability in sph method two new modifications namely a modified poisson pressure equation and a corrective matrix for pressure gradient model are proposed to resolve this shortcoming these two new modifications together with two previously proposed improvements are shown to stabilize and enhance the performance of mps method

entropy of quantum limits in this paper we show that any measure arising as a weak limit of microlocal lifts of eigenfunctions of the laplacian on certain arithmetic manifolds have dimension at least 11 9 and in particular all ergodic components of this measure with respect to the geodesic flow have positive entropy

rigidity of time changes for horocycle flows soit t t un flot preservant la mesure sur un espace de probabilite x on etudie la rigidite des changements de t pour des lots horocycles

torsion homology growth and cycle complexity of arithmetic manifolds let m be an arithmetic hyperbolic 3 manifold such as a bianchi manifold we conjecture that there is a basis for the second homology of m where each basis element is represented by a surface of low genus and give evidence for this we explain the relationship between this conjecture and the study of torsion homology growth

ellipsoidal bgk model for polyatomic molecules near maxwellians a dichotomy in the dissipation estimate abstract we consider the global existence and asymptotic behavior of classical solutions to the ellipsoidal bgk model for polyatomic molecules when the initial data starts sufficiently close to a global polyatomic maxwellian we observe that the linearized relaxation operator is decomposed into a truly polyatomic part and an essentially monatomic part leading to a dichotomy in the dissipative property in the sense that the degeneracy of the dissipation shows an abrupt jump as the relaxation parameter reaches zero accordingly we employ two different sets of micro macro system to derive the full coercivity and close the energy estimate

a method based on the tsallis entropy for characterizing threshold channel bank profiles abstract as a stable channel forms a point is reached when particles shift to motion threshold threshold channel as such the most common challenges related to alluvial channels include the variation in the transverse bank slope s t and channel geometric profile formation the present study introduces a novel reliable method of estimating the transverse slope distribution of stable channel bank profiles in different hydraulic conditions by using the tsallis entropy concept accordingly an equation for calculating s t and subsequently the vertical boundary level of bank profiles is presented based on the principle of maximum entropy the threshold channel bank profile features are defined according to the probability density function and cumulative density function to adjust the general form of the tsallis entropy for this specific engineering problem an extensive detailed study of lagrange multipliers is carried out and a wide range of observational data are used to determine the tsallis entropy model accuracy in measuring the s t of stable channel banks the results indicate that the tsallis entropy model is capable of detecting the ascending trend governing the profiles of stable channel banks in different hydraulic conditions this model exhibits excellent predictive performance with a mean absolute relative error mare of 0 265 and a coefficient of determination r 2 of 0 975 the proposed tsallis entropy based equation can be used to predict river morphology changes for river management plans

rankin selberg without unfolding and bounds for spherical fourier coefficients of maass forms in this paper we study periods of automorphic functions we present a new method which allows one to obtain non trivial spectral identities for weighted sums of certain periods of automorphic functions these identities are modelled on the classical identity of r rankin ra and a selberg se we recall that the rankinselberg identity relates the weighted sum of fourier coefficients of a cusp form to the weighted integral of the inner product of with the eisenstein series e g formula 1 7 below we show how to deduce the classical rankin selberg identity and similar new identities from the uniqueness principle in representation theory also known under the following names the multiplicity one property gelfand pair the uniqueness principle is a powerful tool in representation theory it plays an important role in the theory of automorphic functions we associate a non trivial spectral identity to certain pairs of different triples of gelfand subgroups namely we associate a spectral identity see formula 1 4 below with two triples f h1 g and f h2 g of subgroups in a group g such that pairs g hi and hi f for i 1 2 are strong gelfand pairs having the same subgroup f in the intersection for the notion of gelfand pair that we use see section 1 1 3 we call such a collection g h1 h2 f a strong gelfand formation in the introduction we explain our general idea and describe how to implement it in order to reprove the classical rankin selberg formula we also obtain a new anisotropic analog of the rankin selberg formula we present then an analytical application of these spectral identities towards non trivial bounds for various fourier coefficients of cusp forms the novelty of our results lies mainly in the method as we do not rely on the well known technique of rankin and selberg

asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy we study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions under the shizuta kawashima condition we show that these solutions approach constant equilibrium state in the lp norm at a rate o t m 2 1 1 p as t tends to infty for p in min m 2 infty moreover we can show that we can approximate with a faster order of convergence theconservative part of the solution in terms of the linearized hyperbolic operator for m 2 and by a parabolic equation in the spirit of chapman enskog expansion the main tool is given by a detailed analysis of the green function for the linearized problem

effective equidistribution of shears and applications a shear is a unipotent translate of a cuspidal geodesic ray in the quotient of the hyperbolic plane by a non uniform discrete subgroup of text psl 2 mathbb r possibly of infinite co volume we prove the regularized equidistribution of shears under large translates with effective that is power saving rates we also give applications to weighted second moments of gl 2 automorphic l functions and to counting lattice points on locally affine symmetric spaces

maximum entropy principle and classical evolution equations with source terms abstract we devise a maximum entropy technique to construct approximate time dependent solutions to evolution equations endowed with source terms and consequently not preserving normalization in some special cases the method yields exact solutions it is shown that the present implementation of the maximum entropy prescription always even in the case of approximate solutions preserves the exact functional relationship between the time derivative of the entropy and the time dependent solutions of the evolution equation other properties of the maximum entropy solutions and some illustrative examples are also discussed

bounds for eigenforms on arithmetic hyperbolic 3 manifolds on a family of arithmetic hyperbolic 3 manifolds of square free level we prove an upper bound for the sup norm of hecke maas cusp forms with a power saving over the local geometric bound simultaneously in the laplacian eigenvalue and the volume by a novel combination of diophantine and geometric arguments in a noncommutative setting we obtain bounds as strong as the best corresponding results on arithmetic surfaces

the circle method and bounds for l functions i let f be a hecke maass or holomorphic primitive cusp form of arbitrary level and nebentypus and let chi be a primitive character of conductor m for the twisted l function l s f otimes chi we establish the hybrid subconvex bound begin aligned l left frac 1 2 it f otimes chi right ll m 3 t frac 1 2 frac 1 18 varepsilon end aligned for t in mathbb r the implied constant depends only on the form f and varepsilon

lagrangian versus eulerian integration errors abstract the possibility to use a lagrangian frame to solve problems with large time steps was successfully explored previously by the authors for the solution of homogeneous incompressible fluids and also for solving multi fluid problems idelsohn et al 2012 2014 2013 the strategy used by the authors was named particle finite element method second generation pfem 2 the objective of this paper is to demonstrate in which circumstances the use of a lagrangian frame with particles is more accurate than a classical eulerian finite element method and when large time steps and or coarse meshes may be used

demography of cirsium vulgare in a grazing experiment the complete demographies of 16 populations of cirsium vulgare were followed in a replicated experiment the experiment was a factorial combination of two intensities of sheep grazing in each of three seasons winter grazed or ungrazed spring grazed or ungrazed and summer light or heavy grazing giving eight treatments in two blocks for 6 years from 1987 to 1992 the population sizes of c vulgare were monitored in each of the 16 paddocks after 1989 grazing in spring or winter or increased grazing in summer all increased population sizes population sizes fluctuated widely between years the effects of the grazing treatments and plant sizes on the transitions between nine life history stages were determined

periods subconvexity of l functions and representation theory we describe a new method to estimate the trilinear period on automorphic representations of pg l2 r such a period gives rise to a special value of the triple l function we prove a bound for the triple period which amounts to a subconvexity bound for the corresponding special value our method is based on the study of the analytic structure of the corresponding unique trilinear functional on unitary representations of pg l2 r

subconvex bounds for hecke maass forms on compact arithmetic quotients of semisimple lie groups let h be a semisimple algebraic group k a maximal compact subgroup of g h mathbb r and gamma subset h mathbb q a congruence arithmetic subgroup in this paper we generalize existing subconvex bounds for hecke maass forms on the locally symmetric space gamma backslash g k to corresponding bounds on the arithmetic quotient gamma backslash g for cocompact lattices using the spectral function of an elliptic operator the bounds obtained extend known subconvex bounds for automorphic forms to non trivial k types yielding such bounds for new classes of automorphic representations they constitute subconvex bounds for eigenfunctions on compact manifolds with both positive and negative sectional curvature we also obtain new subconvex bounds for holomorphic modular forms in the weight aspect

extended thermodynamics of fluids and virial equations of state dans la theorie de thermodynamique generalisee de liu et muller en plus des densites de masse de moment et d energie on prend le deviateur de contrainte et le flux thermique comme champs de base equations de champs en thermodynamique generalisee principes physiques de la theorie constitutive relation constitutives equations d etat pour les gaz coefficients du viriel

subconvexity for twisted l functions on gl 3 let q be a large prime and chi the quadratic character modulo q let phi be a self dual cuspidal hecke eigenform for rm sl 3 bbb z and f a hecke maa ss cusp form for gamma 0 q subseteq rm sl 2 bbb z we consider the twisted l functions l s phi times f times chi and l s phi times chi on rm gl 3 times rm gl 2 and rm gl 3 with conductors q 6 and q 3 respectively we prove the subconvexity bounds l 1 2 phi times f times chi ll phi f varepsilon q 5 4 varepsilon quad l 1 2 it phi times chi ll phi t varepsilon q 5 8 varepsilon for any varepsilon 0

triple product formula and the subconvexity bound of triple product l function in level aspect in this paper we derive a nice general formula for the local integrals of triple product formula whenever one of the representations has sufficiently higher level than the other two as an application we generalize venkatesh and woodbury s work on the subconvexity bound of triple product l function in level aspect allowing joint ramifications higher ramifications general unitary central characters and general special values of local epsilon factors

rankin selberg l functions in the level aspect keywords moments rankin selberg convolution level aspect convexity breaking reference tan article 2002 003doi 10 1215 s0012 7094 02 11416 1 record created on 2008 11 14 modified on 2017 05 12

global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy we consider the cauchy problem for a general one dimensional n n hyperbolic symmetrizable system of balance laws it is well known that in many physical examples for instance for the isentropic euler system with damping the dissipation due to the source term may prevent the shock formation at least for smooth and small initial data our main goal is to find a set of general and realistic sufficient conditions to guarantee the global existence of smooth solutions and possibly to investigate their asymptotic behavior for systems which are entropy dissipative a quite natural generalization of the kawashima condition for hyperbolic parabolic systems can be given in this paper we first propose a general framework for this kind of problem by using the so called entropy variables then we go on to prove some general statements about the global existence of smooth solutions under different sets of conditions in particular the present approach is suitable for dealing with most of the physical examples of systems with a relaxation extension our main tools will be some refined energy estimates and the use of a suitable version of the kawashima condition

local maximum entropy approximation schemes a seamless bridge between finite elements and meshfree methods we present a one parameter family of approximation schemes which we refer to as local maximum entropy approximation schemes that bridges continuously two important limits delaunay triangulation and maximum entropy max ent statistical inference local max ent approximation schemes represent a compromise in the sense of pareto optimality between the competing objectives of unbiased statistical inference from the nodal data and the definition of local shape functions of least width local max ent approximation schemes are entirely defined by the node set and the domain of analysis and the shape functions are positive interpolate affine functions exactly and have a weak kronecker delta property at the boundary local max ent approximation may be regarded as a regularization or thermalization of delaunay triangulation which effectively resolves the degenerate cases resulting from the lack or uniqueness of the triangulation local max ent approximation schemes can be taken as a convenient basis for the numerical solution of pdes in the style of meshfree galerkin methods in test cases characterized by smooth solutions we find that the accuracy of local max ent approximation schemes is vastly superior to that of finite elements

the spectral decomposition of shifted convolution sums let pi 1 pi 2 be cuspidal automorphic representations of pgl 2 r qf conductor 1 and hecke eigenvalues lambda pi 1 2 n and let h 0 be an integer for any smooth compactly supported weight functions w 1 w 2 r x c and any y 0 aspectral decomposition of the shifted convolution sum sigma m n h lambda pi 1 vertical bar m vertical bar lambda pi 2 vertical bar n vertical bar root vertical bar mn vertical bar w 1 m y w 2 n y is obtained as an application aspectral decomposition of the dirichlet series graphics is proved for rs 1 2 with polynomial growth on vertical lines in the s aspect and uniformity in the h aspect

an effective ratner equidistribution result for operatorname sl 2 mathbb r ltimes mathbb r 2 let g sl 2 r proportional to r 2 be the affine special linear group of the plane and set gamma sl 2 z proportional to z 2 we prove a polynomially effective asymptotic equidistribution result for the orbits of a 1 dimensional nonhorospherical unipotent flow on gamma g

bounds for gl 3 gl 2 l functions and gl 3 l functions in this paper we will give the subconvexity bounds for self dual gl 3 l functions in the t aspect as well as subconvexity bounds for self dual gl 3 gl 2 l functions in the gl 2 spectral aspect

subconvex equidistribution of cusp forms reduction to eisenstein observables let traverse a sequence of cuspidal automorphic representations of gl2 with large prime level unramified central character and bounded infinity type for g gl1 pgl2 let h g denote the assertion that subconvexity holds for g twists of the adjoint l function of with polynomial dependence upon the conductor of the twist we show that h gl1 implies h pgl2 in geometric terms h pgl2 corresponds roughly to an instance of arithmetic quantum unique ergodicity with a power savings in the error term h gl1 to the special case in which the relevant sequence of measures is tested against an eisenstein series

smooth second order non negative meshfree approximants selected by maximum entropy we present a family of approximation schemes which we refer to as second order maximum entropy max ent approximation schemes that extends the first order local max ent approximation schemes to second order consistency this method retains the fundamental properties of first order max ent schemes namely the shape functions are smooth non negative and satisfy a weak kronecker delta property at the boundary this last property makes the imposition of essential boundary conditions in the numerical solution of partial differential equations trivial the evaluation of the shape functions is not explicit but it is very efficient and robust to our knowledge the proposed method is the first higher order scheme for function approximation from unstructured data in arbitrary dimensions with non negative shape functions as a consequence the approximants exhibit variation diminishing properties as well as an excellent behavior in structural vibrations problems as compared with the lagrange finite elements mls based meshfree methods and even b spline approximations as shown through numerical experiments when compared with usual mls based second order meshfree methods the shape functions presented here are much easier to integrate in a galerkin approach as illustrated by the standard benchmark problems

hyperbolic principal subsystems entropy convexity and subcharacteristic conditions we consider a system of n balance laws compatible with an entropy principle and convex entropy density using the special symmetric form induced by the main field we define the concept of principal subsystem associated with the system we prove that the 2 n 2 principal subsystems are also symmetric hyperbolic and satisfy a subentropy law moreover we can verify that for each principal subsystem the maximum minimum characteristic velocity is not larger smaller than the maximum minimum characteristic velocity of the full system these are the subcharacteristic conditions we present some simple examples in the case of the euler fluid then in the case of dissipative hyperbolic systems we consider an equilibrium principal subsystem and we discuss the consequences in the setting of extended thermodynamics finally in the moments approach to the boltzmann equation we prove as a consequence of the previous result that the maximum characteristic velocity evaluated at the equilibrium state does not decrease when the number of moments increases

moment closure hierarchies for kinetic theories this paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory the first member of the hierarchy is the euler system which is based on maxwellian velocity distributions while the second member is based on nonisotropic gaussian velocity distributions the closure proceeds in two steps the first ensures that every member of the hierarchy is hyperbolic has an entropy and formally recovers the euler limit the second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct navier stokes behavior this is achieved through the introduction of a generalization of the bgk collision operator the simplest such system in three spatial dimensions is a 14 moment closure which also recovers the behavior of the grad 13 moment system when the velocity distributions lie near local maxwellians the closure procedure can be applied to a general class of kinetic theories

uniform distribution of heegner points let e be a modular elliptic curve over q of conductor n let k denote an imaginary quadratic field of discriminant d with n d 1 if p is a prime then there exists a unique zp extension k k such that gal k q acts nontrivially on gal k k the field k is called the anticyclotomic zp extension of k let e k denote the mordell weil group of e over k then a fundamental conjecture of mazur maz predicts that the size of e k is controlled by the prime factorization of n in k equivalently mazur s conjecture relates the size of the mordell weil group to the sign in the functional equation of certain l series the conjecture was verified by greenberg rohrlich and rubin in what mazur calls the exceptional case when e has complex multiplication by k more generally they settled the conjecture for certain abelian varieties with complex multiplication for a discussion of this cm case we refer the reader to gre roh and rub our goal in this paper is to treat the generic case which occurs either when e has no cm or when the field of complexmultiplications is distinct from k under certain conditions on e and k mazur s conjecture predicts that the group e k is finitely generated our main result asserts that this is in fact the case at least when p is an ordinary prime for e or when the class number of k is prime to p the main new ingredient we introduce is that of equidistribution following ideas used by ferrero andwashington to study the cyclotomic invariant more precisely we show that theheegner points associated to definite quaternion algebras are uniformly distributed on the components of a certain curve x and that the elements of a certain galois group act independently in a suitable sense this combined with a special value formula due to gross allows us to conclude that the special values of anticyclotomic l functions are almost always nonzero so that the statement about the mordell weil groups follows from the machinery of euler systems as developed by bertolini and darmon bd

a note on the least prime that splits completely in a nonabelian galois number field we prove a nontrivial estimate for the size of the least rational prime that splits completely in the ring of integers of certain families of nonabelian galois number fields our result complements results of linnik and vinogradov and of pollack who studied this problem in the quadratic and abelian number field settings respectively

weak subconvexity for central values of l functions we describe a general method to obtain weak subconvexity bounds for many classes of l functions we give several examples of our bound and our work has applications to a conjecture of rudnick and sarnak for the mass equidistribution of hecke eigenforms

invariant distributions and time averages for horocycle flows there are infinitely many obstructions to existence of smooth solutions of the cohomological equation uu f where u is the vector field generating the horocycle flow on the unit tangent bundle sm of a riemann m surface of finite area and f is a given function on sm we study the sobolev regularity of these obstructions construct smooth solutions of the cohomological equation and derive asymptotics for the ergodic averages of horocycle flows

extending linear finite elements to quadratic precision on arbitrary meshes the method of finite elements can provide discrete versions of differential operators in general arrangements of nodes linear finite elements defined on a triangulation like delaunays constitute a typical route towards this aim as well as being a tool for interpolation we discuss a procedure to build interpolating functions with quadratic precision from this functional set the idea is to incorporate extend the products of the original functions in order to go from linear precision the property that linear functions are reconstructed exactly to quadratic precision quadratic functions are reconstructed exactly this procedure is applied to the standard galerkin approach in order to study the poisson problem and the direct evaluation of the laplacian we discuss convergence of these problems in 1d and 2d the extended method is shown to be superior in 2d featuring convergence for the direct evaluation of the laplacian in distorted lattices

maximum entropy principle for rarefied polyatomic gases in this chapter we prove in the case of polyatomic rarefied gases that the maximum entropy principle mep gives the same closure of the system as that obtained in the phenomenological et theory with 14 fields discussed in chap 5 the main idea is to consider a generalized distribution function depending not only on the velocity but also on an extra variable that connects with the internal degrees of freedom of a constituent molecule on the basis of mep we again obtain the same binary hierarchy introduced in the previous chapter the one is the usual momentum type f series and the other is the energy type g series the extra variable plays a role in the g series thus we prove the perfect agreement between the et theory and the molecular et theory at least within 14 field theories the agreement for any number of moments will be proved in chap 10

on the uniform equidistribution of long closed horocycles it is well known that on any given hyperbolic surface of finite area a closed horocycle of length becomes asymptotically equidistributed as in this paper we prove that any subsegment of length greater than 1 2 e of such a closed horocycle also becomes equidistributed as the exponent 1 2 e is the best possible and improves upon a recent result by hejhal he3 we give two proofs of the above result our second proof leads to explicit information on the rate of convergence we also prove a result on the asymptotic joint equidistribution of a finite number of distinct subsegments having equal length proportional to

uniform pointwise bounds for matrix coefficients of unitary representations and applications to kazhdan constants let k be a local field and g the group of k rational points of a connected reductive linear algebraic group over k with k semisimple rank g 2 let k be a good maximal compact subgroup of g for a unitary representation of g a vector v in is called kfinite if the subspace spanned bykv is finite dimensional we will use the termk matrix coefficients resp k finite matrix coefficients of to refer to its matrix coefficients with respect to k invariant resp k finite unit vectors following bt we denote by g the subgroup generated by the unipotent k split subgroups of g the main goal of the present paper is to construct a class of uniform pointwise bounds for the k finite matrix coefficients of all infinite dimensional irreducible unitary representations of g or more generally of all unitary representations of g without a non zero g invariant vector let a be a maximal k split torus and a the closed positive weyl chamber of a such that the cartan decomposition g ka k holds where is a finite subset of the

moving least square reproducing kernel methods i methodology and convergence this paper formulates the moving least square interpolation scheme in a framework of the so called moving least square reproducing kernel mlsrk representation in this study the procedure of constructing moving least square interpolation function is facilitated by using the notion of reproducing kernel formulation which as a generalization of the early discrete approach establishes a continuous basis for a partition of unity this new formulation possesses the quality of simplicity and it is easy to implement moreover the reproducing kernel formula proposed is not only able to reproduce any mth order polynomial exactly on an irregular particle distribution but also serves as a projection operator that can approximate any smooth function globally with an optimal accuracy in this contribution a generic m consistency relation has been found which is the essential property of the mlsrk approximation an interpolation error estimate is given to assess the convergence rate of the approximation it is shown that for sufficiently smooth function the interpolant expansion in terms of sampled values will converge to the original function in the sobolev norms as a meshless method the convergence rate is measured by a new control variable dilation parameter of the window function instead of the mesh size h as usually done in the finite element analysis to illustrate the procedure convergence has been shown for the numerical solution of the second order elliptic differential equations in a galerkin procedure invoked with this interpolant in the numerical example a two point boundary problem is solved by using the method and an optimal convergence rate is observed with respect to various norms

the subconvexity problem for rankin selberg l functions and equidistribution of heegner points ii we prove a general subconvex bound in the level aspect for rankin selberg l functions associated with two primitive holomorphic or maass cusp forms over q we use this bound to establish the equidistribution of incomplete galois orbits of heegner points on shimura curves associated with indefinite quaternion algebras over q

the spectral decomposition of shifted convolution sums over number fields let 1 2 be cuspidal automorphic representations of gl2 over a number field f with hecke eigenvalues 1 m 2 m for nonzero integers l1 l2 f and compactly supported functions w1 w2 on f a spectral decomposition of the shifted convolution sum l1t1 l2t2 q0 t1 t2 n 1 t1n 1 2 t2n 1 n t1t2n 2 w1 l1t1 w2 l2t2 is obtained for any nonzero fractional ideal n and any nonzero element q n

the spectral decomposition of theta 2 let theta be an elementary theta function such as the classical jacobi theta function we establish a spectral decomposition and surprisingly strong asymptotic formulas for langle theta 2 varphi rangle as varphi traverses a sequence of hecke translates of a nice enough fixed function the subtlety is that typically theta 2 notin l 2 applications to the subconvexity quantum variance and 4 norm problems we determine all pairs a f g a g h of generalized weighted quasi arithmetic means being square iterative roots of a f g a g h that is the equation a f g a g h circ a f g a g h a f g a g h is solved under three times differentiability of the functions f g h f g h as an application some special cases are presented are indicated

maximisation of the entropy in non equilibrium this author proves that the maximisation of the entropy in non equilibrium is equivalent to the exploitation of the entropy inequality in extended thermodynamics

sparse equidistribution problems period bounds and subconvexity we introduce a geometric method to bound periods of automorphic forms the key features of this method are the use of equidistribution results in place of mean value theorems and the systematic use of mixing and the spectral gap applications are given to equidistribution of sparse subsets of horocycles and to equidistribution of cm points to subconvexity of the triple product period in the level aspect over number fields which implies subconvexity for certain standard and rankin selberg l functions and to bounding fourier coefficients of automorphic forms

on the pair correlation density for hyperbolic angles we prove a conjecture of boca popa zaharescu on the density function for the pair correlation of hyperbolic angles in a growing orbit of a discrete lattice in psl2 r

entropy and global existence for hyperbolic balance laws this paper presents a general result on the existence of global smooth solutions to hyperbolic systems of balance laws in several space variables we propose an entropy dissipation condition and prove the existence of global smooth solutions under initial data close to a constant equilibrium state in addition we show that a system of balance laws satisfies a kawashima condition if and only if its first order approximation namely the hyperbolic parabolic system derived through the chapman enskog expansion satisfies the corresponding kawashima condition the result is then applied to bouchut s discrete velocity bgk models approximating hyperbolic systems of conservation laws

the sup norm problem on the siegel modular space of rank two let f be a square integrable maa ss form on the siegel upper half space mathcal h of rank 2 for the siegel modular group rm sp 4 bbb z with laplace eigenvalue lambda if in addition f is a joint eigenfunction of the hecke algebra and omega is a compact set in rm sp 4 bbb z backslash mathcal h we show the bound f omega infty ll omega 1 lambda 1 delta for some global constant delta0 as an auxiliary result of independent interest we prove new uniform bounds for spherical functions on semisimple lie groups

the subconvexity problem for rankin selberg l functions and equidistribution of heegner points keywords rankin selberg l function subconvexity heegner points reference tan article 2004 002doi 10 4007 annals 2004 160 185 record created on 2008 11 14 modified on 2017 05 12

logarithm laws for flows on homogeneous spaces in this paper we generalize and sharpen d sullivan s logarithm law for geodesics by specifying conditions on a sequence of subsets at t n of a homogeneous space g g a semisimple lie group an irreducible lattice and a sequence of elements ft of g under which t n ftx at is infinite for a e x g the main tool is exponential decay of correlation coefficients of smooth functions ong besides the general higher rank version of sullivan s result as a consequence we obtain a new proof of the classical khinchin groshev theorem on simultaneous diophantine approximation and settle a conjecture recently made by m skriganov

subconvexity bounds for triple l functions and representation theory we describe a new method to estimate the trilinear period on automorphic representations of pgl 2 such a period gives rise to a special value of the triple l function we prove a bound for the triple period which amounts to a subconvexity bound for the corresponding special value of the triple l function our method is based on the study of the analytic structure of the corresponding unique trilinear functional on unitary representations of pgl 2

high order curvilinear finite element methods for lagrangian hydrodynamics the numerical approximation of the euler equations of gas dynamics in a movinglagrangian frame is at the heart of many multiphysics simulation algorithms in this paper we present a general framework for high order lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements this method is an extension of the approach outlined in dobrev et al internat j numer methods fluids 65 2010 pp 1295 1310 and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields including generic finite elements on two and three dimensional meshes with triangular quadrilateral tetrahedral or hexahedral zones we discretize the kinematic variables of position and velocity using a continuous high order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high order parametric mapping from a standard reference element this enables the use of curvilinear zone geometry higher ord

horizontal non vanishing of heegner points and toric periods abstract let f be a totally real number field and a a modular gl 2 type abelian variety over f let k f be a cm quadratic extension let be a class group character over k such that the rankin selberg convolution l s a is self dual with root number 1 we show that the number of class group characters with bounded ramification such that l 1 a 0 increases with the absolute value of the discriminant of k we also consider a rather general rank zero situation let be a cuspidal cohomological automorphic representation over gl 2 a f let be a hecke character over k such that the rankin selberg convolution l s is self dual with root number 1 we show that the number of hecke characters with fixed type and bounded ramification such that l 1 2 0 increases with the absolute value of the discriminant of k the gross zagier formula and the waldspurger formula relate the question to horizontal non vanishing of heegner points and toric periods respectively for both situations the strategy is geometric relying on the zariski density of cm points on self products of a quaternionic shimura variety the recent result 26 31 1 on the andre oort conjecture is accordingly fundamental to the approach