on the upper estimate of the heat kernel of a complete riemannian manifold let m be a complete non compact riemannian manifold whose sectional curvature is bounded between two constants k and k then one expects that the heat diffusion in such a manifold behaves like the heat diffusion in euclidean space the purpose of this paper is to give a justification of such a statement in 5 j cheeger and the third author found a lower estimate of the heat kernel by comparing it with the heat kernel of the space form whose curvature is the lower bound of the curvature of the manifold this lower estimate is sharp if we insist the dependence should be on the lower bound of the ricci curvature alone it remains to give an upper estimate of the heat kernel one does not however expect to have a comparison theorem for the upper bound because it is more sensitive to the geometry of the manifold in fact the heat kernel of the upper hialf space and the heat kernel of the complete hyperbolic manifold with finite volume have quite different behavior this is reflected by the fact that the laplacian has no discrete spectrum in the first case while infinite number of discrete eigenvalues may exist in the latter case what we will prove here is that in any case the heat kernel has to decay in a manner similar to the euclidean heat kernel thus we will prove that for any constant c 4 there exists c1 depending on c t the bound of the curvature of m and x so that for all t e 0 t

quantum entanglement helps in improving economic efficiency we propose an economic regulation approach based on quantum game theory for the government to reduce the abuses of oligopolistic competition theoretical analysis shows that this approach can help government improve the economic efficiency of the oligopolistic market and help prevent monopoly due to incorrect information these advantages are completely attributed to the quantum entanglement a unique quantum mechanical character

boundedness of spectral multipliers of generalized laplacians on compact manifolds with boundary consider a second order strongly elliptic negative semidefinite differential operator l may be a system on a compact riemannian manifold overline m with smooth boundary where the domain of l is defined by a coercive boundary condition classically known results and also recent work in duong et al j funct anal 196 443 485 2002 and duong and mcintosh rev math iberoam 15 233 265 1999 establish sufficient conditions for l infty text bmo l continuity of varphi sqrt l where varphi in s 0 1 mathbb r and l is a suitable elliptic operator using a variant of the cheeger gromov taylor functional calculus due to mauceri et al math res lett 16 861 879 2009 and short time upper bounds on the integral kernel of e tl due to greiner arch ration mech anal 41 168 218 1971 we prove that a variant of such sufficient conditions holds for our operator l

intertwining operators and residues i weighted characters operateurs d entrelacement normalisation groupes reels groupes p adiques representations standard les distributions j m la distribution j m x residus changements de contour les espaces 7b h ac g f s et 7b f ac g f s l application m

the fourier expansion of eisenstein series for 3 the fourier expansions of eisenstein series for gl 3 z are obtained by two methods one analogous to the classical method used by many number theorists including weber in his derivation of the kronecker limit formula the other method is analogous to that used by siegel to obtain fourier expansions of eisenstein series for the siegel modular group the expansions involve matrix argument k bessel functions recently studied by tom bengtson these k bessel functions are natural generalizations of the ordinary k bessel function which arise when considering harmonic analysis on the symmetric space of the general linear group using a certain system of coordinates

determination of the size of the representative volume element for random composites statistical and numerical approach the representative volume element rve plays a central role in the mechanics and physics of random heterogeneous materials with a view to predicting their effective properties a quantitative definition of its size is proposed in this work a rve size can be associated with a given precision of the estimation of the wanted overall property and the number of realizations of a given volume v of microstructure that one is able to consider it is shown to depend on the investigated morphological or physical property the contrast in the properties of the constituents and their volume fractions the methodology is applied to a specific random microstructure namely a two phase three dimensional voronoi mosaic finite element simulations of volumes of different sizes are performed in the case of linear elasticity and thermal conductivity the volumes are subjected to homogeneous strain stress or periodic boundary conditions the effective properties can be determined for large volumes and a small number of realizations conversely smaller volumes can be used providing that a sufficient number of realizations are considered a bias in the estimation of the effective properties is observed for too small volumes for all types of boundary conditions the variance of computed apparent properties for each volume size is used to define the precision of the estimation the key notion of integral range is introduced to relate this error estimation and the definition of the rve size for given wanted precision and number of realizations one is able to provide a minimal volume size for the computation of effective properties the results can also be used to predict the minimal number of realizations that must be considered for a given volume size in order to estimate the effective property for a given precision the rve sizes found for elastic and thermal properties but also for a geometrical property like volume fraction are compared

quantum chinos game winning strategies through quantum fluctuations we apply several quantization schemes to simple versions of the chinos game classically for two players with one coin each there is a symmetric stable strategy that allows each player to win half of the times on average a partial quantization of the game semiclassical allows us to find a winning strategy for the second player but it is unstable w r t the classical strategy however in a fully quantum version of the game we find a winning strategy for the first player that is optimal the symmetric classical situation is broken at the quantum level

terms in the selberg trace formula for 3 ℒ 3 ℛ 3 ℛ associated to eisenstein series coming from a minimal parabolic subgroup in this paper we compute the contribution to the trace formula for sl 3 z of the integrals associated to inner products of eisenstein series we show these reduce to corresponding integrals for a lower rank trace formula plus a few residual terms

conjugacy classes of hyperbolic matrices in and ideal classes in an order a bijection is proved between sl 7s z conjugacy classes of hyperbolic matrices with eigenvalues a1 an which are units in an n degree number field and narrow ideal classes of the ring r z a a bijection between gl n z conjugacy classes and the wide ideal classes which had been known is repeated with a different proof in 1980 peter sarnak was able to obtain an estimate of the growth of the class number of real quadratic number fields using the selberg trace formula and a bijection between hyperbolic elements of s1 2 z and quadratic forms the class number counted was the number of congruence classes of quadratic forms as studied by gauss 1 in this paper we will translate this bijection into modern number theoretic terms by counting ideal classes in a ring of integers associated to a given field in this way a bijection is proved between conjugacy classes of hyperbolic matrices in s1 2 z with a given set of eigenvalues and ideal classes in a certain order i e subring of dimension n over z associated to the ring of integers ok in a real n th degree number field k this more direct method is necessary for generalizing the bijection to higher dimensional cases because sarnak s result depends upon quadratic forms pell s equation and other things which are well understood only ill the case of s1 2 z we must mention the work of latimer and macduffee 3 who first proved theorem 2 in a slightly different fashion important also is the extensive work of taussky 7 9 who simplified the results of latimer and macduffee and extended them in certain directions as well as doing much work on the s1 2 z case it follows from a brief examination of the characteristic polynomial for a matrix a in sl n z that the eigenvalues of a are conjugate units in an extension of q we shall insist in the remainder of this paper that a be hyperbolic with irreducible characteristic polynomial that is a will have distinct real eigenvalues a each of which is of degree n over q proposition 1 if a is an eigenvalue for a matrix a e sl n z then for any field k containing a there exists an eigenvector w ts 1s xn with wi e ok received by the editors march 30 1983 1980 mathematics subject classification primary 10 02 15 02 secondary 15a18 15a36 loc07 tw1984 american mathematical society 0025 5726 84 1 00 25 per page

evolutionary quantum game we present a study of a dynamical quantum game each agent has a memory of her performance over the previous m timesteps and her strategy can evolve in time the game exhibits distinct regimes of optimality for small m the classical game performs better while for intermediate m the relative performance depends on whether the source of qubits is corrupt for large m the quantum players dramatically outperform the classical players by freezing the game into high performing attractors in which evolution ceases

finite element analysis of contact between elastic self affine surfaces finite element methods are used to study nonadhesive frictionless contact between elastic solids with self affine surfaces we find that the total contact area rises linearly with the load at small loads the mean pressure in the contact regions is independent of load and proportional to the root mean square slope of the surface the constant of proportionality is nearly independent of the poisson ratio and roughness exponent and lies between previous analytic predictions the contact morphology is also analyzed connected contact regions have a fractal area and perimeter the probability of finding a cluster of area a c drops as a tau c where tau increases with a decrease in roughness exponent the distribution of pressures shows an exponential tail that is also found in many jammed systems these results are contrasted to simpler models and experiments

the selberg trace formula for sl 3 ℤ sl 3 ℝ so 3 ℝ in this paper we compute the trace formula for sl 3 z in detail and refine it to a greater extent than has previously been done we show that massive cancellation occurs in the parabolic terms leading to a far simpler formula than had been thought possible

asymptotic behaviors of class number sums associated with pell type equations it is well known that the pell equation t 2 du 2 4 has infinitely many integer solutions t u for a given d 0 with d equiv 0 1 bmod 4 and d ne l 2 for any integer l however for a square free integer n ne 1 the equation t 2 du 2 4n does not always have integer solutions and verifying its solubility insolubility is not easy in the present paper we propose the asymptotic formulas of the sum of the class numbers h d of the primitive indefinite binary quadratic forms over the discriminants d 0 for which the pell type equation t 2 du 2 4n has an integer solution to study the distributions of such d

eta invariants of dirac operators on locally symmetric manifolds fibres de dirac determinant de la transformee de cayley operateurs de dirac sur des espaces localement symetriques trace de l operateur de la chaleur impair interpretation cohomologique la formule de la fonction zeta invariants wistes et applications

from infinitesimal to full contact between rough surfaces evolution of the contact area we carry out a statistically meaningful study on self affine rough surfaces in elastic frictionless non adhesive contact we study the evolution of the true contact area under increasing squeezing pressure from zero up to full contact which enables us to compare the numerical results both with asperity based models at light pressures and with persson s contact model for the entire range of pressures a good agreement of numerical results with persson s model is obtained for the shape of the area pressure curve especially near full contact however we obtain qualitatively different results for its derivative at light pressures we investigate the effects of the longest and shortest wavelengths in surface spectrum which control the surface gaussianity and spectrum breadth nayak s parameter we revisit the influence of nayak s parameter which is frequently assumed to play an important role in mechanics of rough contact

contact between representative rough surfaces a numerical analysis of mechanical frictionless contact between rough self affine elastic manifolds was carried out it is shown that the lower cutoff wave number in surface spectra is a key parameter controlling the representativity of the numerical model using this notion we demonstrate that for representative surfaces the evolution of the real contact area with load is universal and independent of the hurst roughness exponent by introducing a universal law containing three constants we extend the study of this evolution beyond the limit of infinitesimal area fractions

representative contact element size determination for micromechanical contact analysis of self affine topographies abstract a generic and straightforward numerical strategy for the determination of the size of representative contact elements rces which are employed in finite element contact homogenization procedures is proposed in this contribution the approach enables the determination of the length height and mesh discretisation of rces that provide a good statistical representation of the contact interface described by a given set of topography properties the case of gaussian self affine and elastic rough profiles under normal frictionless and non adhesive contact is analysed in detail a collection of conditions has been derived for two dimensional problems based on a trade off between the convergence of the real contact area and the computational cost with the increasing width of the roughness power spectrum the restrictions imposed on the length and mesh size can be relaxed allowing to reduce the size of numerical models the corresponding class of problems in three dimensions has also been studied in this case the influence of the numerical scheme adopted for the evaluation of the contact area has been analysed leading to the identification of two bounds which converge for the same value with progressively finer meshes state of the art numerical results fall within the bounded region and the application of the area correction technique proposed by yastrebov et al to the upper node based bound accelerates the convergence of the mesh and renders a good agreement with reference data