eigenvalue analysis of doubly connected plates with different configurations this paper deals with the vibration and buckling analyses of the first order shear deformable rhombic and square plates using a p type variational method the formulation includes rotary inertia and transverse shear terms the full plate is modeled with a single domain defined by a set of geometric points in the plane of the plate square and rectangular plates with a circular hole at the center are treated as the numerical example for the doubly connected plate and are modeled using one quarter of the geometry and only two elements the symmetry about x and y axes with regards to load and boundary conditions are exploited buckling coefficients and natural frequencies are calculated and compared with results from the published sources and the finite element method

the f q mock theta function conjecture and partition ranks in 1944 freeman dyson initiated the study of ranks of integer partitions here we solve the classical problem of obtaining formulas for ne n resp no n the number of partitions of n with even resp odd rank thanks to rademacher s celebrated formula for the partition function this problem is equivalent to that of obtaining a formula for the coefficients of the mock theta function f q a problem with its own long history dating to ramanujan s last letter to hardy little was known about this problem until dragonette in 1952 obtained asymptotic results in 1966 g e andrews refined dragonette s results and conjectured an exact formula for the coefficients of f q by constructing a weak maass poincare series whose holomorphic part is q 1f q24 we prove the andrews dragonette conjecture and as a consequence obtain the desired formulas for ne n and no n

free vibration analysis of rectangular plates with variously shaped holes an approximate method for analyzing the free vibration of rectangular plates with a hole of different shapes is proposed the shapes of the holes are circular semi circular elliptic square rectangular triangular rhombic etc these rectangular plates with a hole can be considered ultimately as a kind of rectangular plates with non uniform thickness a hole in a plate can be considered as an extremely thin part of the plate therefore the free vibration problem of a plate with a hole can be translated into the free vibration problem of the equivalent rectangular plate with non uniform thickness for some plates with different shaped holes the convergency and accuracy of the numerical solutions calculated by the proposed method are investigated

partitions durfee symbols and the atkin garvan moments of ranks atkin and garvan introduced the moments of ranks of partitions in their work connecting ranks and cranks here we consider a combinatorial interpretation of these moments this requires the introduction of a new representation for partitions the durfee symbol and subsequent refinements this in turn leads us to a variety of new congruences for our marked durfee symbols much in the spirit of dyson s original conjectures on the ranks of partitions

almost mean field ising model an algebraic approach we study the thermodynamic limit of the algebraic dynamics for an almost mean field ising model which is a slight generalization of the ising model in the mean field approximation we prove that there exists a family of relevant states on which the algebraic dynamics t can be defined this t defines a group of automorphisms of the algebra obtained by completing the standard spin algebra with respect to the quasiuniform topology defined by our states

congruences for the coefficients of weakly holomorphic modular forms recent works have used the theory of modular forms to establish linear congruences for the partition function and for traces of singular moduli we show that this type of phenomenon is completely general by finding similar congruences for the coefficients of any weakly holomorphic modular form on any congruence subgroup gamma 0 n in particular we give congruences for a wide class of partition functions and for traces of cm values of arbitrary modular functions on certain congruence subgroups of prime level

some remarks on the gelfand naimark segal representations of topological algebras after an appropriate restatement of the gelfand naimark segal construction for topological algebras we prove that there exists an isomorphism among the set cycl a of weakly continuous strongly cyclic representations of a barreled dual separable algebra with unit a the space hilba a of the hilbert spaces that are continuously embedded in a and are invariant under the dual left regular action of a and the set of the corresponding reproducing kernels we show that these isomorphisms are cone morphisms and we prove many interesting results that follow from this fact we discuss how these results can be used to describe cyclic representations on more general inner product spaces

free vibration analysis of rectangular plates with variable thickness abstract an approximate method for analyzing the free vibration of thin and moderately thick rectangular plates with arbitrary variable thickness is proposed the approximate method is based on the green function of a rectangular plate the green function of a rectangular plate with arbitrary variable thickness is obtained as a discrete form solution for deflection of the plate with a concentrated load the discrete form solution is obtained at each discrete point equally distributed on the plate it is shown that the numerical solution for the green function has good convergency and accuracy by applying the green function the free vibration problem of the plate is translated into the eigenvalue problem of the matrix the convergency and accuracy of the numerical solutions for the natural frequency parameter calculated by the proposed method are investigated and the frequency parameters and their modes of free vibration are shown for some rectangular plates

on the explicit construction of higher deformations of partition statistics the modularity of the partition generating function has many important consequences for example asymptotics and congruences for p n in a series of papers the author and ono 12 13 connected the rank a partition statistic introduced by dyson to weak maass forms a new class of functions which are related to modular forms and which were rst considered in 11 here we do a further step towards understanding how weak maass forms arise from interesting partition statistics by placing certain 2 marked durfee symbols introduced by andrews 1 into the framework of weak maass forms to do this we construct a new class of functions which we call quasiweak maass forms because they have quasimodular forms as components as an application we prove two conjectures of andrews it seems that this new class of functions will play an important role in better understanding weak maass forms of higher weight themselves and also their derivatives as a side product we introduce a new method which enables us to prove transformation laws for generating functions over incomplete lattices

algebraic dynamics in o algebras a perturbative approach in this paper the problem of recovering an algebraic dynamics in a perturbative approach is discussed the mathematical environment in which the physical problem is considered is that of algebras of unbounded operators endowed with the quasiuniform topology after some remarks on the domain of the perturbation conditions are given for the dynamics to exist as the limit of a net of regularized linear maps

on the seventh order mock theta functions in a recent paper h we proved the mock theta conjectures these are identities stated by ramanujan in his lost notebook jr2 pp 19 20 involving two of the 5th order mock 0 functions in fact ramanujan gave one such identity for each of the ten 5th order functions as shown in a g1 these ten identities are all equivalent to the two proved in i hi in this paper we prove the corresponding identities for ramanujan s 7th order mock 0 functions and show how they are related to rank differences of partitions to state our results we first introduce some standard notation if q and x are complex numbers with ql 1 and n is a nonnegative integer then

applications of topological algebras of unbounded operators in this paper we discuss some physical applications of topological algebras of unbounded operators the first example is a simple system of free bosons then we consider other models related to this one finally we discuss the time evolution of two interacting models of matter and bosons we show that for all these systems it is possible to build up a common mathematical framework where the existence of the thermodynamical limit of the algebraic dynamics can be conveniently analyzed

dynamic stability of curved panels with cutouts the parametric instability behaviour of curved panels with cutouts subjected to in plane static and periodic compressive edge loadings are studied using finite element analysis the first order shear deformation theory is used to model the curved panels considering the effects of transverse shear deformation and rotary inertia the theory used is the extension of dynamic shear deformable theory according to sanders first approximation for doubly curved shells which can be reduced to love s and donnell s theories by means of tracers the effects of static and dynamic load factors geometry boundary conditions and the cutout parameters on the principal instability regions of curved panels with cutouts are studied in detail using bolotin s method quantitative results are presented to show the effects of shell geometry and load parameters on the stability boundaries results for plates are also presented as special cases and are compared with those available in the literature

q identities for maass waveforms reinterpretation des theoremes de andrews dyson hickerson en termes de q identite pour une certaine forme d onde de maass

free vibration of orthotropic square plates with a square hole an approximate method is extended for analyzing the free vibration problem of orthotropic square plate with a square hole in this paper a square plate with a square hole is transformed into an equivalent square plate with non uniform thickness by considering the hole as an extremely thin part of the equivalent plate therefore the dynamic characteristics of a plate with a hole can be obtained by analyzing the equivalent plate the green function which is the discrete solution for the deflection of the equivalent plate is used to obtain the characteristic equation of the free vibration the effects of the side to thickness ratio hole side to plate side ratio and the variation of the thickness on the frequencies are considered some numerical analyses are carried out for the simply supported orthotropic square plate with a square hole the efficiency and accuracy of the numerical solutions by the present method are investigated

homomorphisms and derivations in proper jcq triples we investigate homomorphisms in proper jcq triples and derivations on proper jcq triples associated with the 3 variable jensen functional equation begin array rcl 2f left frac x y z 2 right f x f y f z end array which was introduced and investigated by park cho and han we moreover prove the hyers ulam rassias stability of homomorphisms in proper jcq triples and of derivations on proper jcq triples this is applied to investigate isomorphisms between proper jcq triples

a boundary perturbation method for circularly periodic plates with a core fundamental frequencies of vibrating circularly periodic plates with a circular core have been determined analytically a boundary perturbation method is developed to extract the fundamental eigenvalue of the governing biharmonic boundary value problem the method is then applied to wavy and polygonal plates with clamped and simply supported outer boundary conditions clamped simply supported and free circular cores are considered approximate analytical formulations of the fundamental frequency for such plates with core are obtained

eulerian series as modular forms in 1988 hickerson proved the celebrated mock theta conjectures a collection of ten identities from ramanujan s lost notebook which express certain modular forms as linear combinations of mock theta functions in the context of maass forms these identities arise from the peculiar phenomenon that two different harmonic maass forms may have the same non holomorphic parts using this perspective we construct several infinite families of modular forms which are differences of mock theta functions

o algebras and quantum dynamics some existence results we discuss the possibility of defining an algebraic dynamics within the settings of o algebras compared to our previous results on this subject the main improvement here is that we are not assuming the existence of some hamiltonian for the full physical system we will show that under suitable conditions the dynamics can still be defined via some limiting procedure starting from a given regularized sequence

new methods and structures in the theory of the multi mode dicke laser model we base a treatment of the dissipative multi mode version of dicke laser model on the theory of completely positive dynamical semigroups and quantum markov processes this leads to new results at both the mathematical and physical levels on the physical side it provides a generalization of the hepp lieb model that admits both chaotic and polychromatic laser radiation on the mathematical side it extends the theory of dynamical semigroups to a regime where the generators are perturbed by unbounded derivations