exponential stabilisation of a simple tree shaped network of timoshenko beams system the stabilisation problem of a forked triple system of timoshenko beams which is a simple tree shaped network is considered in this article suppose that the root of the fork is clamped at the interior node of the fork the displacement and rotational angle of the beams are continuous the shearing force and bending moments of the beams satisfy the transmission conditions the feedback controllers are designed at the exterior tips to stabilise this system then the closed loop system is proved to be well posed by the eigenfrequency analysis together with the asymptotic technique the system is shown to satisfy the spectrum determined growth condition finally this closed loop system is proved to be exponentially stable furthermore a simulation is given to support these results

consistent models of cahn hilliard gurtin equations with neumann boundary conditions abstract in this paper we prove the equivalence between two formulations for generalizations of the cahn hilliard equation based on constitutive equations proposed by gurtin in a parallelepiped associated with mixed periodic neumann boundary conditions it is important to note that in the case of the classical cahn hilliard equation both formulations are useful for the study of the existence and uniqueness of solutions furthermore the interest for taking neumann boundary conditions appears in particular when one takes into account the deformations of the material indeed in that case the order parameter and the displacement are coupled through the boundary conditions as it is generally expected we then obtain some existence and uniqueness results

a sufficient condition on riesz basis with parentheses of non self adjoint operator and application to a serially connected string system under joint feedbacks this paper gives an abstract sufficient condition on riesz basis with parentheses property for the generators of c0 groups in hilbert spaces whose eigenvalues are comprised of some finite unification of separable sets after taking the algebraic multiplicities into account the condition is then applied to the closed loop system of a serially connected string system under joint damping feedbacks to show that there is a family of generalized eigenfunctions that form a riesz basis with parentheses in the state space the spectrum determined growth condition is concluded as a consequence

m dimensional lattice sums of generalized hypergeometric functions representations and convergence criteria for infinite m dimensional lattice sums of generalized hypergeometric functions pfp 1 are deduced by appealing to the principle of mathematical induction in particular we show that such a lattice sum may be expressed essentially as a finite sum of mellin transforms of products of bessel functions of order m 2 and the functions pfp 1 in the lattice sum in addition a direct derivation for the three dimensional case is provided moreover we construct a countably infinite class of null functions on increasingly larger open intervals which are parametrically independent of the functions pfp 1 generating them

a stable and conservative finite difference scheme for the cahn hilliard equation we propose a stable and conservative finite difference scheme to solve numerically the cahn hilliard equation which describes a phase separation phenomenon numerical solutions to the equation is hard to obtain because it is a nonlinear and nearly ill posed problem we design a new difference scheme based on a general strategy proposed recently by furihata and mori the new scheme inherits characteristic properties the conservation of mass and the decrease of the total energy from the equation the decrease of the total energy implies boundedness of discretized sobolev norm of the solution this in turn implies by discretized sobolev s lemma boundedness of max norm of the solution and hence the stability of the solution an error estimate for the solution is obtained and the order is o delta x 2 delta t 2 numerical examples demonstrate the effectiveness of the proposed scheme

method of summation of some slowly convergent series a new method of summation of slowly convergent series is proposed it may be successfully applied to the summation of generalized and basic hypergeometric series as well as some classical orthogonal polynomial series expansions in some special cases our algorithm is equivalent to wynn s epsilon algorithm weniger transformation e j weniger nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series computer physics reports 10 1989 189 371 or the technique recently introduced by cizek et al j cizek j zamastil l skala new summation technique for rapidly divergent perturbation series hydrogen atom in magnetic field journal of mathematical physics 44 3 2003 962 968 in the case of trigonometric series our method is very similar to the homeier s h transformation while in the case of orthogonal series to the k transformation two iterated methods related to the proposed method are considered some theoretical results and several illustrative numerical examples are given

the expansion of a semigroup and a riesz basis criterion problems on the expansion of a semigroup and a criterion for being a riesz basis are discussed in the present paper suppose that a is the generator of a c0 semigroup on a hilbert space and a 1 a 2 a with 2 a is consisted of isolated eigenvalues distributed in a vertical strip it is proved that if 2 a is separated and for each 2 a the dimension of its root subspace is uniformly bounded then the generalized eigenvectors associated with 2 a form an l basis under different conditions on the riesz projection the expansion of a semigroup is studied in particular a simple criterion for the generalized eigenvectors forming a riesz basis is given as an application a heat exchanger problem with boundary feedback is investigated it is proved that the heat exchanger system is a riesz system in a suitable state hilbert space

boundary control of the timoshenko beam it is shown that the timoshenko beam can be uniformly stabilized by means of a boundary control a numerical study on the spectrum is also presented

lattice sums of generalized hypergeometric functions representations and convergence criteria for one dimensional 1d and two dimensional 2d lattice sums of generalized hypergeometric functions pfp 1 are derived by using apparently new integral representations for the latter functions and 1d and 2d forms of the poisson summation formula these lattice sum representations concisely unify and generalize various specializations given previously by several authors and should prove useful in analysing finite size effects in systems subjected to non periodic boundary conditions

linear stability of steady states for thin film and cahn hilliard type equations we study the linear stability of smooth steady states of the evolution equation h t f h xxx x g h h x x ah under both periodic and neumann boundary conditions if a 0 we assume f 1 in particular we consider positive periodic steady states of thin film equations where a 0 and f g might have degeneracies such as f 0 0 as well as singularities like g 0

on crossing event formulas in critical two dimensional percolation several formulas for crossing functions arising in the continuum limit of critical two dimensional percolation models are studied these include watts s formula for the horizontal vertical crossing probability and cardy s new formula for the expected number of crossing clusters it is shown that for lattices where conformal invariance holds they simplify when the spatial domain is taken to be the interior of an equilateral triangle the two crossing functions can be expressed in terms of an equianharmonic elliptic function with a triangular rotational symmetry this suggests that rigorous proofs of watts s formula and cardy s new formula will be easiest to construct if the underlying lattice is triangular the simplification in a triangular domain of schramm s bulk cardy s formula is also studied

on the convective cahn hilliard equation with degenerate mobility abstract in this paper we study the existence of weak solutions for the convective cahn hilliard equation with degenerate mobility based on the schauder type estimates we establish the global existence of classical solutions for regularized problems after establishing some necessary uniform estimates on the approximate solutions we prove the existence of weak solutions the nonnegativity and the finite speed of propagation of perturbations of solutions are also discussed

generalized watson s summation formula for 3 f 2 1 abstract a summation formula is given for 3 f 2 a b c 1 2 a b i 1 2c j 1 with fixed j and arbitrary i i j z this result generalizes the classical watson s theorem which deals with the case i j 0 extensions to the cases of 3f2 a 1 i j a c e 1 i 2c e 1 and 3f2 a b c 1 i a b 1 i j a c 1 are given notice that the case i j 0 corresponds to the classical theorems due to whipple and dixon respectively

riesz basis property of serially connected timoshenko beams in this paper we study the riesz basis property of serially connected timoshenko beams with joint and boundary feedback controls suppose that the left end of the whole beam is clamped and the right end is free at intermediate nodes the displacement and rotational angle of beams are continuous but the shearing force and bending moment could be discontinuous the collocated velocity feedback of the beams at intermediate nodes and the right end are used to stabilize the system we prove that the operator determined by the closed loop system has compact resolvent and generates a c 0 semigroup in an appropriate hilbert space we also show that there is a sequence of the generalized eigenvectors of the operator that forms a riesz basis with parentheses hence the spectrum determined growth condition holds therefore if the imaginary axis is not an asymptote of the spectrum then the closed loop system is exponentially stable finally we give a conclusion remark to explain that our result can be applied not

a study of new hypergeometric transformations the aim of this research paper is to establish a quite general transformation involving hypergeometric functions by the method of elementary manipulation of the series representations certain known as well as new hypergeometric transformations and identities not previously recorded in the literature are then deduced by means of the generalized kummer and dixon theorems obtained earlier by lavoie et al an application of a newly obtained identity is also given

global existence and asymptotics of solutions of the cahn hilliard equation abstract this paper is concerned with the cauchy problem of the cahn hilliard equation u t u 2 u 0 x r n t 0 u t 0 u 0 x x r n first we construct a local smooth solution u t x to the above cauchy problem then by combining some a priori estimates sobolev s embedding theorem and the continuity argument the local smooth solution u t x is extended step by step to all t 0 provided that the smooth nonlinear function u satisfies a certain local growth condition at some fixed point u r and that u 0 x u l 1 r n is suitably small secondly we show that the global smooth solution u t x satisfies the following temporal decay estimates d k u t x u l p r n c 1 t k 4 n 4 1 1 p t 0 k 0 1 here p 1 c 0 is a constant depending on and 0 is any positive constant which can be chosen sufficiently small at last we show that under a strong assumption on the growth of the nonlinear function u at u u the asymptotics of solutions of the above cauchy problem is described by u 0 t n 4 g x t 4 here 0 r n u 0 x u d x g x r n exp 4 i x d

control of a network of euler bernoulli beams abstract the aim is to study the boundary controllability of a system modeling the vibrations of a network of n euler bernoulli beams connected by n vibrating point masses using the classical hilbert uniqueness method the control problem is reduced to the obtention of an observability inequality the solution is then expressed in terms of fourier series so that it is also enough to show that the distance between two consecutive large eigenvalues of the spatial operator involved in this evolution problem is superior to a minimal fixed value this property called spectral gap holds as soon as the roots of a function denoted by f and giving the asymptotic behaviour of the eigenvalues are all simple for a network of n 2 different beams this assumption on the multiplicity of the roots of f denoted by a is proved to be satisfied and controllability follows for higher values of n a numerical approach allows one to prove a in many situations and no counterexample has been found but the problem of giving a general proof of controllability remains open

gauss s 2 f 1 1 cannot be generalized to 2 f 1 x abstract using ideas of jet wimp and richard mcintosh it is proved that gauss s explicit evaluation of 2 f 1 a b c 1 cannot be generalized to 2 f 1 a b c x for arbitrary a b c and x a short proof of wimp s theorem that asserts that 3 f 2 a b c d e 1 cannot be expressed in closed form is also given

a generalization of euler s hypergeometric transformation euler s transformation formula for the gauss hypergeometric function 2 f 1 is extended to hypergeometric functions of higher order unusually the generalized transformation constrains the hypergeometric function parameters algebraically but not linearly its consequences for hypergeometric summation are explored it has as a corollary a summation formula of slater from this formula new one term evaluations of 2 f 1 1 and 3 f 2 1 are derived by applying transformations in the thomae group their parameters are also constrained nonlinearly several new one term evaluations of 2 f 1 1 with linearly constrained parameters are derived as well

exponential stability analysis of xa long chain of coupled vibrating strings with dissipative linkage consider a long chain of coupled vibrating strings where a stabilizer is installed at each internal node and perhaps also at a boundary point the exponential stability of the stabilizers arrangement for this large dynamic structure will be determined through a careful transformation of the coupled wave equations for this structure into an equivalent hyperbolic system and analysis of the eigendeterminant it will be proven that the energy of the system decays uniformly exponentially if there is a stabilizer installed at a boundary point if the stabilizers are installed only at internal nodes it will be proven that the energy may decay either uniformly exponentially or nonuniformly or may not decay at all depending on the different wave speeds and the stabilizers arrangement all possible outcomes have been classified

the fourier collocation method for the cahn hilliard equation abstract in this paper a fourier collocation method for numerically solving cahn hilliard equations with periodic boundary conditions is developed we establish their semidiscrete and fully discrete schemes that inherit the energy dissipation property and mass conservation property from the associated continuous problem we prove existence and uniqueness of the numerical solution and derive the optimal error bounds we perform some numerical experiments which confirm our results

a transformation formula for the generalized hypergeometric series 4f3 1 for positive a and b by employing representations for the mellin transform of the product of two generalized hypergeometric functions 1f2 a2x2 1f2 b2x2 a new transformation formula for the series 4f3 1 is deduced

fast convergent quasipower series for some elementary and special functions abstract the aim of this paper is to prove that many functions having infinitely many poles can be expanded in quasipower series which is convergent in the whole complex plane these new series based on a simple general transformation are given here for numerous elliptic and other similar functions some trigonometric functions some polygamma functions and beta function

irreducible recurrences and representation theorems for 3f2 1 abstract by examining the irreducibility of a certain recurrence we show that the hypergeometric function of the title cannot be represented by gamma functions

on the mellin transform of products of bessel and generalized hypergeometric functions we deduce in an elementary way representations for the mellin transform of a product of bessel functions 0f1 a2x2 and generalized hypergeometric functions pfp 1 b2x2 for a b 0 as a corollary we obtain a transformation formula for p 1fp 1 which was discovered by wimp in 1987 by using bailey s method for the specialization 3f2 1

an analytic method for convergence acceleration of certain hypergeometric series a method is presented for convergence acceleration of the generalized hypergeometric series 3 f 2 with the argument 1 using analytic properties of their terms iterated transformation of the series is performed analytically which results in obtaining new fast converging expansions for some special functions and mathematical constants

hypergeometric identities arising from the elephant random walk abstract a probabilistic approach is provided to establish new hypergeometric identities it is based on the calculation of moments of the limiting distribution of the position of the elephant random walk in the superdiffusive regime

nonnegative solutions of a fourth order nonlinear degenerate parabolic equation elena beretta michiel bertsch roberta dal passo communicated by m guatin o introduction in this paper we study nonnegative solutions of the fourth order equation 0 1 ut u uxxx x o where n is a real positive constant equation 0 1 is a nonlinear parabolic partial differential equation which is degenerate at points at which u vanishes it arises in several applications see the references in 2 4 5 6 in which u x t stands for a nonnegative quantity for example in the study of the dynamics of thin liquid films u denotes the thickness of the film or another relevant nonnegative quantity the case n 1 models the flow in a hele shaw cell while n 3 corresponds to viscous flow on a solid surface without slip driven by surface tension see also 6 7 8 for a related equation it is well known that fourth order equations do not satisfy a maximum principle in particular classical solutions of the linear equation ut u 0 may become negative in finite time bernis 8 friedman 2 have observed that if n is positive equation 0 1 has generalized solutions which remain nonnegative for all times in addition they show that the qualitative positivity of these solutions strongly depends on the value of n in more recent papers by kadanoff et al a combination of numerical calculations and matched asymptotics 4 and the analysis of travelling wave solutions 5 leads to results which suggest a very rich structure of the solutions of 0 1 it is the purpose of the present paper to clarify several aspects of the nonlinear equation 0 1 and its dependence on the parameter n our results lead to several conjectures and open problems as was pointed out in 4 for sufficiently small values of n solutions of 0 1 which are initially strictly positive may vanish at some point x 0 after a finite time to but to the best of our knowledge there is no rigorous proof of this phenomenon in the literature on the other hand it is of particular interest for applications for example if u denotes the thickness of a liquid film it implies that at time to the film breaks at xo

automatic generation of hypergeometric identities by the beta integral method in this article hypergeometric identities or transformations for p 1fp series and for kampe de feriet series of unit arguments are derived systematically from known transformations of hypergeometric series and products of hypergeometric series respectively using the beta integral method in an automated manner based on the mathematica package hyp as a result we obtain some known and some identities which seem to not have been recorded before in literature

group theoretical basis of some identities for the generalized hypergeometric series it is shown that thomae s identity between two 3f2 hypergeometric series of unit argument together with the trivial invariance under separate permutations of numerator and denominator parameters implies that the symmetric group s5 is an invariance group of this series a similar result is proved for the terminating saalschutzian 4f3 series where s6 is shown to be the invariance group of this series or s5 if one parameter is eliminated by using the saalschutz condition here bailey s identity is realized as a permutation of appropriately defined parameters finally the set of three term relations between 3f2 series of unit argument discovered by thomae j thomae j reine angew math 87 26 1879 and systematized by whipple f j whipple proc london math soc 23 104 1925 is shown to be transformed into itself under the action of the group s6 where is a two element group the 12 left cosets of s6 with respect to the invariance group s5 are the structural elements underlying the three

spectrum of a network of euler bernoulli beams abstract a network of n flexible beams connected by n vibrating point masses is considered the spectrum of the spatial operator involved in this evolution problem is studied if 2 is any real number outside a discrete set of values s and if is an eigenvalue then it satisfies a characteristic equation which is given the associated eigenvectors are also characterized if 2 lies in s and if the n beams are identical same mechanical properties another characteristic equation is available it is not the case for different beams no general result can be stated some numerical examples and counterexamples are given to illustrate the impossibility of such a generalization at last the asymptotic behaviour of the eigenvalues is investigated by proving the so called weyl s formula

integrals of jacobi functions in this paper we study f 1 x a 1 x bp a x dx and its partial derivatives with respect to a and b where p a x is the jacobi function our expressions generalize the work of blue gautschi and gatteschi the results are useful to derive integration formulas for integrands with algebraic and logarithmic singularities

output feedback stabilisation of a tree shaped network of vibrating strings with non collocated observation in this article the authors consider the simple tree shaped network of strings with non collocated observation suppose that the network consists of three strings and the displacements of these strings are continuous at the common vertex the sensors and actuators are required to be set at different vertices we propose an observer based output feedback controller to stabilise this network the exponential stability of the closed loop network is obtained based on the riesz basis approach together with estimates of the spectral distribution finally a numerical simulation is given to support these results

the cahn hilliard type equations with periodic potentials and sources we discuss the existence uniqueness and asymptotic estimates of solutions to the cahn hilliard type equations with time periodic potentials and sources

recurrence relations for hypergeometric functions of unit argument we show that the generalized hypergeometric function p 1 p 3fp 2 nn 2 1 a n 0 satisfies a nonhomogeneous recurrence relation of order p a where a 0 when p 3 2 1 is balanced and a 1 otherwise also for us dq n a 4 2 q l n dq 2n a 1 1 n o a homogeneous recurrence relation of order q 1 is given 1 notation the generalized hypergeometric series a a l a 1 00 p 1 p 1 1 p t ail b p e al ai kz k k h b1 k where 1 2 a k f a k f a converges for iz i 0 let x ai i 1 2 p b1 j 1 2 p 2 ck k 1 2 q 2 di i 1 2 q be complex constants we define the functions g 1 n t n 1 m m 2n x 2m 2m n a m m 2n x m t m n bp 21 x m n r 1 bp 2 3 1 f m 2n x m t n m bp 2 p 4p 3l 2n x 2m 1 n m 1 bp 2 f 2n a m t n m ap 1 m 2n x t 1 n m 1 a 2n x 2m 1 n m a j h 3 n t 2n x m n b 1 m n x m s 1 m n 2n a n 1 cq t m q 4 q 3 2n a q 2 n cq 2 3 2 2n x m n dq rn m n cq 2 1 m l2n m 1 n 1 dq xq 2 q l 2n x q 2 n dq here b 1 ci for i q 2 we assume the parameters to be such that all expressions make sense by applying a lemma of wimp 8 we get the alternative forms for gm hm gm n t l p n 1 m n 2n x 2m 2n x t i t n x m m 2n x m t m n 1 bp 2 x t r n x t 1 2 r t 2n x m t n x t 2 bp 2 p 4p3 2n x t 1 n x t 1 bp 2 2n x m t n x t 1 ap f t rn mr t 1 2n x m t 1 n x t 2 a xp 2fp l2 2n x t 1 n x t 1 ap j this content downloaded from 157 55 39 116 on sun 18 sep 2016 06 20 49 utc all use subject to http about jstor org terms 524 stanislaw lewanowicz l1 q 2n x q 2 n 1 m n x m 2n x m mi n cq 2

abstract second order hyperbolic system and applications to controlled network of strings in this paper we study an abstract second order hyperbolic system valued in mathbb c n with appropriate boundary conditions we prove that the system is well posed and associates with a c 0 semigroup in a hilbert state space under certain conditions we show that the spectra of the system operator are located in the vertical strip and that there is a sequence of eigenvectors and generalized eigenvectors that forms a riesz basis with parentheses for the hilbert state space and hence that the system satisfies the spectrum determined growth assumption as applications we investigate the exponential stability of a controlled tree shaped network of 7 strings and a network of n connected strings

an alternative derivation of closed form representations for multidimensional lattice sums of generalized hypergeometric functions some representations for infinite m dimensional lattice sums of generalized hypergeometric functions which were deduced previously by the first named author are rederived here by appealing to an alternative more direct method in particular it is shown that these lattice sums are proportional to a finite sum of meijer s g functions

random continued fractions with beta hypergeometric distribution in a recent paper statist probab lett 78 2008 1711 1721 it has been shown that certain random continued fractions have a density which is a product of a beta density and a hypergeometric function 2f1 in the present paper we fully exploit a formula due to thomae j reine angew math 87 1879 26 73 in order to generalize substantially the class of random continuous fractions with a density of the above form this involves the design of seven particular graphs infinite paths on them lead to random continued fractions with an explicit distribution a careful study about the set of five real parameters leading to a beta hypergeometric distribution is required relying on almost forgotten results mainly due to felix klein

boundary feedback exponential stabilization of a timoshenko beam with both ends free in the present paper we consider the boundary feedback stabilization of a timoshenko beam with both ends free we propose boundary feedback control law that makes the closed loop system dissipative using asymptotic analysis techniques we give explicit asymptotic formula of eigenvalues of the closed loop system and prove the riesz basis property of eigenvectors and generalized eigenvectors by a detailed analysis of spectrum of the closed loop system we show that the closed system is exponentially stable

modeling stabilization and control of serially connected beams many flexible structures consist of a large number of components coupled end to end in the form of a chain in this paper we consider the simplest type of such structures which is formed by n seri

a class of generalized hypergeometric summations abstract summations over the positive integers n of the generalized hypergeometric expressions 1 n p f p 1 n 2 x 2 x 0 are derived in closed form the specialization p 0 for example reduces to known results for schlomilch series in addition we record the apparently not readily available sine and cosine transforms of p f p 1 b 2 x 2 b 0 the latter of which is used together with a form of the poisson summation formula to deduce the aforementioned results

a new two term relation for the 3 f 2 hypergeometric function of unit argument abstract the elementary manipulation of series together with summations of gauss saalschutz and dixon are employed to deduce a two term relation for the hypergeometric function 3f2 1 and a summation formula for the same function neither of which has previously appeared in the literature the two term relation has implications in the calculus of finite differences

asymptotic expansion of a bessel function integral using hypergeometric functions abstract generalized hypergeometric functions are used to extend simplify and complete the analysis of stoyanov and farrel math comput 49 1987 275 279 and of wong math comput 50 1998 229 234 as well as putting their considerations within a wider framework the integral 0 2 sin a cos b j sin j sin d where j is the bessel function of order is analyzed in terms of generalized hypergeometric functions and a complete asymptotic expansion is given for 0 2 j sin j sin d

sonine gegenbauer type integrals abstract representations for complete and incomplete sonine gegenbauer type integrals are given in terms of generalized hypergeometric functions in two and three variables and in terms of neumann type series certain interesting reductions of these integrals are also given in addition an application to a problem in diffraction theory is provided

on the critical case of the weber schafheitlin integral and a certain generalization abstract when the orders of the product of two bessel functions differ by an odd integer we show that the critical case defined in the sequel as the supercritical case of the discontinuous integral of weber and schafheitlin is proportional to a ratio of products of gamma functions the derivation we give is elementary in the sense that it avoids the use of contour integration and the calculus of residues we consider also a generalization of the later integral by essentially replacing one of the bessel functions by the hypergeometric function 1 f 2 as a byproduct of this investigation we deduce whipple s transformation formula for a well poised 6 f 5 1 and allied results