certain families of series associated with the hurwitz lerch zeta function abstract the history of problems of evaluation of series associated with the riemann zeta function can be traced back to christian goldbach 1690 1764 and leonhard euler 1707 1783 many different techniques to evaluate various series involving the zeta and related functions have since then been developed the authors show how elegantly certain families of series involving the hurwitz lerch zeta function can be evaluated by starting with a single known identity for the hurwitz lerch zeta function some of the special cases of these series identities are also shown to lead to certain known families of summation formulas involving the hurwitz zeta function

probabilistic analysis of a generalization of the unit clause literal selection heuristics for the k satisfiability problem abstract two algorithms for the k satisfiability problem are presented and a probabilistic analysis is performed the analysis is based on an instance distribution which is parametrized to simulate a variety of sample characteristics the algorithms assign values to literals appearing in a given instance of k satisfiability one at a time until a solution is found or it is discovered that further assignments cannot lead to finding a solution one algorithm chooses the next literal from a unit clause if one exists and randomly from the set of remaining literals otherwise the other algorithm uses a generalization of the unit clause rule as a heuristic for selecting the next literal at each step a literal is chosen randomly from a clause containing the least number of literals the algorithms run in polynomial time and it is shown that they find a solution to a random instance of k satisfiability with probability bounded below by a constant greater than zero for two different ranges of parameter values it is also shown that the second algorithm mentioned finds a solution with probability approaching one for a wide range of parameter values

ramanujan formula for the generalized stirling approximation abstract the aim of this paper is to improve ramanujan s formula for approximation of the factorial function starting from burnside s formula in contradistinction with the classical formula that starts from stirling s formula

on some slowly convergent series involving the hurwitz zeta function we shall extract the essence of the adamchik srivastava generating function method analysis munich 18 1998 131 by proving the most far reaching ramanujan yoshimoto formula and by showing that some of the results stated in srivastava and choi series associated with the zeta and related functions kluwer academic publishers dordrecht 2001 are simple consequences of the above mentioned formula

evolutionary topology optimization using design space adjustment based on fixed grid design space optimization for topology based on fixed grid is proposed and its superiority to conventional topology optimization is shown in the conventional topology optimization the design domain is fixed it is however desirable to make the design domain evolve into a better one during optimization process by increasing or decreasing the number of design pixels or variables which we call design space optimization a breakthrough in obtaining sensitivities when design space expands has been made recently with necessary mathematical background but due to coupling effect and others sensitivity results have not been satisfactory three innovative implementations are developed in this paper firstly the proper characteristics of artificial material are defined the second one is to decouple neighbouring elements for exact design space sensitivities the previous design space optimization has been tedious because only one layer can be added so the third innovation is a new expansion strategy with multi layers based on design space sensitivities as a result the proposed evolutionary method can get an optimum much faster than ever before especially for large scale problems it is also conjectured that this gives higher probability of getting the global optimum as confirmed by numerical examples

mathieu series and associated sums involving the zeta functions almost twelve decades ago mathieu investigated an interesting series s r in the study of elasticity of solid bodies since then many authors have studied various problems arising from the mathieu series s r in various diverse ways in this paper we present a relationship between the mathieu series s r and certain series involving the zeta functions by means of this relationship we then express the mathieu series s r in terms of the trigamma function j z or equivalently the hurwitz or generalized zeta function z s a accordingly various interesting properties of s r can be obtained from those of j z and z s a among other results certain integral representations of s r are deduced here by using the aforementioned relationships among s r j z and z s a

some pitfalls for experimenters with random sat abstract we consider the use of random cnf formulas in evaluating the performance of sat testing algorithms and in particular the role that the phase transition phenomenon plays in this use examples from the literature illustrate the importance of understanding the properties of formula distributions prior to designing an experiment we expect this to be of increasing importance in the field

integrals involving a function associated with the euler maclaurin summation formula the authors first evaluate sums of certain series involving the riemann zeta function by using the theory of the double gamma function with or without the use of these results the authors then establish seberal integrals involving a certain periodic function which is associated for example with the euler maclaurin summation formula finally by introducing some new mathematical constants several families of definite integrals involving logarithms of gamma functions are considered relevant connections of the results presented here with those given in earlier works are also pointed out

critical behavior in the computational cost of satisfiability testing abstract in previous work we employed finite size scaling a method from statistical mechanics to explore the crossover from the sat regime of k sat where almost all randomly generated expressions are satisfiable to the unsat regime where almost all are not in this work we extend the experiments to cover critical behavior in the computational cost we find that the median computational cost takes on a universal form across the transition regime finite size scaling accounts for its dependence on n the number of variables and on m the number of clauses in the k cnf expression we also inquire into the sources of the complexity by studying distributions of computational cost in the sat phase we observe an unusually wide range of costs the median cost increases linearly with n while the mean is significantly increased over the median by a small fraction of cases in which exponentially large costs are incurred we show that the large spread in cost of finding assignments is mainly due to the variability of running time of the davis putnam dp procedure used to determine the satisfiability of our expressions in particular if we consider a single satisfiable expression and run dp many times each time randomly relabelling the variables in the expression the resulting distribution of costs nearly reproduces the distribution of costs encountered by running dp search once on each of many such randomly generated satisfiable expressions there are intriguing similarities and differences between these effects and kinetic phenomena studied in statistical physics in glasses and in spin glasses

sums associated with the zeta function abstract we evaluate the sums of certain classes of series involving the riemann zeta function by using the theory of the double gamma function which has recently been revived in the study of determinants of laplacians relevant connections with various known results are also pointed out

a multi resolution method for 3d multi material topology optimization abstract this paper presents a multi resolution implementation in 3d for multi material topology optimization problem an alternating active phase algorithm where the problem at hand is divided into a series of the traditional material void phase topology optimization is employed for the multi material problem different levels of discretization are used for the displacement mesh design variable mesh and density mesh which provides higher resolution designs for the solutions a projection scheme is employed to compute the element densities from design variables and control the length scale of the material density simple block coordinate descent method similar to the gauss seidel technique is used to solve the subproblems several 3d numerical examples are presented to demonstrate the ease and the effectiveness of the proposed implementation incorporating the multi resolution method into the multi material approach robust designs with improved resolution can be achieved for real life problems with complex geometries

a note on some alternating series involving zeta and multiple zeta values in this article we consider various generalizations of euler s famous relation gamma sum n geq 2 1 n frac zeta n n linking euler s constant gamma to special values of the riemann zeta function at positive integers among other things we highlight the existence of a very similar relation for the apostol vu harmonic zeta function which have never been noticed before

fault tolerance of random graphs with respect to connectivity mean field approximation for semidense random graphs the fault tolerance of random graphs with unbounded degrees with respect to connectivity is investigated which relates to the reliability of wireless sensor networks with unreliable relay nodes the model evaluates the network breakdown probability that a graph is disconnected after stochastic node removal to establish a mean field approximation for the model we propose the cavity method for finite systems the analysis enables us to obtain an approximation formula for random graphs with any number of nodes and an arbitrary degree distribution in addition its asymptotic analysis reveals that the phase transition occurs in semidense random graphs whose average degree grows logarithmically these results which are supported by numerical simulations coincide with the mathematical results indicating successful predictions by the mean field approximation for unbounded but not dense random graphs

computational simulation of trabecular adaptation progress in human proximal femur during growth abstract there are a large number of clinical and experimental studies that analyzed trabecular architecture as a result of bone adaptation however only a limited amount of quantitative data is currently available on the progress of trabecular adaptation during growth in this paper we proposed a two step numerical simulation method that predicts trabecular adaptation progress during growth using a recently developed topology optimization algorithm design space optimization dso under the hypothesis that the mechanisms of dso are functionally equivalent to those of bone adaptation we applied the proposed scheme to trabecular adaptation simulation in human proximal femur for the simulation the full trabecular architecture in human proximal femur was represented by a two dimensional fe model with 50 m resolution in step 1 we determined a reference value that regulates trabecular adaptation in human proximal femur in step 2 we simulated trabecular adaptation in human proximal femur during growth with the reference value derived in step 1 we analyzed the architectural and mechanical properties of trabecular patterns through iterations from the comparison with experimental data in the literature we showed that in the early growth stage trabecular adaptation was achieved mainly by increasing bone volume fraction or trabecular thickness while in the later stage of the development the trabecular architecture gained higher structural efficiency by increasing structural anisotropy with a relatively low level of bone volume fraction or trabecular thickness we demonstrated that the proposed numerical framework predicted the growing progress of trabecular bone that has a close correlation with experimental data

the coc algorithm part ii topological geometrical and generalized shape optimization abstract after outlining analytical methods for layout optimization and illustrating them with examples the coc algorithm is applied to the simultaneous optimization of the topology and geometry of trusses with many thousand potential members the numerical results obtained are shown to be in close agreement up to twelve significant digits with analytical results finally the problem of generalized shape optimization finding the best boundary topology and shape is discussed

certain classes of series involving the zeta function the authors apply the theory of the double gamma function which was recently revived in the study of determinants of laplacians to evaluate some families of series involving the riemann zeta function introducing a presumably new mathematical constant in the theory of the double gamma function they also systematically evaluate a definite integral of the double gamma function and various classes of series associated with zeta functions some of these definite integrals are expressed in terms of quotients of double gamma functions

asymptotics of the solution to the conductivity equation in the presence of adjacent circular inclusions with finite conductivities abstract we consider the conductivity problem in the presence of adjacent circular inclusions with constant conductivities when two inclusions get closer and their conductivities degenerate to zero or infinity the gradient of the solution can be arbitrary large in this paper we derive an asymptotic formula of the solution which characterizes the gradient blow up of the solution in terms of conductivities of inclusions as well as the distance between inclusions the asymptotic formula is expressed in bipolar coordinates in terms of the lerch transcendent function and it is valid for inclusions with arbitrary constant conductivities we illustrate our results with numerical calculations

performance prediction and preselection for optimization and heuristic solution procedures the operations research literature contains numerous studies on the design and application of optimization and heuristic solution procedures these studies identify a particular optimization problem suggest a general solution procedure and then customize that procedure to improve its efficiency and or accuracy in contrast this paper shows how to use existing solution procedures more effectively we develop a methodology for predicting the relative performance of alternative procedures using easily computed problem characteristics this methodology enables us for any given data set to preselect a solution procedure we apply this preselection methodology to the 0 1 knapsack problem for which two successful optimization procedures dynamic programming and branch and search are available extensive computational testing indicates that substantial savings in average computation time are achieved the benefits of our work include faster and cheaper identification of effective solution procedures as well as an improved understanding of the relationship between problem characteristics and the performance of various procedures our methodology can be applied to many optimization problems to develop easily implemented guidelines for selecting appropriate solution procedures

new summation relations for the stieltjes constants the stieltjes constants have been of interest for over a century yet their detailed behaviour remains under investigation these constants appear in the laurent expansion of the hurwitz zeta funct

the kink phenomenon in fejer and clenshaw curtis quadrature the fejer and clenshawcurtis rules for numerical integration exhibit a curious phenomenon when applied to certain analytic functions when n the number of points in the integration rule increases the error does not decay to zero evenly but does so in two distinct stages for n less than a critical value the error behaves like o 2n where is a constant greater than 1 for these values of n the accuracy of both the fejer and clenshawcurtis rules is almost indistinguishable from that of the more celebrated gausslegendre quadrature rule for larger n however the error decreases at the rate o n i e only half as fast as before convergence curves typically display a kink where the convergence rate cuts in half in this paper we derive explicit as well as asymptotic error formulas that provide a complete description of this phenomenon

sums of certain series of the riemann zeta function abstract the object of the present paper is to investigate systematically several interesting families of summation formulas involving infinite series of the riemann zeta function many of the various results which are unified and generalized here in a remarkably simple manner have received considerable attention in recent years we also present a brief account of a number of analogous results associated with the hurwitz s generalized zeta function

solving satisfiability via boltzmann machines boltzmann machines bms are proposed as a computational model for the solution of the satisfiability sat problem in the propositional calculus setting conditions that guarantee consensus function maxima for configurations of the bm associated with solutions to the satisfaction problem are given experimental results that show a linear behavior of bms solving the satisfiability problem are presented and discussed

design space optimization using a numerical design continuation method summary a generalized optimization problem in which design space is also a design to be found is de9ned and a numerical implementation method is proposed in conventional optimization only a portion of structural parameters is designated as design variables while the remaining set of other parameters related to the design space are often taken for granted a design space is speci9ed by the number of design variables and the layout or con9guration to solve this type of design space problems a simple initial design space is selected and gradually improved while the usual design variables are being optimized to make the design space evolve into a better one one may increase the number of design variables but in this transition there are discontinuities in the objective and constraint functions accordingly the sensitivity analysis methods based on continuity will not apply to this discontinuous stage to overcome the di culties a numerical continuation scheme is proposed based on a new concept of a pivot phase design space two new categories of structural optimization problems are formulated and concrete examples shown copyright 2001 john wiley sons ltd

a homogenization method for shape and topology optimization abstract shape and topology optimization of a linearly elastic structure is discussed using a modification of the homogenization method introduced by bendsoe and kikuchi together with various examples which may justify validity and strength of the present approach for plane structures

generating hard satisfiability problems abstract we report results from large scale experiments in satisfiability testing as has been observed by others testing the satisfiability of random formulas often appears surprisingly easy here we show that by using the right distribution of instances and appropriate parameter values it is possible to generate random formulas that are hard that is for which satisfiability testing is quite difficult our results provide a benchmark for the evaluation of satisfiability testing procedures

parallelized structural topology optimization for eigenvalue problems a parallel topology optimization method is proposed to deal with large scale structural eigenvalue related design problems while existing parallel methods have been employed mainly for finite element analysis the present work deals with the entire parallel process of analysis and topology optimization using a parallel processing technique in the framework of the physical domain decomposition method the sensitivity analysis and design variable update are performed independently in each subdomain with minimum data communication among subdomains a successive estimation strategy over design iterations is proposed to expedite the design optimization process the preconditioned conjugate gradient method and the subspace iteration method are used as parallel solvers several numerical examples are considered to show the scalability and effectiveness of the present parallel approach in handling large scale design problems

carlitz s q bernoulli and q euler numbers and polynomials and a class of generalized q hurwitz zeta functions in this paper we systematically recover the identities for the q eta numbers h k and the q eta polynomials h k x presented by carlitz l carlitz q bernoulli numbers and polynomials duke math j 15 1948 987 1000 which we define here via generating series rather than via the difference equations of carlitz following a method developed by kaneko et al m kaneko n kurokawa m wakayama a variation of euler s approach to the riemann zeta function kyushu j math 57 2003 175 192 for a canonical q extension of the riemann zeta function we investigate a similarly constructed q extension of the hurwitz zeta function the details of this investigation disclose some interesting connections among q eta polynomials carlitz s q bernoulli polynomials b k x e polynomials and the q bernoulli polynomials that emerge from the q extension of the hurwitz zeta function discussed here

some generalizations of the apostol bernoulli and apostol euler polynomials abstract the main object of this paper is to give analogous definitions of apostol type see t m apostol on the lerch zeta function pacific j math 1 1951 161 167 and h m srivastava some formulas for the bernoulli and euler polynomials at rational arguments math proc cambridge philos soc 129 2000 77 84 for the so called apostol bernoulli numbers and polynomials of higher order we establish their elementary properties derive several explicit representations for them in terms of the gaussian hypergeometric function and the hurwitz or generalized zeta function and deduce their special cases and applications which are shown here to lead to the corresponding results for the classical bernoulli numbers and polynomials of higher order

topological design for vibrating structures the topological optimization technique using micro scale voids with the homogenization method for stress analysis of perforated structures has been applied to solve stiffness maximization problem with success here the homogenization design technique is extended to design problems concerning vibrating structures an extended optimization algorithm is also derived to maximize a set of eigenvalues as well as to identify the topology design for specified eigenvalues to characterize forced vibration of a structure

certain classes of series associated with the zeta function and multiple gamma functions abstract the authors apply the theory of multiple gamma functions which was recently revived in the study of the determinants of the laplacians in order to evaluate some families of series involving the riemann zeta function by introducing a certain mathematical constant they also systematically evaluate this constant and some definite integrals of the triple gamma function various classes of series associated with the zeta function are expressed in closed forms many of these results are also used here to compute the determinant of the laplacian on the four dimensional unit sphere s 4 explicitly

large scale topology optimization in 3d using parallel computing we consider large scale topology optimization of elastic continua in 3d using the regularized intermediate density control introduced in 1 the nested approach is used i e equilibrium is solved at each iteration to get a high quality resolution of realistic designs in 3d problems involving several hundreds of thousand finite elements are solved in order to deal with problems of this size parallel computing is used in combination with domain decomposition the equilibrium equations are solved by a preconditioned conjugate gradient algorithm and the optimization part is solved using sequential convex programming several numerical results obtained from computations performed on a cray parallel computer are presented

further series representations for ζ 2n 1 for a natural number n we propose and develop yet another family of rapidly converging series representations for the riemann zeta function z 2n 1 these developments lead us naturally to the problem of computation of the derivatives z 1 2n and z n a of the riemann and hurwitz zeta functions respectively we also briefly indicate relevant connections of the results considered here with many other known series representations for z 2n 1

certain classes of series associated with the zeta and related functions a fascinatingly large number of seemingly independent solutions of the so called basler problem of evaluating the riemann zeta function z s when s 2 which was of vital importance to leonhard euler 1707 1783 and the bernoulli brothers jakob bernoulli 1654 1705 and johann bernoulli 1667 1748 have appeared in the mathematical literature ever since euler first solved this problem in the year 1736 the main object of this two part series of lectures is to present some recent developments on the evaluations and representations of z s when email protected email protected 1 n being the set of natural numbers we emphasize upon several interesting classes of rapidly convergent series representations for z 2n 1 email protected n which have been developed in recent years in two of many computationally useful special cases considered here it is observed that z 3 can be represented by means of series which converge much more rapidly than that in euler s celebrated formula as well as the series used recently by roger apery 1916 1994 in his proof of the irrationality of z 3 symbolic and numerical computations using mathematica version 4 0 for linux show among other things that only 50 terms of one of these series are capable of producing an accuracy of seven decimal places

empirically derived estimates of the complexity of labeling line drawings of polyhedral scenes abstract several results have been obtained in the past about the complexity of understanding line drawings of polyhedral scenes kirousis and papadimitriou 1988 have shown that the problem of labeling line drawings of trihedral scenes is np complete the human brain however seems to grasp at a glance the 3d structure associated with a line drawing a possible explanation of this discrepancy offered by kirousis and papadimitriou themselves is that the worst case complexity does not reflect the real difficulty of labeling line drawings which might be far less in the average or in typical cases however no statistical analysis has ever been carried out to test this conjecture the core of this paper is an algorithm for the generation of random instances of polyhedral scenes random instances of line drawings are then obtained as perspective projections of these scenes and can be used as an input to standard labeling algorithms so as to derive experimental estimates of the complexity of these algorithms the results indicate that the median case complexity is linear in the number of junctions this substantiates the conjecture that typical instances of line drawings are easy to label and may help explain the ease by which the brain is able to solve the problem

the determinant of one dimensional polyharmonic operators of arbitrary order abstract we obtain an explicit expression for the regularised spectral determinant of the polyharmonic operator p n 1 n x 2 n on 0 t with dirichlet boundary conditions and n a positive integer and show that it satisfies the asymptotics log det p n n 2 log n 7 3 2 2 3 2 log t 4 n 2 o n for large n this is a consequence of sharp upper and lower bounds for log det p n valid for all n and which coincide in the terms up to order n these results form the basis to analyse more general operators with nonconstant coefficients and show that the corresponding determinants have a similar asymptotic behaviour

some generalizations of the apostol genocchi polynomials and the stirling numbers of the second kind abstract recently the authors introduced some generalizations of the apostol bernoulli polynomials and the apostol euler polynomials see q m luo h m srivastava j math anal appl 308 2005 290 302 and q m luo taiwanese j math 10 2006 917 925 the main object of this paper is to investigate an analogous generalization of the genocchi polynomials of higher order that is the so called apostol genocchi polynomials of higher order for these generalized apostol genocchi polynomials we establish several elementary properties provide some explicit relationships with the apostol bernoulli polynomials and the apostol euler polynomials and derive various explicit series representations in terms of the gaussian hypergeometric function and the hurwitz or generalized zeta function we also deduce their special cases and applications which are shown here to lead to the corresponding results for the genocchi and euler polynomials of higher order by introducing an analogue of the stirling numbers of the second kind that is the so called stirling numbers of the second kind we derive some basic properties and formulas and consider some interesting applications to the family of the apostol type polynomials furthermore we also correct an error in a previous paper q m luo h m srivastava comput math appl 51 2006 631 642 and pose two open problems on the subject of our investigation

series involving the zeta function and multiple gamma functions the theory of multiple gamma functions which was recently revived in the study of the determinants of the laplacians was applied in several earlier works in order to evaluate some families of series involving the riemann zeta function as well as to compute the determinants of the laplacians here in the present paper the authors address the converse problem and apply various known or new formulas for series associated with the zeta and related functions with a view to developing the corresponding theory of multiple gamma functions and then using these series to compute the determinants of the laplacians on the n dimensional unit sphere s n n 5 6 7 explicitly

fixed grid techniques for phase change problems a review summary the aim of this paper is to categorize the major fixed grid formulations and solution methods for conduction controlled phase change problems using a two phase model of a solid liquid phase change the basic enthalpy equation is derived starting from this equation a number of alternative formulations are obtained all the formulations are reduced to a standard form from this standard form finite element and finite volume discretizations are developed these discretizations are used as the basis for a number of fixed grid numerical solution techniques for solidification phase change systems in particular various apparent capacity and source based enthalpy methods are explored

improving multiresolution topology optimization via multiple discretizations summary unlike the traditional topology optimization approach that uses the same discretization for finite element analysis and design optimization this paper proposes a framework for improving multiresolution topology optimization imtop via multiple distinct discretizations for 1 finite elements 2 design variables and 3 density this approach leads to high fidelity resolution with a relatively low computational cost in addition an adaptive multiresolution topology optimization amtop procedure is introduced which consists of selective adjustment and refinement of design variable and density fields various two dimensional and three dimensional numerical examples demonstrate that the proposed schemes can significantly reduce computational cost in comparison to the existing element based approach copyright 2012 john wiley sons ltd

some families of the hurwitz lerch zeta functions and associated fractional derivative and other integral representations the main object of this paper is to present in a unified manner a number of fractional derivative and other integral representations for several general families of the hurwitz lerch zeta functions relevant connections of the results presented here with those obtained in earlier works are also indicated precisely

multiphase dynamics in arbitrary geometries on fixed cartesian grids in this work a mixed eulerian lagrangian algorithm calledelafint eulerian lagrangian algorithm for interface tracking is developed further and applied to compute flows with solid fluid and fluid fluid interfaces the method is capable of handling fluid flows in the presence of both irregularly shaped solid boundaries and moving boundaries on a fixed cartesian grid the field equations are solved on the underlying fixed grid using a collocated variable pressure based formulation the moving boundary is tracked explicitly by the lagrangian translation of marker particles the moving boundary passes through the grid and the immersed boundary technique is used to handle its interaction with the underlying grid the internal solid boundaries are dealt with by using a cut cell technique particular attention is directed toward conservation and consistency in the vicinity of both phase boundaries the complex geometry feature has been tested for a variety of flow problems the performance of the immersed boundary representation is demonstrated in the simulation of newtonian liquid drops the combination of the two features is then employed in the simulation of motion of drops through constricted tubes the capabilities developed here can be useful for solving flow problems involving moving and stationary complex boundaries

solutions to shape and topology eigenvalue optimization problems using a homogenization method a solution strategy to find the shape and topology of structures that maximize a natural frequency is presented the methodology is based on a homogenization method and the representation of the shape of the structure as a material property the problem is formulated as a reinforcement problem in which a given structure is reinforced using a prescribed amount of material two dimensional plane elasticity problems are considered examples are presented for illustration

reducing dimensionality in topology optimization using adaptive design variable fields topology optimization methodologies typically use the same discretization for the design variable and analysis meshes analysis accuracy and expense are thus directly tied to design dimensionality and optimization expense this paper proposes leveraging properties of the heaviside projection method hpm to separate the design variable field from the analysis mesh in continuum topology optimization hpm projects independent design variables onto element space over a prescribed length scale a single design variable therefore influences several elements creating a redundancy within the design that can be exploited to reduce the number of independent design variables without significantly restricting the design space the algorithm begins with sparse design variable fields and adapts these fields as the optimization progresses the technique is demonstrated on minimum compliance maximum stiffness problems solved using continuous optimization and genetic algorithms for the former the proposed algorithm typically identifies solutions having objective functions within 1 of those found using full design variable fields computational savings are minor to moderate for the minimum compliance formulation with a single constraint and are substantial for formulations having many local constraints when using genetic algorithms solutions are consistently obtained on mesh resolutions that were previously considered intractable copyright 2009 john wiley sons ltd

spectral functions special functions and the selberg zeta function the functional determinant of an eigenvalue sequence as defined by zeta regularization can be simply evaluated by quadratures we apply this procedure to the selberg trace formula for a compact riemann surface to find a factorization of the selberg zeta function into two functional determinants respectively related to the laplacian on the compact surface itself and on the sphere we also apply our formalism to various explicit eigenvalue sequences reproducing in a simpler way classical results about the gamma function and the barnesg function concerning the latter our method explains its connection to the selberg zeta function and evaluates the related glaisher kinkelin constanta

elliptic extensions of the apostol bernoulli and apostol euler polynomials in this paper we investigate the elliptic analogues of the apostol bernoulli and apostol euler polynomials and obtain the closed expressions of sums of products for these elliptic type polynomials some interesting special cases are also shown

some two sided inequalities for multiple gamma functions and related results there is an abundant literature on inequalities for the euler s gamma function c and its various related functions yet only very recently several authors began to study inequalities for the barnes double gamma function c 2 here in this paper we aim at presenting several two sided inequalities for the multiple gamma functions c n n 2 3 4 5 in our investigation of these two sided inequalities for the multiple gamma functions c n n 2 3 4 5 we employ and extend a method based upon taylor s formula and express email protected n 1 x as series involving the zeta functions we also give a more convenient explicit form of the multiple gamma functions c n email protected n n being the set of positive integers the main two sided inequalities for the multiple gamma functions c n n 2 3 4 5 which we have presented in this paper are presumably new and their derivations provide a fruitful insight into the corresponding problem for the multiple gamma functions c n when email protected 6

asymptotic expansions of the hurwitz lerch zeta function abstract the hurwitz lerch zeta function z s a is considered for large and small values of a c and for large values of z c with arg a z 1 and s c this function is originally defined as a power series in z convergent for z 1 s c and 1 a n an integral representation is obtained for z s a which define the analytical continuation of the hurwitz lerch zeta function to the cut complex z plane c 1 from this integral we derive three complete asymptotic expansions for either large or small a and large z these expansions are accompanied by error bounds at any order of the approximation numerical experiments show that these bounds are very accurate for real values of the asymptotic variables

backtracking algorithms for disjunctions of temporal constraints abstract we extend the framework of simple temporal problems studied originally by dechter meiri and pearl to consider constraints of the form x 1 y 1 r 1 x n y n r n where x 1 x n y 1 y n are variables ranging over the real numbers r 1 r n are real constants and n 1 this is a wide class of temporal constraints that can be used to model a variety of problems in temporal reasoning scheduling planning and temporal constraint databases we have implemented several progressively more efficient algorithms for the consistency checking problem for this class of temporal constraints backtracking backjumping three variations of forward checking and forward checking with backjumping we have partially ordered the above algorithms according to the number of visited search nodes and the number of performed consistency checks although our problem is non binary our results agree with the results of kondrak and van beek who consider only binary constraints we have also studied the performance of the above algorithms experimentally using randomly generated sets of data and job shop scheduling problems the experiments with random instances allowed us to locate the hard region for this class of problems the results show that hard problems occur at a critical value of the ratio of disjunctions to variables

some integral and asymptotic formulas associated with the hurwitz zeta function the main object of this paper is to present an easily accessible integral representation of the partial sum l u x a 0 n x n a u of the hurwitz zeta function z u a which entails a number of important implications for l u x a and z u a and for their derivatives furthermore a new proof is given for a fundamental summation formula contained in theorem 3 below which is shown to possess numerous further consequences and applications relevant connections of the results obtained here with those considered in many other earlier and recent works are also discussed

a new efficient convergence criterion for reducing computational expense in topology optimization reducible design variable method summary a new efficient convergence criterion named the reducible design variable method rdvm is proposed to save computational expense in topology optimization there are two types of computational costs one is to calculate the governing equations and the other is to update the design variables in conventional topology optimization the number of design variables is usually fixed during the optimization procedure thus the computational expense linearly increases with respect to the iteration number some design variables however quickly converge and some other design variables slowly converge the idea of the proposed method is to adaptively reduce the number of design variables on the basis of the history of each design variable during optimization using the rdvm those design variables that quickly converge are not considered as design variables for the next iterations this means that the number of design variables can be reduced to save the computational costs of updating design variables then the iteration will repeat until the number of design variables becomes 0 in addition the proposed method can lead to faster convergence of the optimization procedure which indeed is a more significant time saving it is also revealed that the rdvm gives identical optimal solutions as those by conventional methods we confirmed the numerical efficiency and solution effectiveness of the rdvm with respect to two types of optimization static linear elastic minimization and linear vibration problems with the first eigenvalue as the objective function for maximization copyright 2012 john wiley sons ltd

an engineer s approach to optimal material distribution and shape finding abstract the fundamental aim of shape optimization involves the optimal distribution of mass in space observing global and local design constraints the practical realization in applied mechanics can be performed by introducing a foam like material with variable density as discussed by bendsoe and kikuchi this paper uses for the evaluation of material properties a simple energy approach the application is extended to three dimensional domains multiple loading cases are also considered further the approach is implemented in a preoptimizer for optimal shape finding

some q extensions of the apostol bernoulli and the apostol euler polynomials of order n and the multiple hurwitz zeta function abstract in this paper we first investigate several further interesting properties of the multiple hurwitz lerch zeta function n z s a which was introduced recently by choi et al j choi d s jang h m srivastava a generalization of the hurwitz lerch zeta function integral transform spec funct 19 2008 we then introduce and investigate some q extensions of the multiple hurwitz lerch zeta function n z s a the apostol bernoulli polynomials b k n x of order n and the apostol euler polynomials e k n x of order n relevant connections of the results presented here with those obtained in earlier works are also indicated precisely

evaluation of series with hurwitz and lerch zeta function coefficients by using hankel contour integrals we introduce a new technique for evaluation of series with zeta coefficients and also for evaluation of certain integrals involving the loggamma function this technique is based on hankel integral representations of the hurwitz zeta the lerch transcendent the digamma and loggamma functions