simulation of the continuous time random walk of the space fractional diffusion equations in this article we discuss the solution of the space fractional diffusion equation with and without central linear drift in the fourier domain and show the strong connection between it and the a stable levy distribution 0 a 2 we use some relevant transformations of the independent variables x and t to find the solution of the space fractional diffusion equation with central linear drift which is a special form of the space fractional fokker planck equation which is useful in studying the dynamic behaviour of stochastic differential equations driven by the non gaussian levy noises we simulate the continuous time random walk of these models by using the monte carlo method

vibration of arbitrarily shaped triangular plates with elastically restrained edges abstract a solution method is proposed for the vibration analysis of arbitrarily shaped triangular plates with elastically restrained edges an arbitrarily shaped triangular plate is first mapped into a right angled isosceles triangular plate and subsequently stretched to form a square plate by padding to it another right angled isosceles triangular plate of near zero thickness the displacement function is then expressed as a two dimensional fourier cosine series supplemented by several one dimensional series introduced to improve the convergence and accuracy of the displacement solution regardless of the shapes and boundary conditions of the triangular plate the final stiffness and mass matrices can always be calculated analytically which makes the current solution method highly efficient in implementations numerical examples are presented to verify the applicability of the proposed method to triangular plates of different shapes and perhaps more importantly different boundary conditions the current method can be easily extended to plates with heterogeneous material properties variable thickness non uniform elastic restraints etc

on the relationship between combinatorial and lp based lower bounds for np hard scheduling problems enumerative approaches to solving optimization problems such as branch and bound require a subroutine that produces a lower bound on the value of the optimal solution in the domain of scheduling problems the requisite lower bound has typically been derived from either the solution to a linear programming lp relaxation of the problem or the solution to a combinatorial relaxation in this paper we investigate from a theoretical perspective the relationship between several lp based lower bounds and combinatorial lower bounds for three scheduling problems in which the goal is to minimize the average weighted completion time of the jobs scheduled we establish a number of facts about the relationship between these different sorts of lower bounds including the equivalence of certain lp based lower bounds for these problems to combinatorial lower bounds used in successful branch and bound algorithms as a result we obtain the first worst case analysis of the quality of the lower bounds delivered by these combinatorial relaxations

two agent scheduling in a flowshop abstract in this paper we study two agent scheduling in a two machine flowshop the cost function is the weighted sum of some common regular functions including the makespan and the total completion time specifically we consider two problems namely the problem to minimize the weighted sum of both agents makespan and the problem to minimize the weighted sum of one agent s total completion time and the other agent s makespan for the first problem we give an ordinary np hardness proof and a pseudo polynomial time algorithm we also analyze the performance of treating the problem using johnson s rule and propose an approximation algorithm based on johnson s rule for the second problem we propose an approximation algorithm based on linear programming relaxation of the problem finally we show that some simple algorithms can be used to solve special cases of the two problems

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

scheduling to minimize average completion time off line and on line approximation algorithms in this paper we introduce two general techniques for the design and analysis of approximation algorithms for np hard scheduling problems in which the objective is to minimize the weighted sum of the job completion times for a variety of scheduling models these techniques yield the first algorithms that are guaranteed to find schedules that have objective function value within a constant factor of the optimum in the first approach we use an optimal solution to a linear programming relaxation in order to guide a simple list scheduling rule consequently we also obtain results about the strength of the relaxation our second approach yields on line algorithms for these problems in this setting we are scheduling jobs that continually arrive to be processed and for each time t we must construct the schedule until time t without any knowledge of the jobs that will arrive afterwards our on line technique yields constant performance guarantees for a variety of scheduling environments and in some cases essentially matches the performance of our off line lp based algorithms

fractional fokker planck equation for nonlinear stochastic differential equations driven by non gaussian levy stable noises the fokker planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by gaussian noises however there are both theoretical and empirical reasons to consider similar equations driven by strongly non gaussian noises in particular they yield strongly non gaussian anomalous diffusion which seems to be relevant in different domains of physics in this paper we therefore derive a fractional fokker planck equation for the probability distribution of particles whose motion is governed by a nonlinear langevin type equation which is driven by a levy stable noise rather than a gaussian we obtain in fact a general result for a markovian forcing we also discuss the existence and uniqueness of the solution of the fractional fokker planck equation

a variable kinematic ritz formulation for vibration study of quadrilateral plates with arbitrary thickness a new variable kinematic ritz method applied to free vibration analysis of arbitrary quadrilateral thin and thick isotropic plates is presented carrera s unified formulation and the versatile pb 2 ritz method are properly combined to build a powerful yet simple modeling and solution framework the proposed technique allows to generate arbitrarily accurate ritz solutions from a large variety of refined two dimensional plate theories by expanding so called ritz fundamental nuclei of the plate mass and stiffness matrices theoretical development of the present methodology is described in detail convergence and accuracy of the method are examined through several examples on thin moderately thick and very thick plates of rectangular skew trapezoidal and general quadrilateral shapes with an arbitrary combination of clamped free and simply supported edges present results are compared with existing three dimensional solutions from open literature maximum and average differences of various higher order plate theories and three dimensional results are also presented with the aim of providing useful guidelines on the choice of appropriate plate theory to get a desired accuracy on frequency parameters

the achievable region approach to the optimal control of stochastic systems summary the achievable region approach seeks solutions to stochastic optimization problems by characterizing the space of all possible performances the achievable region of the system of interest and optimizing the overall system wide performance objective over this space this is radically different from conventional formulations based on dynamic programming the approach is explained with reference to a simple two class queuing system powerful new methodologies due to the authors and co workers are deployed to analyse a general multiclass queuing system with parallel servers and then to develop an approach to optimal load distribution across a network of interconnected stations finally the approach is used for the first time to analyse a class of intensity control problems

submodular function minimization submodular functions often arise in various fields of operations research including discrete optimization game theory queueing theory and information theory in this survey paper we give overview on the fundamental properties of submodular functions and recent algorithmic devolopments of their minimization

transverse vibration of simply supported elliptical and circular plates using boundary characteristic orthogonal polynomials in two variables abstract the first four frequencies and mode shapes have been computed for elliptical and circular plates of uniform thickness with simply supported edges by employing orthogonal polynomials in the rayleigh ritz method in general this is found to give better results than traditional methods successive approximations have been worked out to ensure convergence comparisons have been made with existing results in some cases calculations have been done for several values of b a i e the ratio of the semi major and semi minor axes mode shapes have been used to obtain three dimensional plots of plates in displaced configurations

stronger lagrangian bounds by use of slack variables applications to machine scheduling problems lagrangian relaxation is a powerful bounding technique that has been applied successfully to manynp hard combinatorial optimization problems the basic idea is to see annp hard problem as an easy to solve problem complicated by a number of nasty side constraints we show that reformulating nasty inequality constraints as equalities by using slack variables leads to stronger lower bounds the trick is widely applicable but we focus on a broad class of machine scheduling problems for which it is particularly useful we provide promising computational results for three problems belonging to this class for which lagrangian bounds have appeared in the literature the single machine problem of minimizing total weighted completion time subject to precedence constraints the two machine flow shop problem of minimizing total completion time and the single machine problem of minimizing total weighted tardiness

moving least square ritz method for vibration analysis of plates this paper presents a novel numerical method the moving least square ritz method mls ritz for free vibration analysis of classical thin plates the proposed method utilizes the strength of the moving least square approach to define the ritz trial function for the transverse displacement of the plates a set of points is pre selected on the calculation domain of a plate that forms the basis for the mls ritz trial function the edge support conditions of the plate are satisfied by forcing the boundary points to meet the geometric boundary conditions of the plate via a point substitution technique virtual points points outside the plate domain are introduced for clamped edges to improve the convergence and accuracy of the calculations square and right angled isosceles triangular plates of various combinations of edge support conditions are selected to examine the validity and accuracy of the mls ritz method extensive convergence studies are carried out to investigate the influence of the mls mesh size the mls support radius the number of gaussian integration points and the shape of the mls weight function on the proposed method comparing with the existing ritz methods the mls ritz method is highly stable and accurate and is extremely flexible for dealing with plates of arbitrary shapes and boundary conditions

axisymmetric vibration of circular plates and its analog in elliptical plates using characteristic orthogonal polynomials the axisymmetric vibration of circular plates and its analog in elliptic plates with clamped simply supported and free boundary conditions are investigated using boundary characteristic orthogonal polynomials in the rayleigh ritz method modified polar coordinates are employed to analyze the vibration of elliptical plates with circular plates as a special case axisymmetric vibration of circular plates and its analog in elliptical plates with concentric nodal elipses require only one dimensional shape functions in the rayleigh ritz method the first six natural frequencies and the parameters associated with nodal ellipses are tabulated

vibration analysis of arbitrarily shaped plates using beam characteristic orthogonal polynomials in the semi analytical finite strip method abstract a semi analytical finite strip method mapping arbitrarily shaped plates into a natural co ordinate plane using serendipity functions is presented the product of normalized beam characteristic orthogonal polynomials and hermitian polynomials form the displacement function for the strip in the natural co ordinate domain flexural free vibration analysis of various shaped plates is performed results show that as long as the plate is modelled by high enough degree mapping functions for the specific applications requested the flexural frequencies obtained are in excellent agreement with those found in the literature

numerical convergence of simple and orthogonal polynomials for the unilateral plate buckling problem using the rayleigh ritz method unilateral buckling is a contact problem whereby buckling is confined to take place in only one lateral direction for plate structures this can occur when a thin steel plate is juxtaposed with a rigid concrete medium and the steel may only buckle locally away from the concrete core this paper investigates the use of simple and orthogonal polynomials in the rayleigh ritz method for unilateral plate buckling the orthogonal polynomials used are the classical chebyshev types 1 and 2 legrende hermite and laguerre the study presents a comparison between the efficiency of the polynomial based displacement functions with regard to elastic bilateral and unilateral plate buckling where efficiency is measured as a function of their convergence characteristics some buckling solutions for plates with varying boundary conditions and in plane shear loads are also provided as an illustration copyright 1999 john wiley sons ltd

approximation bounds for a general class of precedence constrained parallel machine scheduling problems an important class of scheduling problems concerns parallel machines and precedence constraints we consider precedence delays which associate with each precedence constraint a certain amount of time that must elapse between the completion and start times of the corresponding jobs together with ordinary precedence constraints release dates and delivery times can be modeled in this manner we present a 4 approximation algorithm for the total weighted completion time objective for this general class of problems the algorithm is a rather simple form of list scheduling the list is in order of job midpoints derived from a linear programming relaxation our analysis unifies and simplifies that of a number of special cases heretofore separately studied while actually improving many of the former approximation results

minimizing weighted completion times with deadlines we examine a one machine scheduling problem whose objective is to minimize the weighted sum of completion times subject to deadline constraints we synthesize and extend current known theory and derive precedence relations between jobs these relationships along with tight new bounding criteria are incorporated in a branch and bound solution procedure

on partially inexact hss iteration methods for the complex symmetric linear systems in space fractional cnls equations the space fractional coupled nonlinear schrdinger cnls equations are discretized by an implicit conservative difference scheme with the fractional centered difference formula which is unconditionally stable the coefficient matrix of the discretized linear system is equal to the sum of a complex scaled identity matrix and a symmetric positive definite diagonal plus toeplitz matrix the hermitian and skew hermitian splitting hss method and the partially inexact hss pihss method are employed to solve the discretized linear system in the inner iteration processes of the hss method we only need to solve the linear sub systems associated with the hermitian part inexactly by the conjugate gradient cg method resulting in pihss iteration method theoretical analyses show that both hss and pihss methods are unconditionally convergent numerical examples are given to demonstrate the effectiveness of the hss iteration and the pihss iteration

from the space time fractional integral of the continuous time random walk to the space time fractional diffusion equations a short proof and simulation abstract in this paper i prove the relation between the integral equation of the continuous time random walk ctrw and the space time fractional diffusion equations by using the definitions of the weyl fractional derivatives and integrals i generalize a transformation theorem between the independent variables of the solution of the space time fractional diffusion equation stfde and the solution of the space time fractional fokker planck equation stffpe i simulate the symmetric and the non symmetric random walks for the two mentioned models i use the asymptotic behavior of the mittag leffler function for generating the waiting time random variable and use the levy flight distribution function to generate the jump width random variable for the both models the simulation results are investigated for different values of the space and time fractional orders

two agent scheduling to minimize the total cost abstract two agents each having his own set of jobs compete to perform their own jobs on a common processing resource each job of the agents has a weight that specifies its importance the cost of the first agent is the maximum weighted completion time of his jobs while the cost of the second agent is the total weighted completion time of his jobs we consider the scheduling problem of determining the sequence of the jobs such that the total cost of the two agents is minimized we provide a 2 approximation algorithm for the problem show that the case where the number of jobs of the first agent is fixed is np hard and devise a polynomial time approximation scheme for this case

the constrained minimum weighted sum of job completion times problem we consider the problem of minimizing the weighted sum of job completion times on a single machine subject to certain job weights with an additional side constraint on the weighted sum of job completion times with respect to different job weights this problem is np hard and we provide a polynomial time approximation scheme for this problem our method is based on lagrangian relaxation mixed with carefully guessing the positions of certain jobs in the schedule

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

free vibration of regular polygonal plates with simply supported edges the free vibration of regular polygonal plates with simply supported edges is studied by the dynamical analogy with membranes a regular polygonal membrane is formed on a rectangular membrane by fixing several segments with the reaction forces acting on all edges of an actual polygonal membrane regarded as unknown harmonic loads the stationary response of the membrane to these loads is expressed by the eigenfunctions of the extended rectangular membrane without internal supports the force distributions along the edges are expanded into fourier sine series with unknown coefficients and the homogeneous equations for the coefficients are derived by restraint conditions on the edges the natural frequencies and the mode shapes of the actual membrane are determined by calculating the eigenvalues and eigenvectors of the equations the method is applied to an equilateral triangular through a regular decagonal membrane the natural frequencies and mode shapes are calculated numerically and the effect of the shape of membrane is discussed the numerical values obtained for polygonal membranes are immediately converted into those of simply supported polygonal plates

transverse vibrations of a trapezoidal cantilever plate of variable thickness n atural frequencies of a trapezoidal cantilever plate of variable thickness which model an aircraft wing structure approximately are determined using energy techniques characteristic orthogonal polynomials in two variables are constructed to describe the structural deflections which are used in the rayleigh ritz method to obtain the natural frequencies the fundamental natural frequencies for different parameter values are also obtained using a deflection function containing an optimized exponent the first technique can be used to obtain the natural frequencies and corresponding mode shapes for the preliminary design of aircraft wing structures

single machine scheduling polyhedra with precedence constraints we consider nonpreemptive single machine scheduling subject to precedence constraints we define feasible schedules by the vector of the job completion times and study the structure of the convex hull of all feasible schedules called the scheduling polyhedron p we derive classes of valid inequalities for p and necessary and sufficient conditions under which they are facet inducing our main result is a complete description of the minimal linear system defining p when the precedence constraints are series parallel moreover this system consists of two classes of facet inducing inequalities associated with series and parallel compositions respectively if the precedence constraints are not series parallel we present another class of facet inducing inequalities for p associated with induced z subgraphs we also show that the convex hull of all preemptive feasible schedules is identical to p if and only if the precedence constraints form an out forest

single machine scheduling with precedence constraints we discuss the problem of sequencing precedence constrained jobs on a single machine to minimize the average weighted completion time this problem has attracted much attention in the mathematical programming community since sidney s pioneering work in 1975 sidney j b 1975 decomposition algorithms for single machine scheduling with precedence relations and deferral costs operations research23 283 298 we look at the problem from a polyhedral perspective and uncover a relation between sidney s decomposition theorem and different linear programming relaxations more specifically we present a generalization of sidney s result which particularly allows us to reason that virtually all known 2 approximation algorithms are consistent with his decomposition moreover we establish a connection between the single machine scheduling problem and the vertex cover problem indeed in the special case of series parallel precedence constraints we prove that the sequencing problem can be seen as a special case of the vertex cover problem we also argue that this result is true for general precedence constraints if one can show that a certain integer program represents a valid formulation of the sequencing problem finally we give a 3 2 approximation algorithm for two dimensional partial orders and we also provide a characterization of the active inequalities of a linear programming relaxation in completion time variables

structure of a simple scheduling polyhedron in a one machine nonpreemptive scheduling problem the feasible schedules may be defined by the vector of the corresponding job completion times for given positive processing times the associated simple scheduling polyhedronp is the convex hull of these feasible completion time vectors the main result of this paper is a complete description of the minimal linear system definingp we also give a complete combinatorial description of the face lattice ofp and a simple o n logn separation algorithm this algorithm has potential usefulness in cutting plane type algorithms for more difficult scheduling problems

the free flexural vibration of right triangular isotropic and orthotropic plates abstract a simple straighforward rayleigh ritz analysis is given for the determination of an eigenproblem for the free flexural vibration of thin right triangular plates having any combination of the classical free simply supported or clamped boundary conditions simple polynomials are used as the admissible functions and a recurrence relationship facilitates the evaluation of the necessary integrals the analysis is developed for specially orthotropic plates but numerical results are given primarily for the isotropic case

a polyhedral study of the cardinality constrained knapsack problem a cardinality constrained knapsack problem is a continuous knapsack problem in which no more than a specified number of nonnegative variables are allowed to be positive this structure occurs for example in areas such as finance location and scheduling traditionally cardinality constraints are modeled by introducing auxiliary 0 1 variables and additional constraints that relate the continuous and the 0 1 variables we use an alternative approach in which we keep in the model only the continuous variables and we enforce the cardinality constraint through a specialized branching scheme and the use of strong inequalities valid for the convex hull of the feasible set in the space of the continuous variables to derive the valid inequalities we extend the concepts of cover and cover inequality commonly used in 0 1 programming to this class of problems and we show how cover inequalities can be lifted to derive facet defining inequalities we present three families of non trivial facet defining inequalities that are lifted cover inequalities finally we report computational results that demonstrate the effectiveness of lifted cover inequalities and the superiority of the approach of not introducing auxiliary 0 1 variables over the traditional mip approach for this class of problems

computational geometry an introduction from the reviews this book offers a coherent treatment at the graduate textbook level of the field that has come to be known in the last decade or so as computational geometry the book is well organized and lucidly written a timely contribution by two founders of the field it clearly demonstrates that computational geometry in the plane is now a fairly well understood branch of computer science and mathematics it also points the way to the solution of the more challenging problems in dimensions higher than two

application of a series type method to vibration of orthotropic rectangular plates with mixed boundary conditions the object of this paper is to show an application of a series type method to the free vibration of an orthotropic rectangular plate with mixed boundary conditions the rectangular plate considered is elastically constrained or clamped along a few parts of its edge and simply supported on the remainder a frequency equation is derived to accommodate rectangular orthotropy of the plate by the extension of a previously developed method and subsequent algebraic manipulation leads to the improved equation yielding natural frequencies of the plate with very good accuracy the method is demonstrated for numerical examples where one two or three parts are constrained along the boundary of the square plate and the effects of varying constraint and orthotropic parameters on the natural frequencies and mode shapes are studied

anomalous diffusion modeling by fractal and fractional derivatives this paper makes an attempt to develop a fractal derivative model of anomalous diffusion we also derive the fundamental solution of the fractal derivative equation for anomalous diffusion which characterizes a clear power law this new model is compared with the corresponding fractional derivative model in terms of computational efficiency diffusion velocity and heavy tail property the merits and distinctions of these two models of anomalous diffusion are then summarized

three dimensional elasticity solutions to vibration of cantilevered skewed trapezoids an accurate three dimensional elasticity model for determining the free vibration response of skewed trapezoidal plates is presented the method is formulated on the basis of a linear small strain three dimensional elasticity theory with the ritz minimization procedure the solution method uses sets of uniquely defined one and twodimensional polynomial functions to approximate the trial displacements in the thickness and surface directions respectively these functions are orthogonally generated and have been proven to be highly efficient and numerically stable the proposed technique yields natural frequencies and mode shapes for a wide range of cantilevered skewed trapezoidal plates of arbitrary planform the accuracy of these results whenever possible is validated through comparison with the analytical and experimental data parametric investigations on the vibration behavior of cantilevered trapezoidal plates with respect to different thickness ratios skew angles and chord ratios have been carried out for the first time the presence of surface parallel symmetric thickness modes for these plates is demonstrated in vivid three dimensional mode shape plots

fundamental frequency of clamped plates with circularly periodic boundaries abstract a boundary perturbation method is developed to determine the fundamental frequency of vibrating plates the method is then applied to wavy star shape and polygonal plates with clamped boundary conditions approximate analytical solutions of the fundamental frequency are obtained with an accuracy of o e4 where e is the deviation from the unit circle

tight bounds for permutation flow shop scheduling in flow shop scheduling there are m machines and n jobs such that every job has to be processed on the machines in the fixed order 1 m in the permutation flow shop problem it is also required that each machine process the set of all jobs in the same order formally given n jobs along with their processing times on each machine the goal is to compute a single permutation of the jobs n n that minimizes the maximum job completion time makespan of the schedule resulting from the previously best known approximation guarantee for this problem was o m log m 1 2 sviridenko m 2004 a note on permutation flow shop problem ann oper res 129 247 252 in this paper we obtain an improved o min m1 2 n1 2 approximation algorithm for the permutation flow shop scheduling problem by finding a connection between the scheduling problem and the longest increasing subsequence problem our approximation ratio is relative to the lower bounds of maximum job length and maximum machine load and is the best possible such result this also resolves an open question from potts et al potts c d shmoys d williamson 1991 permutation vs nonpermutation flow shop schedules oper res lett 10 281 284 by algorithmically matching the gap between permutation and nonpermutation schedules we also consider the weighted completion time objective for the permutation flow shop scheduling problem using a natural linear programming relaxation and our algorithm for the makespan objective we obtain an o min m1 2 n1 2 approximation algorithm for minimizing the total weighted completion time improving on the previously best known guarantee of em for any constant e 0 smutnicki c 1998 some results of the worst case analysis for flow shop scheduling eur j oper res 109 66 87 we give a matching lower bound on the integrality gap of our linear programming relaxation

application of two dimensional orthogonal plate function to flexural vibration of skew plates abstract a set of two dimensional orthogonal plate functions is used as an admissible deflection function for the study of the flexural vibration of skew plates by the rayleigh ritz method from a prescribed starting function satisfying the boundary conditions the higher terms in the two dimensional orthogonal plate functions are generated by using the gram schmidt orthogonalization process the method is applied to obtain results for a few particular rhombic plates with different support conditions at various skew angles where possible the numerical results presented are compared with the values obtained by other numerical methods in the literature the results should be of considerable value and practical significance in design applications

vibration analysis of skew fibre reinforced composite laminated plates the vibration of skew laminated composite plates with simply supported and clamped edges is studied the skew plate is mapped into a unit square by linear transformation orthogonal polynomials are used with the ritz method to determine the natural frequencies the effects of skew angle and lamination scheme on natural frequencies are studied results are tabulated for different lamination schemes and compared to available studies in the literature

the free flexural vibration of isotropic and orthotropic general triangular shaped plates abstract the rayleigh ritz method is used with simple polynomials as admissible functions to obtain an eigenvalue equation for the free flexural vibration of thin isotropic and specially orthotropic general triangular plates the plates may have any combination of the classical free simply supported or clamped boundary conditions the convergence and accuracy of the solution is illustrated and numerical results are presented for a variety of isotropic plates and for orthotropic cantilever plates

robust structural topology optimization considering boundary uncertainties in classical deterministic topology optimization the effect of the possible boundary variations on the performance of the structure is not taken into account which may lead to designs that are very sensitive to manufacturing errors as a consequence the performance of the real structure may be far from optimal and even not meet the design requirements in the present paper structural topology optimization considering the uncertainty of boundary variations is considered via level set approach in order to make the optimal designs less sensitive to the possible boundary variations we choose the compliance and fundamental frequency of structure enduring the worst case perturbation as the objective function for ensuring the robustness of the optimal solution with use of the schwarz inequality the original bi level optimization problem is transformed to a single level optimization problem which can be solved efficiently numerical examples demonstrate the effectiveness of the proposed approach

buckling and vibration of polar orthotropic circular plate resting on winkler foundation buckling and vibrational behavior of polar orthotropic circular plates of linearly varying thickness is presented on the basis of classical plate theory the plate is resting on winkler type foundation an approximate solution has been obtained by ritz method which employs basis functions based upon static deflection of polar orthotropic plates the effect of elastic foundation and that of orthotropy on the natural frequency of plate has been illustrated for different values of taper parameter flexibility parameter in plane force and nodal diameter the critical buckling load for clamped and simply supported plates have been obtained a comparison of results with those available in literature has been presented

random walks with infinite spatial and temporal moments the continuous time random walk of montroll and weiss has been modified by scher and lax to include a coupled spatial temporal memory we treat novel cases for the random walk and the corresponding generalized master equation when combinations of both spatial and temporal moments of the memory are infinite the asymptotic properties of the probability distribution for being at any lattice site as a function of time and its variance are calculated the resulting behavior includes localized diffusive wavelike and levy s stable laws for the appropriate scaled variable we show that an infinite mean waiting time can lead to long time diffusive behavior while a finite mean waiting time is not sufficient to ensure the same

sharing supermodular costs we study cooperative games with supermodular costs we show that supermodular costs arise in a variety of situations in particular we show that the problem of minimizing a linear function over a supermodular polyhedron a problem that often arises in combinatorial optimization has supermodular optimal costs in addition we examine the computational complexity of the least core and least core value of supermodular cost cooperative games we show that the problem of computing the least core value of these games is strongly np hard and in fact is inapproximable within a factor strictly less than 17 16 unless p np for a particular class of supermodular cost cooperative games that arises from a scheduling problem we show that the shapley value which in this case is computable in polynomial time is in the least core while computing the least core value is np hard

numerical experiments on the determination of natural frequencies of transverse vibrations of rectangular plates of non uniform thickness abstract a comparison of natural frequencies of transverse vibration of thin rectangular plates of non uniform thickness with different combinations of boundary conditions is presented in this paper as obtained by using the following methodologies 1 the rayleigh ritz method with characteristic orthogonal polynomial shape functions 2 the rayleigh ritz method with a shape function which includes two exponents that are to be determined by minimizing the fundamental frequency coefficient 3 the optimized kantorovich method which has been proposed rather recently 4 the finite element method the results are presented in tabular form and discussed

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

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

free transverse vibrations of thin plates with discontinuous boundary conditions vibrations of circular and rectangular plates clamped on part of the boundary and simply supported along the remainder are analyzed by means of a method of perturbation of boundary conditions this approach appears to be simple and straightforward giving excellent results for the first mode and its versatility permits to extend it to higher modes of vibration without difficulty furthermore it is shown that the fundamental frequency coefficient can also be determined using a modified galerkin approach and very simple polynomial coordinate functions which yield good engineering accuracy

a polyhedral approach to single machine scheduling problems we report new results for a time indexed formulation of nonpreemptive single machine scheduling problems we give complete characterizations of all facet inducing inequalities with integral coefficients and right hand side 1 or 2 for the convex hull of the set of feasible partial schedules i e schedules in which not all jobs have to be started furthermore we identify conditions under which these facet inducing inequalities are also facet inducing for the original polytope which is the convex hull of the set of feasible complete schedules i e schedules in which all jobs have to be started to obtain insight in the effectiveness of these classes of facet inducing inequalities we develop a branch and cut algorithm based on them we evaluate its performance on the strongly np hard single machine scheduling problem of minimizing the weighted sum of the job completion times subject to release dates

decompositions network flows and a precedence constrained single machine scheduling problem we present an in depth theoretical algorithmic and computational study of a linear programming lp relaxation to the precedence constrained single machine scheduling problem 1 prec s jw jc jto minimize a weighted sum of job completion times on the theoretical side we study the structure of tight parallel inequalities in thelp relaxation and show thatevery permutation schedule that is consistent with sidney s decomposition has total cost no more than twice the optimum on the algorithmic side we provide a parametric extension to sidney s decomposition and show that a finest decomposition can be obtained by essentially solving a parametric minimum cut problem finally we report results obtained by an algorithm based on these developments on randomly generated instances with up to 2 000 jobs

optimal mechanism design for a sequencing problem with two dimensional types we study the design of mechanisms for a sequencing problem where the types of job agents consist of processing times and waiting costs that are private to the jobs in the bayes nash setting we seek to find a sequencing rule and incentive compatible payments that minimize the total expected payments that have to be made to the agents it is known that the problem can be efficiently solved when jobs have single dimensional types here we address the problem with two dimensional types we show that the problem can be solved in polynomial time by linear programming techniques answering an open problem formulated by heydenreich et al our implementation is randomized and truthful in expectation remarkably it also works when types are correlated across jobs the main steps are a compactification of an exponential size linear programming formulation and a convex decomposition algorithm that allows us to implement the optimal linear programming solution in addition by means of computational experiments we generate some new insights into the implementability in different equilibria

flexural vibration of polygonal plates using characteristic orthogonal polynomials in two variables a set of characteristic orthogonal polynomials in two variables is used as deflection functions to obtain the natural frequencies and mode shapes of polygonal plates by the rayleigh ritz method the set of orthogonal polynomials is constructed by employing the gram schmidt orthogonalization procedure the first six natural frequencies are numerically evaluated for triangular plates of different configurations by using these orthogonal functions and the corresponding mode shapes are plotted results are compared with those obtained previously by other methods

langevin equations for continuous time levy flights we consider the combined effects of a power law l evy step distribution characterized by the step index f and a power law waiting time distribution characterized by the time index g on the long time behavior of a random walker the main point of our analysis is a formulation in terms of coupled langevin equations which allows in a natural way for the inclusion of external force fields in the anomalous case for f2 and g1 the dynamic exponent z locks onto the ratio f g drawing on recent results on l evy flights in the presence of a random force field we also find that this result is independent of the presence of weak quenched disorder for d below the critical dimension mathit d mathit c 2f 2 the disorder is relevant corresponding to a nontrivial fixed point for the force correlation function