derived category automorphisms from mirror symmetry inspired by the homological mirror symmetry conjecture of kontsevich 30 we construct new classes of automorphisms of the bounded derived category of coherent sheaves on a smooth quasi projective variety msc 2000 18e30 14j32

spatiotemporal complexity of the cubic quintic nonlinear schrodinger equation the integrability of the cubic quintic nonlinear schrodinger equation is investigated numerically by analytically studying the linear stability of the homogeneous state and numerically solving such a continuum hamiltonian dynamic system the authors show that the quintic nonlinear term leads to a spatiotemporal complexity of wave fields and illustrate that this behaviour is associated with the stochastic partition of energy in fourier modes in addition they show the presence of the stochastic motion is due to the homoclinic orbit crossings

fast joint estimation of silhouettes and dense 3d geometry from multiple images we propose a probabilistic formulation of joint silhouette extraction and 3d reconstruction given a series of calibrated 2d images instead of segmenting each image separately in order to construct a 3d surface consistent with the estimated silhouettes we compute the most probable 3d shape that gives rise to the observed color information the probabilistic framework based on bayesian inference enables robust 3d reconstruction by optimally taking into account the contribution of all views we solve the arising maximum a posteriori shape inference in a globally optimal manner by convex relaxation techniques in a spatially continuous representation for an interactively provided user input in the form of scribbles specifying foreground and background regions we build corresponding color distributions as multivariate gaussians and find a volume occupancy that best fits to this data in a variational sense compared to classical methods for silhouette based multiview reconstruction the proposed approach does not depend on initialization and enjoys significant resilience to violations of the model assumptions due to background clutter specular reflections and camera sensor perturbations in experiments on several real world data sets we show that exploiting a silhouette coherency criterion in a multiview setting allows for dramatic improvements of silhouette quality over independent 2d segmentations without any significant increase of computational efforts this results in more accurate visual hull estimation needed by a multitude of image based modeling approaches we made use of recent advances in parallel computing with a gpu implementation of the proposed method generating reconstructions on volume grids of more than 20 million voxels in up to 4 41 seconds

optimization engineering techniques for the exact solution of np hard combinatorial optimization problems abstract the design of effective exact enumerative algorithms for finding the optimal solution of a given np hard combinatorial optimization problem whose mathematical model is given by an integer linear program is considered the commonly used approaches i e dynamic programming branch and bound branch and cut and branch and price are shortly described since the most effective algorithm to be used for finding the optimal solution of a given problem strongly depends on the specific instance to be solved then the best results are often obtained by using hybrid algorithms i e by combining different approaches according to what can be called an optimization engineering technique to illustrate the above mentioned approach the well known 0 1 knapsack problem asymmetric travelling salesman problem and 2 constraint bin packing problem are considered

parallel approximation algorithms for bin packing we study the parallel complexity of polynomial heuristics for the bin packing problem we show that some well known and simple moethods like first fit decreasing are p complete and it is hence very unlikely that they can be efficiently parallelized on the other hand we exhibit an optimal nc algorithm that achieves the same performance bound as does ffd finally we discuss parallelization of polynomial approximation algorithms for bin packing based on discretization

numerical analysis of free vibrations of laminated composite conical and cylindrical shells discrete singular convolution dsc approach a numerical study on the free vibration analysis for laminated conical and cylindrical shell is presented the analysis is carried out using love s first approximation thin shell theory and solved using discrete singular convolution dsc method numerical results in free vibrations of laminated conical and cylindrical shells are presented graphically for different geometric and material parameters free vibrations of isotropic cylindrical shells and annular plates are treated as special cases the effects of circumferential wave number number of layers on frequencies characteristics are also discussed the numerical results show that the present method is quite easy to implement accurate and efficient for the problems considered

geometry of the modulational instability iii homoclinic orbits for the periodic sine gordon equation in this paper the homoclinic geometric structure of the integrable sine gordon equation under periodic boundary conditions is developed specifically focus is given to orbits homoclinic to n tori simple examples of such homoclinic orbits are constructed and a physical interpretation of these states is given a labeling is provided which identifies and catalogues all such orbits these orbits are related in a one to one manner to linearized instabilities explicit formulas for all homoclinic orbits are given in terms of backlund transformations

periodic and chaotic behaviour in a reduction of the perturbed korteweg de vries equation the dynamical behaviour of a reduction of the forced and damped korteweg de vries equation is studied numerically chaos arising from subharmonic instability and homoclinic crossings are observed both period doubling bifurcations and the melnikov sequence of subharmonic bifurcations are found and lead to chaotic behaviour here characterised by a positive lyapunov exponent supporting theoretical analysis includes the construction of periodic solutions and homoclinic orbits and their behaviour under perturbation using melnikov functions

fully dynamic planarity testing with applications this paper introduces compressed certificates for planarity biconnectivity and triconnectivity in planar graphs and proves many structural properties of certificates in planar graphs as an application of our compressed certificates we develop efficient dynamic planar algorithms in particular we consider the following three operations on a planar graph g i insert an edge if the resultant graph remains planar ii delete an edge and iii test whether an edge could be added to the graph without violating planarity we show how to support each of the above operations in o n 2 3 time where n is the number of vertices in the graph the bound for tests and deletions is worst case while the bound for insertions is amortized this is the first algorithm for this problem with sub linear running time and it affirmatively answers a question posed in epstein et al 1992 we use our compressed certificates for biconnectivity and triconnectivity to maintain the biconnected and triconnected components of a dynamic planar graph the time bounds are the same o n 2 3 worst case time per edge deletion o n 2 3 amortized time per edge insertion and o n 2 3 amortized time per edge insertion and o n 2 3 worst case time to check whether two vertices are either biconnected or triconnected

homoclinic crossings and pattern selection the correlations between a homoclinic orbit hmo and coherent patterns in the nonlinear schr odinger model are discussed in a hamiltonian situation two independent patterns are revealed to exist one corresponds to a motion within an hmo and the other outside of an hmo the study further illustrates when the hamiltonian constraint is released the significance of an hmo on the patterns dynamics by presenting the irregular hmo crossings and the resulting chaotic selections between the patterns

modeling of biological population problems using the element free kp ritz method a degenerate parabolic equation arising in the spatial diffusion of biological population is analyzed using the mesh free kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes effectiveness of the mesh free kp ritz method for biological population model is investigated by numerical examples in this paper the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

the binary network flow problem is logspace complete for p abstract it is shown that the problem of whether the maximum flow in a given network exceeds a given natural number is logspace many one complete for p if the edge capacities are presented in binary even if the problem is restricted to acyclic graphs this improves a result by goldschlager et al 1982 that this problem is logspace turing complete for p

influence of boundary conditions on the frequency characteristics of a rotating truncated circular conical shell the influence of boundary conditions on the frequency characteristics of a rotating conical shell is studied using the galerkin method the results obtained include the relationships between the frequency parameter and circumferential wavenumber and between the frequency parameter and rotating velocity at various cone angles under different boundary conditions the variation of the frequency characteristics at various vibrational modes is also shown in order to validate the present analysis several comparisons of the numerical results with those published are made one comparison is for an infinitely long rotating cylindrical shell other comparisons are for the non rotating conical shells as is expected these comparisons show very good agreement

solving airline crew scheduling problems by branch and cut the crew scheduling problem is one that has been studied almost continually for the past 40 years but all prior approaches have always approximated the problem of finding an optimal schedule for even the smallest of an airline s fleets the problem is especially important today since costs for flying personnel of major u s carriers have grown and now often exceed 1 3 billion a year and are the second largest item next to fuel cost of the total operating cost of major u s carriers thus even small percentage savings amount to substantial dollar amounts we present a branch and cut approach to solving to proven optimality large set partitioning problems arising within the airline industry we first provide some background related to this important application and then describe the approach for solving representative problems in this problem class the branch and cut solver generates cutting planes based on the underlying structure of the polytope defined by the convex hull of the feasible integer points and incorporates these cuts into a tree search algorithm that uses automatic reformulation procedures heuristics and linear programming technology to assist in the solution numerical experiments are reported for a sample of 68 large scale real world crew scheduling problems these problems include both pure set partitioning problems and set partitioning problems with side constraints these base constraints represent contractual labor requirements and have heretofore not been represented explicitly in the construction of crew schedules thus making it impossible to provide any measure of how far the obtained solution was from optimality an interesting result of obtaining less costly schedules is that the crews themselves are happier with the schedules because they spend more of their duty time flying than waiting on the ground

dynamic properties of cubic nonlinear schrodinger equation with varying nonlinear parameter the dynamic properties of the cubic nonlinear schrodinger equation are investigated numerically using the symplectic scheme euler centred scheme we discuss the dynamic behaviour of the cubic nonlinear schrodinger equation with varying nonlinear parameter the results show that the system exhibits regular recurrence for weakly nonlinearity we also illustrate that the system will exhibit varying dynamic behaviour with increasing nonlinear parameter i e the system will show the homoclinic orbit hmo crossing quasi recurrence pseudorecurrence irregular motion or stochastic motion for a strongly nonlinear constants

on the use of orthogonal polynomials in the rayleigh ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates series composed of recently proposed orthogonal polynomial functions are used in the rayleigh ritz method to generate results for a number of flexural vibration and buckling problems for rectangular isotropic and orthotropic plates it is demonstrated that the approach yields excellent results not only for natural frequencies and buckling loads but also for the more sensitive mode shape bending moment and shear force distribution problem

the free vibrations of tapered rectangular plates using a new set of beam functions with the rayleigh ritz method abstract in19991999 academic pressacademic pressthis paper the free vibrations of a wide range of non uniform rectangular plates in one or two directions are considered the domain of the plate is bounded by copyright x 1a a and y 1b b in rectangular co ordinates the thickness of the plate is continuously varying and proportional to the power functionxsyt a variety of tapered rectangular plates can be described by giving the taper factors s and t different values s and t may be given arbitrary real numbers if both 1 0 and 1 0 or arbitrary non negative numbers if 1 0 or 1 0 the uniform rectangular plate is a special case by letting both s and t equal to zero a new set of admissible functions which are the static solutions of the tapered beam or a strip taken from the tapered rectangular plate under an arbitrary static load expanded into a taylor series is developed unlike conventional admissible functions the set of static beam functions will vary appropriately with the thickness variation of the plate the eigenfrequency equation is obtained by the use of the rayleigh ritz method a general computer program has been compiled and some numerical results are tabulated on the basis of comparison with available results in the literature it is shown that the first few eigenfrequencies can be obtained with good accuracy by using only a small number of terms of the static beam functions

i o efficient algorithms for the minimum cut problem on unweighted undirected graphs the problem of finding the minimum cut of an undirected unweighted graph is studied on the external memory model first a lower bound of e v sort v on the number of i os is shown for the problem where v is the number of vertices and e is the number of edges then the following are presented for m b 2 1 a minimum cut algorithm that uses o c log e rm msf v e frac v b rm sort v i os here msf v e is the number of i os needed to compute a minimum spanning tree of the graph and c is the value of the minimum cut the algorithm performs better on dense graphs than the algorithm of 7 which requires o e c 2 v log v c i os when executed on the external memory model for a fat graph for 0 the maximum tree packing of the graph is at least 1 c 2 our algorithm computes a minimum cut in o c loge msf v e sort e i os 2 a randomized algorithm that computes minimum cut with high probability in o c log e cdot rm msf v e rm sort e log 2 v frac v b rm sort v log v i os 3 a 2 e minimum cut algorithm that requires o e v msf v e i os and performs better on sparse graphs than our exact minimum cut algorithm

facet identification for the symmetric traveling salesman polytope several procedures for the identification of facet inducing inequalities for the symmetric traveling salesman polytope are given an identification procedure accepts as input the support graph of a point which does not belong to the polytope and returns as output some of the facet inducing inequalities violated by the point a procedure which always accomplishes this task is calledexact otherwise it is calledheuristic we give exact procedures for the subtour elimination and the 2 matching constraints based on the gomory hu and padberg rao algorithms respectively efficient reduction procedures for the input graph are proposed which accelerate these two algorithms substantially exact and heuristic shrinking conditions for the input graph are also given that yield efficient procedures for the identification of simple and general comb inequalities and of some elementary clique tree inequalities these procedures constitute the core of a polytopal cutting plane algorithm that we have devised and programmed to solve a substantial number of large scale problem instances with sizes up to 2392 nodes to optimality

vibration of pretwisted cantilever shallow conical shells abstract this paper presents a mathematical model to investigate the effects of initial twist on the vibratory characteristics of cantilever shallow conical shells the energy functional is minimized according to the ritz procedure to arrive at the governing eigenvalue equation a set of orthogonally generated two dimensional polynomials associated with a basic function which accounts for the boundary expressions and constraints is introduced to approximate the in plane and transverse displacement amplitude functions the complete procedure has been automated to compute the vibration frequencies and mode shapes for exemplary problems in the numerical experiments the convergence of eigenvalues is confirmed by increasing the degrees of polynomials employed in the admissible shape functions to enhance the existing literature a set of first known frequency parameters is presented the paper highlights the important effects of angle of twist on the vibration frequencies and mode shapes of conical shells the fundamental physical frequency decreases monotonically for a longer conical shell the result shows that an increase in the angle of twist does not ensure higher torsional stiffness for a conical shell which is in contradiction with previous observation for a pretwisted beam or plate the symmetry of modes is absent when the angle of twist is non zero

solving the asymmetric travelling salesman problem with time windows by branch and cut many optimization problems have several equivalent mathematical models it is often not apparent which of these models is most suitable for practical computation in particular when a certain application with a specific range of instance sizes is in focus our paper addresses the asymmetric travelling salesman problem with time windows atsp tw from such a point of view the real world application we aim at is the control of a stacker crane in a warehouse we have implemented codes based on three alternative integer programming formulations of the atsp tw and more than ten heuristics computational results for real world instances with up to 233 nodes are reported showing that a new model presented in a companion paper outperforms the other two models we considered at least for our special application and that the heuristics provide acceptable solutions

parallel algorithms for minimum cuts and maximum flows in planar networks algorithms are given that compute maximum flows in planar directed networks either in o log n 3 parallel time using o n 4 processors or o log n 2 parallel time using o n 6 processors the resource consumption of these algorithms is dominated by the cost of finding the value of a maximum flow when such a value is given or when the computation is on an undirected network the bound is o log n 2 time using o n 3 processors no efficient parallel algorithm is known for the maximum flow problem in general networks

bipartite perfect matching is in quasi nc we show that the bipartite perfect matching problem is in quasi mathsf nc 2 that is it has uniform circuits of quasi polynomial size n o log n and o log 2 n depth previously only

vibrational responses of antisymmetric angle ply laminated conical shell by the methods of polynomial based differential quadrature and fourier expansion based differential quadrature abstract vibrational response of antisymmetric angle ply laminated conical shell based on transverse shear deformation theory is analyzed in this research the equilibrium and corresponding boundary equations including the extension coupling terms are derived in terms of displacement and rotational components two types of differential quadrature methods dqm including polynomial based differential quadrature pdq and fourier expansion based differential quadrature fdq are applied to convert the existing differential equations to algebraic equations after discretization of existing differential equations the eigenvalue equation system for the functional value in the whole domain is established and solved a series of numerical tests are carried out to validate the present approach that highly accurate results are obtained only few grid points finally the parametric studies are performed to illustrate the effects of different boundary conditions fiber angle and number of layers and also various aspect ratio of the shell including thickness to radius ratio length to radius on the frequency parameter

effects of initial twist and thickness variation on the vibration behaviour of shallow conical shells abstract a thorough computational investigation is presented into the effects of initial twist and thickness variation on the vibratory characteristics of cantilevered pretwisted thin shallow conical shells with generally varying thickness an energy approach with the ritz minimization procedure is employed to arrive at a governing eigenvalue equation the admissiblepb 2shape functions which comprise sets of mathematically complete two dimensional orthogonal polynomials and a basic function are introduced to account for the boundary constraints and to approximate the three dimensional displacements of the conical shell the effects of angle of twist thickness variation and geometric parameters on the vibration response are presented in a comprehensive parametric study which provides useful new design data selected vibration mode shapes are also included to enhance the existing literature it is found that an increase in the angle of twist does not necessarily increase the torsional stiffness on the contrary the fundamental frequencies is reduced in the present analysis it is also observed that non zero angle of twist and non uniform chordwise thickness variation cause the absent of vibration mode symmetry

implementing an efficient minimum capacity cut algorithm in this paper we present an efficient implementation of theo mn n2 logn time algorithm originally proposed by nagamochi and ibaraki 1992 for computing the minimum capacity cut of an undirected network to enhance computation various ideas are added so that it can contract as many edges as possible in each iteration to evaluate the performance of the resulting implementation we conducted extensive computational experiments and compared the results with that of padberg and rinaldi s algorithm 1990 which is currently known as one of the practically fastest programs for this problem the results indicate that our program is considerably faster than padberg and rinaldi s program and its running time is not significantly affected by the types of the networks being solved

differential quadrature and rayleigh ritz methods to determine the fundamental frequencies of simply supported rectangular plates with linearly varying thickness abstract in this paper differential quadrature and rayleigh ritz methods are presented for computation of the fundamental frequency of simply supported homogeneous isotropic thin rectangular plates with the thickness tapering linearly in one direction the complete analytical formulation and solution procedure is presented for both methods results obtained by these two methods are compared with available results in the literature and by the finite element method effects of the level of discretization aspect and taper ratios are also presented

a new approach to the minimum cut problem this paper present a new approach to finding minimum cuts in undirected graphs the fundamental principle is simple the edges in a graph s minimum cut form an extremely small fraction of the graph s edges using this idea we give a randomized strongly polynomial algorithm that finds the minimum cut in an arbitrarily weighted undirected graph with high probability the algorithm runs in o n 2 log 3 n time a significant improvement over the previous o mn time bounds based on maximum flows it is simple and intuitive and uses no complex data structures our algorithm can be parallelized to run in rnc with n 2 processors this gives the first proof that the minimum cut problem can be solved in rnc the algorithm does more than find a single minimum cut it finds all of them with minor modifications our algorithm solves two other problems of interest our algorithm finds all cuts with value within a multiplicative factor of of the minimum cut s in expected o n 2 time or in rnc with n 2 processors the problem of finding a minimum multiway cut of graph into r pieces is solved in expected o n 2 r 1 time or in rnc with n 2 r 1 processors the trace of the algorithm s execution on these two problems forms a new compact data structure for representing all small cuts and all multiway cuts in a graph this data structure can be efficiently transformed into the more standard cactus representing for minimum cuts

separating clique trees and bipartition inequalities having a fixed number of handles and teeth in polynomial time many important cutting planes have been discovered for the traveling salesman problem among them are the clique tree inequalities and the more general bipartition inequalities little is known in the way of exact algorithms for separating these inequalities in polynomial time in the size of the fractional point x which is being separated an algorithm is presented here that separates bipartition inequalities of a fixed number of handles and teeth which includes clique tree inequalities of a fixed number of handles and teeth in polynomial time

a branch and cut algorithm for the resolution of large scale symmetric traveling salesman problems an algorithm is described for solving large scale instances of the symmetric traveling salesman problem stsp to optimality the core of the algorithm is a polyhedral cutting plane procedure that exploits a subset of the system of linear inequalities defining the convex hull of the incidence vectors of the hamiltonian cycles of a complete graph the cuts are generated by several identification procedures that have been described in a companion paper whenever the cutting plane procedure does not terminate with an optimal solution the algorithm uses a tree search strategy that as opposed to branch and bound keeps on producing cuts after branching the algorithm has been implemented in fortran two different linear programming lp packages have been used as the lp solver the implementation of the algorithm and the interface with one of the lp solvers is described in sufficient detail to permit the replication of our experiments computational results are reported with up to 42 stsps with sizes rangin

a polyhedral approach to the asymmetric traveling salesman problem several branch and bound algorithms for the exact solution of the asymmetric traveling salesman problem atsp based on the assignment problem ap relaxation have been proposed in the literature these algorithms perform very well for some instances e g those with uniformly random integer costs but very poorly for others the aim of this paper is to evaluate the effectiveness of a branch and cut algorithm exploiting atsp specific facet defining cuts to be used to attack hard instances that cannot be solved by the ap based procedures from the literature we present new separation algorithms for some classes of facet defining cuts and a new variable pricing technique for dealing with highly degenerate primal lp problems a branch and cut algorithm based on these new results is designed and evaluated through computational analysis on several classes of both random and real world instances the outcome of the research is that on hard instances the branch and cut algorithm clearly outperforms the best ap based algorithms from the literature

implementing the dantzig fulkerson johnson algorithm for large traveling salesman problems dantzig fulkerson and johnson 1954 introduced the cutting plane method as a means of attacking the traveling salesman problem this method has been applied to broad classes of problems in combinatorial optimization and integer programming in this paper we discuss an implementation of dantzig et al s method that is suitable for tsp instances having 1 000 000 or more cities our aim is to use the study of the tsp as a step towards understanding the applicability and limits of the general cutting plane method in large scale applications

a p complete graph partition problem abstract the different than majority labelling dtml problem has a simple polynomial time sequential algorithm the labelling given by this algorithm is called the lexicographical first dtml in this paper we show that the lf dtml problem is p complete furthermore we show that even when restricted to planar graphs the lf dtml problem remains p complete

dynamical survey of the dual power zakharov kuznetsov burgers equation with external periodic perturbation abstract we investigate the dynamical behavior of the newly introduced dual power zakharov kuznetsov burgers equation using bifurcation theory of planar dynamical systems we study bifurcations of traveling wave solutions of the dual power zakharov kuznetsov burgers equation in presence and absence of viscosity effect in presence of an external periodic perturbation we discuss the periodic and chaotic motions of the perturbed dual power zakharov kuznetsov burgers equation by analyzing phase projection analysis time series analysis poincare section and sensitivity analysis the effect of viscosity plays an important role in the transition from chaotic motion to periodic motion of the perturbed dual power zakharov kuznetsov burgers equation

dynamic behaviors and soliton solutions of the modified zakharov kuznetsov equation in the electrical transmission line the modified zakharov kuznetsov mzk equation in the electrical transmission line is investigated in this paper different expressions on the parameters in the mzk equation are given by means of the hirota method bilinear forms and soliton solutions of the mzk equation are obtained linear stability analysis yields the instability condition for such soliton solutions we find that the soliton amplitude becomes larger when the inductance l and capacitance c 0 decrease phase plane analysis is conducted on the mzk equation for the properties at equilibrium points then we investigate the perturbed mzk equation which can be proposed when the external periodic force is considered both the weak and developed chaotic motions are observed our results indicate that the two chaotic motions can be manipulated with certain relation between the absolute values of nonlinear terms and the perturbed one we also find that the chaotic motions can be weakened with the absolute values of l and c 0 decreased

lower bounds in a parallel model without bit operations we define a natural and realistic model of parallel computation called the pram model without bit operations it is like the usual pram model the main difference being that no bit operations are provided it encompasses virtually all known parallel algorithms for weighted combinatorial optimization and algebraic problems in this model we prove that for some large enough constant b the mincost flow problem for graphs with n vertices cannot be solved deterministically or with randomization in sqrt n b expected time using 2 sqrt n b processors this is so even if we restrict every cost and capacity to be an integer nonnegative if it is a capacity of bitlength at most an for some large enough constant a a similar lower bound is also proved for the max flow problem it follows that these problems cannot be solved in our model deterministically or with randomization in omega n c expected time with 2 omega n c processors where c is an appropriate positive constant and n is the total bitlength of the input since these problems were known to be p complete this provides concrete support for the belief that p completeness implies high parallel complexity and for the p not nc conjecture our lower bounds also extend to the pram model with limited bit operations which provides instructions for parity and left or right shift by one bit our proof is based on basic algebraic geometry so we investigate if the algebrogeometric approach could also work for the p versus nc problem our results support this possibility and a close analysis of the limitation of our technique in this context suggests that such a proof of p not nc should somehow use geometric invariant theory in a deep way

vibrations of circular cylindrical shells theory and experiments in the present paper a method for analysing linear and nonlinear vibrations of circular cylindrical shells having different boundary conditions is presented the method is based on the sanders koiter theory displacement fields are expanded in a mixed double series based on harmonic functions and chebyshev polynomials simply supported and clamped clamped boundary conditions are analysed as well as connections with rigid bodies in the latter case experiments are carried out comparisons with experiments and finite element analyses show that the technique is computationally efficient and accurate in modelling linear vibrations of shells with different boundary conditions an application to large amplitude of vibration shows that the technique is effective also in the case of nonlinear vibration comparisons with the literature confirm the accuracy of the approach the method proposed is a general framework suitable for analysing vibration of circular cylindrical shells both in the case of linear and nonlinear vibrations r 2007 elsevier ltd all rights reserved

solution of large scale symmetric travelling salesman problems in this paper we report on a cutting plane procedure with which we solved symmetric travelling salesman problems of up to 1000 cities to optimality our implementation is based on a fast lp solver ibm s mpsx and makes effective use of polyhedral results on the symmetric travelling salesman polytope we describe the important ingredients of our code and give an extensive documentation of its computational performance

free vibration of a conical shell with variable thickness abstract an analysis is presented for the free vibration of a truncated conical shell with variable thickness by use of the transfer matrix approach the applicability of the classical thin shell theory is assumed and the governing equations of vibration of a conical shell are written as a coupled set of first order differential equations by using the transfer matrix of the shell once the matrix has been determined by quadrature of the equations the natural frequencies and the mode shapes of vibration are calculated numerically in terms of the elements of the matrix under any combination of boundary conditions at the edges the method is applied to truncated conical shells with linearly parabolically or exponentially varying thickness and the effects of the semi vertex angle truncated length and varying thickness on the vibration are studied

minimizing symmetric submodular functions we describe a purely combinatorial algorithm which given a submodular set functionf on a finite setv finds a nontrivial subseta ofv minimizingf a f v a this algorithm an extension of the nagamochi ibaraki minimum cut algorithm as simplified by stoer and wagner m stoer f wagner a simple min cut algorithm proceedings of the european symposium on algorithms esa 94 lncs 855 springer berlin 1994 pp 141 147 and by frank a frank on the edge connectivity algorithm of nagamochi and ibaraki laboratoire artemis imag universite j fourier grenbole 1994 minimizes any symmetric submodular function using o v 3 calls to a function value oracle 1998 the mathematical programming society inc published by elsevier science b v

small min cut polyhedra we study small min cut polyhedra for directed and undirected complete graphs we give the ideal descriptions of the polyhedra for undirected graphs with up to seven nodes and for directed graphs with up to five nodes and generalize the inequalities for complete graphs with arbitrary number of nodes the facial structure of the polyhedra turns out to be unexpectedly rich

diagnosing infeasibilities in network flow problems we consider the problem of finding a feasible flow in a directed networkg n a in which each nodei n has a supplyb i and each arc i j a has a zero lower bound on flow and an upper bounduij it is well known that this feasibility problem can be transformed into a maximum flow problem it is also well known that there is no feasible flow in the networkg if and only if there is a subsets of nodes such that the net supplies of the nodes ins exceeds the capacity of the arcs emanating froms such a sets is called a witness of infeasibility or simply awitness of the network flow problem in the case that there are many different witnesses for an infeasible problem a small cardinality witness may be preferable in practice because it is generally easier for the user to assimilate and may provide more guidance to the user on how to identify the cause of the infeasibility here we show that the problem of finding a minimum cardinality witness is np hard we also consider the problem of determining aminimal witness that is a witnesss such that no proper subset ofs is also a witness in this paper we show that we can determine a minimal witness by solving a sequence of at mostn maximum flow problems moreover if we use the preflow push algorithm to solve the resulting maximum flow problems and organize computations properly then the total time taken by the algorithm is comparable to that of solving a single maximum flow problem this approach determines a minimal cardinality witness in o n2m1 2 time using simple data structures and in o nm logn time using the standard implementation of the dynamic tree data structures we also show that the recognition version of the minimal witness problem is equivalent to a recognition version of a related problem known as theminimum rooted cut problem 1998 the mathematical programming society inc published by elsevier science b v

vibration characteristics of thin rotating cylindrical shells with various boundary conditions abstract an analysis is presented for the vibration characteristics of thin rotating cylindrical shells with various boundary conditions by use of fourier series expansion method based on sanders shell equations the governing equations of motion which take into account the effects of centrifugal and coriolis forces as well as the initial hoop tension due to rotating are derived the displacement field is expressed as a product of fourier series expressions which represents the axial modal displacements and trigonometric functions which represents the circumferential modal displacements stokes transformation is employed to derive the derivatives of the fourier series expressions then through the process of formula derivation an explicit expression of the exact frequency equation can be obtained for a thin rotating cylinder with classical boundary conditions of any type once the frequency equation has been determined the frequencies are calculated numerically to validate the present analysis comparisons between the results of the present method and previous studies are performed and very good agreement is achieved finally the method is applied to investigate the vibration characteristics of thin rotating cylindrical shells under various boundaries and the results are presented

numerical analysis of generalized regularized long wave equation using the element free kp ritz method abstract a numerical analysis of the generalized regularized long wave grlw equation by application of the element free kp ritz method is performed to approximate the displacement field an element free kernel particle estimation is employed and a system of nonlinear discrete equations is achieved by using the ritz minimization procedure to the energy expressions validation of the present numerical solutions with the exact results has been conducted by numerical examples and evidenced a good agreement

an efficient algorithm for the minimum capacity cut problem given a finite undirected graph with nonnegative edge capacities the minimum capacity cut problem consists of partitioning the graph into two nonempty sets such that the sum of the capacities of edges connecting the two parts is minimum among all possible partitionings the standard algorithm to calculate a minimum capacity cut due to gomory and hu 1961 runs in o n4 time and is difficult to implement we present an alternative algorithm with the same worst case bound which is easier to implement and which was found empirically to be far superior to the standard algorithm we report computational results for graphs with up to 2000 nodes

complex variable boundary element free method for two dimensional elastodynamic problems abstract we proposed a new direct meshless boundary integral equation technique the complex variable boundary element free method cvbefm based on the complex variable moving least squares cvmls approximation and the boundary element free method befm to study the two dimensional elastodynamic problems with the cvmls approximation the trial function of a two dimensional problem is formed with a one dimensional basis function the number of unknown coefficients in the trial function of the cvmls approximation is less than that in the trial function of the moving least squares mls approximation therefore it requires fewer nodes in the meshless method which formed from the cvmls approximation than that formed from the mls approximation with no lose of precision the laplace transform is used to formulate the boundary integral equations of the two dimensional elastodynamics and then the formulae of the cvbefm for two dimensional elastodynamic problems are derived the cvbefm is a direct numerical method in which the basic unknown quantities are the real solutions of the nodal variables moreover in the cvbefm the boundary conditions can be applied directly and easily that leads to a greater computational precision in this paper we selected a few numerical examples to illustrate the applicability of the cvbefm

approximating unweighted connectivity problems in parallel given an integer i k 0 can be achieved by an nc approximation algorithm this paper considers the more general case where k is polylogarithmic in the size of the input graph and presents the first nc approximation algorithm with a performance ratio of 1 924 for this case we also consider the vertex analogue of this problem in which we require k vertex connectivity instead of k edge connectivity we present the first nc approximation algorithm with a performance ratio of 1 931 for the special case where the input integer k is fixed to be 3 2001 elsevier science

minimum cuts in near linear time we significantly improve known time bounds for solving the minimum cut problem on undirected graphs we use a semiduality between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling techniques we give a randomized monte carlo algorithm that finds a minimum cut in an m edge n vertex graph with high probability in o m log 3 n time we also give a simpler randomized algorithm that finds all minimum cuts with high probability in o m log 3 n time this variant has an optimal rnc parallelization both variants improve on the previous best time bound of o n 2 log 3 n other applications of the tree packing approach are new nearly tight bounds on the number of near minimum cuts a graph may have and a new data structure for representing them in a space efficient manner

the complexity of markov decision processes we investigate the complexity of the classical problem of optimal policy computation in markov decision processes all three variants of the problem finite horizon infinite horizon discounted and infinite horizon average cost were known to be solvable in polynomial time by dynamic programming finite horizon problems linear programming or successive approximation techniques infinite horizon we show that they are complete for p and therefore most likely cannot be solved by highly parallel algorithms we also show that in contrast the deterministic cases of all three problems can be solved very fast in parallel the version with partially observed states is shown to be pspace complete and thus even less likely to be solved in polynomial time than the np complete problems in fact we show that most likely it is not possible to have an efficient on line implementation involving polynomial time on line computations and memory of an optimal policy even if an arbitrary amount of precomputation is allowed finally the variant of the problem in which there are no observations is shown to be np complete

efficient separation routines for the symmetric traveling salesman problem i general tools and comb separation this is the first of a series of two papers dedicated to efficient separation heuristics for violated inequalities in the context of solving to optimality instances of the traveling salesman problem via branch and cut in this paper we give the basic ideas behind these heuristics and design heuristics for comb separation the second paper will deal with more complex inequalities such as clique tree star or path and ladder inequalities and give computational results

free vibration analysis of conical shells via the element free kp ritz method in this paper we consider the free vibration analysis of thin conical shells under different boundary conditions the analysis is carried out using the element free kp ritz method the present study is based on the classical thin shell theory the kernel particle kp functions are employed in hybridized form with harmonic functions to approximate the two dimensional displacement field in order to examine the numerical stability of the present approach convergence studies are performed based on the influences of the support size and the number of nodes to verify the accuracy of this method comparisons of the present results are made with results available in the open literature this study also examines in detail the effects of semi vertex angles and boundary conditions on the frequency characteristics of the conical shells

dynamics of the generalized kp mew burgers equation with external periodic perturbation the generalized kadomtsevpetviashvili modified equal width burgers kp mew burgers equation is introduced for the first time the qualitative change of the traveling wave solutions of the kp mew burgers equation is studied using numerical simulations considering an external periodic perturbation the periodic and chaotic motions of the perturbed kp mew burgers equation are investigated by using the phase projection analysis time series analysis poincare section and bifurcation diagram the parameter a nonlinear coefficient plays a crucial role in the periodic motions and chaotic motions through period doubling route to chaos of the perturbed kp mew burgers equation

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

chaotic transport and integrable instabilities in a near integrable many particle hamiltonian lattice abstract this paper is a report of detailed numerical experiments on a large dimensional hamiltonian lattice which arises as a nearly integrable discretization of the periodic sine gordon equation through four different one parameter families of initial data we focus on the interplay between numerically observable near integrable behavior quantified by modern statistical diagnostics and the integrable pde solutions and phase space geometry associated with the initial data transitions are observed within each family from quasiperiodic behavior to chaotic motion which is sometimes accompanied by transport toward equipartition these transitions in the near integrable system are correlated with integrable features of the initial data in particular transitions from neutrally stable to exponentially unstable sine gordon solutions and associated homoclinic orbits geometrically these correspond to transitions from neutrally stable tori to whiskered tori our results indicate that 1 positive lyapunov exponents our messure of chaos in near integrable orbits coincide one to one with integrable pde instabilities and homoclinic orbits 2 the statistical transition to equipartition of energy on a long fixed timescale occurs only if but not necessarily if there are integrable instabilities and associated whiskered tori the rate of transport appears to depend on the amplitude of the homoclinic degrees of freedom 3 isolated cases of discreteness induced instabilities and action transport are observed these return to quasiperiodic flow at finer discretizations 4 a simple measure such as energy of the initial data is not an accurate predictor of chaotic or recurrent behavior one family of initial data exhibits as the energy increases alternating windows of quasiperiodic and chaotic orbits

a simple parallel algorithm for the maximal independent set problem two basic design strategies are used to develop a very simple and fast parallel algorithms for the maximal independent set mis problem the first strategy consists of assigning identical copies o

scan first search and sparse certificates an improved parallel algorithm for k vertex connectivity given a graph g v e a certificate of k vertex connectivity is an edge subset e subset e such that the subgraph v e is k vertex connected if and only if g is k vertex connected let n and m denote the number of vertices and edges a certificate is called sparse if it contains o kn edges for undirected graphs this paper introduces a graph search called the scan first search and shows that a certificate with at most k n 1 edges can be computed by executing scan first search k times in sequence on subgraphs of g for each of the parallel distributed and sequential models of computation the complexity of scan first search matches the best complexity of any graph search on that model in particular the parallel scan first search runs in o log n time using c n m processors on a crcw pram where c n m is the number of processors needed to find a spanning tree in each connected component in o log n time and the parallel certificate algorithm runs in o k log n time us

a taxonomy of problems with fast parallel algorithms the class nc consists of problems solvable very fast in time polynomial in log n in parallel with a feasible polynomial number of processors many natural problems in nc are known in this paper an attempt is made to identify important subclasses of nc and give interesting examples in each subclass the notion of nc 1 reducibility is introduced and used throughout problem r is nc 1 reducible to problem s if r can be solved with uniform log depth circuits using oracles for s problems complete with respect to this reducibility are given for many of the subclasses of nc a general technique the parallel greedy algorithm is identified and used to show that finding a minimum spanning forest of a graph is reducible to the graph accessibility problem and hence is in nc 2 solvable by uniform boolean circuits of depth o log 2 n and polynomial size the class logcfl is given a new characterization in terms of circuit families the class det of problems reducible to integer determinants is defined and many examples given a new problem complete for deterministic polynomial time is given namely finding the lexicographically first maximal clique in a graph this paper is a revised version of s a cook 1983 in proceedings 1983 intl found comut sci conf lecture notes in computer science vol 158 pp 78 93 springer verlag berlin new york

discrete and continuous models for partitioning problems recently variational relaxation techniques for approximating solutions of partitioning problems on continuous image domains have received considerable attention since they introduce significantly less artifacts than established graph cut based techniques this work is concerned with the sources of such artifacts we discuss the importance of differentiating between artifacts caused by discretization and those caused by relaxation and provide supporting numerical examples moreover we consider in depth the consequences of a recent theoretical result concerning the optimality of solutions obtained using a particular relaxation method since the employed regularizer is quite tight the considered relaxation generally involves a large computational cost we propose a method to significantly reduce these costs in a fully automatic way for a large class of metrics including tree metrics thus generalizing a method recently proposed by strekalovskiy and cremers ieee conference on computer vision and pattern recognition pp 1905 1911 2011

an nc algorithm for minimum cuts we show that the minimum cut problem for weighted undirected graphs can be solved in nc using three separate and independently interesting results the first is an m 2 n processor nc algorithm for finding a 2 epsilon approximation to the minimum cut the second is a randomized reduction from the minimum cut problem to the problem of obtaining a 2 epsilon approximation to the minimum cut this reduction involves a natural combinatorial set isolation problem that can be solved easily in rnc the third result is a derandomization of this rnc solution that requires a combination of two widely used tools pairwise independence and random walks on expanders we believe that the set isolation approach will prove useful in other derandomization problems the techniques extend to two related problems we describe nc algorithms finding minimum k way cuts for any constant k and finding all cuts of value within any constant factor of the minimum another application of these techniques yields an nc algorithm for finding a em sparse k connectivity certificate for all polynomially bounded values of k previously an nc construction was only known for polylogarithmic values of k

the maximum flow problem is log space complete for p the space complexity of the maximum flow problem is investigated it is shown that the problem is log space complete for deterministic polynomial time thus the maximum flow problem probably has no algorithm which needs only o logk n storage space for any constant k another consequence is that there is probably no fast parallel algorithm for the maximum flow problem

vibration of shallow conical shells with shear flexibility a first order theory a formulation of shear deformation theory implemented numerically for the prediction of vibratory characteristics of shallow conical shell panels is presented the derivation of thickness shear is assumed in a linear approximation the lame parameter for the transverse shear strain component which has previously been neglected is considered this consideration accounts for the replacement of a term in transverse strain distribution through the shell thickness which results in linear transverse shear strain distribution in contrast to the constant distribution hitherto known to researchers in this field the energy integral which incorporates the shear deformation and rotary inertia is minimized to derive the governing eigen matrix equation a set of benchmark frequency solutions is presented for two exemplary conical shells the cantilever and the fully clamped shells some selected mode shapes in terms of mid surface contour plots and three dimensional meshes are also illustrated

a branch and cut framework for the consistent traveling salesman problem abstract we develop an exact solution framework for the consistent traveling salesman problem this problem calls for identifying the minimum cost set of routes that a single vehicle should follow during the multiple time periods of a planning horizon in order to provide consistent service to a given set of customers each customer may require service in one or multiple time periods and the requirement for consistent service applies at each customer location that requires service in more than one time period this requirement corresponds to restricting the difference between the earliest and latest vehicle arrival times across the multiple periods to not exceed some given allowable limit we present three mixed integer linear programming formulations for this problem and introduce a new class of valid inequalities to strengthen these formulations the new inequalities are used in conjunction with traditional traveling salesman inequalities in a branch and cut framework we test our framework on a comprehensive set of benchmark instances which we compiled by extending traveling salesman instances from the well known tsplib library into multiple periods and show that instances with up to 50 customers requiring service over a 5 period horizon can be solved to guaranteed optimality our computational experience suggests that enforcing arrival time consistency in a multi period setting can be achieved with merely a small increase in total routing costs

a survey and comparison of discrete and continuous multi label optimization approaches for the potts model we present a survey and a comparison of a variety of algorithms that have been proposed over the years to minimize multi label optimization problems based on the potts model discrete approaches based on markov random fields as well as continuous optimization approaches based on partial differential equations can be applied to the task in contrast to the case of binary labeling the multi label problem is known to be np hard and thus one can only expect near optimal solutions in this paper we carry out a theoretical comparison and an experimental analysis of existing approaches with respect to accuracy optimality and runtime aimed at bringing out the advantages and short comings of the respective algorithms systematic quantitative comparison is done on the graz interactive image segmentation benchmark this paper thereby generalizes a previous experimental comparison klodt et al 2008 from the binary to the multi label case

periodic and chaotic behaviour in a reduced form of the perturbed generalized korteweg de vries and kadomtsev petviashvili equations abstract the dynamical behaviour of a reduced form of the perturbed generalized korteweg de vries and kadomtsev petviashvili equations extension of the korteweg de vries equation to two space variables are studied in this paper harmonic solutions of non resonance and primary resonance are obtained using the perturbation method chaotic motion under harmonic excitations is studied using the melnikov method a wide range of solutions for the reduced perturbed generalized korteweg de vries equations in which non linear phenomena appearing within transition from regular harmonic response periodic solutions to chaotic motion are obtained using the time integration runge kutta method when chaos is found it is detected by examining the phase plane the poincare map the sensitivity solution of the solution to initial conditions and by calculating the largest lyapunov exponent