a geometric optimization approach to detecting and intercepting dynamic targets using a mobile sensor network a methodology is developed to deploy a mobile sensor network for the purpose of detecting and capturing mobile targets in the plane the sensing pursuit problem considered in this paper is analogous to the marco polo game in which a pursuer marco must capture multiple mobile targets that are sensed intermittently and with very limited information the competing objectives exhibited by this problem arise in a number of surveillance and monitoring applications in this paper the mobile sensor network consists of a set of robotic sensors that must track and capture mobile targets based on the information obtained through cooperative detections when these detections form a satisfactory target track a mobile sensor is switched to pursuit mode and deployed to capture the target in minimum time since the sensors are installed on robotic platforms and have limited range the geometry of the platforms and of the sensors fields of view play a key role in obstacle avoidance and target detection a new cell decomposition approach is presented to determine the probability of detection and the cost of operating the sensors from the geometric properties of the network and its workspace the correctness and complexity of the algorithm are analyzed proving that the termination time is a function of the network parameters and of the number of required detections

searching and pebbling abstract we relate the search number of an undirected graph g with the minimum and maximum of the progressive pebble demands of the directed acyclic graphs obtained by orienting g towards this end we introduce node searching a slight variant of searching in which an edge is cleared by placing searchers on both of its endpoints we also show that the minimum number of searchers necessary to node search a graph equals its vertex separator plus one

weak formulation based haar wavelet method for solving differential equations the haar wavelet based discretization method for solving differential equations is developed nonlinear burgers equation is considered as a test problem both strong and weak formulations based approaches are discussed the discretization scheme proposed is based on the weak formulation an attempt is made to combine the advantages of the fem and haar wavelets the obtained numerical results have been validated against a closed form analytical solution as well as fem results good agreement with the exact solution has been observed

numerical solutions of variable order time fractional 1 1 and 1 2 dimensional advection dispersion and diffusion models abstract a numerical scheme based on haar wavelets coupled with finite differences is suggested to study variable order time fractional partial differential equations tfpdes the technique is tested on 1 1 dimensional advection dispersion and 1 2 dimensional advection diffusion equations in the proposed scheme time fractional derivative is firstly approximated by quadrature formula and then finite differences are combined with one and two dimensional haar wavelets with the help of suggested method the tfpdes convert to a system of algebraic equations which is easily solvable also convergence of the proposed scheme has been discussed which is an important part of the present work for validation the obtained results are matched with earlier work and exact solutions computations illustrate that the proposed scheme has better outcomes

dynamic formulation for geometrically exact sandwich shells abstract extending our recent works on geometrically exact sandwich beams and one dimensional plates see e g vu quoc and ebcio lu 1995 vu quoc and deng 1995c vu quoc and deng 1995a we present here a geometrically exact sandwich shell theory entirely in terms of stress resultants which accommodates finite deformations in membrane bending and transverse shear the motion of the shell are referred directly to the inertial frame the transverse fiber of the sandwich shell has a motion identical to that of a chain of three rigid links connected by revolute joints an important approximated theory is developed from the general nonlinear equations the classical linear theory is recovered by the consistent linearization

treewidth computations ii lower bounds for several applications it is important to be able to compute the treewidth of a given graph and to find tree decompositions of small width reasonably fast good lower bounds on the treewidth of a graph can amongst others help to speed up branch and bound algorithms that compute the treewidth of a graph exactly a high lower bound for a specific graph instance can tell that a dynamic programming approach for solving a problem is infeasible for this instance this paper gives an overview of several recent methods that give lower bounds on the treewidth of graphs

inverse formulation for geometrically exact stress resultant shells the inverse elastostatics method tackles a class of problems in which the deformed geometry and the applied load are known while the initial geometry and the stress in the deformed state are to be determined the method is imperative for many biomechanics applications particularly for image based stress analysis of living organs as the geometry captured by imaging often correspond to a pre deformed configuration 3 4 the computational aspects of inverse elastostatics i e the inverse formulations have been established for general elastic solids 1 2 3 in this work the inverse formulation of thin walled structures modeled as geometrically exact stress resultant shell 5 is presented the inverse formulation builds on a fundamental assumption of the elastic media that the stress depends on local relative motion of the body if either the reference or the deformed configuration is given the other can be found from the elastostatic equilibrium the shell formulation follows the same logic albeit involving shell kinematics and kinetics regardless of the additional assumptions introduced in the shell theory the fundamental premise underlying inverse analysis remains the same in the proposed formulation the inverse problem is solved by using the standard week form of shell balance equations which are yet parameterized and linearized in terms of the inverse motion to facilitate an effective numerical computation an invariant approached is used to formulate the constitutive equations a consistent reduction from 3d energy function is also introduced numerical examples involving both isotopic and anisotropic materials are provided for validating the formulation applications to several biological thin walled structures demonstrate the practical utility of the method

numerical solution of evolution equations by the haar wavelet method an efficient numerical method for solution of nonlinear evolution equations based on the haar wavelets approach is proposed the method is tested in the case of burgers and sine gordon equations numerical results obtained by computer simulation are compared with other available solutions these calculations demonstrate that the accuracy of the haar wavelet solutions is quite high even in the case of a small number of grid points

a non uniform haar wavelet method for numerically solving two dimensional convection dominated equations and two dimensional near singular elliptic equations abstract a non uniform haar wavelet based collocation method has been developed in this paper for two dimensional convection dominated equations and two dimensional near singular elliptic partial differential equations in which traditional haar wavelet method produces oscillatory solutions or low accurate solutions the main idea behind the proposed method is to transform the computation of numerical solution of considered partial differential equations to computation of solution of a linear system of equations this process is done by discretizing space variables with non uniform haar wavelets to confirm efficiency of the proposed method seven benchmark problems are solved and the obtained results are compared with exact solutions and with local meshless methods finite element method finite difference method and polynomial collocation method numerical experiments show that the proposed method gives convincing results even in less number of collocation nodes

finite graph automata for linear and boundary graph languages graph grammars can be regarded as a generalization of context free grammars from strings to graphs over the past 30 years a rich theory of graph grammars and their languages has been developed however there are no graph automata there is no duality between generative and recognizing devices as it is known for the chomsky hierarchy of formal languages here we introduce graph automata as devices for the recognition of sets of undirected node labelled graphs a graph automaton consists of a finite state control a finite set of instructions and a collection of heads or guards it reads an input graph in a systematic way and performs a graph search directed by the instructions as our main results we show that finite graph automata recognize exactly the set of graph languages generated by linear nce graph grammars and that alternating finite graph automata recognize exactly the languages of boundary graph grammars finally we generalize some automata theoretic properties from string to graph automata integrate the connectivity of graphs into graph automata and explain why graph automata cannot be generalized to deal with dynamic edge relabellings and ence graph languages

harmonic wavelets towards the solution of nonlinear pde in this paper harmonic wavelets which are analytically defined and band limited are studied together with their differentiable properties harmonic wavelets were recently applied to the solution of evolution problems and more generally to describe evolution operators in order to consider the evolution of a solitary profile and to focus on the localization property of wavelets it seems to be more expedient to make use of functions with limited compact support either in space or in frequency the connection coefficients of harmonic wavelets are explicitly computed in the following at any order and characterized by some recursive formulas in particular they are functionally and finitely defined by a simple formula for any order of the basis derivatives

the complexity of searching a graph t parsons originally proposed and studied the following pursuit evasion problem on graphs members of a team of searchers traverse the edges of a graph g in pursuit of a fugitive who moves along the edges of the graph with complete knowledge of the locations of the pursuers what is the smallest number s g of searchers that will suffice for guaranteeing capture of the fugitive it is shown that determining whether s g k for a given integer k is np complete for general graphs but can be solved in linear time for trees we also provide a structural characterization of those graphs g with s g k for k 1 2 3

solving integral and differential equations by the aid of non uniform haar wavelets a modification of the haar wavelet method for which the stepsize of the argument is variable is proposed to establish the efficiency of the method three test problems for which exact solution is known are considered computer simulations show clear preference of the suggested method compared with the haar wavelet method of a constant stepsize

linear rank width and linear clique width of trees we show that for every forest t the linear rank width of t is equal to the path width of t and the linear clique width of t equals the path width of t plus two provided that t contains a path of length three it follows that both linear rank width and linear clique width of forests can be computed in linear time using our characterization of linear rank width of forests we determine the set of minimal excluded acyclic vertex minors for the class of graphs of linear rank width at most k

a c k n 5 approximation algorithm for treewidth we give an algorithm that for an input n vertex graph g and integer k 0 in time 2 o k n either outputs that the treewidth of g is larger than k or gives a tree decomposition of g of width at most 5k 4 this is the first algorithm providing a constant factor approximation for treewidth which runs in time single exponential in k and linear in n treewidth based computations are subroutines of numerous algorithms our algorithm can be used to speed up many such algorithms to work in time which is single exponential in the treewidth and linear in the input size

geometrically exact sandwich shells the static case the present formulation offers a general method for analyzing the static response of geometrically exact sandwich shells undergoing large deformation the layer directors at a point in the reference surface are connected to each other by universal joints and form a chain of rigid links finite rotations of the directors in every layer are allowed with shear deformation independently accounted for in each layer the thickness and the length of each layer can be arbitrary thus allowing the modeling of an important class of multilayer structures having ply drop offs the present formulation is thus suitable to model shell structures with patches of constrained viscoelastic materials or of piezoelectric materials the nonlinear weak form of the governing equations of equilibrium is constructed here and then the linearization of the weak form and the associated inextensible directors update are derived leading to a symmetric tangent stiffness matrix a galerkin finite element projection of the linearized equilibrium equations results in a system of nonlinear algebraic equations in which the interpolation accounts for the finite rotations of the directors we present extensive numerical examples including sandwich shells with three identical layers and ply drop offs to illustrate the applicability and versatility of the proposed formulation

an algebraic theory of graph reduction we show how membership in classes of graphs definable in monadic second order logic and of bounded treewidth can be decided by finite sets of terminating reduction rules the method is constructive in the sense that we describe an algorithm which will produce from a formula in monadic second order logic and an integer k such that the class defined by the formula is of treewidth k a set of rewrite rules that reduces any member of the class to one of finitely many graphs in a number of steps bounded by the size of the graph this reduction system corresponds to an algorithm that runs in time linear in the size of the graph

treewidth computations i upper bounds for more and more applications it is important to be able to compute the treewidth of a given graph and to find tree decompositions of small width reasonably fast this paper gives an overview of several upper bound heuristics that have been proposed and tested for the problem of determining the treewidth of a graph and finding tree decompositions each of the heuristics produces tree decompositions whose width may be larger than the optimal width however experiments show that in many cases the heuristics give tree decompositions whose width is close to the exact treewidth of the input graphs

parallel algorithms with optimal speedup for bounded treewidth we describe the first parallel algorithm with optimal speedup for constructing minimum width tree decompositions of graphs of bounded treewidth on n vertex input graphs the algorithm works in o log n 2 time using o n operations on the erew pram we also give faster parallel algorithms with optimal speedup for the problem of deciding whether the treewidth of an input graph is bounded by a given constant and for a variety of problems on graphs of bounded treewidth including all decision problems expressible in monadic second order logic on n vertex input graphs the algorithms use o n operations together with o log n log n time on the erew pram or o log n time on the crcw pram

approximate search strategies for weighted trees the problems of classical searching and connected searching of weighted trees are known to be computationally hard in this work we give a polynomial time 3 approximation algorithm that finds a connected search strategy of a given weighted tree this in particular yields constant factor approximation algorithms for the non connected classical searching problems and for the weighted pathwidth problem for this class of graphs

edge and node searching problems on trees in this paper we show that there is a natural correspondence between a tree s edge search strategy and its node search strategy by doing so we simplify the previous linear time algorithm for determining the edge search number of a tree and improve the running time of a previous algorithm for constructing an edge search strategy or plan for a tree containing n vertices from o n log n to o n time

the vertex separation and search number of a graph abstract we relate two concepts in graph theory and algorithmic complexity namely the search number and the vertex separation of a graph let s g denote the search number and vs g denote the vertex separation of a connected undirected graph g we show that vs g s g vs g 2 and we give a simple transformation from g to g such that vs g s g we characterize those trees having a given vertex separation and describe the smallest such trees we also note that there exist trees for which the difference between search number and vertex separation is indeed 2 we give algorithms that for any tree t compute vs t in linear time and compute an optimal layout with respect to vertex separation in time o n log n vertex separation has previously been related to progressive black white pebble demand and has been shown to be identical to a variant of search number node search number and to path width which has been related to gate matrix layout cost all these properties are known to be computationally intractable for fixed k an o n log 2 n algorithm is known which decides whether a graph has path width at most k

on the physical meaning of the dynamical equations governing geometrically exact multilayer shells in this paper the physical meaning of the equations governing geometrically exact multilayer shells is provided through a totally new derivation by means of dynamic equilibrium consideration starting from a 3 d continuum setting in curvilinear coordinates the theory is valid for large deformation and large overall motion as characteristic of geometrically exact formulations the dynamic equilibrium derivation offers a clear physical insight into the meaning of the terms in the equations of motion such insight was not afforded by previous derivations based on the principle of virtual power in particular we obtain directly the balance of angular momentum in true resultant couples without the need to use the constitutive restriction as in our previous papers moreover we also obtain here new expressions for the inertia operators that will greatly simplify the computational formulation when compared to our previous work in addition an analytical justification of the inertial operators is also provided the present formulation is independent of any kinematic assumption along the shell director and is in particular valid for the case of shells with variable length director e g for modeling through the thickness deformation and higher order kinematic assumptions

digraph decompositions and monotonicity in digraph searching graph decompositions such as tree decompositions and associated width measures have been the focus of much attention in structural and algorithmic graph theory in particular it has been found that many otherwise intractable problems become tractable on graph classes of bounded tree width more recently proposals have been made to define a similar notion to tree width for directed graphs several proposals have appeared so far supported by algorithmic applications in this paper we explore the limits of algorithmic applicability of digraph decompositions and show that various natural candidates for problems which potentially could benefit from digraphs having small directed width remain np complete even on almost acyclic graphs closely related to graph and digraph decompositions are graph searching games an important property of graph searching games is monotonicity and a large number of papers addresses the question whether particular variants of these games are monotone however so far for two natural types of graph searching games underlying dag and kelly decompositions the question whether they are monotone was still open we settle this issue by showing that both variants the visible and the inert invisible graph searching games on directed graphs are non monotone

complexity of node coverage games modern software systems may exhibit a nondeterministic behavior due to many unpredictable factors in this work we propose the node coverage game a two player turn based game played on a finite game graph as a formalization of the problem to test such systems each node in the graph represents a functional equivalence class of the software under test sut one player the tester wants to maximize the node coverage measured by the number of nodes visited when exploring the game graphs while his opponent the sut wants to minimize it an optimal test would maximize the cover and it is an interesting problem to find the maximal number of nodes that the tester can guarantee to visit irrespective of the responses of the sut we show that the decision problem of whether the guarantee is less than a given number is np complete we also discuss two extensions of our result and present a testing procedure based on our result when the sut is not so hostile we establish that the decision problem of maximal node coverage guarantee of non deterministic game graphs is np complete we present two variations of node coverage game with np complete decision problem complexity we also provide an adaptive procedure that employs an np procedure to generate test cases with maximal coverage guarantee and reevaluate the mcg and regenerate test cases when the sut is not so hostile

self organized critical state of sandpile automaton models we study a general bak tang wiesenfeld type automaton model of self organized criticality in which the toppling conditions depend on local height but not on its gradient we characterize the critical state and determine its entropy for an arbitrary finite lattice in any dimension the two point correlation function is shown to satisfy a linear equation the spectrum of relaxation times describing the approach to the critical state is also determined exactly

a fast wavelet multigrid method to solve elliptic partial differential equations abstract in this paper we present a wavelet based multigrid approach to solve elliptic boundary value problems encountered in mathematical physics the system of equations arising from finite difference discretization is represented in wavelet basis these equations are solved using multiresolution properties of wavelets characterized by sparse matrices having condition number o 1 together with a multigrid strategy for accelerating convergence the filter coefficients of d 2 k k 2 3 4 from daubechies family of wavelets are used to demonstrate the effectiveness and efficiency of the method the distinguishing feature of the method is it works as both solver and preconditioner as a consequence it avoids instability minimizes error and speeds up convergence compared to the classical multigrid method this approach requires substantially shorter computation time at the same time meeting accuracy requirements it is found that just one cycle is enough for the convergence of wavelet multigrid scheme whereas normally 7 8 cycles are required in classical multigrid schemes to meet the same accuracy numerical examples show that the scheme offers a fast and robust technique for elliptic pde s

recognizing hyperelliptic graphs in polynomial time abstract based on analogies between algebraic curves and graphs baker and norine introduced divisorial gonality a graph parameter for multigraphs related to treewidth multigraph algorithms and number theory various equivalent definitions of the gonality of an algebraic curve translate to different notions of gonality for graphs called stable gonality and stable divisorial gonality we consider so called hyperelliptic graphs multigraphs of gonality 2 in any meaning of graph gonality and provide a safe and complete set of reduction rules for such multigraphs this results in an algorithm to recognize hyperelliptic graphs in time o m n log n where n is the number of vertices and m the number of edges of the multigraph a corollary is that we can decide with the same runtime whether a two edge connected graph g admits an involution such that the quotient g is a tree

monotony properties of connected visible graph searching search games are attractive for their correspondence with classical width parameters for instance the invisible search number a k a node search number of a graph is equal to its pathwidth plus 1 and the visible search number of a graph is equal to its treewidth plus 1 the connected variants of these games ask for search strategies that are connected i e at every step of the strategy the searched part of the graph induces a connected subgraph we focus on monotone search strategies i e strategies for which every node is searched exactly once the monotone connected visible search number of an n node graph is at most o logn times its visible search number first we prove that this logarithmic bound is tight precisely we prove that there is an infinite family of graphs for which the ratio monotone connected visible search number over visible search number is w logn second we prove that as opposed to the non connected variant of visible graph searching recontamination helps for connected visible search precisely we prove that for any k 4 there exists a graph with connected visible search number at most k and monotone connected visible search number k

simple linear time algorithms to test chordality of graphs test acyclicity of hypergraphs and selectively reduce acyclic hypergraphs chordal graphs arise naturally in the study of gaussian elimination on sparse symmetric matrices acyclic hypergraphs arise in the study of relational data bases rose tarjan and lueker siam j c

adaptive wavelet algorithms for elliptic pde s on product domains with standard isotropic approximation by piecewise polynomials of fixed order in a domain d subset of r d the convergence rate in terms of the number n of degrees of freedom is inversely proportional to the space dimension d this so called curse of dimensionality can be circumvented by applying sparse tensor product approximation when certain high order mixed derivatives of the approximated function happen to be bounded in l 2 it was shown by nitsche 2006 that this regularity constraint can be dramatically reduced by considering best n term approximation from tensor product wavelet bases when the function is the solution of some well posed operator equation dimension independent approximation rates can be practically realized in linear complexity by adaptive wavelet algorithms assuming that the infinite stiffness matrix of the operator with respect to such a basis is highly compressible applying piecewise smooth wavelets we verify this compressibility for general non separable elliptic pdes in tensor domains applications of the general theory developed include adaptive galerkin discretizations of multiple scale homogenization problems and of anisotropic equations which are robust i e independent of the scale parameters resp of the size of the anisotropy

adaptive multiscale wavelet galerkin analysis for plane elasticity problems and its applications to multiscale topology design optimization the multiscale galerkin formulation of two dimensional elasticity problems is presented for easy interpolation and boundary handlings as well as efficient adaptive analysis two dimensional interpolation wavelets are used as the multiscale trial functions in the galerkin formulation after the validity of the present multiscale adaptive method is verified with some benchmark problems the present wavelet based method is applied to the multiscale topology optimization that progresses design resolution levels dyadically from low to high levels by this application we show the potential of the multiscale method and the possibility of developing a fully integrated analysis and topology design optimization in the multiscale multiresolution setting

an efficient numerical algorithm for multi dimensional time dependent partial differential equations abstract an efficient and robust numerical scheme based on haar wavelets and finite differences is suggested for the solution of two dimensional time dependent linear and nonlinear partial differential equations pdes excellent feature of the scheme is the conversion of linear and non linear pdes to algebraic equations which are comparatively easy to handle convergence of the scheme which guarantees small error norm as the resolution level increases is also an important part of this work different error norms are computed to check efficiency of the technique computations verify accuracy flexibility and low computational cost of the method

a linear time algorithm for finding tree decompositions of small treewidth in this paper we give for constant k a linear time algorithm that given a graph g v e determines whether the treewidth of g is at most k and if so finds a tree decomposition of g with treewidth at most k a consequence is that every minor closed class of graphs that does not contain all planar graphs has a linear time recognition algorithm another consequence is that a similar result holds when we look instead for path decompositions with pathwidth at most some constant k

a combinatorial li yau inequality and rational points on curves we present a method to control gonality of nonarchimedean curves based on graph theory let k denote a complete nonarchimedean valued field we first prove a lower bound for the gonality of a curve over the algebraic closure of k in terms of the minimal degree of a class of graph maps namely one should minimize over all so called finite harmonic graph morphisms to trees that originate from any refinement of the dual graph of the stable model of the curve next comes our main result we prove a lower bound for the degree of such a graph morphism in terms of the first eigenvalue of the laplacian and some volume of the original graph this can be seen as a substitute for graphs of the li yau inequality from differential geometry although we also prove that the strict analogue of the original inequality fails for general graphs finally we apply the results to give a lower bound for the gonality of arbitrary drinfeld modular curves over finite fields and for general congruence subgroups vargamma of vargamma 1 that is linear in the index vargamma 1 vargamma with a constant that only depends on the residue field degree and the degree of the chosen infinite place this is a function field analogue of a theorem of abramovich for classical modular curves we present applications to uniform boundedness of torsion of rank two drinfeld modules that improve upon existing results and to lower bounds on the modular degree of certain elliptic curves over function fields that solve a problem of papikian

refined shear deformation models for composite laminates with finite rotations abstract for arbitrary multilayered shell structures made particularly of composite material layers a refined finite rotation theory with seven independent displacement variables is developed approximating the displacement field by a cubic series expansion of thickness coordinates this model allows a quadratic shear deformation distribution across the thickness procedures are given permitting a unique determination of the first order displacement term in the case of finite rotations kinematic relations are formulated in two alternative forms suitable for both classical and isoparametric finite element formulations the constitutive relations presented model orthotropic material properties varying arbitrarily across the thickness this third order single layer theory is then transformed by introducing further constraints into three simplified models a third order theory with five independent displacement variables a mindlin reissner type theory and a kirchhoff love type theory these four models differ however from each other essentially in the constraints imposed on the first and third order displacement variables a significant advantage for a unified finite element development finally the mindlin reissner type theory is generalized to a layer wise model being the most predictive one in dealing with local interlaminar effects the theoretical models are transformed into adequate finite shell elements and then compared by means of appropriate examples concerning their prediction capability also examples are given demonstrating their applicability to finite rotation phenomena

treewidth distance on phylogenetic trees in this article we study the treewidth of the display graph an auxiliary graph structure obtained from the fusion of phylogenetic i e evolutionary trees at their leaves earlier work has shown that the treewidth of the display graph is bounded if the trees are in some formal sense topologically similar here we further expand upon this relationship we analyse a number of reduction rules commonly used in the phylogenetics literature to obtain fixed parameter tractable algorithms in some cases the subtree reduction the reduction rules behave similarly with respect to treewidth while others the cluster reduction behave very differently and the behaviour of the chain reduction is particularly intriguing because of its link with graph separators and forbidden minors we also show that the gap between treewidth and tree bisection and reconnect tbr distance can be infinitely large and that unlike for example planar graphs the treewidth of the display graph can be as much as linear in its number of vertices a number of other auxiliary results are given we conclude with a discussion and list a number of open problems

numerical solutions of two dimensional sobolev and generalized benjamin bona mahony burgers equations via haar wavelets abstract this work addresses numerical method based on haar wavelets and finite differences to solve two dimensional linear nonlinear sobolev and non linear generalized benjamin bona mahony burgers ngbbmb equations the temporal part is discretized using finite differences while spatial part is approximated by two dimensional haar wavelets with this strategy computing solution of two dimensional pdes reduces to computing solution of linear system of algebraic equations collocation approach is then applied to determine the wavelet coefficients from linear system this paper shows that two dimensional haar wavelets are suitable and effective for two dimensional linear and non linear pdes for validation of the proposed scheme different problems have been solved and error norms l l 2 are computed computation verifies that current scheme has good outcome

the monadic second order logic of graphs i recognizable sets of finite graphs abstract the notion of a recognizable set of finite graphs is introduced every set of finite graphs that is definable in monadic second order logic is recognizable but not vice versa the monadic second order theory of a context free set of graphs is decidable

using divergence free wavelets for the numerical solution of the 2 d stationary navier stokes equations a galerkin wavelet scheme is presented for solving the 2 d stationary navier stokes equations using the scaling generator of the divergence free wavelets moreover some boundary generators are constructed to improve the approximation accuracy finally the optimal error estimates and the numerical results are reported

recontamination does not help to search a graph this paper is concerned with a game on graphs called graph searching the object of this game is to clear all edges of a contaminated graph clearing is achieved by moving searchers a kind of token along the edges of the graph according to clearing rules certain search strategies cause edges that have been cleared to become contaminated again megiddo et al 9 conjectured that every graph can be searched using a minimum number of searchers without this recontamination occurring that is without clearing any edge twice in this paper this conjecture is proved this places the graph searching problem in np completing the proof by megiddo et al that the graph searching problem is np complete furthermore by eliminating the need to consider recontamination this result simplifies the analysis of searcher requirements with respect to other properties of graphs

monotonicity of non deterministic graph searching in graph searching a team of searchers are aiming at capturing a fugitive moving in a graph in the initial variant called invisible graph searching the searchers do not know the position of the fugitive until they catch it in another variant the searchers permanently know the position of the fugitive i e the fugitive is visible this latter variant is called visible graph searching a search strategy that catches any fugitive in such a way that the part of the graph reachable by the fugitive never grows is called monotone a priori monotone strategies may require more searchers than general strategies to catch any fugitive this is however not the case for visible and invisible graph searching two important consequences of the monotonicity of visible and invisible graph searching are 1 the decision problem corresponding to the computation of the smallest number of searchers required to clear a graph is in np and 2 computing optimal search strategies is simplified by taking into account that there exist some that never backtrack fomin et al f v fomin p fraigniaud n nisse nondeterministic graph searching from pathwidth to treewidth in proceedings of the 30th international symposium on mathematical foundations of computer science mfcs 05 2005 pp 364 375 introduced an important graph searching variant called non deterministic graph searching that unifies visible and invisible graph searching in this variant the fugitive is invisible and the searchers can query an oracle that permanently knows the current position of the fugitive the question of the monotonicity of non deterministic graph searching was however left open in this paper we prove that non deterministic graph searching is monotone in particular this result is a unified proof of monotonicity for visible and invisible graph searching as a consequence the decision problem corresponding to non deterministic graph searching belongs to np moreover the exact algorithms designed by fomin et al do compute optimal non deterministic search strategies

fugitive search games on graphs and related parameters abstract the goal of a fugitive search game on a graph is to trap a fugitive that hides on the vertices of the graph by systematically placing searchers on the vertices the fugitive is assumed to have complete knowledge of the graph and of the searchers moves but is restricted to move only along paths whose vertices are not guarded by searchers the search number of the graph is the least number of searchers necessary to trap the fugitive variants of the fugitive search game have been related to important graph parameters like treewidth and pathwidth in this paper we introduce a class of fugitive search games where the searchers do not see the fugitive and the fugitive can only move just before a searcher is placed on the vertex it occupies letting the fugitive s speed i e the maximum number of edges the fugitive can traverse at a single move vary we get different games we show that if the speed of the fugitive is unbounded then the search number minus 1 is equal to the treewidth of the graph while if the speed is 1 then the search number minus 1 is equal to a polynomially computable graph parameter which is called width or alternatively linkage and is studied in the context of the constraint satisfaction and boolean satisfiability problems we also show that in the above two cases the search number remains the same even if we consider only search strategies that at every step further restrict the fugitive s possible resorts this monotonicity property is usually expressed as recontamination does not help moreover we give an equivalent characterization of the search number for any given fugitive speed in terms of an elimination ordering of the vertices of the graph using this characterization we show that for any graph if the length of any chordless cycle is bounded by a constant s s 3 then the treewidth of the graph plus 1 is equal to the search number for fugitive speed s 2

fast edge searching and fast searching on graphs given a graph g v e in which a fugitive hides on vertices or along edges graph searching problems are usually to find the minimum number of searchers required to capture the fugitive in this paper we consider the problem of finding the minimum number of steps to capture the fugitive we introduce the fast edge searching problem in the edge search model which is the problem of finding the minimum number of steps called the fast edge search time to capture the fugitive we establish relations between the fast edge searching and the fast searching that is the problem of finding the minimum number of searchers to capture the fugitive in the fast search model while the family of graphs whose fast search number is at most k is not minor closed for any positive integer k 2 we show that the family of graphs whose fast edge search time is at most k is minor closed we establish relations between the fast fast edge searching and the node searching these relations allow us to transform the problem of computing node search numbers to the problem of computing fast edge search numbers or fast search numbers using these relations we prove that the problem of deciding given a graph g and an integer k whether the fast edge search number of g is less than or equal to k is np complete and it remains np complete for eulerian graphs we also prove that the problem of determining whether the fast edge search number of g is half of the number of odd vertices in g is np complete and it remains np complete for planar graphs with maximum degree 4 we present a linear time approximation algorithm for the fast edge search time that always delivers solutions of at most 1 v 1 e 1 times the optimal value this algorithm also gives us a tight upper bound on the fast search number of graphs we also show a lower bound on the fast search number using the minimum degree and the number of odd vertices

the natural integral equations of plane elasticity problem and its wavelet methods in this paper we apply interpolatory hermite type trigonometric wavelet to investigate the numerical solution of the natural boundary integral equation of plane elasticity problem by galerkin method in our fast algorithm the computational formulae of entries of the stiffness matrix yield simple close form and for one 2 j 3x2 j 3 stiffness matrix we only need to compute 2 2 j 2 2 j 1 entries the error estimates of the approximate solution are given and the test examples are presented in the end

numerical solution of two dimensional elliptic pdes with nonlocal boundary conditions in the present paper two numerical methods are analyzed for the solution of two dimensional poisson equation with two different types of nonlocal boundary conditions the first numerical method is a collocation method based on haar wavelet whereas the second numerical method is a meshless method based on different types of radial basis functions rbfs a two point boundary condition and an integral boundary condition are the two types of nonlocal boundary conditions considered in the present work for the collocation method based on haar wavelet a new approach is formulated which involves the approximation of a fourth order mixed derivative by a haar expansion which is integrated subsequently to get wavelet approximation of the solution for the meshless method based on rbfs the algorithm is implemented using two different splitting schemes with and without shape parameter splitting for numerical solution of the model the comparative analysis of the meshless methods with and without shape parameter splitting scheme is performed between themselves as well as with the haar wavelet accuracy and efficiency wise performance is confirmed through application of the algorithms on the benchmark tests

connected graph searching in the graph searching game the opponents are a set of searchers and a fugitive in a graph the searchers try to capture the fugitive by applying some sequence of moves that include placement removal or sliding of a searcher along an edge the fugitive tries to avoid capture by moving along unguarded paths the search number of a graph is the minimum number of searchers required to guarantee the capture of the fugitive in this paper we initiate the study of this game under the natural restriction of connectivity where we demand that in each step of the search the locations of the graph that are clean i e non accessible to the fugitive remain connected we give evidence that many of the standard mathematical tools used so far in classic graph searching fail under the connectivity requirement we also settle the question on the price of connectivity that is how many searchers more are required for searching a graph when the connectivity demand is imposed we make estimations of the price of connectivity on general graphs and we provide tight bounds for the case of trees in particular for an n vertex graph the ratio between the connected searching number and the non connected one is o logn while for trees this ratio is always at most 2 we also conjecture that this constant ratio upper bound for trees holds also for all graphs our combinatorial results imply a complete characterization of connected graph searching on trees it is based on a forbidden graph characterization of the connected search number we prove that the connected search game is monotone for trees i e restricting search strategies to only those where the clean territories increase monotonically does not require more searchers a consequence of our results is that the connected search number can be computed in polynomial time on trees moreover we show how to make this algorithm distributed finally we reveal connections of this parameter to other invariants on trees such as the horton strahler number

haar wavelet method for solving fisher s equation in this paper we develop an accurate and efficient haar wavelet solution of fisher s equation a prototypical reaction diffusion equation the solutions of fisher s equation are characterized by propagating fronts that can be very steep for large values of the reaction rate coefficient there is an ongoing effort to better adapt haar wavelet methods to the solution of differential equations with solutions that resemble shock waves or fronts typical of hyperbolic partial differential equations moreover the use of haar wavelets is found to be accurate simple fast flexible convenient small computation costs and computationally attractive

on search games that include ambush we present a stochastic game that models ambush search in a finite region q which has area but no other structure the searcher can search a unit area of q in unit time or adopt an ambush mode for a certain period the searcher captures the hider when the searched region contains the hider s location or if the hider moves while the searcher is in ambush mode the payoff in this zero sum game is the capture time our game is motivated by the still unsolved princess and monster game on a star graph with a large number of leaves

computing the vertex separation of unicyclic graphs we describe an o n log n algorithm for the computation of the vertex separation of unicyclic graphs the algorithm also computes a linear layout with optimal vertex separation in the same time bound pathwidth node search number and vertex separation are different ways of defining the same notion path decompositions and search strategies can be derived from linear layouts the algorithm applies existing linear time techniques for the computation of the vertex separation of trees together with corresponding optimal layouts we reformulate the earlier work on the linear time computation of optimal layouts a polynomial time algorithm for the problem on unicyclic graphs can be inferred from existing more general methods for graphs of fixed treewidth since unicyclic graphs have treewidth two but the time complexity of the resulting method would seem to be an inordinately high order polynomial our algorithm we claim is practical the addition of one edge to a tree does seem to require a considerably more elaborate algorithm

a partial k arboretum of graphs with bounded treewidth the notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies this survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class also some mutual relations between such classes are discussed

dynamics of geometrically exact sandwich beams 1 d plates computational aspects a galerkin projection of the complete equations of motion of geometrically exact sandwich beams applicable to 1 d plates is presented here the beam can take any arbitrary initial position in the 2 d space each layer of the beam can have different material constants with no restriction on the mass distribution and layer thickness further each layer can take on different length thus allowing the modeling of multilayer structures with ply drop offs finite rotation and shear deformation are accommodated for in each layer the deformed cross section of the beam is continuous piecewise linear the continuity of displacement across the interlayer boundaries is exactly enforced extensive numerical examples including sandwich beams with three identical layers sandwich structures with ply drop off free flying and spin up maneuver of sandwich beams are presented to illustrate the applicability and versatility of the proposed formulation

mixed searching and proper path width abstract this paper considers a mixed search game which is a natural generalization of edge search and node search games extensively studied so far we establish a relationship between the mixed search number of a graph g and the proper path width of g introduced by the authors in a previous paper we also prove complexity results

haar wavelet collocation method for three dimensional elliptic partial differential equations a new collocation method based on haar wavelet is presented for numerical solution of three dimensional elliptic partial differential equations with dirichlet boundary conditions an important advantage of the method is that it can be applied to both linear as well as nonlinear problems the algorithm based on this new method is simple and can be easily implemented in any programming language experimental rates of convergence of the proposed method are calculated which are in agreement with theoretical results the proposed method is applied to several benchmark problems from the literature including linear and nonlinear elliptic problems as well as systems of elliptic partial differential equations the numerical experiments confirm the accuracy and diverse applicability of the method

optimal and sublogarithmic time randomized parallel sorting algorithms this paper assumes a parallel ram random access machine model which allows both concurrent reads and concurrent writes of a global memory the main result is an optimal randomized parallel algorithm for integer sort i e for sorting n integers in the range 1 n this algorithm costs only logarithmic time and is the first known that is optimal the product of its time and processor bounds is upper bounded by a linear function of the input size also given is a deterministic sublogarithmic time algorithm for prefix sum in addition this paper presents a sublogarithmic time algorithm for obtaining a random permutation of n elements in parallel and finally sublogarithmic time algorithms for general sort and integer sort are presented our sub logarithmic general sort algorithm is also optimal

some np complete problems similar to graph isomorphism the graph isomorphism problem has so far resisted attempts at determining its complexity status it has not been shown to be np complete nor in p in this paper several altered or generalized versions of the isomorphism problem are presented and shown to be np complete one of these is the problem of determining whether a given graph has a fixed point free automorphism some speculation is made on the possible implications of these results on deciding the complexity status of isomorphism various classes and hierarchies of problems in np are discussed

discontinuous legendre wavelet element method for elliptic partial differential equations abstract by incorporating the legendre multiwavelet into the discontinuous galerkin dg method this paper presents a novel approach for solving poisson s equation with dirichlet boundary which is known as the discontinuous legendre multiwavelet element dlwe method derive an adaptive algorithm for the method and estimate the approximating error of its numerical fluxes one striking advantage of our method is that the differential operator boundary conditions and numerical fluxes involved in the elementwise computation can be done with lower time cost numerical experiments demonstrate the validity of this method furthermore this paper generalizes the dlwe method to the general elliptic equations defined on a bounded domain and describes the possibilities of constructing optimal adaptive algorithm the proposed method and its generalizations are also applicable to some other kinds of partial differential equations

on minimum cost edge searching we consider the problem of finding edge search strategies of minimum cost the cost of a search strategy is the sum of searchers used in the clearing steps of the search one of the natural questions is whether it is possible to find a search strategy that minimizes both the cost and the number of searchers used to clear a given graph g we call such a strategy ideal we prove by an example that ideal search strategies do not exist in general on the other hand we provide a formula for the cost of clearing complete graphs from our construction it follows that an ideal search strategy of a complete graph does exist and can be calculated efficiently for general graphs g we give a polynomial time o logn approximation algorithm for finding minimum cost search strategies we also prove that recontamination does not help to obtain minimum cost edge search strategies

a spectral collocation method based on integrated chebyshev polynomials for two dimensional biharmonic boundary value problems this paper reports a new spectral collocation method for numerically solving two dimensional biharmonic boundary value problems the construction of the chebyshev approximations is based on integration rather than conventional differentiation this use of integration allows i the imposition of the governing equation at the whole set of grid points including the boundary points and ii the straightforward implementation of multiple boundary conditions the performance of the proposed method is investigated by considering several biharmonic problems of first and second kinds more accurate results and higher convergence rates are achieved than with conventional differential methods

optimal solid shells for non linear analyses of multilayer composites ii dynamics abstract we are presenting a simple low order solid shell element formulation having only displacement degrees of freedom dofs i e without rotational dofs that has an optimal number of parameters to pass the patch tests and thus allows for efficient and accurate analyses of large deformable multilayer shell structures using elements at extremely high aspect ratio with the dynamics referred to a fixed inertial frame the elements can be used to analyze multilayer shell structures undergoing large overall motion the formulation of this element is based on the mixed hu washizu variational principle leading to a novel enhancing strain tensor enhanced assumed strain eas method that renders the computation particularly efficient with improved in plane and out of plane bending behavior poisson thickness locking especially in refined analyses of composite structures involving a large number of high aspect ratio layers the energy momentum conserving algorithm in the context of current solid shell element is presented we discuss the eas formulation based on the displacement gradient and its complexity compared to formulation on the green lagrange strain shear locking and curvature thickness locking are treated using the assumed natural strain ans method the element has an optimal combination of the ans method and the minimal number of eas parameters required to pass the plate bending patch test numerical examples involving dynamic analyses with conservation of energy and momentum of multilayer shell structures having a large range of element aspect ratios are presented several implicit direct integration methods with without numerical dissipation are used and compared in terms of the accuracy stability and cost in multilayer shell structure finally we note that the topic in this paper is a fitting dedication to professor ekkehard ramm who has made important pioneering contributions in this research direction

an annotated bibliography on guaranteed graph searching graph searching encompasses a wide variety of combinatorial problems related to the problem of capturing a fugitive residing in a graph using the minimum number of searchers in this annotated bibliography we give an elementary classification of problems and results related to graph searching and provide a source of bibliographical references on this field

fast mixed searching and related problems on graphs abstract in this paper we introduce the fast mixed search model which is a combination of the fast search model and the mixed search model given a graph g in which a fugitive hides on vertices or along edges the fast mixed search problem is to find the minimum number of searchers to capture the fugitive in the fast mixed search model we establish a relation between the fast mixed search problem and the induced path cover problem we also consider relations between the fast mixed search problem and other graph search problems we prove that fast mixed searching from leaves is np complete and it remains np complete for planar graphs with maximum degree 3 we also prove that fast mixed searching between leaves is np complete and it remains np complete for graphs with maximum degree 4 we present linear time algorithms for computing the fast mixed search number and optimal search strategies of some classes of graphs including trees cacti and proper interval graphs

wavelet based quasilinearization method for semi linear parabolic initial boundary value problems finite difference free wavelets based quasilinearization methods developed for spibvp fisher huxley and newell whitehead segel equations solved very efficiently comparison study provided for quasilinearization based on haar and legendre wavelets proposed approach performs better than the methods in the recent literature in this paper numerical methods based on quasilinearization and haar and legendre wavelets to solve a class of semi linear parabolic initial boundary value problem spibvp have been presented the haar and legendre wavelet methods have been successfully combined with quasilinearization to solve spibvp efficiently the presented numerical scheme has been illustrated using appropriate examples including fisher equation and the obtained results show that the proposed numerical scheme is robust and easy to apply

on shear correction factors in the non linear theory of elastic shells abstract theoretical values of two correction factors s 5 6 and t 7 10 are established for the respective transverse shear stress resultants and stress couples within the general dynamically and kinematically exact six field theory of elastic shells these values do not depend on the shell material symmetry geometry of the base surface the shell thickness or any kind of kinematic and or dynamic constraints the analysis is based on the complementary energy density following from the transverse shear stresses acting only on the shell cross section the appropriate quadratic and cubic distributions of the stresses across the thickness allow one to derive the consistent constitutive equations for the transverse shear stress resultants and stress couples with s and t as the respective correction factors four numerical examples of highly non linear shell structures illustrate the influence of different values of s and t on the results in particular some influence of t is noticed on the placement of bifurcation points in dynamic problem of flight of three intersecting plates analysed with newmark type temporal algorithm the value of t influences the moment at which the relative error of total energy of the system begins to grow indefinitely leading to the solution failure

solving pdes with the aid of two dimensional haar wavelets two dimensional haar wavelets are applied for solution of the partial differential equations pdes the proposed method is mathematically simple and fast to demonstrate the efficiency of the method two test problems solution of the diffusion and poisson equations are discussed computer simulation showed that the method guarantees the necessary exactness already for a small number of grid points

monotonicity in digraph search problems in this paper we study the monotonicity and complexity of five digraph search problems directed searching mixed directed searching internal directed searching internal strong searching and internal weak searching in the first three search problems both searchers and intruder must follow the edge directions when they move along edges in the internal strong search problem the intruder must move in the edge directions but searchers need not in the internal weak search problem searchers must move in the edge directions but the intruder need not there are three actions for searchers in the first two search problems placing removing and sliding and there are only two actions for searchers in the last three internal search problems placing and sliding note that the internal strong searching is a strong version of the internal directed searching the internal weak searching is a weak version of the internal directed searching and the internal edge searching is an analogy of the internal directed searching on undirected graphs we prove that the first three problems are monotonic and the last two problems are non monotonic respectively it is interesting that the internal directed searching is monotonic while the internal strong searching the internal weak searching and the internal edge searching are all non monotonic we also show that the first four problems are np complete and the last problem is np hard we solve the open problem on whether a non monotonic searching problem can be np complete

csp duality and trees of bounded pathwidth we study non uniform constraint satisfaction problems definable in monadic datalog stratified by the use of non linearity we show how such problems can be described in terms of homomorphism dualities involving trees of bounded pathwidth and in algebraic terms for this we introduce a new parameter for trees that closely approximates pathwidth and can be characterised via a hypergraph searching game

multilayer shells geometrically exact formulation of equations of motion we present here a formulation for geometrically exact multilayer shells where the number of layers is completely arbitrary and not necessarily restricted to three as in the case of sandwich shells based entirely in terms of stress resultants the formulation accommodates finite deformation in membrane bending and shear deformation typical of geometrically exact formulation the kinematics of the shell is referred directly to an inertial frame and not by means of a floating frame the motion of a transverse fiber of an n layer shell is exactly that of a chain of n rigid links connected by universal joints in three dimensional space the kinematics of deformation in each layer is expressed in terms of the deformation of an arbitrary layer chosen as a reference layer the thickness and side dimensions of each layer are also arbitrary these features allow a convenient modeling of multilayer shells with ply drop offs we also show that the present formulation reduces exactly to the case of multilayer beams