a darbo fixed point theory approach towards the existence of a functional integral equation in a banach algebra abstract this paper investigates the nonlinear functional integral equation comprising of hadamard fractional operator using the concept of measure of non compactness existence of solutions in banach algebra has been studied under certain relevant assumptions in conjunction with fixed point theory finally an example has been considered to substantiate the validity of the result

nondecreasing solutions of a quadratic integral equation of urysohn type applying the technique associated with measures of noncompactness we prove the existence of nondecreasing solutions of a quadratic integral equation of urysohn type in the space of real functions defined and continuous on a closed bounded interval

theoretical underpinnings for maximal clique enumeration on perturbed graphs the problem of enumerating the maximal cliques of a graph is a computationally expensive problem with applications in a number of different domains sometimes the benefit of knowing the maximal clique enumeration mce of a single graph is worth investing the initial computation time however when graphs are abstractions of noisy or uncertain data the mce of several closely related graphs may need to be found and the computational cost of doing so becomes prohibitively expensive here we present a method by which the cost of enumerating the set of maximal cliques for related graphs can be reduced by using the mce for some baseline graph the mce for a modified or perturbed graph may be obtained by enumerating only the maximal cliques that are created or destroyed by the perturbation when the baseline and perturbed graphs are relatively similar the difference set between the two mces can be overshadowed by the maximal cliques common to both thus by enumerating only the difference set between the baseline and perturbed graphs mces the computational cost of enumerating the maximal cliques of the perturbed graph can be reduced we present necessary and sufficient conditions for enumerating difference sets when the perturbed graph is formed by several different types of perturbations we also present results of an algorithm based on these conditions that demonstrate a speedup over traditional calculations of the mce of perturbed real biological networks

on quadratic integral equation of fractional orders abstract we present an existence theorem for a nonlinear quadratic integral equations of fractional orders arising in the queuing theory and biology in the banach space of real functions defined and continuous on a bounded and closed interval the concept of measure of noncompactness and a fixed point theorem due to darbo are the main tool in carrying out our proof

monotonic solutions of a class of quadratic integral equations of volterra type using the technique associated with measures of noncompactness we prove the existence of monotonic solutions of a class of quadratic integral equation of volterra type in the banach space of real functions defined and continuous on a bounded and closed interval

monotonic solutions of a perturbed quadratic fractional integral equation abstract we present an existence theorem for monotonic solutions of a perturbed quadratic fractional integral equation in c 0 1 the concept of a measure of noncompactness and a fixed point theorem due to darbo are the main tools in carrying out our proof finally we give an example for indicating the natural realizations of our abstract result presented in the paper

plate vibration under irregular internal supports this paper studies the problem of plate vibration under complex and irregular internal support conditions such a problem has its widely spread industrial applications and has not been addressed in the literature yet partially due to the numerical difficulties a novel computational method discrete singular convolution dsc is introduced for solving this problem the dsc algorithm exhibits controllable accuracy for approximations and shows excellent flexibility in handling complex geometries boundary conditions and internal support conditions convergence and comparison studies are carried out to check the validity and accuracy of the dsc method case studies are considered to the combination of a few different boundary conditions and irregular internal supports the latter are generated by using an image processing algorithm completely independent verifications are conducted by using the established pb 2 ritz method which is available for two relatively simpler support patterns the morphology of the first few eigenmodes is found to be localized to largest support free spatial regions

on the solutions to a class of nonlinear integral equations arising in transport theory existence and uniqueness for the solutions to a class of nonlinear equations arising in transport theory are investigated in terms of a real parameter which can take on positive and negative values on the basis of contraction mapping and positivity properties of the relevant nonlinear operator iteration schemes are proposed and their convergence either pointwise or in norm is studied

on a perturbed quadratic fractional integral equation of abel type we present an existence theorem for monotonic solutions of a perturbed quadratic fractional integral equation in c 0 1 our equation contains the famous chandrasekhar integral equation as a special case the concept of the measure of noncompactness related to monotonicity introduced by j banas and l olszowy and a fixed point theorem due to darbo are the main tools in carrying out our proof moreover we give an example for indicating the natural realizations of our abstract result presented in this paper

on the complexity of fixed parameter clique and dominating set we provide simple faster algorithms for the detection of cliques and dominating sets of fixed order our algorithms are based on reductions to rectangular matrix multiplication we also describe an improved algorithm for diamonds detection

on the superposition operator and integrable solutions of some functional equations on etudie les equations x t f t x t et x t f t x t dans l espace l 1 a b equipe de la topologie de la convergence faible on montre que ces equations ont des solutions integrables qui sont additionnellement des fonctions monotones p p

monotonic solutions of a convolution functional integral equation in this paper we show that a very general convolution functional integral equation has at least one monotonic solution in the space of lebesgue integrable functions on an unbounded interval a suitable combination of the technique associated with measures of noncompactness in both the weak and the strong sense and the darbo fixed point is the main tool in our analysis

on syntactic versus computational views of approximability we attempt to reconcile the two distinct views of approximation classes syntactic and computational syntactic classes such as max snp permit structural results and have natural complete problems while computational classes such as apx allow us to work with classes of problems whose approximability is well understood our results provide a syntactic characterization of computational classes and give a computational framework for syntactic classes we compare the syntactically defined class max snp with the computationally defined class apx and show that every problem in apx can be placed i e has approximation preserving reduction to a problem in max snp our methods introduce a simple yet general technique for creating approximation preserving reductions which shows that any well approximable problem can be reduced in an approximation preserving manner to a problem which is hard to approximate to corresponding factors the reduction then follows easily from the recent nonapproximability results for max snp hard problems we demonstrate the generality of this technique by applying it to other classes such as max snp rmax 2 and min f pi 2 1 which have the clique problem and the set cover problem respectively as complete problems the syntactic nature of max snp was used by papadimitriou and yannakakis j comput system sci 43 1991 pp 425 440 to provide approximation algorithms for every problem in the class we provide an alternate approach to demonstrating this result using the syntactic nature of max snp we develop a general paradigm nonoblivious local search useful for developing simple yet efficient approximation algorithms we show that such algorithms can find good approximations for all max snp problems yielding approximation ratios comparable to the best known for a variety of specific max snp hard problems nonoblivious local search provably outperforms standard local search in both the degree of approximation achieved and the efficiency of the resulting algorithms

monotonic solutions of urysohn integralequation on unbounded interval abstract in this paper we investigate a nonlinear urysohn integral equation on unboundedinterval we show that under some assumptions that the equation has monotonic solutions belonging to the space of functions being lebesgue integrable on unbounded interval the main tool used in our study is the technique associated with measures of weak noncompactness and measures of noncompactness in strong sense

existence results for nonlinear integral equations the schauder tychonoff theorem in locally convex topological hausdorff spaces and a nonlinear alternative of leray schauder type are used to establish some existence results for volterra and hammerstein integral equations

solvability of a nonlinear integral equation of volterra type the aim of this paper is to investigate a class of integral equation of volterra type and its solvability in the space of continuous and bounded functions on r the main tool used in our considerations is the technique associated with measures of noncompactness

on approximating the number of k cliques in sublinear time we study the problem of approximating the number of k cliques in a graph when given query access to the graph we consider the standard query model for general graphs via 1 degree queries 2

a fixed point theorem for condensing operators and applications to hammerstein integral equations in banach spaces abstract we prove a fixed point theorem of furi pera type for condensing operators this will then be used to establish the existence of solutions to certain integral equations of hammerstein type in banach spaces

on the parameterized complexity of approximating dominating set we study the parameterized complexity of approximating the k dominating set domset problem where an integer k and a graph g on n vertices are given as input and the goal is to find a dominating set of size at most f k k whenever the graph g has a dominating set of size k when such an algorithm runs in time t k poly n i e fpt time for some computable function t it is said to be an f k fpt approximation algorithm for k domset whether such an algorithm exists is listed in the seminal book of downey and fellows 2013 as one of the most infamous open problems in parameterized complexity this work gives an almost complete answer to this question by showing the non existence of such an algorithm under w 1 fpt and further providing tighter running time lower bounds under stronger hypotheses specifically we prove the following for every computable functions t f and every constant e 0 assuming w 1 fpt there is no f k fpt approximation algorithm for k domset assuming the exponential time hypothesis eth there is no f k approximation algorithm for k domset that runs in t k no k time assuming the strong exponential time hypothesis seth for every integer k 2 there is no f k approximation algorithm for k domset that runs in t k nk e time assuming the k sum hypothesis for every integer k 3 there is no f k approximation algorithm for k domset that runs in t k n k 2 e time previously only constant ratio fpt approximation algorithms were ruled out under sf w 1 fpt and log1 4 m k fpt approximation algorithms were ruled out under eth chen and lin focs 2016 recently the non existence of an f k fpt approximation algorithm for any function f was shown under gap eth chalermsook et al focs 2017 note that to the best of our knowledge no running time lower bound of the form nd this allows us to easily apply known techniques to solve them

the free vibration of a type of tapered beams this paper studies the vibrational characteristics of tapered beams with continuously varying rectangular cross section of depth and breadth proportional to xs and xt respectively where both s and t are arbitrary real numbers for a truncated beam and arbitrary positive numbers for a sharp ended beam and x is the axial co ordinate measured from the sharp end of the beam the bernoulli euler theory of bending is used to describe the motion of the beam a new set of beam functions are developed as the admissible functions which are the complete solution of the tapered beam under an arbitrary static load expanded into a taylor series the eigenfrequency equation is obtained by the rayleigh ritz method the accuracy is assured from the convergency and comparison studies the effect of the location of the taylor series expanding point on the convergency is discussed the analysis shows that the present approach is convergent for arbitrary truncation factor by taking the midpoint of the beam as the expanding point of the taylor series numerical results are tabulated for three different tapered beams with various boundary conditions and truncation factors it is shown that the eigenfrequencies can be obtained with high accuracy by using only a small number of terms of the static beam functions 2000 elsevier science s a all rights reserved

on a perturbed functional integral equation of urysohn type abstract we study the existence of monotonic solutions for a perturbed functional integral equation of urysohn type in the space of lebesgue integrable functions on an unbounded interval the technique associated with measures of noncompactness in both the weak and the strong sense and the darbo fixed point are the main tool to prove our main result

existence theory for nonlinear fredholm and volterra integral equations on half open intervals in this chapter we present existence theory for the nonlinear fredholm integral equation y t h t smallint 0 t k t s g s y s ds 4 1 1 and the nonlinear volterra integral equation y t h t smallint 0 t k t s g s y s ds 4 1 2 when both are defined on the compact interval 0 t naturally we first concern ourselves with existence principles for both equations

eigenfrequencies of tapered rectangular plates with intermediate line supports the free vibrations of a wide range of tapered rectangular plates with an arbitrary number of intermediate line supports in one or two directions are investigated the domain of the plate is bounded by x a a 0 1 and y b b 0 1 in the rectangular co ordinates the thickness of the plate is continuously varying and proportional to a power function xsyt a variety of tapered rectangular plates can be described by giving the taper factors s and t various values the intermediate line supports run parallel to the edges of the plate a new set of admissible functions which are the static solutions of the tapered beam with intermediate point supports or a strip taken from the plate structure in one or the other direction under a taylor series of loads is developed consistent convergency independent of the truncation factors and of the plate can be obtained by taking the midpoint of the beam as the expanding point of the taylor series unlike conventional admissible functions this set of static beam functions can appropriately vary with the thickness variation of the plate the eigenfrequency equation of the plate is derived by the rayleigh ritz approach a general computer program has been compiled it can be seen that the convergency of the numerical computation is very rapid and that the first few eigenfrequencies can be obtained with good accuracy by using only a small number of terms of the static beam functions sets of first time reported eigenfrequency data are included for future reference

on integral equations of urysohn volterra type the existence of solutions to urysohn volterra equation in a locally convex topological hausdorff space has been established the schauder tychonoff theorem is the main tool in our analysis

the worst case time complexity for generating all maximal cliques and computational experiments we present a depth first search algorithm for generating all maximal cliques of an undirected graph in which pruning methods are employed as in the bron kerbosch algorithm all the maximal cliques generated are output in a tree like form subsequently we prove that its worst case time complexity is o 3n 3 for an n vertex graph this is optimal as a function of n since there exist up to 3n 3 maximal cliques in an n vertex graph the algorithm is also demonstrated to run very fast in practice by computational experiments

application of simulation function and measure of noncompactness for solvability of nonlinear functional integral equations and introduction to an iteration algorithm to find solution abstract the aim of this article is to investigate the existence of solution for the nonlinear functional integral equations with the help of measure of noncompactness simulation function and generalized darbo fixed point theorem also we provided example for the applicability of obtained results to the theory of integral equations also we introduce an iteration algorithm by modified homotopy perturbation and adomian decomposition method to find solution of the above problem with high accuracy finally we have a discussion about convergence and upper bound of error

investigation on the existence of solutions for some nonlinear functional integral equations abstract we prove an existence theorem for a nonlinear integral equation which is a volterra counterpart of an integral equation arising in traffic theory using the technique of the measure of noncompactness in banach algebra we prove an existence theorem for a nonlinear functional integral equation basic fixed point theorems such as darbo s theorem are employed to obtain the aforementioned aims in banach algebra

solvability of urysohn integral equation in this paper we present the existence theorem of integrable solutions of urysohn integral equation in the class of monotonic functions the proof of that theorem is based on the fixed point theorem associated with the notion of a measure of noncompactness

regular edge labeling of 4 connected plane graphs and its applications in graph drawing problems abstract in this paper we extend the concept of the regular edge labeling for general plane graphs and for triconnected triangulated plane graphs to 4 connected triangulated plane graphs we present two different linear time algorithms for constructing such a labeling by using regular edge labeling we present a new linear time algorithm for constructing rectangular dual of planar graphs our algorithm is simpler than previously known algorithms the coordinates of the rectangular dual constructed by our algorithm are integers while the one constructed by known algorithms are real numbers our second regular edge labeling algorithm is based on canonical ordering of 4 connected triangulated plane graphs by using this technique we present a new algorithm for constructing visibility representation of 4 connected planar graphs our algorithm reduces the size of the representation by a factor of 2 for such graphs

on existence of integrable solutions of a functional integral equation under caratheodory conditions abstract we study the solvability of a functional integral equation in the space of lebesgue integrable functions on an unbounded interval using the conjunction of the technique of measures of weak noncompactness with the classical schauder fixed point principle we show that the equation in question is solvable in the mentioned function space our existence result is obtained under the assumption that functions involved in the investigated functional integral equation satisfy caratheodory conditions moreover that result generalizes several ones obtained earlier in many research papers and monographs

fixed points and best proximity points in contractive cyclic self maps satisfying constraints in closed integral form with some applications this paper investigates the existence of best proximity points and the potential fixed points of p cyclic self maps which are defined on the union of a finite set of subsets of a certain uniform metric space under several integral type contractive conditions the corresponding properties of the associated restricted composed maps from any of the subsets to itself are also dealt with in a formal context the above subsets of the uniform metric space are not assumed to necessarily intersect but the case when they intersect leads to particular results of the general case in the sense that best proximity points become fixed points common fixed points and best proximity points of pairs of self maps on the above subsets of the uniform metric space are also investigated

planar orientations with low out degree and compaction of adjacency matrices abstract we consider the problem of orienting the edges of a planar graph in such a way that the out degree of each vertex is minimized if for each vertex v the out degree is at most d then we say that such an orientation is d bounded we prove the following results each planar graph has a 5 bounded acyclic orientation which can be constructed in linear time each planar graph has a 3 bounded orientation which can be constructed in linear time a 6 bounded acyclic orientation and a 3 bounded orientation of each planar graph can each be constructed in parallel time o log n log n on an erew pram using o n log n log n processors as an application of these results we present a data structure such that each entry in the adjacency matrix of a planar graph can be looked up in constant time the data structure uses linear storage and can be constructed in linear time

free vibration analysis of tapered rectangular plates by differential quadrature method a semi analytical approach abstract the particular type of thin rectangular plate configurations considered in the present work are the ones having two opposite edges simply supported and are of varying thickness between the other two edges the boundary conditions at these two edges may be quite general the plates may isotropic or specially orthotropic for the numerical solution to evaluate the free vibration characteristics of such plates a semi analytical approach is adopted first by using the trigonometric sine functions for the mode shape between the simply supported edges the eigenvalue partial differential equation is reduced to an ordinary differential equation the solution of the reduced equation is then carried out by the differential quadrature method on the basis of comparison with the available results in the published literature it is believed that this solution method is capable of yielding highly accurate results moreover the very small computation times required for the evaluation of the vibration characteristics demonstrate the high computational efficiency of the method and point to its possible use in the real time analysis and design of vibrating plate systems

monotonic solutions of a quadratic integral equation of volterra type abstract we study a nonlinear quadratic integral equation of volterra type in the banach space of real functions defined and continuous on a bounded and closed interval with the help of a suitable measure of noncompactness we show that the mentioned integral equation has monotonic solutions

the global attractivity and asymptotic stability of solution of a nonlinear integral equation abstract in this paper we employ the fixed point theorem to study the existence of an integral equation and obtain the global attractivity and asymptotic stability of solutions of the equation some new results are given

on a quadratic fractional hammerstein volterra integral equation with linear modification of the argument abstract we study the existence of monotonic solutions of a quadratic fractional hammerstein volterra integral equation with linear modification of the argument the quadratic integral equation studied below contains as a special case numerous integral equations encountered in the theory of radiative transfer and in the kinetic theory of gases we show that the quadratic fractional hammerstein volterra integral equation with linear modification of the argument has a monotonic solution in the banach space of all real functions defined and continuous on a bounded and closed interval the concept of measure of noncompactness and a fixed point theorem due to darbo are the main tools in carrying out our proof

on monotonic solutions of an integral equation of volterra type with supremum abstract using a technique associated with measures of noncompactness we prove the existence of nondecreasing solutions of an integral equation of volterra type in c 0 1

an equation of hammerstein type arising in particle transport theory an equation of hammerstein type arising in particle transport theory is derived a sufficient condition for the existence of a solution to it is obtained via a simple application of the contracting mapping principle

threesomes degenerates and love triangles the 3sum problem is to decide given a set of n real numbers whether any three sum to zero it is widely conjectured that a trivial o n2 time algorithm is optimal on the real ram and optimal even in the nonuniform linear decision tree model over the years the consequences of this conjecture have been revealed this 3sum conjecture implies n2 lower bounds on numerous problems in computational geometry and a variant of the conjecture for integer inputs implies strong lower bounds on triangle enumeration dynamic graph algorithms and string matching data structures in this article we refute the conjecture that 3sum requires n2 in the real ram and refute more forcefully the conjecture that its complexity is n2 in the linear decision tree model in particular we prove that the decision tree complexity of 3sum is o n3 2s log n and give two subquadratic 3sum algorithms a deterministic one running in o n2 log n log log n 2 3 time and a randomized one running in o n2 log log n 2 log n time with high probability our results lead directly to improved bounds on the decision tree complexity of k variate linear degeneracy testing for all odd k 3 finally we give a subcubic algorithm for a generalization of the min product over real valued matrices and apply it to the problem of finding zero weight triangles in edge weighted graphs we give a depth o n5 2s log n decision tree for this problem as well as a deterministic algorithm running in time o n3 log log n 2 log n

arboricity and subgraph listing algorithms in this paper we introduce a new simple strategy into edge searching of a graph which is useful to the various subgraph listing problems applying the strategy we obtain the following four algorithms the first one lists all the triangles in a graph g in o a g m time where m is the number of edges of g and a g the arboricity of g the second finds all the quadrangles in o a g m time since a g is at most three for a planar graph g both run in linear time for a planar graph the third lists all the complete subgraphs k l of order l in o la g l 2 m time the fourth lists all the cliques in o a g m time per clique all the algorithms require linear space we also establish an upper bound on a g for a graph g a g leqq lceil 2m n 1 2 rceil where n is the number of vertices in g

on a functional integral equation with deviating arguments we study the solvability of a functional integral equation with deviating arguments where our investigations take place in the space of lebesgue integrable functions on an unbounded interval in this space we show that our functional integral equation has at least one nonnegative and nonincreasing solution the proof of our main result is based on a suitable combination of the technique associated with measures of noncompactness in both the weak and the strong sense and the darbo fixed point in the end we conclude an example to illustrate our abstract results

the numerical solution of nonlinear two dimensional volterra fredholm integral equations of the second kind based on the radial basis functions approximation with error analysis in this paper we present a numerical method for solving two dimensional nonlinear volterra fredholm integral equations of the second kind the method approximates the solution by the discrete collocation method based on radial basis functions rbfs constructed on a set of disordered data the proposed method is meshless since it does not require any background mesh or domain elements error analysis of this method is also investigated numerical examples which compare the proposed method with 2d tfs method 4 approve its supremacy in terms of accuracy and computational cost using various rbfs we have concluded that mq rbf is the best choice for the proposed method

hardness of rna folding problem with four symbols abstract an rna sequence is a string composed of four types of nucleotides a c g and u the goal of the rna folding problem is to find a maximum cardinality set of crossing free pairs of the form a u or c g in a given rna sequence the problem is central in bioinformatics and has received much attention over the years abboud backurs and williams focs 2015 demonstrated a conditional lower bound for a generalized version of the rna folding problem based on a conjectured hardness of the k clique problem their lower bound requires the rna sequence to have at least 36 types of symbols making the result not applicable to the rna folding problem in real life i e alphabet size 4 in this paper we present an improved lower bound that works for the alphabet size 4 case we also investigate the dyck edit distance problem which is a string problem closely related to rna folding we demonstrate a reduction from rna folding to dyck edit distance with alphabet size 10 this leads to a much simpler proof of the conditional lower bound for dyck edit distance problem given by abboud backurs and williams focs 2015 and lowers the alphabet size requirement

vibration analysis of multi span plates having orthogonal straight edges abstract an accurate numerical technique is developed for flexural vibration of rectangular and l shaped plates continuous over rigid supports with arbitrary number of spans a set of orthogonally generated two dimensional plates function is used in the rayleigh ritz method to determine the natural frequencies of the plate systems several numerical examples are presented and the results obtained where possible are compared with the known solutions in the literature the present method is proven to be extremely versatile in solving a broad class of the aforementioned problems

monotonic solutions of a quadratic integral equation of fractional order abstract in the paper we indicate an error made in the proof of the main result of the paper m a darwish on quadratic integral equation of fractional orders j math anal appl 311 2005 112 119 moreover we provide correct proof of a slightly modified version of the mentioned result the main tool used in our proof is the technique associated with the hausdorff measure of noncompactness

existence of solutions to singular integral equations abstract nonnegative solutions are established for singular integral equations of the form y t h t t 0 k t s f s y s ds for t 0 t here f may be singular at y 0

online parameterized dictionary matching with one gap abstract we study the online parameterized dictionary matching with one gap problem pdmog which is the following preprocess a dictionary d of d patterns where each pattern contains a special gap symbol that can match any string so that given a text t arriving online a character at a time we can report all the patterns from d that parameterized match to suffixes of the text that has arrived so far before the next character arrives two equal length strings are a parameterized match if there exists a bijection on the alphabets such that one string matches the other under the bijection the gap symbols are associated with bounds determining the possible lengths of matching strings online dictionary matching with one gap dmog captures the difficulty in a bottleneck procedure for cyber security as many digital signatures of viruses manifest themselves as patterns with a single gap parameterized match captures possible encryption of the patterns we also define the strict pdmog problem in which subpatterns of the same dictionary pattern should be parameterized matched via the same bijection this captures situations where subpatterns of a dictionary pattern are encoded simultaneously we study this problem for special case called alphabet saturated dictionairy where every subpattern contains all characters of the dictionary alphabet we use the following parameters to describe our results d is the total size of the dictionary not including the gaps plsc is the longest parameterized suffix chain of subpatterns in d op is the number of parameterized patterns occurrences in t and are the minimum left and maximum right gap borders in the non uniformly bounded dictionary case g d is the degeneracy of the graph g d representing dictionary d this graph is classified as sparse or dense according the value of the g d and plsc parameters we obtain o d preprocessing time space and o g d plsc plsc max m o p query time per text character algorithm for online pdmog with sparse graph dictionaries o d d preprocessing time space and o plsc d plsc max m o p query time per text character algorithm for online pdmog with dense graph dictionaries o d preprocessing time space and o g d plsc o p query time per text character algorithm for strict pdmog with alphabet saturated dictionaries these results are parallel to the ones obtained for the dictionary with one gap dmog problem almost matching the lower bounds achieved for this problem 7 while the parameter g d can be as large as d and much lager if the dictionary has non uniform gap boundaries and the parameter plsc could theoretically be as large as d in many practical situations these parameters are actually small the strength of our work is in achieving results that explore and exploit small values for these parameters thus supplying algorithms that are suitable for some practical cyber security needs

eigenfrequencies of line supported rectangular plates abstract a set of series consisting of a combination of free vibrating beam functions and polynomials is used as the admissible functions in the rayleigh ritz method to study the problem of the flexural vibration of thin uniform thickness orthotropic rectangular plates which may be continuous over several supports in one or two directions in practice which kind of free vibrating beam functions are used is determined by the boundary conditions of the plate the starting order of the beam eigenfunctions and the number of terms in the polynomials in each direction depend on the number of intermediate line supports in that direction the coefficients of the polynomials are decided by the boundary conditions of the plate and the locations of the line supports some numerical results are given for the simply supported and or clamped rectangular plates with two and three spans in one and two directions it is demonstrated that the method may be used to tackle such plate problems and has considerable accuracy and fast convergence compared with the available results the difficulty of application not being greater than any other methods

main memory triangle computations for very large sparse power law graphs finding counting and or listing triangles three vertices with three edges in massive graphs are natural fundamental problems which have recently received much attention because of their importance in complex network analysis here we provide a detailed survey of proposed main memory solutions to these problems in a unified way we note that previous authors have paid surprisingly little attention to space complexity of main memory solutions despite its both fundamental and practical interest we therefore detail space complexities of known algorithms and discuss their implications we also present new algorithms which are time optimal for triangle listing and beats previous algorithms concerning space needs they have the additional advantage of performing better on power law graphs which we also detail we finally show with an experimental study that these two algorithms perform very well in practice allowing us to handle cases which were previously out of reach

counting triangles in massive graphs with mapreduce graphs and networks are used to model interactions in a variety of contexts there is a growing need to quickly assess the characteristics of a graph in order to understand its underlying structure some of the most useful metrics are triangle based and give a measure of the connectedness of mutual friends this is often summarized in terms of clustering coefficients which measure the likelihood that two neighbors of a node are themselves connected computing these measures exactly for large scale networks is prohibitively expensive in both memory and time however a recent wedge sampling algorithm has proved successful in efficiently and accurately estimating clustering coefficients in this paper we describe how to implement this approach in mapreduce to deal with massive graphs we show results on publicly available networks the largest of which is 132m nodes and 4 7b edges as well as artificially generated networks using the graph500 benchmark the largest of which has 240m nodes and 8 5b edges

arboricity h index and dynamic algorithms we propose a new data structure for manipulating graphs called h graph which is particularly suited for designing dynamic algorithms the structure itself is simple consisting basically of a triple of elements for each vertex of the graph the overall size of all triples is o n m for a graph with n vertices and m edges we describe algorithms for performing the basic operations related to dynamic applications as insertions and deletions of vertices or edges and adjacency queries the data structure employs a technique first described by chiba and nishizeki chiba nishizeki arboricity and subgraph listing algorithms siam j comput 14 1 1985 210 223 and relies on the arboricity of graphs using the proposed data structure we describe several dynamic algorithms for solving problems as listing the cliques of a given size recognizing diamond free graphs and finding simple simplicial and dominated vertices these algorithms are the first of their kind to be proposed in the literature in fact the dynamic algorithms for the above problems lead directly to new static algorithms and using the data structure we also design new static algorithms for the problems of counting subgraphs of size 4 recognizing cop win graphs and recognizing strongly chordal graphs the complexities of all of the proposed static algorithms improve over the complexities of the so far existing algorithms for graphs of low arboricity in addition for the problems of counting subgraphs of size 4 and recognizing diamond free graphs the improvement is general

vibration and buckling of tapered rectangular plates with two opposite edges simply supported and the other two edges elastically restrained against rotation abstract the paper describes an application of a method of power series expansions to the free vibration and buckling problems of isotropic rectangular plates with linear thickness variation the plates are simply supported on the two opposite edges parallel to the direction of thickness variation and the other two edges are elastically restrained against rotation by the present method one can solve exactly the governing equation with variable coefficients the choice of the origin for the power series expansion plays an important role in obtaining rapid convergence and accurate results the effects of thickness variation and rotational stiffness of the elastic spring on the eigenvalues and mode shapes are shown numerically and graphically on the basis of new results obtained by the present exact analysis

map graphs we consider a modified notion of planarity in which two nations of a map are considered adjacent when they share any point of their boundaries not necessarily an edge as planarity requires such adjacencies define a map graph we give an np characterization for such graphs derive some consequences regarding sparsity and coloring and survey some algorithmic results

on floor plan of plane graphs a floor plan is a rectangle partitioned into a set of disjoint rectilinear polygonal regions called modules a floor plan f represents a plane graph g as follows each vertex of g corresponds to a module of f and two vertices are adjacent in g iff their corresponding modules share a common boundary floor plans find applications in vlsi chip design if a module m is a union of k disjoint rectangles m is called a k rectangle module it was shown in k h yeap and m sarrafzadeh siam j comput 22 1993 pp 500 526 that every triangulated plane graph g has a floor plan using 1 2 and 3 rectangle modules in this paper we present a simple linear time algorithm that constructs a floor plan for g using only 1 and 2 rectangle modules

map graphs having witnesses of large girth abstract a half square of a bipartite graph b x y e b has one color class of b as vertex set say x two vertices are adjacent whenever they have a common neighbor in y if g v e g is the half square of a planar bipartite graph b v w e b then g is called a map graph and b is a witness of g map graphs generalize planar graphs and have been introduced and investigated by chen grigni and papadimitriou stoc 1998 j acm 2002 they proved that recognizing map graphs is in np by proving the existence of a witness soon later thorup focs 1998 claimed that recognizing map graphs is in p by providing an n 120 time algorithm for n vertex input graphs in this note we give good characterizations and efficient recognition for half squares of bipartite graphs with girth at least a given integer g 8 it turns out that map graphs having witnesses of girth at least g are precisely the graphs whose vertex clique incidence bipartite graph is planar and of girth at least g our structural characterization implies an o n 2 m time algorithm for recognizing if a given n vertex m edge graph g is such a map graph

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

on monotonic solutions of an integral equation of volterra type using a technique associated with measures of noncompactness we prove the existence of nondecreasing solutions to integral equations of volterra type in c 0 1

extended dynamic subgraph statistics using h index parameterized data structures we present techniques for maintaining subgraph frequencies in a dynamic graph using data structures that are parameterized in terms of h the h index of the graph our methods extend previous results of eppstein and spiro for maintaining statistics for undirected subgraphs of size three to directed subgraphs and to subgraphs of size four for the directed case we provide a data structure to maintain counts for all 3 vertex induced subgraphs in o h amortized time per update for the undirected case we maintain the counts of size four subgraphs in o h 2 amortized time per update these extensions enable a number of new applications in bioinformatics and social networking research

new applications of clique separator decomposition for the maximum weight stable set problem graph decompositions such as decomposition by clique separators and modular decomposition are of crucial importance for designing efficient graph algorithms clique separators in graphs were used by tarjan as a divide and conquer approach for solving various problems such as the maximum weight stable set mws problem colouring and minimum fill in the basic tool is a decomposition tree of the graph whose leaves have no clique separator so called atoms and the problem can be solved efficiently on the graph if it is efficiently solvable on its atoms we give new examples where the clique separator decomposition works well for the mws problem our results improve and extend various recently published results in particular we describe the atom structure for some new classes of graphs whose atoms are p 5 free the p 5 is the induced path with five vertices and obtain new polynomial time results for the mws problem the complexity of this problem on the class of p 5 free graphs is still unknown

fixed parameter tractability and completeness ii on completeness for w 1 abstract for many fixed parameter problems that are trivially solvable in polynomial time such as k dominating set essentially no better algorithm is presently known than the one which tries all possible solutions other problems such as feedback vertex set exhibit fixed parameter tractability for each fixed k the problem is solvable in time bounded by a polynomial of degree c where c is a constant independent of k in a previous paper the w hierarchy of parameterized problems was defined and complete problems were identified for the classes w t for t 2 our main result shows that independent set is complete for w 1

tau approximation method for the weakly singular volterra hammerstein integral equations in this paper we propose a useful method based on the tau method with arbitrary bases to find the numerical solution of weakly singular voletrra hammerstein integral equations in this scheme an operational approach using the orthogonal polynomial bases is presented for converting the problem under consideration to its matrix vector representation error analysis of this method is also presented some numerical examples are provided to illustrate the accuracy and computational efficiency of the method

the application of a new finite strip to the free vibration of rectangular plates of varying complexity abstract a new finite strip method is applied to the vibration of rectangular plates with complicated boundary and internal support conditions based on the classical thin plate theory and displacement formulation the new finite strip element is conforming with formula continuity the displacement function of the strip element is expressed as the product of cubic hermitian functions in the transverse direction and a set of computed static modes in the longitudinal direction by means of a continuous beam computer program these longitudinal modes can be computeda priori numerical examples are given to demonstrate the versatility accuracy and efficiency of the element

induced subgraph isomorphism the complexity of the subgraph isomorphism problem where the pattern graph is of fixed size is well known to depend on the topology of the pattern graph here we present two results which in contrast provide evidence that no topology of an induced subgraph of fixed size can be substantially easier to detect or count than an independent set of related size we show that any fixed pattern graph having a maximum independent set of size k that is disjoint from other maximum independent sets is not easier to detect as an induced subgraph than an independent set of size k it follows in particular that an induced path on 2 k 1 vertices is not easier to detect than an independent set on k vertices and that an induced cycle on 2k vertices is not easier to detect than an independent set on k vertices in view of linear time upper bounds on the detection of induced path of length two and three our lower bound is tight similar corollaries hold for the detection of induced complete bipartite graphs and an induced paw and its generalizations we show also that for an arbitrary pattern graph h on k vertices with no isolated vertices there is a simple subdivision of h resulting from splitting each edge into a path of length four and attaching a distinct path of length three at each vertex of degree one that is not easier to detect or count than an independent set on k vertices respectively next we show that the so called diamond and its generalizations on k vertices are not easier to detect as induced subgraphs than an independent set on three vertices or an independent set on k vertices respectively for c 4 we give a weaker evidence of its hardness in terms of an independent set on three vertices finally we derive several results relating the complexity of the edge colored variant of induced subgraph isomorphism to that of the standard variant

existence of solutions of functional integral equations of convolution type using a new construction of a measure of noncompactness on l p r let l p r denote the space of lebesgue integrable functions on r with the standard norm x p 0 x t p d t 1 p first we define a new measure of noncompactness on the spaces l p r 1 p in addition we study the existence of entire solutions for a class of nonlinear functional integral equations of convolution type using darbo s fixed point theorem which is associated with the new measure of noncompactness we provide some examples to demonstrate that our results are applicable whereas the previous results are not

a new decomposition technique for maximal clique enumeration for sparse graphs abstract given a graph we are interested in the question of finding all its maximal cliques this question models the community detection problem and has been extensively studied here we approach it under the light of an important graph parameter the degeneracy of a graph g is the smallest integer k such that every subgraph of g contains a vertex of degree at most k using a new decomposition technique we present two output sensitive algorithms for the maximal clique enumeration problem the first one has enumeration time depending only on the degeneracy of the graph this is the first such result in the literature this algorithm requires that the cliques are stored in memory thus we propose a second one which has enumeration time depending on the degeneracy and the maximum degree and which only requires memory polynomial in the degeneracy of the graph besides the space to store the graph itself then we show that this algorithm can be easily parallelized as a by product of our decomposition technique we propose new algorithms for the maximum clique and p clique problems as well as an approximation algorithm counting maximal cliques with approximation ratio the maximum clique size