stochastic and mixed flower graphs stochasticity is introduced to a well studied class of recursively grown graphs u v flower nets which have power law degree distributions as well as small world properties when u 1 the stochastic variant interpolates between different deterministic flower graphs thus adding flexibility to the model the random multiplicative growth process involved however leads to a spread ensemble of networks with finite variance for the number of links nodes and loops nevertheless the degree exponent and loopiness exponent attain unique values in the thermodynamic limit of infinitely large graphs we also study a class of mixed flower networks closely related to the stochastic flowers but which are grown recursively in a deterministic way the deterministic growth of mixed flower nets eliminates ensemble spreads and their recursive growth allows for exact analysis of their uniquely defined mixed properties

the optimal p version approximation of singularities on polyhedra in the boundary element method we consider elliptic boundary value problems on three dimensional polyhedral domains we describe the three types of singular components that arise in the solution edge vertex and edge vertex singularities we analyze the approximation of the traces of each of each of these different types of singularities by polynomial subspaces on the boundary as the polynomial degree p tends to infinity the p version we establish asymptotic rates of convergence that are optimal in the h t norm over the boundary for 0 leq t leq 1 we apply these results to a galerkin boundary element method bem formulation for a model neumann problem obtaining the optimal convergence rate for the p version bem over polyhedral domains

exact solution for mean first passage time on a pseudofractal scale free web the explicit determinations of the mean first passage time mfpt for trapping problem are limited to some simple structure e g regular lattices and regular geometrical fractals and determining mfpt for random walks on other media especially complex real networks is a theoretical challenge in this paper we investigate a simple random walk on the the pseudofractal scale free web psfw with a perfect trap located at a node with the highest degree which simultaneously exhibits the remarkable scale free and small world properties observed in real networks we obtain the exact solution for the mfpt that is calculated through the recurrence relations derived from the structure of psfw the rigorous solution exhibits that the mfpt approximately increases as a power law function of the number of nodes with the exponent less than 1 we confirm the closed form solution by direct numerical calculations we show that the structure of psfw can improve the efficiency of transport by diffusion compared with some other structure such as regular lattices sierpinski fractals and t graph the analytical method can be applied to other deterministic networks making the accurate computation of mfpt possible

enumeration of maximal irredundant sets for claw free graphs abstract domination is one of the classical subjects in structural graph theory and in graph algorithms the minimum dominating set problem and many of its variants are np complete and have been studied from various algorithmic perspectives one of those variants called irredundance is highly related to domination for example every minimal dominating set of a graph g is also a maximal irredundant set of g in this paper we study the enumeration of the maximal irredundant sets of a claw free graph we show that an n vertex claw free graph has o 1 9341 n maximal irredundant sets and these sets can be enumerated in the same time we complement the aforementioned upper bound with a lower bound by providing a family of graphs having 1 5848 n maximal irredundant sets

p adaptive boundary elements this paper presents the implementation of an adaptive philosophy to plane potential problems using the direct boundary element method after some considerations about the state of the art and a discussion of the standard approach features the possibility of separately treating the modelling of variables and their interpolation through hierarchical shape functions is analysed then the proposed indicators and estimators are given followed by a description of a small computer program written for an ibm pc finally some examples show the kind of results to be expected

the p version of the boundary element method for weakly singular operators on piecewise plane open surfaces we study piecewise polynomial approximations in negative order sobolev norms of singularities which are inherent to neumann data of elliptic problems of second order in polyhedral domains the worst case of exterior crack problems in three dimensions is included as an application we prove an optimal a priori error estimate for the p version of the bem with weakly singular operators on polyhedral lipschitz surfaces and piecewise plane open screens

solvability of singular second order m point boundary value problems abstract let f 0 1 r 2 r be a function satisfying caratheodory s conditions and 1 t e t l 1 0 1 let i 0 1 a i r i 1 m 2 0 1 2 m 2 1 be given this paper is concerned with the problem of existence of a c 1 0 1 solution for the m point boundary value problem x f t x t x t e t 0 t 1 0 1 x 0 0 x 1 i 1 m 2 a i x i the proof of our main result is based upon the leray schauder continuation theorem

construction of equilibrated singular basis functions without a priori knowledge of analytical singularity order in this paper a novel method is presented to construct singular basis functions for solving harmonic and bi harmonic problems with weak singularities such bases are found without any knowledge of the singularity order the singular bases are constructed by choosing a series as a tensor product of chebyshev polynomials and trigonometrical functions in radial and angular directions respectively and applying weak form of the governing equation with such features the singular bases are categorized as the equilibrated basis functions the constructed singular functions can be utilized as a complementary part to the smooth part of the approximation in the solution of problems with singularities to demonstrate the efficiency of employing such singular bases they are used in a boundary node method through the solution of some examples selected from the well known literature the capability of the method is shown it will be demonstrated that the main function and its derivatives are excellently approximated at very close neighborhood of the singular point the method may especially be found useful for those who research on the extended finite element method or similar ideas

global bifurcation phenomena for singular one dimensional p laplacian in this paper we present global existence results for the following problem p p u t h t f u t 0 a e in 0 1 u 0 u 1 0 where p x x p 2x p 1 a positive parameter and h a nonnegative measurable function on 0 1 which may be singular at t 0 and or t 1 and f c r r with r 0 by applying the global bifurcation theorem and figuring the shape of unbounded subcontinua of solutions we obtain many different types of global existence results of positive solutions we also obtain existence results of sign changing solutions for p when f is an odd symmetric function

a global bifurcation phenomenon for second order singular boundary value problems we establish an existence result of unbounded continuum of solutions from the trivial branch for a second order singular boundary value problem as an application we prove several existence and multiplicity results of positive solutions for certain singular boundary value problems

positive solutions to singular multi point dynamic eigenvalue problems with mixed derivatives abstract this paper considers a singular m point dynamic eigenvalue problem on time scales t p t u t f t u t t 0 1 t u 0 i 1 m 2 a i u i u 1 p 1 u 1 i 1 m 2 b i p i u i we allow f t w to be singular at w 0 and t 0 by constructing the green s function and studying its positivity eigenvalue intervals in which there exist positive solutions of the above problem are obtained by making use of the fixed point index theory

the optimal rate of convergence of the p version of the boundary element method in two dimensions we introduce the jacobi weighted besov and sobolev spaces in the one dimensional setting in the framework of these spaces we analyze lower and upper bounds for approximation errors in the p version of the boundary element method for hypersingular and weakly singular integral operators on polygons we prove the optimal rate of convergence for the p version in the energy norms of and respectively

the optimal convergence rate of the p version of the finite element method optimal error estimates for the p version of the finite element method in two dimensions are proven for the case when u in h k omega or u has singularities induced by the corners of the domain the case of nonhomogenous essential boundary conditions is also analyzed

an o n m time algorithm for finding a minimum weightdominating set in a permutation graph farber and keil algorithmica 4 1989 pp 221 236 presented an o n 3 time algorithm for finding a minimum weight dominating set in permutation graphs this result was improved to o n 2 log 2n by tsai and hsu sigal 90 algorithms lecture notes in computer science springer verlag new york 1990 pp 109 117 and to o n n m by the authors of this paper inform process lett 37 1991 pp 219 224 respectively in this paper we introduce a new faster algorithm that takes only o n m time to solve the same problem where m is the number of edges in a graph of n vertices

on hp error estimation in the bem for a three dimensional helmholtz exterior problem the purpose of the paper is to give an a priori convergence estimate for the hp adaptive boundary element method the method is used to solve an exterior helmholtz boundary value problem with the robin s boundary condition in the three dimensional space the mathematical model describes an acoustic wave scattering problem on a bounded elastic solid where time harmonic process is assumed the estimate consists of three parts which correspond to influence of three errors caused by interpolation of functions geometry and an incident wave

on the h p version of the boundary element method for symm s integral equation on polygons abstract in this paper we present the numerical implementation of and numerical experiments for the galerkin approximation of symm s integral equation using the h p and h p methods numerical results obtained using an adaptive algorithm are also given the theoretical results for these methods are summarized and are compared with the experimental results

the h p and h p versions of the finite element methods in 1 dimension part iii the adaptive h p version abstract the paper is the third and final part in the series of three devoted to the detailed analysis of the three basic versions of the finite element method in one dimension the first part analyzed the p version and the second part concentrated on the h and h p version this paper analyzes a theoretical frame of the adaptive h p version and based on it the authors provide concrete algorithm for the one dimensional problem it is proven that in the case that the solution has x sub alpha type singularity the adaptive algorithm give an exponential rate of convergence very close to the optimal one analyzed in the second part of the paper additional keyword error analysis

sturm type problems for singular p laplacian boundary value problems in this paper the eigenvalue problem of singular p laplacian boundary value problems is discussed which is a generalization of the classical sturmian theorem for second order ordinary differential equations as an application the existence of solutions to singular boundary value problem is discussed

domination number and minimum dominating sets in pseudofractal scale free web and sierpinski graph abstract the minimum dominating set mds problem is a fundamental subject of theoretical computer science and has found vast applications in different areas including sensor networks protein interaction networks and structural controllability however the determination of the size of a mds and the number of all mdss in a general network is np hard and it thus makes sense to seek particular graphs for which the mds problem can be solved analytically in this paper we study the mds problem in the pseudofractal scale free web and the sierpinski graph which have the same number of vertices and edges for both networks we determine explicitly the domination number as well as the number of distinct mdss we show that the pseudofractal scale free web has a unique mds and its domination number is only half of that for the sierpinski graph which has many mdss we argue that the scale free topology is responsible for the difference of the size and number of mdss between the two studied graphs which in turn indicates that power law degree distribution plays an important role in the mds problem and its applications in scale free networks

the h p version of the boundary element method for transmission problems with piecewise analytic data this paper analyzes the rate of convergence of the h p version of the boundary element galerkin method for transmission problems with piecewise analytic data based on the regularity of solutions of integral equations in terms of countably nonmed spaces we design the geometric mesh on the interface gamma and the boundary element subspace containing piecewise polynomials with varying degrees we prove that the boundary element galerkin solution converges exponentially fast to the solution of the integral equation in the h 1 2 gamma times h 1 2 gamma norm

positive solutions of singular sublinear emden fowler boundary value problems abstract this paper is about the dirichlet boundary value problem of singular sublinear emden fowler equations a necessary and sufficient condition for the existence of positive solutions to this problem has been obtained by using the method of lower and upper solutions the uniqueness of positive solutions has also been discussed

one dimensional p laplacian with a strong singular indefinite weight i eigenvalue abstract in this paper we prove the existence of eigenvalues for the problem p u t h t p u t 0 a e in 0 1 u 0 u 1 0 where p s s p 2 s p 1 is a real parameter and the indefinite weight h is a nonnegative measurable function on 0 1 which may be singular at 0 and or 1 and h 0 on any compact subinterval in 0 1 we derive similar properties of eigenvalues as known in linear case p 2 or continuous case h c 0 1 if h satisfies 0 1 t p 1 1 t p 1 h t d t when 1 p 2 and 0 1 2 p 1 s 1 2 h d d s 1 2 1 p 1 1 2 s h d d s when p 2 respectively for the result we establish the c 1 regularity of all solutions at the boundary for the above problem as well as the following problem p u t h t f u t 0 a e in 0 1 u 0 u 1 0 where f c r r s f s 0 for s 0 f is odd and f s p s is bounded above as s 0

maximum matchings and minimum dominating sets in apollonian networks and extended tower of hanoi graphs abstract the apollonian networks display the remarkable power law and small world properties as observed in most realistic networked systems their dual graphs are extended tower of hanoi graphs which are obtained from the tower of hanoi graphs by adding a special vertex linked to all its three extreme vertices in this paper we study analytically maximum matchings and minimum dominating sets in apollonian networks and their dual graphs both of which have found vast applications in various fields e g structural controllability of complex networks for both networks we determine their matching number domination number the number of maximum matchings as well as the number of minimum dominating sets

pfaffian orientations and perfect matchings of scale free networks counting perfect matchings is of great interest in theoretical computer science mathematics among other disciplines however explicitly determining the number of perfect matchings of general graphs is a challenge in this paper we present a first analytical study of the enumeration problem of perfect matchings on scale free networks which are ubiquitous in real life systems we focus on two iteratively growing scale free networks one is fractal while the other is non fractal for each network we construct an orientation and prove that it is pfaffian then based on the connection between the number of perfect matchings and determinant of the skew adjacency matrix corresponding to a pfaffian orientation we derive the recursive expressions for the number of perfect matchings of the networks at two successive iterations furthermore using the recursive relations we show that for both scale free networks their entropy is zero which is in sharp contrast to the previously obtained results for other networks without scale free behavior but having the same average degree as the studied networks such as square lattice and honeycomb lattice whose entropies are larger than zero our results indicate from another angle that scale free networks have a distinct architecture in comparison with those lattices lacking the power law property

isogemetric analysis and symmetric galerkin bem isogeometric approach applied to boundary element methods is an emerging research area see e g simpson et al 2012 33 in this context the aim of the present contribution is that of investigating from a numerical point of view the symmetric galerkin boundary element method sgbem devoted to the solution of 2d boundary value problems for the laplace equation where the boundary and the unknowns on it are both represented by b splines de boor 2001 9 we mainly compare this approach which we call iga sgbem with a curvilinear sgbem aimi et al 1999 2 which operates on any boundary given by explicit parametric representation and where the approximate solution is obtained using lagrangian basis both techniques are further compared with a standard conventional sgbem approach aimi et al 1997 1 where the boundary of the assigned problem is approximated by linear elements and the numerical solution is expressed in terms of lagrangian basis several examples will be presented and discussed underlying benefits and drawbacks of all the above mentioned approaches

multilevel additive schwarz method for the h p version of the galerkin boundary element method we study a multilevel additive schwarz method for the h p version of the galerkin boundary element method with geometrically graded meshes both hypersingular and weakly singular integral equations of the first kind are considered as it is well known the h p version with geometric meshes converges exponentially fast in the energy norm however the condition number of the galerkin matrix in this case blows up exponentially in the number of unknowns m we prove that the condition number p of the multilevel additive schwarz operator behaves like o mlog 2 m as a direct consequence of this we also give the results for the 2 level preconditioner and also for the h p version with quasi uniform meshes numerical results supporting our theory are presented

a p extension of the symmetric boundary element method abstract this paper describes an implementation of the symmetric galerkin boundary element method for plane potential and elasticity problems on domains with polygonal boundaries the method makes use of the hyper singular boundary integral equations for the normal derivatives of the unknown function we discuss an integration technique which is sufficiently robust to handle p extensions on geometrically graded meshes computer times required compare favorably with corresponding finite element methods we present numerical results obtained by a uniform p extension for various mixed boundary value problems we demonstrate that the same convergence rates can be obtained by the symmetric variational boundary element method as with p extensions of the finite element method on the basis of the p extension process a reliable error estimate based on extrapolation from a sequence of p levels can be obtained this is a unique feature of the variational methods as compared to the classical collocation approach the error estimate remains valid even for boundary element analysis employing substructures and mixed discretizations with boundary elements and finite elements

bifurcation of nodal radial solutions for a prescribed mean curvature problem on an exterior domain abstract we investigate the existence and multiplicity of nodal radial solutions for a prescribed mean curvature problem on the exterior domain of a ball using the global bifurcation theory moreover we establish the asymptotic behavior of the solutions on the subcontinua which bifurcate from a trivial branch all results are obtained by considering a radially equivalent second order problem with a singular weight

efficient sub 5 approximations for minimum dominating sets in unit disk graphs abstract a unit disk graph is the intersection graph of n congruent disks in the plane dominating sets in unit disk graphs are widely studied due to their applicability in wireless ad hoc networks because the minimum dominating set problem for unit disk graphs is np hard numerous approximation algorithms have been proposed in the literature including some ptass however since the proposal of a linear time 5 approximation algorithm in 1995 the lack of efficient algorithms attaining better approximation factors has aroused attention we introduce an o n m algorithm that takes the usual adjacency representation of the graph as input and outputs a 44 9 approximation this approximation factor is also attained by a second algorithm which takes the geometric representation of the graph as input and runs in o n log n time regardless of the number of edges additionally we propose a 43 9 approximation which can be obtained in o n 2 m time given only the graph s adjacency representation it is noteworthy that the dominating sets obtained by our algorithms are also independent sets

the treatment of nonhomogeneous dirichlet boundary conditions by thep version of the finite element method the paper addresses the problem of the implementation of nonhomogeneous essential dirichlet type boundary conditions in thep version of the finite element method

additive schwarz algorithms for the p version of the galerkin boundary element method we study some additive schwarz algorithms for the p version galerkin boundary element method applied to some weakly singular and hypersingular integral equations of the first kind both non overlapping and overlapping methods are considered we prove that the condition numbers of the additive schwarz operators grow at most as 1 log p 2 independently of h where p is the degree of the polynomials used in the galerkin boundary element schemes and h is the mesh size thus we show that additive schwarz methods which were originally designed for finite element discretisation of differential equations are also efficient preconditioners for some boundary integral operators which are non local operators

study of singular boundary value problems for second order impulsive differential equations this paper studies the existence of extremal solutions for a class of singular boundary value problems of second order impulsive differential equations by using the method of upper and lower solutions and the monotone iterative technique criteria of the existence of extremal solutions are established

inapproximability of dominating set on power law graphs we prove the first logarithmic lower bounds for the approximability of the minimum dominating set problem for the case of connected power law graphs for being a size parameter and the power law exponent we give also a best up to now upper approximation bound for this problem in the case of the parameters 2 we develop also a new functional method for proving lower approximation bounds and display a sharp approximation phase transition area between approximability and inapproximability of the underlying problems our results depend on a method which could be also of independent interest

nodal solutions of second order boundary value problems with superlinear or sublinear nonlinearities abstract we consider boundary value problems for nonlinear second order differential equations of the form u a t f u 0 t 0 1 u 0 u 1 0 where a c 1 0 1 0 with a t 0 0 for some t 0 0 1 and f r r is continuous with f s s 0 for s 0 we establish existence and multiplicity results for nodal solutions of the problems if either f 0 0 f or f 0 f 0 where f s s approaches f 0 and f as s approaches 0 and respectively we use bifurcation techniques to prove our main results

the approximation theory for the p version of the finite element method the purpose of this article is to present the approximation theory underlying the p version of the finite element method by exploiting the relationship between polynomial approximation and certain weighted sobolev spaces which are identified as the domains of positive real powers of the legendre operator this one dimensional result is generalized via a tensor product construction to yield a nonconforming piecewise polynomial approximation result in the usual unweighted sobolev spaces on triangulated domains of r n it is then shown that essentially the same result holds for approximation by conforming piecewise polynomials provided that the function being approximated possesses the same degree of conformality across the common boundaries of adjacent simplices and the same homogeneous boundary conditions inverse results are given for the special case of approximation in l 2

minimal dominating sets in graph classes combinatorial bounds and enumeration abstract the number of minimal dominating sets that a graph on n vertices can have is known to be at most 1 715 9 n this upper bound might not be tight since no examples of graphs with 1 570 5 n or more minimal dominating sets are known for several classes of graphs we substantially improve the upper bound on the number of minimal dominating sets at the same time we give algorithms for enumerating all minimal dominating sets where the running time of each algorithm is within a polynomial factor of the proved upper bound for the graph class in question in several cases we provide examples of graphs containing the maximum possible number of minimal dominating sets for graphs in that class thereby showing the corresponding upper bounds to be tight

a hypersingular boundary integral method for two dimensional screen and crack problems we analyze hypersingular integral equations on a curved open smooth arc in r 2 that model either curved cracks in an elastic medium or the scattering of acoustic and elastic waves at a hard screen by using the mellin transformation we obtain sharp regularity results for the solution of these equations in sobolev spaces in the form of singular expansions in particular we show that the expansions do not contain logarithmic singularities

the h p boundary element method for solving 2 and 3 dimensional problems abstract in this survey paper we report on recent developments of the hp version of the boundary element method we consider weakly singular and hypersingular integral equations on polygons and polyhedral surfaces we show that the galerkin solutions computed with the hp version on geometric meshes converge exponentially fast towards the exact solutions of the integral equations the implementation of the hp version of the boundary element method is discussed and adaptive algorithms are given model problems for the coupling of finite elements and boundary elements are also considered numerical results are presented which underline the theoretical results

efficient algorithms for the domination problems on interval and circular arc graphs this paper first presents a unified approach to design efficient algorithms for the weighted domination problem and its three variants i e the weighted independent connected and total domination problems on interval graphs given an interval model with endpoints sorted these algorithms run in time o n or o n log log n where n is the number of vertices the results are then extended to solve the same problems on circular arc graphs in o n m time where m is the number of edges of the input graph

on the number of minimal dominating sets on some graph classes a dominating set in a graph is a subset of vertices such that each vertex is either in the dominating set or adjacent to some vertex in the dominating set it is known that graphs have at most o 1 7159 n minimal dominating sets in this paper we establish upper bounds on this maximum number of minimal dominating sets for split graphs cobipartite graphs and interval graphs for each of these graph classes we provide an algorithm to enumerate them for split and interval graphs we show that the number of minimal dominating sets is at most 3 n 3 1 4423 n which is the best possible bound this settles a conjecture by couturier et al sofsem 2012 1 for cobipartite graphs we lower the o 1 5875 n upper bound from couturier et al to o 1 4511 n

existence result for a singular nonlinear boundary value problem at resonance we study the existence of solutions of the second order boundary value problems u t 2u t a t g u t h t a e t 0 1 u acloc 0 1 u 0 u 1 0 where g r r is continuous a h z lloc1 0 1 01t z t dt the proof of the main result is based upon the lyapunov schmidt procedure and the connectivity properties of the solution set of parametrized families of compact vector fields

node deletion problems on bipartite graphs a set of problems which has attracted considerable interest recently is the set of node deletion problems the general node deletion problem can be stated as follows given a graph find the minimum number of nodes whose deletion results in a subgraph satisfying property r in ly this problem was shown to be np complete for a large class of properties the class of properties that are hereditary on induced subgraphs using a small number of reduction schemes from the node cover problem since the node cover problem becomes polynomial on bipartite graphs it might be hoped that this is the case with other node deletion problems too in this paper we characterize those properties for which the bipartite restriction of the node deletion problem is polynomial and those for which it remains np complete similar results follow for analogous problems on other structures such as families of sets hypergraphs and 0 1 matrices for example in the case of matrices our result states that ifm is a class of 0 1 matrices which is closed under permutation and deletion of rows and columns then finding the largest submatrix inm of a matrix is polynomial if the matrices ofm have bounded rank and np complete otherwise 1 introduction a common approach when faced with an np complete problem c k gj is to restrict its input domain with the hope that the problem may become solvable in polynomial time under the restriction in fact it turns out that sometimes this is the case for example the node cover problem np complete on general graphs k can be solved efficiently when restricted to bipartite graphs this follows from k6nig s theorem that the node covering number of a bipartite graph equals the number of edges in a maximum matching and moreover a minimum node cover can be found efficiently from a maximum matching when the graph is bipartite see for example la in other cases however the node cover problem continues to be np complete under restriction for example the node cover problem on planar graphs gjs much work has been done recently kd ly ldl on a class of problems called the node deletion or maximum subgraph problems the general node deletion problem can be stated as follows given a graph or digraph g find a set of nodes of minimum cardinality whose deletion results in a graph or digraph satisfying a property r several of the known np complete problems such as the node cover the max clique the feedback node set k as well as some polynomial problems such as the connectivity of a graph e it can be formulated in an obvious way as node deletion problems by specifying appropriately the property r

the h p and h p versions of the finite element method in 1 dimension this paper is the first one in the series of three which are addressing in detail the properties of the three basic versions of the finite element method in the one dimensional setting the main emphasis is placed on the analysis when the exact solution has singularity of x type the first part analyzes thep version the second theh version and generalh p version and the final third part addresses the problems of the adaptiveh p version

the p version of the finite element method for constraint boundary conditions abstract this paper addresses the implementation of general constraint boundary conditions for a system of equations by the p version of the finite element method by constraint boundary conditions the authors mean conditions where some relation between the components is prescribed at the boundary optimal error bounds are proven keywords convergence sobolev spaces

enumerating minimal connected dominating sets in graphs of bounded chordality enumerating objects of specified type is one of the principal tasks in algorithmics in graph algorithms one often enumerates vertex subsets satisfying a certain property we study the enumeration of all minimal connected dominating sets of an input graph from various graph classes of bounded chordality we establish enumeration algorithms as well as lower and upper bounds for the maximum number of minimal connected dominating sets in such graphs in particular we present algorithms to enumerate all minimal connected dominating sets of chordal graphs in time o 1 7159 n of split graphs in time o 1 3803 n and of at free strongly chordal and distance hereditary graphs in time o 3 n 3 where n is the number of vertices of the input graph our algorithms imply corresponding upper bounds for the number of minimal connected dominating sets for these graph classes

analytic regularity of stokes flow on polygonal domains in countably weighted sobolev spaces we investigate the analytic regularity of the stokes problem in a polygonal domain r2 with straight sides and piecewise analytic data we establish a shift theorem in weighted sobolev spaces of arbitrary order with explicit control of the order dependence of the constants the shift theorem in the framework of countably weighted sobolev spaces implies in particular interior analyticity and gevrey type analytic regularity near the corners

nonresonant nonlinear singular problems in the limit circle case existence results are presented for the resonant singular boundary value problem tfrac 1 p py prime prime lambda m qy f t y a e on 0 1 with limt 0 py y 1 0 here we donot assume int 0 1 tfrac ds p s infty but only that int 0 1 tfrac 1 p s left int 0 s p x q x dx right tfrac 1 2 ds infty

solution of elastic scattering problems in linear acoustics using h p boundary element methods abstract a simplified model problem reduced from the general class of elastic scattering problems is analyzed both classical helmholtz and hypersingular formulations are discussed and a general h p boundary element method based on the burton miller combination of both approaches is formulated a simple l 2 residual a posteriori error estimate is discussed as a basis of adaptive h or p refinements

dimer coverings on the sierpinski gasket we present the number of dimer coverings nd n on the sierpinski gasket sgd n at stage n with dimension d equal to two three four or five when the number of vertices denoted as v n of the sierpinski gasket is an even number nd n is the number of close packed dimers when the number of vertices is an odd number no close packed configurations are possible and we allow one of the outmost vertices uncovered the entropy of absorption of diatomic molecules per site defined as s mathit sg d lim n to infty ln n d n v n is calculated to be ln 2 3 exactly for sg2 the numbers of dimers on the generalized sierpinski gasket sgd b n with d 2 and b 3 4 5 are also obtained exactly with entropies equal to ln 6 7 ln 28 12 ln 200 18 respectively the number of dimer coverings for sg3 is given by an exact product expression such that its entropy is given by an exact summation expression the upper and lower bounds for the entropy are derived in terms of the results at a certain stage for sgd n with d 3 4 5 as the difference between these bounds converges quickly to zero as the calculated stage increases the numerical value of s mathit sg d with d 3 4 5 can be evaluated with more than a hundred significant figures accurate

pseudofractal scale free web we find that scale free random networks are excellently modeled by simple deterministic graphs our graph has a discrete degree distribution degree is the number of connections of a vertex which is characterized by a power law with exponent gamma 1 ln 3 ln 2 properties of this compact structure are surprisingly close to those of growing random scale free networks with gamma in the most interesting region between 2 and 3 we succeed to find exactly and numerically with high precision all main characteristics of the graph in particular we obtain the exact shortest path length distribution for a large network ln n 1 the distribution tends to a gaussian of width approximately sqrt ln n centered at l approximately ln n we show that the eigenvalue spectrum of the adjacency matrix of the graph has a power law tail with exponent 2 gamma

on the convergence of the p version of the boundary element galerkin method abstract the authors consider various physical problems which may be formulated in terms of integral equations of the first kind including the two dimensional screen neumann and dirichlet problems in acoustics and crack problems in elasticity sharp regularity results for the solutions are available for these problems proven is the convergence of the p version for some galerkin boundary element schemes based on the integral equation formulations it is shown that the rate of convergence obtained by our method is twice that for the usual h version

solution of elastic scattering problems in linear acoustics using h p boundary element method abstract the work is a continuation of 1 a simplified 3d model problem reduced from the general class of elastic scattering problems is analyzed focusing attention on such practical details of the 3d implementation as a triangles based h p approximation and corresponding data structure integration of singular integrals and its effect on theoretically optimal rates of convergence a posteriori error estimation and sample adaptive strategies

the p version of the finite element method in the p version of the finite element method the triangulation is fixed and the degree p of the piecewise polynomial approximation is progressively increased until some desired level of precision is reached in this paper we first establish the basic approximation properties of some spaces of piecewise polynomials defined on a finite element triangulation these properties lead to an a priori estimate of the asymptotic rate of convergence of the p version the estimate shows that the p version gives results which are not worse than those obtained by the conventional finite element method called the h version in which h represents the maximum diameter of the elements when quasi uniform triangulations are employed and the basis for comparison is the number of degrees of freedom furthermore in the case of a singularity problem we show under conditions which are usually satisfied in practice that the rate of convergence of the p version is twice that of the h version with quasi uniform mesh inve

singular dirichlet problem for ordinary differential equation with impulses abstract the paper deals with the impulsive dirichlet problem u t f t u t u t u 0 a u t b u t j i j u t j u t j m j u t j j 1 p where f car 0 t r 2 f has time singularities at t 0 and t t i j m j c 0 r a b r we prove the existence of a solution to this problem under the assumption that there exist lower and upper functions associated with the problem our proofs are based on the schauder fixed point theorem and on the method of a priori estimates

optimal greedy algorithms for indifference graphs abstract a fundamental problem in social sciences and management is understanding and predicting decisions made by individuals various groups or the society as a whole in this context one important concept is the notion of indifference we characterize the class of indifference graphs that is graphs which arise in the process of quantifying indifference relations in particular we show that these graphs are characterized by the existence of a special ordering of their vertices as it turns out this ordering leads naturally to optimal greedy algorithms for a number of computational problems including coloring finding a shortest path between two vertices computing a maximum matching the center and a hamiltonian path

enumeration and maximum number of minimal dominating sets for chordal graphs abstract we study the enumeration of the minimal dominating sets and upper bounds for the number of such sets in chordal graphs we show that the maximum number of minimal dominating sets of an n vertex chordal graph is at most 1 5048 n and prove that these sets can be enumerated in time o 1 5048 n in this way we improve the previous upper bound of 1 5214 n recently established by abu khzam and heggernes and narrow the gap between the upper bound and the known lower bound of 1 4422 n

existence and multiplicity results for nonlinear boundary value problems this paper studies the existence of positive solutions for a class of boundary value problems of elliptic degenerate equations by using bifurcation and fixed point index theories in the frame of approximation arguments the criteria of the existence multiplicity and nonexistence of positive solutions are established

positive solutions for singular m point boundary value problems with positive parameter in this paper some new existence results for positive solutions for a class of singular m point boundary value problems with parameter be obtained

mathematical foundation of adaptive boundary element methods abstract in this paper we review some mathematical aspects of adaptive boundary element methods in brief and give some a posteriori local error estimates for the h version and the p version

nodal solutions for singular nonlinear eigenvalue problems abstract we are concerned with determining values of r for which there exist nodal solutions of the boundary value problems u r a t f u 0 0 t 1 u 0 u 1 0 where r is a parameter and a 0 1 0 is continuous and satisfies 0 0 1 t 1 t a t d t the proof of our main result is based on bifurcation techniques