a numerical method for a class of non linear integro differential equations on the half line we design and analyse a numerical method for the solution of the following second order integro differential boundary value problem n y g y email protected 0 k x g x dx d y g y p y g 0 0 limy g y 0 which arises in the study of the kinetic theory of dusty plasmas the method we propose represents a first insight into the numerical solution of more complicated problems and consists of a discretization of the differential and integral terms and of an iteration process to solve the resulting non linear system under suitable hypotheses we prove the convergence we will show the characteristics of the method by means of some numerical simulations

out of plane vibrations of curved non uniform beams of constant radius the governing differential equations for out of plane vibrations of curved non uniform beams of constant radius are derived two physical parameters are introduced to simplify the analysis the explicit relations between the flexural displacement its first three order derivatives and the torsional displacement are derived with these explicit relations the two coupled governing characteristic differential equations can be decoupled and reduced to a sixth order ordinary differential equation with variable coefficients in the torsional displacement it is shown that if the material and geometric properties of the beam are in arbitrary polynomial forms of spatial variable then exact solutions for the out of plane vibrations of the beam can be obtained the derived explicit relations can also be used to reduce the difficulty in experimental measurements finally the influence of taper ratio center angle and arc length on the first two natural frequencies of the beams is illustrated

analytical and numerical approaches to nonlinear galloping of internally resonant suspended cables a study is carried out on nonlinear multimodal galloping of suspended cables a consistent model of a curved cable beam geometrically nonlinear and able to torque recently formulated by the authors is used the model accounts for quasi steady aerodynamic forces including the effect of static swing of the cable and dynamic twist of the cross section complementary solution methods are employed namely finite difference and galerkin spatial discretization followed by numerical time integration or galerkin spatial discretization in conjunction with multiple scale perturbation analysis the different techniques are applied to a cable close to the first cross over point at which a number of internal resonances exist branches of periodic solutions and their stability are evaluated as functions of wind velocity the existence of branches of quasi periodic solutions originating from narrow unstable intervals and propagating elsewhere is also proved qualitative and quantitative results furnished by the different investigation tools are compared among them and the importance of the various components of motion accounted or neglected in the reduced models is discussed

anti modularity and anti community detecting in complex networks abstract many networks of interest in sciences and social research can be divided naturally into anti communities the problem of detecting and characterizing such anti community structure has attracted recent attention in this paper we first define the anti modularity as a quantitative measure of anti community partitioning on a network we also theoretically and empirically show the reliability of anti modularity as a measurement of the quality of an anti community partitioning a label propagation algorithm lpad for anti community detection is proposed experimental results on synthetic and real world networks show that our algorithm lpad can obtain higher quality anti community partitioning than other methods

subgraph centrality in complex networks we introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network smaller subgraphs are given more weight than larger ones which makes this measure appropriate for characterizing network motifs we show that the subgraph centrality c s i can be obtained mathematically from the spectra of the adjacency matrix of the network this measure is better able to discriminate the nodes of a network than alternate measures such as degree closeness betweenness and eigenvector centralities we study eight real world networks for which c s i displays useful and desirable properties such as clear ranking of nodes and scale free characteristics compared with the number of links per node the ranking introduced by c s i for the nodes in the protein interaction network of s cereviciae is more highly correlated with the lethality of individual proteins removed from the proteome

perturbation results for the estrada index in weighted networks the logarithm of the estrada index has been proposed recently as a spectral measure to character efficiently the robustness of complex networks in this paper we explore the estrada index in weighted networks and develop various perturbation results based on spectral graph theory it is shown that the robustness of a network may be enhanced even when some edge weights are reduced this is of particular theoretical and practical significance to network design and optimization

finding community structure in networks using the eigenvectors of matrices we consider the problem of detecting communities or modules in networks groups of vertices with a higher than average density of edges connecting them previous work indicates that a robust approach to this problem is the maximization of the benefit function known as modularity over possible divisions of a network here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix which plays a role in community detection similar to that played by the graph laplacian in graph partitioning calculations this result leads us to a number of possible algorithms for detecting community structure as well as several other results including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong the algorithms and measures proposed are illustrated with applications to a variety of real world complex networks

gaussianization of the spectra of graphs and networks theory and applications abstract matrix functions of the adjacency matrix are very useful for understanding important structural properties of graphs and networks such as communicability node centrality bipartivity and many more they are also intimately related to the solution of differential equations describing dynamical processes on graphs and networks here we propose a new matrix function based on the gaussianization of the adjacency matrix of a graph this function gives more weight to a selected reference eigenvalue ref which may be located in any region of the graph spectra we show here that this matrix function can be derived from physical models that consider the interactions between nearest and next nearest neighbors in the graph we first obtain a few mathematical results for the trace of this matrix function when ref 1 h 1 for simple graphs as well as for random graphs we also provide a combinatorial interpretation of this index in terms of subgraphs in the graph and in terms of the competition pressure among agents in a complex system finally we apply this index to the study of magnetic properties of molecules emerging due to spin interactions as well as to studying the temporal evolution of the international trade network in the period 1992 2002 in both cases we give a clear phenomenological interpretation of the processes described

a note on new bounds for the estrada index abstract let g be a graph on n vertices and 1 2 n their eigenvalues the estrada index of g is defined as e e g i 1 n e i in this paper we obtain new upper and lower bounds on the estrada index of a given graph considering numerical inequalities present in the literature

an increasing sequence of lower bounds for the estrada index of graphs and matrices abstract let g be a graph on n vertices and 1 2 n its eigenvalues the estrada index of g is defined as e e g i 1 n e i in this work we use an increasing sequence converging to the 1 to obtain an increasing sequence of lower bounds for e e g in addition we generalize this succession for the estrada index of an arbitrary symmetric nonnegative matrix

understanding how both the partitions of a bipartite network affect its one mode projection abstract it is a well known fact that the degree distribution dd of the nodes in a partition of a bipartite network influences the dd of its one mode projection on that partition however there are no studies exploring the effect of the dd of the other partition on the one mode projection in this article we show that the dd of the other partition in fact has a very strong influence on the dd of the one mode projection we establish this fact by deriving the exact or approximate closed forms of the dd of the one mode projection through the application of generating function formalism followed by the method of iterative convolution the results are cross validated through appropriate simulations

three dimensional free vibrations of a circular arch using the theory of a cosserat point small deformation three dimensional free vibrations of a circular arch with uniform rectangular cross section have been investigated by using different theoretical approaches and by experimental verification special emphasis has been focused on a numerical formulation which models each element of the arch using the theory of a cosserat point comparison has been made with accurate three dimensional numerical modeling of the arch using the computer program ansys also three dimensional beam elements in the computer programs ansys and i deas have been considered along with an exact solution of approximate model equations of the arch the results indicate that appropriate modeling of rotary inertia is necessary to predict accurate frequencies associated with torsional out of plane modes moreover in its general form the theory of a cosserat point is a fully nonlinear theory that has already been tested for buckling of beams and arches therefore the success of the cosserat theory for the dynamic problem considered in this paper suggests that the theory of a cosserat point can be used for more complicated nonlinear dynamic problems of thin rod like structures

superconvergent derivative recovery for lagrange triangular elements of degree p on unstructured grids in this paper we develop a postprocessing derivative recovery scheme for the finite element solution u h on general unstructured but shape regular triangulations in the case of continuous piecewise polynomials of degree p geq 1 by applying the global l 2 projection q h and a smoothing operator s h the recovered p th derivatives s h m q h partial p u h superconverge to the exact derivatives partial p u based on this technique we are able to derive a local error indicator depending only on the geometry of corresponding element and the p 1 st derivatives approximated by partial s h m q h partial p u h we provide several numerical examples illustrating the effectiveness of our schemes we also observe that higher order elements are likely to require more conservative refinement strategies to create meshes corresponding to optimal orders of convergence

analysis of weighted networks the connections in many networks are not merely binary entities either present or not but have associated weights that record their strengths relative to one another recent studies of networks have by and large steered clear of such weighted networks which are often perceived as being harder to analyze than their unweighted counterparts here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph allowing us to apply standard techniques for unweighted graphs to weighted ones as well we give a number of examples of the method including an algorithm for detecting community structure in weighted networks and a simple proof of the maximum flow minimum cut theorem

interior two dimensional acoustic modelling and modal analysis using isogeometric approach abstract in this paper the interior two dimensional acoustic modelling and modal analysis are presented in the framework of isogeometric analysis iga the acoustic domain governed by the helmholtz equation is parameterized and analysed by non uniform rational lagrange nurl basis which can construct exact geometry model inherently like non uniform rational b spines nurbs and can provide a more straightforward way than nurbs to impose dirichlet boundary conditions the verification and versatility of iga using nurl are assessed in the investigation of a unit square domain and a unit circular domain by comparison with analytical solutions furthermore a quadrilateral domain with concave or convex conics is studied and some innovative results are presented which can be the benchmark data for other algorithm researches the effects of geometric weight and aspect ratio on acoustic eigenvalue and eigenmode of the quadrilateral domain are investigated in detail

non linear galloping of sagged cables in 1 2 internal resonance the aeroelastic behaviour of a flexible elastic suspended cable driven by mean wind speed blowing perpendicularly to the cable s plane is investigated by applying the galerkin procedure to the partial differential equations of motion and using an in plane and an out of plane mode as shape functions a two d o f model is derived the discrete equations are coupled through quadratic and cubic terms arising both from geometric and aerodynamic effects the associated linear frequencies are assumed to be in an almost 1 2 ratio so that internal resonance occurs the multiple scale perturbation method is employed to obtain a set of three amplitude modulation equations whose coefficients depend on the mean wind speed which is assumed as control parameter two perturbative solutions are developed each based on a different assumption about the order of magnitude of the static displacements produced by steady state wind forces analytical results are then compared with direct numerical integrations of discrete non linear equations by performing a bifurcation analysis the existence of several equilibrium branches is proved the relative importance of geometric and aerodynamic non linearities is discussed through simplified models the influence on critical and postcritical behaviour of several parameters including geometrical cable parameters detuning and non symmetric flow effects is investigated the important role played by the steady state forces is highlighted

on the estrada index conjecture abstract let g be a simple graph of order n with m edges let the adjacency spectrum be 1 2 n 1 n of g where 1 2 n 1 n the estrada index of a graph g is ee g i 1 n e i in j a pena i gutman j rada estimating the estrada index linear algebra appl 427 2007 70 76 pena et al posed a conjecture that the star s n has maximum estrada index for any tree of order n and the path p n has minimum estrada index for any tree of order n or any connected graph of order n in this paper we have proved that the star has maximum estrada index for any tree also we obtain that the path has minimum estrada index for any connected graph with m 1 8 n 4 or m n 2 6 moreover we give better lower bound on estrada index for any connected graph

a unified approach for nonlinear vibration analysis of curved structures using non uniform rational b spline representation abstract a novel procedure for the nonlinear vibration analysis of curved beam is presented the non uniform rational b spline nurbs is combined with the euler bernoulli beam theory to define the curvature of the structure the governing equation of motion and the general frequency formula using the nurbs variables is applicable for any type of curvatures is developed the galerkin procedure is implemented to obtain the nonlinear ordinary differential equation of curved system and the multiple time scales method is utilized to find the corresponding frequency responses as a case study the nonlinear vibration of carbon nanotubes with different shapes of curvature is investigated the effect of oscillation amplitude and the waviness on the natural frequency of the curved nanotube is evaluated and the primary resonance case of system with respect to the variations of different parameters is discussed for the sake of comparison of the results obtained with those from the molecular dynamic simulation the natural frequencies evaluated from the proposed approach are compared with those reported in literature for few types of carbon nanotube simulation

spectral measures of bipartivity in complex networks we introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network spectral graph theory is used to quantify how close to bipartite a network is and the extent to which individual nodes and edges contribute to the global network bipartivity it is shown that the bipartivity characterizes the network structure and can be related to the efficiency of semantic or communication networks trophic interactions in food webs construction principles in metabolic networks or communities in social networks

on network bipartivity systems with two types of agents with a preference for heterophilous interaction produces networks that are more or less close to bipartite we propose two measures quantifying the notion of bipartivity the two measures one well known and natural but computationally intractable one computationally less complex but also less intuitive are examined on model networks that continuously interpolates between bipartite graphs and graphs with many odd circuits we find that the bipartivity measures increase as we tune the control parameters of the test networks to intuitively increase the bipartivity and thus conclude that the measures are quite relevant we also measure and discuss the values of our bipartivity measures for empirical social networks constructed from professional collaborations internet communities and field surveys here we find as expected that networks arising from romantic online interaction have high and professional collaboration networks have low bipartivity values in some other cases probably due to low average degree of the network the bipartivity measures cannot distinguish between romantic and friendship oriented interaction

communicability in complex networks we propose a new measure of the communicability of a complex network which is a broad generalization of the concept of the shortest path according to the new measure most of the real world networks display the largest communicability between the most connected popular nodes of the network assortative communicability there are also several networks with the disassortative communicability where the most popular nodes communicate very poorly to each other using this information we classify a diverse set of real world complex systems into a small number of universality classes based on their structure dynamic correlation in addition the new communicability measure is able to distinguish finer structures of networks such as communities into which a network is divided a community is unambiguously defined here as a set of nodes displaying larger communicability among them than to the rest of the nodes in the network

on maximum estrada indices of k trees abstract the estrada index of a graph g is defined as ee g i 1 n e i where 1 2 n are the eigenvalues of the adjacency matrix of g let t n k be the set of the k trees of order n in this paper we characterize the graphs among t n k having the first resp the second largest estrada index

function gradient and hessian recovery using quadratic edge bump functions an approximate error function for the discretization error on a given mesh is obtained by projecting via the energy inner product the functional residual onto the space of continuous piecewise quadratic functions which vanish on the vertices of the mesh conditions are given under which one can expect this hierarchical basis error estimator to give efficient and reliable function recovery asymptotically exact gradient recovery and convergent hessian recovery in the square norms one does not find similar function recovery results in the literature the analysis given here is based on a certain superconvergence result which has been used elsewhere in the analysis of gradient recovery methods numerical experiments are provided which demonstrate the effectivity of the approximate error function in practice

graph animals subgraph sampling and motif search in large networks we generalize a sampling algorithm for lattice animals connected clusters on a regular lattice to a monte carlo algorithm for graph animals i e connected subgraphs in arbitrary networks as with the algorithm in n kashtan et al bioinformatics 20 1746 2004 it provides a weighted sample but the computation of the weights is much faster linear in the size of subgraphs instead of superexponential this allows subgraphs with up to ten or more nodes to be sampled with very high statistics from arbitrarily large networks using this together with a heuristic algorithm for rapidly classifying isomorphic graphs we present results for two protein interaction networks obtained using the tandem affinity purification tap method one of escherichia coli with 230 nodes and 695 links and one for yeast saccharomyces cerevisiae with roughly ten times more nodes and links we find in both cases that most connected subgraphs are strong motifs z scores 10 or antimotifs z scores 10 when the null model is the ensemble of networks with fixed degree sequence strong differences appear between the two networks with dominant motifs in e coli being nearly bipartite graphs and having many pairs of nodes that connect to the same neighbors while dominant motifs in yeast tend towards completeness or contain large cliques we also explore a number of methods that do not rely on measurements of z scores or comparisons with null models for instance we discuss the influence of specific complexes like the 26s proteasome in yeast where a small number of complexes dominate the k cores with large k and have a decisive effect on the strongest motifs with 6 8 nodes we also present zipf plots of counts versus rank they show broad distributions that are not power laws in contrast to the case when disconnected subgraphs are included

in plane and out of plane free vibrations of curved beams with variable sections we present an approximate method to study the analysis for both the in plane and out of plane free vibration of horizontally curved beams with arbitrary shapes and variable cross sections the characteristic equation for free vibration can be derived by applying the green function which is obtained as a discrete type solution of differential equations governing the flexural behaviour of the curved beam under the action of a concentrated load

on the numerical solution of a class of nonstandard sturm liouville boundary value problems the paper deals with the numerical solution of a nonstandard sturm liouville boundary value problem on the half line where the coefficients of the differential terms depend on the unknown function by means of a scalar integral operator by using a finite difference discretization a truncated quadrature rule and an iterative procedure we construct a numerical method whose convergence is proved the order of convergence and the truncation at infinity are also discussed finally some numerical tests are given to show the performance of the method

the effect of temperature on the large amplitude vibrations of curved beams the thermoelastic geometrically nonlinear vibrations of isotropic straight and curved beams are studied using p version hierarchical finite elements first order shear deformation theory is followed and both the longitudinal displacements and inertia are taken into account the nonlinear equations of motion are solved in the time domain by newmark s method the influence of parameters like the temperature variation the thickness and the ratio of curvature on the beams nonlinear dynamics is studied periodic and non periodic motions are found

spectra of real world graphs beyond the semicircle law results on the spectra of adjacency matrices corresponding to models of real world graphs we find that when the number of links grows as the number of nodes the spectral density of uncorrelated random matrices does not converge to the semicircle law furthermore the spectra of real world graphs have specific features depending on the details of the corresponding models in particular scale free graphs develop a trianglelike spectral density with a power law tail while small world graphs have a complex spectral density consisting of several sharp peaks these and further results indicate that the spectra of correlated graphs represent a practical tool for graph classification and can provide useful insight into the relevant structural properties of real networks

topological evolution in dense granular materials a complex networks perspective abstract one of the great challenges in the science of complex materials materials capable of emergent behavior such as self organized pattern formation is deciphering their inherent structural design principles as they deform in response to external loads we have been exploring the efficacy of techniques from complex networks to the study of dense granular materials as a means to i uncover such design principles and ii identify suitable metrics that quantify the evolution of structure during deformation herein we characterize the developing network structure and loss of connectivity in a quasistatically deforming granular medium from the perspective of complex networks attention is paid to the evolution of the contact and contact force networks at the local or mesoscopic level i e a particle and its immediate neighbors as well as the macroscopic level we explore network motifs and other topological properties at these multiple length scales in an attempt to find that which best correlates with the constitutive properties of nonaffine deformation and dissipation spatially and with respect to strain key processes or rearrangement events that cause loss of connectivity within the material domain e g microbanding and force chain buckling are investigated network statistics of these processes previously shown to be major sources of energy dissipation and nonaffine deformation are then tied to corresponding trends observed in the evolving macroscopic network it is shown that consideration of the unweighted contact network alone is insufficient to tie dissipation to loss of material connectivity

random walks along the streets and canals in compact cities spectral analysis dynamical modularity information and statistical mechanics different models of random walks on the dual graphs of compact urban structures are considered analysis of access times between streets helps to detect the city modularity the statistical mechanics approach to the ensembles of lazy random walkers is developed the complexity of city modularity can be measured by an informationlike parameter which plays the role of an individual fingerprint of genius loci global structural properties of a city can be characterized by the thermodynamic parameters calculated in the random walk problem

asymptotically exact a posteriori error estimators part i grids with superconvergence in part i of this work we develop superconvergence estimates for piecewise linear finite element approximations on quasi uniform triangular meshes where most pairs of triangles sharing a common edge form approximate parallelograms in particular we first show a superconvergence of the gradient of the finite element solution uh and to the gradient of the interpolant ui we then analyze a postprocessing gradient recovery scheme showing that q h nabla u h is a superconvergent approximation to nabla u here qh is the global l2 projection in part ii we analyze a superconvergent gradient recovery scheme for general unstructured shape regular triangulations this is the foundation for an a posteriori error estimate and local error indicators

extremal graphs for estrada indices abstract let g be a simple undirected connected graph the signless laplacian estrada laplacian estrada and estrada indices of a graph g is the sum of the exponentials of the signless laplacian eigenvalues laplacian eigenvalues and eigenvalues of g respectively the present work derives an upper bound for the estrada index of a graph as a function of its chromatic number in the family of graphs whose color classes have order not less than a fixed positive integer the graphs for which the upper bound is tight is obtained additionally an upper bound for the estrada index of the complement of a graph in the previous family of graphs with two color classes is given a nordhaus gaddum type inequality for the laplacian estrada index when g is a bipartite graph with color classes of order not less than 2 is presented moreover a sharp upper bound for the estrada index of the line graph and for the signless laplacian index of a graph in terms of connectivity is obtained

can we have superconvergent gradient recovery under adaptive meshes we study adaptive finite element methods for elliptic problems with domain corner singularities our model problem is the two dimensional poisson equation results of this paper are twofold first we prove that there exists an adaptive mesh gauged by a discrete mesh density function under which the recovered gradient by the polynomial preserving recovery ppr is superconvergent second we demonstrate by numerical examples that an adaptive procedure with an a posteriori error estimator based on ppr does produce adaptive meshes that asatisfy our mesh density assumption and the recovered gradient by ppr is indeed superconvergent in the adaptive process

dependence centrality similarity measuring the diversity of profession levels of interests abstract to understand the relations between developers and software we study a collaborative coding platform from the perspective of networks including follower networks dependence networks and developer project bipartite networks through the analyzing of degree distribution pagerank and degree dependent nearest neighbors centrality we find that the degree distributions of all networks have a power law form except the out degree distributions of dependence networks the nearest neighbors centrality is negatively correlated with degree for developers but fluctuates around the average for projects in order to measure the diversity of profession levels of interests a new index called dependence centrality similarity is proposed and the correlation between dependence centrality similarity and degree is investigated the result shows an obvious negative correlations between dependence centrality similarity and degree

on extremal bipartite unicyclic graphs abstract let u n be the set of connected bipartite unicyclic graphs with n vertices here we consider the extremal graphs in u n with respect to both the estrada index of themselves and the kirchhoff index of their complements we find that the first two and the last one unicyclic graphs in u n according to these two orderings are coincident

returnability in complex directed networks digraphs the concept of returnability is proposed for complex directed networks digraphs it can be seen as a generalization of the concept of reciprocity two measures of the returnability are introduced we establish closed formulas for the calculation of the returnability measures which are also related to the digraph spectrum the two measures are calculated for simple examples of digraphs as well as for real world complex directed networks and are compared with the reciprocity

in plane and out of plane motions of an extensible semi circular pipe conveying fluid abstract in plane and out of plane motions of a semi circular pipe conveying fluid are analyzed in this paper assuming that the centerline of the semi circular pipe is extensible nonlinear equations of in plane and out of plane motions are derived according to the extended hamilton principle the lagrange nonlinear strain theory and the euler bernoulli beam theory are used to derive the equations the derived equations of motion are discretized by applying the galerkin method linearized equations around the equilibrium position are obtained from the discretized equations and then the dynamic characteristics of the pipe are investigated in addition some modelling issues which are related to the nonlinearity of the circumferential strain and stress are discussed this study finds that a semi circular pipe conveying fluid does not lose stability even at a high fluid velocity although a model using the lagrange nonlinear strain and the corresponding nonlinear stress yields the most accurate computational results of the natural frequencies a model using the lagrange strain and a linearized stress is recommended to compute the natural frequencies efficiently while still maintaining accuracy

on extremal bipartite bicyclic graphs abstract let b n be the set of all connected bipartite bicyclic graphs with n vertices the estrada index of a graph g is defined as ee g i 1 n e i where 1 2 n are the eigenvalues of the adjacency matrix of g and the kirchhoff index of a graph g is defined as kf g i j r i j where r i j is the resistance distance between vertices v i and v j in g the complement of g is denoted by g in this paper sharp upper bound on ee g resp kf g of graph g in b n is established the corresponding extremal graphs are determined respectively furthermore by means of some newly created inequalities the graph g in b n with the second maximal ee g resp kf g is identified as well it is interesting to see that the first two bicyclic graphs in b n according to these two orderings are mainly coincident

fixed point iterations for a class of nonstandard sturm liouville boundary value problems abstract the paper examines a particular class of nonlinear integro differential equations consisting of a sturm liouville boundary value problem on the half line where the coefficient of the differential term depends on the unknown function by means of a scalar integral operator in order to handle the nonlinearity of the problem we consider a fixed point iteration procedure which is based on considering a sequence of classical sturm liouville boundary value problems in the weak solution sense the existence of a solution and the global convergence of the fixed point iterations are stated without resorting to the banach fixed point theorem moreover the unique solvability of the problem is discussed and several examples with unique and non unique solutions are given

complex networks and economics abstract as the first step toward a study of complex networks in economics we consider business networks categorized into bipartite networks through empirical study we show the possibility that business networks will fall into the scale free category to have an idea about the clustering coefficient and the averaged path length for bipartite networks we perform a one mode reduction we calculate the quantities for networks constructed by banks and companies before after a merger among banks and quantitatively show that the merger among banks increases the cliquishness of companies and decreases the typical separation between two companies

in plane free vibration of a single crystal silicon ring in this paper the natural frequencies and the associated mode shapes of in plane free vibration of a single crystal silicon ring are analyzed it is found that the si 1 1 1 ring is two dimensionally isotropic in the 1 1 1 plane for elastic constants but three dimensionally anisotropic while the si 1 0 0 ring is fully anisotropic hamilton s principle is used to derive the equations of vibration which is a set of partial differential equations with coefficients being periodic in polar variable expressing the radial and tangential displacements in sinusoidal form with non predetermined amplitudes and through the integration with respect to the circumferential variable the original governing equations in partial differential form can be converted into the amplitude equations in ordinary differential form the exact expressions for frequencies and mode shapes are obtained it is found that for si 1 0 0 rings the frequencies of a pair of modes which are equal for an isotropic ring split due to the anisotropic effect only for the second in plane vibration mode the phenomena of frequency splitting and degenerate modes can be proved either based on the conservation of averaged mechanical energy or by the concept of crystallographic symmetry groups when the single crystal silicon is replaced by the polycrystalline silicon which is isotropic in elastic constants the derived equations for frequencies correctly predict the vanishing of the phenomenon of frequency splitting

spectral centrality measures in complex networks complex networks are characterized by heterogeneous distributions of the degree of nodes which produce a large diversification of the roles of the nodes within the network several centrality measures have been introduced to rank nodes based on their topological importance within a graph here we review and compare centrality measures based on spectral properties of graph matrices we shall focus on pagerank pr eigenvector centrality ev and the hub and authority scores of the hits algorithm we derive simple relations between the measures and the in degree of the nodes in some limits we also compare the rankings obtained with different centrality measures

on a numerical method for a homogeneous nonlinear nonlocal elliptic boundary value problem abstract in this work we develop a numerical method for the equation 0 1 u t d t u x u x 2 n 1 0 x 0 1 u 0 a u 1 b we begin by establishing a priori estimates and the existence and uniqueness of the solution to the nonlinear auxiliary problem via the schauder fixed point theorem from this analysis we then prove the existence and uniqueness to the problem above by defining a continuous compact mapping utilizing the a priori estimates and the brouwer fixed point theorem next we analyze a discretization of the above problem and show that a solution to the nonlinear difference problem exists and is unique and that the numerical procedure converges with error h we conclude with some examples of the numerical process

on maximum estrada indices of bipartite graphs with some given parameters abstract the estrada index of a graph g is defined as e e g i 1 n e i where 1 2 n are the eigenvalues of the adjacency matrix of g in this paper we characterize the unique bipartite graph with maximum estrada index among bipartite graphs with given matching number and given vertex connectivity edge connectivity respectively

free vibrations of circular arches a review abstract in this paper a critical brief review of the free dynamics of circular arches is presented under the classical hypotheses that 1 the dimensions of the cross section are small in comparison with the radius 2 the axis is inextensible and 3 shear forces and rotatory inertia are neglected a simple yet efficient method is proposed which allows one to take into account quite naturally the cross section variations and the presence of flexible supports a number of other approaches are also briefly illustrated from the ritz and galerkin methods to the finite element techniques and their numerical performances are compared for a wide range of examples uniform arches with rotationally flexible and axially flexible supports have been extensively examined together with three different kinds of stepped arches and two different arches with linearly varying cross section whenever possible a comparison with available exact solutions is also performed the agreement among all these methods is generally good even if there are some theoretical discrepancies to be pointed out

applications of estrada indices and energy to a family of compound graphs abstract to track the gradual change of the adjacency matrix of a simple graph g into the signless laplacian matrix v nikiforov in 35 suggested the study of the convex linear combination a adjacency matrix a g d g 1 a g for 0 1 where a g and d g are the adjacency and the diagonal vertex degrees matrices of g respectively taking this definition as an idea the next matrix was considered for a b r the matrix a a b defined by a a b g a d g b a g extends the previous adjacency matrix this matrix is designated the a b adjacency matrix of g both adjacency matrices are examples of universal matrices already studied by w haemers in this paper we study the a b adjacency spectra for a family of compound graphs formed by disjoint balanced trees whose roots are identified to the vertices of a given graph in consequence new families of cospectral adjacency laplacian and signless laplacian graphs new hypoenergetic graphs graphs whose energy is less than its vertex number and new explicit formulae for estrada signless laplacian estrada and laplacian estrada indices of graphs were obtained moreover sharp upper bounds of the above indices for caterpillars in terms of length of the path and of the maximum number of its pendant vertices are given

ultraconvergence of high order fems for elliptic problems with variable coefficients in this paper we investigate local ultraconvergence properties of the high order finite element method fem for second order elliptic problems with variable coefficients under suitable regularity and mesh conditions we show that at an interior vertex which is away from the boundary with a fixed distance the gradient of the post precessed kth k ge 2 k 2 order finite element solution converges to the gradient of the exact solution with order mathcal o h k 2 mathrm ln h 3 o hk 2 lnh 3 the proof of this ultraconvergence property depends on a new interpolating operator some new estimates for the discrete green s function a symmetry theory derived in 26 and the richardson extrapolation technique in 20 numerical experiments are performed to demonstrate our theoretical findings

local ultraconvergence of high order finite element method by interpolation postprocessing technique for elliptic problems with constant coefficients abstract assume that u x satisfies the problem l u x x i a i j u x j f x x u x 0 x in this article using interpolation postprocessing technique we will investigate the local ultraconvergence of the primal variable and the derivative of finite element approximation of u x using piecewise polynomials of degrees bi k k 3 over a rectangular partition assume that k 3 is odd and x 0 is an interior vertex satisfying x 0 c using the new interpolation postprocessing formula presented in this study we show that the primal variable and the derivative of the post processed finite element solution using piecewise of degrees bi k k 3 at x 0 converge to the primal variable and the derivative of the exact solution with order o h k 3 ln h under suitable regularity and mesh conditions respectively finally we use numerical experiments to illustrate our theoretical findings

approximating spectral sums of large scale matrices using stochastic chebyshev approximations computation of the trace of a matrix function plays an important role in many scientific computing applications including applications in machine learning computational physics e g lattice qua

spectral properties of unimodular lattice triangulations random unimodular lattice triangulations have been recently used as an embedded random graph model which exhibit a crossover behavior between an ordered large world and a disordered small world behavior using the ergodic pachner flips that transform such triangulations into another and an energy functional that corresponds to the degree distribution variance markov chain monte carlo simulations can be applied to study these graphs here we consider the spectra of the adjacency and the laplacian matrix as well as the algebraic connectivity and the spectral radius power law dependencies on the system size can clearly be identified and compared to analytical solutions for periodic ground states for random triangulations we find a qualitative agreement of the spectral properties with well known random graph models in the microcanonical ensemble analytical approximations agree with numerical simulations in the canonical ensemble a crossover behavior can be found for the algebraic connectivity and the spectral radius thus combining large world and small world behavior in one model the considered spectral properties can be applied to transport problems on triangulation graphs and the crossover behavior allows a tuning of important transport quantities

stability of synchronized states in networks of phase oscillators the stability of synchronized states frequency locked states in networks of phase oscillators is investigated for several network topologies it is shown that for some topologies there is more than one stable synchronized state according to the sign of coupling strength between oscillators it is also shown that in some cases the synchronized state corresponds to zero order parameter

superconvergence of quadratic finite elements on mildly structured grids superconvergence estimates are studied in this paper on quadratic finite element discretizations for second order elliptic boundary value problems on mildly structured triangular meshes for a large class of practically useful grids the finite element solution u h is proven to be superclose to the inter polant u i and as a result a postprocessing gradient recovery scheme for u h can be devised the analysis is based on a number of carefully derived identities in addition to its own theoretical interests the result in this paper can be used for deriving asymptotically exact a posteriori error estimators for quadratic finite element methods

on the numerical solution of a nonlocal boundary value problem we study a nonlinear boundary value problem involving a nonlocal integral operator in the coefficients of the unknown function provided sufficient conditions for the existence and uniqueness of the solution for its approximation we propose a numerical method consisting of a classical discretization of the problem and an algorithm to solve the resulting nonlocal and nonlinear algebraic system by means of some iterative procedures the second order of convergence is assured by different sufficient conditions which can be alternatively used in dependence on the given data the theoretical results are confirmed by several numerical tests

on maximum estrada indices of graphs with given parameters abstract for a graph g with eigenvalues 1 2 n its estrada index is defined as ee g i 1 n e i we determine the unique graphs with maximum estrada indices among graphs with given number of cut vertices connectivity and edge connectivity respectively

topological structural classes of complex networks we use theoretical principles to study how complex networks are topologically organized at large scale using spectral graph theory we predict the existence of four different topological structural classes of networks these classes correspond respectively to highly homogenous networks lacking structural bottlenecks networks organized into highly interconnected modules with low inter community connectivity networks with a highly connected central core surrounded by a sparser periphery and networks displaying a combination of highly connected groups quasicliques and groups of nodes partitioned into disjoint subsets quasibipartites here we show by means of the spectral scaling method that these classes really exist in real world ecological biological informational technological and social networks we show that neither of three network growth mechanisms random with uniform distribution preferential attachment and random with the same degree sequence as real network is able to reproduce the four structural classes of complex networks these models reproduce two of the network classes as a function of the average degree but completely fail in reproducing the other two classes of networks

analysis of recovery type a posteriori error estimators for mildly structured grids some recovery type error estimators for linear finite elements are analyzed under o h 1 0 regular grids superconvergence of order o h 1 0 p is established for recovered gradients by three different methods as a consequence a posteriori error estimators based on those recovery methods are asymptotically exact

nonlinear vibration of a curved beam under uniform base harmonic excitation with quadratic and cubic nonlinearities abstract this paper presents nonlinear vibration analysis of a curved beam subject to uniform base harmonic excitation with both quadratic and cubic nonlinearities the galerkin method is employed to discretize the governing equations a high dimensional model that can take nonlinear model coupling into account is derived and the incremental harmonic balance ihb method is employed to obtain the steady state response of the curved beam the cases investigated include softening stiffness hardening stiffness and modal energy transfer the stability of the periodic solutions for given parameters is determined by the multi variable floquet theory using hsu s method particular attention is paid to the anti symmetric response with and without excitation as the excitation frequency is close to the first and third natural frequencies of the system the results obtained with the ihb method compare very well with those obtained via numerical integration

random neighborhood graphs as models of fracture networks on rocks structural and dynamical analysis abstract we propose a new model to account for the main structural characteristics of rock fracture networks rfns the model is based on a generalization of the random neighborhood graphs to consider fractures embedded into rectangular spaces we study a series of 29 real world rfns and find the best fit with the random rectangular neighborhood graphs rrngs proposed here we show that this model captures most of the structural characteristics of the rfns and allows a distinction between small and more spherical rocks and large and more elongated ones we use a diffusion equation on the graphs in order to model diffusive processes taking place through the channels of the rfns we find a small set of structural parameters that highly correlates with the average diffusion time in the rfns we found analytically some bounds for the diameter and the algebraic connectivity of these graphs that allow to bound the diffusion time in these networks we also show that the rrngs can be used as a suitable model to replace the rfns in the study of diffusion like processes indeed the diffusion time in rfns can be predicted by using structural and dynamical parameters of the rrngs finally we also explore some potential extensions of our model to include variable fracture apertures the possibility of long range hops of the diffusive particles as a way to account for heterogeneities in the medium and possible superdiffusive processes and the extension of the model to 3 dimensional space

the estrada index of evolving graphs abstract the estrada index of a simple graph g with adjacency matrix a is defined as ee g trace e a it can be used in a range of fields as an efficient measuring tool an evolving graph g 1 g 2 g n is a time ordered sequence of graphs over a fixed set of vertices by using the natural definition of a walk on the evolving graph that respects the arrow of time we extend the static estrada index to accommodate this promising dynamic setting we find that although asymmetry is raised intrinsically by time s arrow the dynamic estrada index is order invariant we establish some lower and upper bounds for the dynamic estrada index in terms of the numbers of vertices and edges illustrative examples are worked out to demonstrate the computations involved

estimating the estrada index abstract let g be a graph on n vertices and let 1 2 n be its eigenvalues the estrada index of g is a recently introduced graph invariant defined as ee i 1 n e i we establish lower and upper bounds for ee in terms of the number of vertices and number of edges also some inequalities between ee and the energy of g are obtained

superconvergence and gradient recovery of linear finite elements for the laplace beltrami operator on general surfaces superconvergence results and several gradient recovery methods of finite element methods in flat spaces are generalized to the surface linear finite element method for the laplace beltrami equation on general surfaces with mildly structured triangular meshes for a large class of practically useful grids the surface linear finite element solution is proven to be superclose to an interpolant of the exact solution of the laplace beltrami equation and as a result various postprocessing gradient recovery including simple and weighted averaging local and global l 2 projections and zienkiewicz and zhu z z schemes are devised and proven to be a better approximation of the true gradient than the gradient of the finite element solution numerical experiments are presented to confirm the theoretical results

free non linear vibration of a rotating thin ring with the in plane and out of plane motions free non linear vibration of a rotating thin ring with a constant speed is analyzed when the ring has both the in plane and out of plane motions the geometric non linearity of displacements is considered by adopting the lagrange strain theory for the circumferential strain instead of the infinitesimal strain theory by using hamilton s principle the coupled non linear partial differential equations are derived which describe the out of plane bending and torsional motions as well as the in plane bending and extensional motions during deriving the equations of motion we discuss how to model the circumferential stress and strain in order to consider the geometric non linearity four models are established three non linear models and one linear model for the four models the linearized equations of motion are obtained in the neighbourhood of the steady state equilibrium position based on the linearized equations of the four cases the natural frequencies are computed at various rotational speeds and then they are compared through the comparison this study recommends which model is appropriate to describe the non linear behaviour more precisely

the estrada index of trees the estrada index of a graph g is defined as ee g i 1ne i where 1 2 n are the eigenvalues of its adjacency matrix we determine the unique tree with maximum estrada index among the set of trees with given number of pendant vertices as applications we determine trees with maximum estrada index among the set of trees with given matching number independence number and domination number respectively finally we give a proof of a conjecture in j li x li l wang the minimal estrada index of trees with two maximum degree vertices match commun math comput chem 64 2010 799 810 on trees with minimum estrada index among the set of trees with two adjacent vertices of maximum degree

bounds of the extended estrada index of graphs abstract let g be a graph on n vertices and 1 2 n the eigenvalues of its extended adjacency matrix the extended estrada index ee ex is defined as the sum of the terms e i i 1 2 n in this paper we establish lower and upper bounds for ee ex in terms of the number of vertices and the number of edges and characterize the extremal graphs also the bounds for ee ex of some special graphs are obtained

on the numerical solution of some nonlinear and nonlocal boundary value problems the modeling of various physical questions often leads to nonlinear boundary value problems involving a nonlocal operator which depends on the unknown function in the entire domain rather than at a single point in order to answer an open question posed by j r cannon and d j galiffa we study the numerical solution of a special class of nonlocal nonlinear boundary value problems which involve the integral of the unknown solution over the integration domain starting from cannon and galiffa s results we provide other sufficient conditions for the unique solvability and a more general convergence theorem moreover we suggest different iterative procedures to handle the nonlocal nonlinearity of the discrete problem and show their performances by some numerical tests

the estrada index of unicyclic graphs abstract the estrada index of a graph g is defined as ee g i 1 n e i where 1 2 n are the eigenvalues of g we determine the unique unicyclic graph with maximum estrada index the unique bipartite unicyclic graph with maximum estrada index and the unique bipartite unicyclic graph of a given bipartition with maximum estrada index we also show that only two graphs are possible to be the unicyclic graph s with minimum estrada index