on the existence and multiplicity of positive periodic solutions for first order vector differential equation abstract in this paper we consider the existence and multiplicity of positive periodic solutions for first order vector differential equation x t f t x t 0 a e t 0 under the periodic boundary value condition x 0 x here is a positive constant and f 0 r n r n is a caratheodory function some existence and multiplicity results of positive periodic solutions are derived by using a fixed point theorem in cones

a recursive approach to local mesh refinement in two and three dimensions abstract the newest vertex strategy for local refinement in two dimensions is reviewed and discussed a recursive algorithm for local refinement of tetrahedral meshes in three dimensions based on similar bisection strategy is described the recursive approach requires certain restrictions on the initial mesh on the other hand under this condition the refinement process can be kept as local as needed and it can be fully inverted simple data structures and derefinement algorithms are also outlined

remarks on first and second order periodic boundary value problems on etudie les problemes aux valeurs limites periodiques d ordre 1 et 2 suivants u f t u u 0 u 2 et u f t u u 0 u 2 u 0 u 2 on obtient l existence de solutions extremales comme limites d iterees monotones

quality local refinement of tetrahedral meshes based on bisection we present a three dimensional 3 d local refinement algorithm for tetrahedral meshes based on a bisection procedure the quality of refined meshes is guaranteed in terms of a tetrahedron shape measure eta specifically it is proved that the algorithm creates a finite number which only depends on the number of tetrahedra in the initial mesh of classes of similar tetrahedra in all refined tetrahedra furthermore if bf t is a tetrahedron in the original mesh and bf t i n is any refined tetrahedron of bf t then eta bf t i n geq c eta bf t where c is a positive constant independent of bf t and the number of refinements it is also proved that for any interior face in the final mesh the absolute value of the difference of the bisection levels of the two adjacent tetrahedra incident on the face is leq 2 which indicates that local refinements on tetrahedra can be smoothly extended to their neighbors the expected time complexity of the algorithm is o n wh

nonlinear boundary value problems for first order impulsive functional differential equations this paper is concerned with solutions of nonlinear boundary value problems for a class of first order functional differential equations we introduce new concept of lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid obviously we extend previous results

red refinements of simplices into congruent subsimplices abstract we show that in dimensions higher than two the popular red refinement technique commonly used for simplicial mesh refinements and adaptivity in the finite element analysis and practice never yields subsimplices which are all acute even for an acute father element as opposed to the two dimensional case in the three dimensional case we prove that there exists only one tetrahedron that can be partitioned by red refinement into eight congruent subtetrahedra that are all similar to the original one

periodic boundary value problems for a class of functional differential equations in this paper we show that the method of upper and lower solutions coupled with the monotone iterative technique is valid to obtain constructive proofs of existence of solutions for nonlinear periodic boundary value problems of functional differential equations without assuming properties of monotonicity in the nonlinear part

monotone method for second order delayed differential equations with boundary value conditions in this paper we investigate the existence of extremal solutions of boundary value problems for second order differential equations with delayed arguments we show that a lower and upper solution method has been applied successfully to such problems an one sided lipschitz condition with corresponding constants is important assumption in our research

stability and convergence of finite element approximation schemes for harmonic maps this article discusses stability and convergence of approximation schemes for harmonic maps a finite element discretization of an iterative algorithm due to f alouges is introduced and shown to be stable and convergent in general only on acute type triangulations an break a posteriori criterion is proposed which allows us to monitor sufficient conditions for weak convergence to a harmonic map on general triangulations and for adaptive mesh refinement numerical break experiments show that an adaptive strategy automatically refines triangulations in neighborhoods of typical point singularities and thereby underline its efficiency

second order periodic boundary value problems on time scales in this paper we study the existence of solutions of periodic boundary value problem for second order nonlinear dynamic equations on time scales for this purpose we use two methods here first sign properties of the green s function are investigated and existence results of bounded solutions of nonlinear boundary value problems are established as a result of schauder fixed point theorem second the monotone method is discussed to assure the existence and uniqueness of solutions of such periodic boundary value problems on time scales

convergent finite element discretization of the multi fluid nonstationary incompressible magnetohydrodynamics equations we propose a convergent implicit stabilized finite element discretization of the nonstationary incompressible magnetohydrodynamics equations with variable density viscosity and electric conductivity the discretization satisfies a discrete energy law and a discrete maximum principle for the positive density and iterates converge to weak solutions of the limiting problem for vanishing discretization parameters a simple fixed point scheme together with an appropriate stopping criterion is proposed which decouples the computation of density velocity and magnetic field and inherits the above properties provided a mild mesh constraint holds computational studies are provided

periodic boundary value problem for first order impulsive functional differential equations this paper discusses the periodic boundary value problem for a class of first order impulsive functional differential equations we establish several existence results under weaker hypotheses by using the leray schauder alternative the lower and upper solution method and the monotone iterative technique the corresponding results in the literature are improved or extended some examples are also given to illustrate the advantage of the results

discrete minimum and maximum principles for finite element approximations of non monotone elliptic equations uniform lower and upper bounds for positive finite element approximations to semilinear elliptic equations in several space dimensions subject to mixed dirichlet neumann boundary conditions are derived the main feature is that the non linearity may be non monotone and unbounded the discrete minimum principle provides a positivity preserving approximation if the discretization parameter is small enough and if some structure conditions on the non linearity and the triangulation are assumed the discrete maximum principle also holds for degenerate diffusion coefficients the proofs are based on stampacchia s truncation technique and on a variational formulation both methods are settled on careful estimates on the truncation operator

an approach to refining three dimensional tetrahedral meshes based on delaunay transformations a technique for refining three dimensional tetrahedral meshes is proposed in this paper the proposed technique is capable of treating arbitrary unstructured tetrahedral meshes convex or non convex with multiple regions resulting in high quality constrained delaunay triangulations the tetrahedra generated are of high quality nearly equilateral sliver tetrahedra which present a real problem to many algorithms are not produced with the new method the key to the generation of high quality tetrahedra is the iterative application of a set of topological transformations based on the voronoi delaunay theory and a reposition of nodes technique the computational requirements of the proposed technique are in linear relationship with the number of nodes and tetrahedra making it ideal for direct employment in a fully automatic finite element analysis system for 3 d adaptive mesh refinement application to some test problems is presented to show the effectiveness and applicability of the new method

positive solution for system of nonlinear first order pbvps on time scales abstract in this paper we are concerned with the following system of nonlinear first order periodic boundary value problems on time scale t x i t f i t x 1 t x 2 t x n t 0 t 0 t x i 0 x i t i 1 2 n where f i 0 t 0 n r is continuous and there exists a constant m i 0 such that m i x i f i t x 1 x 2 x n 0 for x 1 x 2 x n 0 n t 0 t some existence criteria of positive solution are established by using a fixed point theorem for operators on cone

monotone method for first order functional differential equations we study periodic boundary value problems relative to a general class of first order functional differential equations for this class of problems we develop the monotone iterative technique our formulation is very general including delay differential equations functional differential equations with maxima and integro differential equations but the case where the operator defining the functional dependence is not necessarily lipschitzian is also considered

monotone method for first order functional differential equations with retardation and anticipation abstract this paper discusses first order functional differential equations with retardation and anticipation by using the method of upper and lower solutions coupled with monotone iterative technique new existence results are obtained which improve known results in the literature

existence of triple positive solutions of two point right focal boundary value problems on time scales we consider the following boundary value problem 1 n 1y d n t 1 p 1f t y s n 1 t email protected a b t y d n a 0 email protected email protected p 1 y d n s b 0 email protected email protected n 1 where n 2 1 p n 1 is fixed and t is a time scale by applying fixed point theorems for operators on a cone existence criteria are developed for triple positive solutions of the boundary value problem we also include examples to illustrate the usefulness of the results obtained

waveform relaxation methods for periodic differential functional systems the convergence of waveform relaxation methods applied to a periodic differential functional system is studied the continuous dependence is also discussed

on nonobtuse simplicial partitions this paper surveys some results on acute and nonobtuse simplices and associated spatial partitions these partitions are relevant in numerical mathematics including piecewise polynomial approximation theory and the finite element method special attention is paid to a basic type of nonobtuse simplices called path simplices the generalization of right triangles to higher dimensions in addition to applications in numerical mathematics we give examples of the appearance of acute and nonobtuse simplices in other areas of mathematics

triggering cascades on strongly connected directed graphs consider the following process of activation on a strongly connected directed graph g v e with threshold function v n in round zero a set of vertices called the seeds are active thereafter a vertex v v is activated in a round if it has at least v active in neighbors in the previous round once a vertex is activated it remains active sets of seeds activating all vertices after a finite number of rounds are known in the literature as irreversible dynamic monopolies a k a perfect target sets corresponding to g with v deg v for all v v where deg v denotes the indegree of v and 0 1 this paper proves the existence of an irreversible dynamic monopoly of size no more than max 4 92 v 1

periodic boundary value problem for first order impulsive delay differential equations in this paper by means of the method of upper and lower solutions and the monotone iterative technique the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsive delay differential equations is considered

periodic boundary value problems for impulsive integro differential equations of mixed type by developing a comparison result and using the monotone iterative technique we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for first order nonlinear impulsive integro differential equations of mixed type

discrete maximum principles for finite element solutions of nonlinear elliptic problems with mixed boundary conditions one of the most important problems in numerical simulations is the preservation of qualitative properties of solutions of the mathematical models by computed approximations for problems of elliptic type one of the basic properties is the continuous maximum principle in our work we present several variants of the maximum principles and their discrete counterparts for scalar second order nonlinear elliptic problems with mixed boundary conditions the problems considered are numerically solved by the continuous piecewise linear finite element approximations built on simplicial meshes sufficient conditions providing the validity of the corresponding discrete maximum principles are presented geometrically they mean that the employed meshes have to be of acute or nonobtuse type depending of the type of the problem finally some examples of real life problems where the preservation of maximum principles plays an important role are presented

existence and approximation of solutions for nonlinear functional differential equations with periodic boundary value conditions abstract this paper is concerned with the existence and approximation of solutions for a class of first order functional differential equations with periodic boundary conditions we present a new comparison result and extend previous results

periodic solutions of functional dynamic equations with infinite delay abstract in this paper sufficient criteria are established for the existence of periodic solutions of some functional dynamic equations with infinite delays on time scales which generalize and incorporate as special cases many known results for differential equations and for difference equations when the time scale is the set of the real numbers or the integers respectively the approach is mainly based on the krasnosel ski fixed point theorem which has been extensively applied in studying existence problems in differential equations and difference equations but rarely applied in studying dynamic equations on time scales this study shows that one can unify such existence studies in the sense of dynamic equations on general time scales

periodic boundary value problems for second order impulsive integro differential equations by developing a new comparison result and using the monotone iterative technique we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for second order nonlinear impulsive integro differential equations of mixed type

acute type refinements of tetrahedral partitions of polyhedral domains we present a new technique to perform refinements on acute type tetrahedral partitions of a polyhedral domain provided that the center of the circumscribed sphere around each tetrahedron belongs to the tetrahedron the resulting family of partitions is of acute type thus all the tetrahedra satisfy the maximum angle condition both these properties are highly desirable in finite element analysis

remarks on periodic boundary value problems for functional differential equations we extend some results on existence and approximation of solution for a class of first order functional differential equations with periodic boundary conditions we show the validity of the monotone iterative technique under weaker hypotheses and present some examples

periodic boundary value problem for first order impulsive functional differential equations in this paper by means of the method of upper and lower solutions and the monotone iterative technique the existence of minimal and maximal solutions of the periodic boundary value problem for first order impulsive functional differential equations is considered

periodic boundary value problems for delay differential equations with impulses existence and approximation of solutions for an impulsive delay differential equation with periodic boundary value conditions are presented we use comparison principles and monotone iterative techniques

an iterative method for functional differential equations a suitable periodic boundary conditions for a functional differential equations email protected t f t x x t are conditions of the form x 0 q x 2 p q in this paper we use the notion of upper and lower solutions coupled with monotone iterative method to prove the existence of solutions of this periodic boundary value problem

existence and approximation of solutions for discontinuous functional differential equations in this paper existence of solutions of initial value problems for discontinuous functional differential equations is investigated firstly by applying the method of upper and lower solutions which may be discontinuous some existence results of extremal solutions are obtained furthermore we also develop a monotone iterative technique for obtaining extremal solutions which are obtained as limits of monotone sequences

on the maximum angle condition for linear tetrahedral elements synge s maximum angle condition for triangular elements is generalized to tetrahedral elements for the generalized condition it is proved that tetrahedra may degenerate in a certain way and the error of the standard linear interpolation remains o h in the w p 1 omega norm for sufficiently smooth functions and p in 1 infty

local majorities coalitions and monopolies in graphs a review this paper provides an overview of recent developments concerning the process of local majority voting in graphs and its basic properties from graph theoretic and algorithmic standpoints

positive solutions to nonlinear first order pbvps with parameter on time scales abstract in this paper we consider the following nonlinear first order periodic boundary value problem with parameter on a time scale t x t p t x t f x t t 0 t t x 0 x t where 0 is a parameter for suitable 0 some existence multiplicity and nonexistence criteria of positive solutions are established by using well known results from the fixed point index

two point right focal eigenvalue problems on time scales we consider the following right focal boundary value problem 1 n 1y d n t email protected 1 p 1f t y s n 1 t email protected a b t y d i a 0 0 0 n 2 1

an existence result on noncompact intervals for second order functional differential inclusions in this paper we investigate the existence of mild solutions on an infinite interval for second order functional differential inclusions in banach spaces we shall make use of a theorem of ma which is an extension to multivalued maps on locally convex topological spaces of schaefer s theorem

twin positive solutions of nonlinear first order boundary value problems on time scales abstract in this paper we consider the following nonlinear first order boundary value problem on time scale t x t f x t t 0 t t x 0 x t where 0 1 some existence criteria for at least two positive solutions are established by using the well known twin fixed point theorem due to avery and henderson

positive solutions for first order periodic boundary value problem this paper discusses the existence and multiplicity of positive solutions for the following first order periodic boundary value problemx t f t x t 0 0

existence and nonexistence of positive solutions for second order time scale systems abstract this paper is concerned with the following system on time scale t u i t f i u 1 t u 2 t u n t 0 t 0 t t u i 0 0 u i 2 t i 1 2 n where 0 t t and t 0 by using the theory of the fixed point index we investigate the effect of 2 t on the existence and nonexistence of positive solution for the above system in sublinear cases the results obtained are even new for the special cases of difference system and differential system as well as in the general time scale setting

a trapping principle and convergence result for finite element approximate solutions of steady reaction diffusion systems we consider nonlinear elliptic systems with mixed boundary conditions on a convex polyhedral domain rn these are nonlinear divergence form generalizations of u f u where f is outward pointing on the trapping region boundary the motivation is that of applications to steady state reaction diffusion systems also included are reaction diffusion convection systems which satisfy the einstein relations for which the cole hopf transformation is possible for maximum generality the theory is not tied to any specific application we are able to demonstrate a trapping principle for the piecewise linear galerkin approximation defined via a lumped integration hypothesis on integrals involving f by use of variational inequalities results of this type have previously been obtained for parabolic systems by estep larson and williams and for nonlinear elliptic equations by karatson and korotov recent minimum and maximum principles have been obtained by jungel and unterreiter for nonlinear elliptic equations we make use of special properties of the element stiffness matrices induced by a geometric constraint upon the simplicial decomposition this constraint is known as the non obtuseness condition it states that the inward normals associated with an arbitrary pair of an element s faces determine an angle with nonpositive cosine dr g nescu dupont and scott have constructed an example for which the discrete maximum principle fails if this condition is omitted we also assume vertex communication in each element in the form of an irreducibility hypothesis on the off diagonal elements of the stiffness matrix there is a companion convergence result which yields an existence theorem for the solution this entails a consistency hypothesis for interpolation on the boundary and depends on the tabata construction of simple function approximation based on barycentric regions

combinatorial model and bounds for target set selection the adoption of everyday decisions in public affairs fashion movie going and consumer behavior is now thoroughly believed to migrate in a population through an influential network the same diffusion process when being imitated by intention is called viral marketing this process can be modeled by a directed graph g v e with a threshold t v for every vertex v v where v becomes active once at least t v of its in neighbors are already active a perfect target set is a set of vertices whose activation will eventually activate the entire graph and the perfect target set selection problem ptss asks for the minimum such initial set it is known chen 2008 6 that ptss is hard to approximate even for some special cases such as bounded degree graphs or majority thresholds we propose a combinatorial model for this dynamic activation process and use it to represent ptss and its variants by linear integer programs this allows one to use standard integer programming solvers for solving small size ptss instances we also show combinatorial lower and upper bounds on the size of the minimum perfect target set our upper bound implies that there are always perfect target sets of size at most v 2 and 2 v 3 under majority and strict majority thresholds respectively both in directed and undirected graphs this improves the bounds of 0 727 v and 0 7732 v found recently by chang and lyuu 2010 5 for majority and strict majority thresholds in directed graphs and matches their bound under majority thresholds in undirected graphs furthermore our proof is much simpler and we observe that some of these bounds are tight one interesting and perhaps surprising implication of our lower bound for undirected graphs is that it is easy to get a constant factor approximation for ptss for relatively balanced graphs e g bounded degree graphs nearly regular graphs with a more than majority threshold that is t v deg v for every v v and some constant 1 2 whereas no polylogarithmic approximation exists for more than majority graphs

periodic boundary value problem for non lipschitzian impulsive functional differential equations we consider a class of first order impulsive functional differential equations where the functional dependence is not necessarily a lipschitzian function the new maximum principle improves and extends previous results and uniqueness of solution between a lower and an upper solution for a particular nonlinear problem is presented we give conditions for existence of extremal solutions in an interval delimited by a lower and an upper solution

on the equivalence of regularity criteria for triangular and tetrahedral finite element partitions in this note we examine several regularity criteria for families of simplicial finite element partitions in r d email protected 2 3 these are usually required in numerical analysis and computer implementations we prove the equivalence of four different definitions of regularity often proposed in the literature the first one uses the volume of simplices the others involve the inscribed and circumscribed ball conditions and the minimal angle condition

an algebraic discrete maximum principle in hilbert space with applications to nonlinear cooperative elliptic systems discrete maximum principles are derived for finite element discretizations of nonlinear elliptic systyems with cooperative and weakly diagonally dominant coupling the results are achieved via an algebraic discrete maximum principle organized in a hilbert space framework and in the case of simplicial elements are obtained under weakened acute type conditions for the finite element fe meshes

existence of solutions of boundary value problems for differential equations with delayed arguments we study the existence and approximation of solution of boundary value problems for differential equations with delayed arguments sufficient conditions are established for the existence of a unique solution or extremal ones of the given problem a monotone iterative technique is applied

existence and multiplicity of positive solutions to nonlinear first order pbvps on time scales in this paper we consider the following nonlinear first order periodic boundary value problems on time scales x d t p t x s t f x t email protected 0 t t x 0 x s t some new existence and multiplicity criteria of positive solutions are established by using several well known fixed point theorems

local nonobtuse tetrahedral refinements around an edge in this note we show how to generate and conformly refine nonobtuse tetrahedral meshes locally around and towards an edge so that all dihedral angles of all resulting tetrahedra remain nonobtuse the proposed technique can be used e g for a numerical treatment of solution singularities and also for various mesh adaptivity procedures near the reentrant corners of cylindric type 3d domains

on monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations abstract in this paper we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions of first and second order periodic boundary value problems and periodic solutions of functional differential equations we obtain some new results relative to the lower solution and upper solution with

monotone iterative method for first order functional difference equations with nonlinear boundary value conditions in this paper we show that the method of monotone iterative coupled with the upper and lower solutions is valid to obtain constructive proofs to the existence of solutions for first order functional difference equations with nonlinear boundary value conditions an example is given to illustrate the results obtained

discrete maximum principle for fe solutions of the diffusion reaction problem on prismatic meshes in this paper we analyse the discrete maximum principle dmp for a stationary diffusion reaction problem solved by means of prismatic finite elements we derive geometric conditions on the shape parameters of the prismatic partitions which guarantee validity of the dmp the presented numerical tests show the sharpness of the obtained conditions

discontinuous functional differential equations with delayed or advanced arguments we provide new results on the existence of extremal solutions for discontinuous differential equations with a deviated argument which can be either delayed or advanced the boundary condition is allowed to be discontinuous and to depend functionally on the unknown solution

dynamic monopolies and feedback vertex sets in hexagonal grids in a majority conversion process the vertices of a graph can be in one of the two states colored or uncolored and these states are dynamically updated so that a vertex becomes colored at a certain time period if at least half of its neighbors were in the colored state in the previous time period a dynamic monopoly is a set of vertices in a graph that when initially colored will eventually cause all vertices in the graph to become colored this paper establishes a connection between dynamic monopolies and the well known feedback vertex sets which are sets of vertices whose removal results in an acyclic graph more specifically we show that dynamic monopolies and feedback vertex sets are equivalent in graphs wherein all vertices have degree 2 or 3 we use this equivalence to provide exact values for the minimum size of dynamic monopolies of planar hexagonal grids as well as upper and lower bounds on the minimum size of dynamic monopolies of cylindrical and toroidal hexagonal grids for these last two topologies the respective upper and lower bounds differ by at most one

some new results on the existence of positive solutions for the one dimensional p laplacian boundary value problems on time scales abstract this paper is devoted to using the leggett williams fixed point theorem to derive some sufficient conditions for the existence of triple positive solutions to a type of p laplacian boundary value problems on time scales the interesting point is that the nonlinear term f depends on the first order delta derivative explicitly

advanced differential equations with nonlinear boundary conditions we investigate the existence of solutions for advanced differential equations with nonlinear boundary conditions sufficient conditions when the problem has extremal solutions or a unique solution are formulated linear advanced differential inequalities are also discussed

adaptive finite element method assisted by stochastic simulation of chemical systems stochastic models of chemical systems are often analyzed by solving the corresponding fokker planck equation which is a drift diffusion partial differential equation for the probability distribution function efficient numerical solution of the fokker planck equation requires adaptive mesh refinements in this paper we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system by observing the stochastic trajectory for a relatively short amount of time the areas of the state space with nonnegligible probability density are identified by refining the finite element mesh in these areas and coarsening elsewhere a suitable mesh is constructed and used for the computation of the stationary probability density numerical examples demonstrate that the presented method is competitive with existing a posteriori methods

the optimal refinement strategy for 3 d simplicial meshes 3 d mesh refinement strategies are the object of interest in the present paper the dependence of finite element solutions on various refinement procedures is discussed a new refinement strategy which is optimal with respect to the measure of degeneracy for all canonical domains is obtained comparisons with known refinement techniques are made some isoparametric examples are presented

multiple positive solutions for functional dynamic equations on time scales in this paper we study the following functional dynamic equation on time scales f u d t a t f u t u m t 0 email protected 0 t t u t email protected t email protected r 0 t u 0 b 0 u d 0 0 u d t 0 where f r r is an increasing homeomorphism and a positive homomorphism and f 0 0 by using the well known leggett williams fixed point theorem existence criteria for multiple positive solutions are established an example is also given to illustrate the main results

on the shape of tetrahedra from bisection we present a procedure for bisecting a tetrahedron t successively into an infinite sequence of tetrahedral meshes j 0 91 g2 which has the following properties 1 each mesh sfn is conforming 2 there are a finite number of classes of similar tetrahedra in all the 3n n 0 3 for any tetrahedron t7 in s7n jj t cl1 t where ti is a tetrahedron shape measure and cl is a constant 4 3 j c2 1 2 ni3j t where d t denotes the diameter of tetrahedron t1 and c2 is a constant estimates of cl and c2 are provided properties 2 and 3 extend similar results of stynes and adler and of rosenberg and stenger respectively for the 2 d case the diameter bound in property 4 is better than one given by kearfott

bounding the sizes of dynamic monopolies and convergent sets for threshold based cascades consider the following reversible cascade on a simple directed graph g v e in round zero a set of vertices called the seeds are active in round email protected z a vertex email protected v is activated deactivated if at least resp fewer than f v of its in neighbors are active in round k 1 where f v n an irreversible cascade is defined similarly except that active vertices cannot be deactivated two specific candidates for the threshold function f are f m a j v s t r i c email protected deg v 1 email protected and f r v email protected email protected deg v where deg v denotes the indegree of email protected v and email protected 0 1 an irreversible dynamic monopoly is a set of seeds that leads all vertices to activation after finitely many rounds of the irreversible cascade with email protected m a j s t r i c t a set of vertices s is said to be convergent if no vertex will ever change its state from active to inactive or vice versa once the set of active vertices equals s this paper shows that an irreversible dynamic monopoly of size at most v email protected can be found in polynomial in v time if g is strongly connected furthermore we show that for any constant e 0 all email protected 0 1 email protected r email protected email protected ln e r n 1 and with probability 1 n w 1 every convergent set of the erdos renyi random graph g n p has size o email protected or n o email protected our result on convergent sets holds for both the reversible and irreversible cascades

global and local refinement techniques yielding nonobtuse tetrahedral partitions preservation of basic qualitative properties for example the maximum principle ofthe solution of partial differential equations by its finite element approximations is an important goal in mathematical modelling and simulation nonobtuse tetrahedral partitions and linear finite elements guarantee the validity of the discrete analogues of the maximum principle for a wide class of parabolic and elliptic problems in order to get more accurate approximation we often need to refine the used partitions globally or locally in this paper we first propose two variants of global refinement techniques which produce nonobtuse face to face tetrahedral partitions second we present a new local refinement technique which generates nonobtuse face to face tetrahedral partitions in a neighbourhood of a given vertex

double positive solutions of three point boundary value problems for p laplacian dynamic equations on time scales a new double fixed point theorem is applied to investigate the existence of at least double positive solutions of three point boundary value problems for p laplacian dynamic equations on a time scale

existence of solutions to nonlinear first order pbvps on time scales abstract in this paper we are concerned with the following nonlinear first order periodic boundary value problem on time scales x t p t x t g t x t t 0 t t x 0 x t some new existence criteria of at least one solution are established by using novel inequalities and the well known schaefer fixed point theorem