criteria for generalized invex monotonicities abstract in this paper under appropriate conditions we establish that i if the gradient of a function is strictly pseudo monotone then the function is strictly pseudo invex ii if the gradient of a function is quasi monotone then the function is quasi invex and iii if the gradient of a function is strong pseudo monotone then the function is strong pseudo invex

criteria for quasi convexity and pseudo convexity relationships and comparisons a first order criterion for pseudo convexity and second order criteria for quasi convexity and pseudo convexity are given for twice differentiable functions on open convex sets the relationships between these second order criteria and other known criteria are also analysed finally the numbers of operations required to verify these criteria are calculated and compared

a variational like inequality for multifunctions with applications abstract we study a variational like inequality problem for a multifunction a certain relevant complementarity problem is defined we establish some existence theorems for the above two problems an application to convex mathematical programming is also shown

constructing and predicting solitary pattern solutions for nonlinear time fractional dispersive partial differential equations building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics physics and engineering in this work a new analytical technique for constructing and predicting solitary pattern solutions of time fractional dispersive partial differential equations is proposed based on the generalized taylor series formula and residual error function the new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software for method evaluation and validation the proposed technique was applied to three different models and compared with some of the well known methods the resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct as well as the prediction of solitary pattern solutions for time fractional dispersive partial differential equations

characterization of a condition related to a class of preinvex functions in the theory of invex functions a very important role is played by the so called condition c we present a convenient characterization of this condition in terms of starlike sets and projections

relationships between vector variational like inequality and optimization problems abstract in this paper we will establish the relationships between vector variational like inequality and optimization problems we will be able to identify the vector critical points the weakly efficient points and the solutions of the weak vector variational like inequality problem under conditions of pseudo invexity these conditions are more general those existing in the literature

a finite volume scheme for two phase immiscible flow in porous media in this paper we prove the convergence of a numerical method for solving two phase immiscible incompressible flow in porous media the method combines an upwind time implicit finite volume scheme for the saturation equation hyperbolic parabolic type and a centered finite volume scheme for the chavent global pressure equation elliptic type the capillary pressure is not neglected and we study the case when the diffusion term in the saturation equation is weakly degenerated estimates on the approximate solution are proven then by using compactness theorems we obtain a limit when the size of the discretization goes to zero and we prove that this limit is the unique weak solution of the problem that we study

efficiency through variational like inequalities with lipschitz functions in this work first we introduce several notions of invexity and pseudoinvexity for a locally lipschitz function by means of the generalized jacobian we study relationships between these concepts in particular the implications between preinvexity and invexity next we obtain necessary and sufficient optimality conditions for efficient and weak efficient solutions of finite dimensional non necessarily pareto vector optimization problems with locally lipschitz objective functions through solutions of vector variational like inequality problems these conditions are stated via the generalized jacobian and under pseudoinvexity hypotheses and they show that a vector optimization problem can be reformulated as a vector variational like inequality problem this work extends and improves several previous papers where the objective function of the vector optimization problem is assumed to be differentiable or being locally lipschitz the authors consider the componentwise subdifferential based on the clarke s generalized gradients of the components of the objective function throughout the paper some simple examples are given in order to illustrate the main concepts and results

the locally stabilized finite volume method for incompressible flow a locally stabilized finite volume method for the two dimensional incompressible flow governed by stationary stokes and navier stokes equations is investigated in this work a macroelement condition is introduced for constructing the local stabilized formulation for the problem the optimal l 2 error estimate of u h p h determined by stokes equations is also deduced some numerical examples are provided to check the efficiency of this method

criteria for generalized invex monotonicities without condition c in this paper some necessary conditions of strictly pseudo invex monotonicity and quasi invex monotonicity are established with the condition that is affine in the first argument and skew instead of condition c

generalized invex monotonicity abstract in this paper the generalized invex monotone functions are defined as an extension of monotone functions a series of sufficient and necessary conditions are also given that relate the generalized invexity of the function with the generalized invex monotonicity of its gradient function this new class of functions will be important in order to characterize the solutions of the variational like inequality problem and mathematical programming problem

asymptotic dynamics of short waves in nonlinear dispersive models multiple scale perturbation theory well known for long waves is extended to the study of the far field behavior of short waves commonly called ripples it is proved that the benjamin char21 bona char21 mahony char21 peregrine equation can support the propagation of short waves this result contradicts the benjamin hypothesis that short waves do not propagate in this model and closes a part of the old controversy over different solutions for the korteweg char21 de vries and benjamin char21 bona char21 mahony char21 peregrine equations we have shown that in a short wave analysis a nonlinear quadratic klein gordon char21 type equation replaces the ubiquitous korteweg char21 de vries equation of the long wave approach moreover the kink solutions of ensuremath varphi 4 and sine gordon equations are understood as an asymptotic behavior of short waves to all orders it is proved that the antikink solution of the ensuremath varphi 4 model which was never obtained perturbatively occurs as a perturbation expansion in the wave number k in the short wave limit

the finite volume element method for diffusion equations on general triangulations this paper develops discretization error estimates for the finite volume element method on general triangulations of a polygonal domain in mathcal r 2 using a special type of control volume the theory applies to diffusion equations of the form begin gathered nabla a nabla u f quad text in omega hfill u 0 quad text on partial omega hfill end gathered under fairly general conditions the theory establishes o h estimates of the error in a discrete mathcal h 1 seminorm under an additional assumption concerning local uniformity of the triangulation the estimate is improved to o h 2

some relations between variational like inequality problems and vectorial optimization problems in banach spaces in this work we will establish some relations between variational like inequality problems and vectorial optimization problems in banach spaces under invexity hypotheses this paper extends the earlier work of ruiz garzon et al g ruiz garzon r osuna gomez a rufian lizana relationships between vector variational like inequality and optimization problems european j oper res 157 2004 113 119

some errors estimates for the box method we define and analyze several variants of the box method for discretizing elliptic boundary value problems in the plane our estimates show the error to be comparable to a standard galerkin finite element method using piecewise linear polynomials

some characterizations of strongly preinvex functions in this paper a new class of generalized convex function is introduced which is called the strongly preinvex function we study some properties of strongly preinvex function in particular we establish the equivalence among the strongly preinvex functions strongly invex functions and strongly monotonicity under some suitable conditions as special cases one can obtain several new and previously known results for preinvex invex functions

the mortar finite volume method with the crouzeix raviart element for elliptic problems abstract we construct and analyse a mortar finite volume method for the discretization for selfadjoint elliptic boundary value problems in r 2 this method is based on the mortar crouzeix raviart non conforming finite element spaces we prove the optimal order h 1 norm and l 2 norm error estimates between the exact solution and the mortar finite volume approximation of the elliptic problems

an integrable equation governing short waves in a long wave model the dynamics of a nonlinear and dispersive long surface capillary gravity wave model equation is studied analytically in its short wave limit we exhibit its lax pair and some non trivial conserved quantities through a change of functions an unexpected connection between this classical surface water wave model and the sine gordon or sinh gordon equation is established numerical and analytical studies show that in spite of integrability their solutions can develop singularities and multivaluedness in finite time these features can be traced to the fact that the surface tension term in the energy involves second order derivatives it would be interesting to see in an experiment whether such singularities actually appear for which surface tension would be specifically responsible

generalized invexity of nonsmooth functions abstract in this paper the concepts of weak invexity and weak quasi invexity are introduced and the relations among several kinds of generalized invexity are studied for nonsmooth functions by means of the properties of limiting subdifferentials in addition the relations between generalized invexity of a nonsmooth function and generalized invariant monotonicity of its limiting subdifferential mapping are researched our results here are an extension and generalization of those presented by m soleimani damaneh

on the finite volume element method the finite volume element method fve is a discretization technique for partial differential equations it uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations then restricts the admissible functions to a finite element space to discretize the solution this paper develops discretization error estimates for general selfadjoint elliptic boundary value problems with fve based on triangulations with linear finite element spaces and a general type of control volume we establisho h estimates of the error in a discreteh 1 semi norm under an additional assumption of local uniformity of the triangulation the estimate is improved too h 2 results on the effects of numerical integration are also included

nonlinear asymptotic short wave models in fluid dynamics nonlinear monochromatic short surface waves in ideal fluids are studied and by the general consideration of wave dynamics and perturbative methods a simple and effective multiscale approach is devised for nonlinear asymptotic short wave dynamics in dispersive systems in particular the evolution of a monochromatic surface wave in an ideal fluid is shown to lead to a modified green naghdi system of equations and a green naghdi system with surface tension short surface waves exist in these systems and the nonlinear asymptotic analysis produces the nonlinear model equations that govern their dynamics particular solutions are shown moreover the method allows for a general classification of classical model equations as boussinesq benjamin bona mahony peregrine and camassa holm equations their related nonlinear short wave model limits are then derived a relation between the short wave limit of the integrable camassa holm equation and the harry dym hierarchy is finally unveiled

preconditioning the bidomain model with almost linear complexity the bidomain model is widely used in electro cardiology to simulate spreading of excitation in the myocardium and electrocardiograms it consists of a system of two parabolic reaction diffusion equations coupled with an ode system its discretisation displays an ill conditioned system matrix to be inverted at each time step simulations based on the bidomain model therefore are associated with high computational costs in this paper we propose a preconditioning for the bidomain model either for an isolated heart or in an extended framework including a coupling with the surrounding tissues the torso the preconditioning is based on a formulation of the discrete problem that is shown to be symmetric positive semi definite a block lu decomposition of the system together with a heuristic approximation referred to as the monodomain approximation are the key ingredients for the preconditioning definition numerical results are provided for two test cases a 2d test case on a realistic slice of the thorax based on a segmented heart medical image geometry a 3d test case involving a small cubic slab of tissue with orthotropic anisotropy the analysis of the resulting computational cost both in terms of cpu time and of iteration number shows an almost linear complexity with the problem size i e of type nlog a n for some constant a which is optimal complexity for such problems

exchange price equilibria and variational inequalities the aim of this paper is to show the relevance of the concept and the theory of variational inequalities in the study of economic equilibria

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

finite volume methods for convection diffusion problems derivation stability and error analysis in both discrete h 1 and l 2 norms for cell centered finite volume approximations of convection diffusion problems are presented various upwind strategies are investigated the theoretical results are illustrated by numerical examples

integrability of the modified generalised vakhnenko equation integrability of the modified generalised vakhnenko equation is investigated systematically based on binary bell polynomials its bilinear representation n soliton solutions bilinear backlund transformation and lax pair are succinctly constructed moreover the conservation laws of the modified generalised vakhnenko equation are discussed by using corresponding lax pair furthermore the quasiperiodic solution of the modified generalised vakhnenko equation is presented by applying hirota direct method and riemann theta function the asymptotic behavior of the one periodic wave is analyzed in details it is shown that the one periodic wave solution tends to the one soliton solution under a small amplitude limit 0 finally the new n soliton solutions of the standard vakhnenko equation are presented it would be specially mentioned that all the results of modified generalised vakhnenko equation can be reduced to the generalised vakhnenko equation and standard vakhnenko equation under the special case of 1 and 1 0 respectively

on the coupling of finite volume and discontinuous galerkin method for elliptic problems the coupling of cell centered finite volume method with primal discontinuous galerkin method is introduced in this paper for elliptic problems convergence of the method with respect to the mesh size is proved numerical examples confirm the theoretical rates of convergence advantages of the coupled scheme are shown for problems with discontinuous coefficients or anisotropic diffusion matrix

integrable discretizations for the short wave model of the camassa holm equation the link between the short wave model of the camassa holm equation sche and bilinear equations of the two dimensional toda lattice equation is clarified the parametric form of the n cuspon solution of the sche in casorati determinant is then given based on the above finding integrable semi discrete and full discrete analogues of the sche are constructed the determinant solutions of both semi discrete and fully discrete analogues of the sche are also presented

on the accuracy of the finite volume element method for diffusion equations on composite grids this paper develops the finite volume element fve method which is similar to the so called control volume finite element method but tailored to composite grid applications fve is described for the general two dimensional diffusion equation in divergence form o h 3 2 discretization error estimates are then developed for the case of triangular elements these results are improved to o h 2 using a special modification involving rectilinear elements at the grid interface

fractal structure of ferromagnets the singularity structure analysis following the weiss tabor carnevale approach j weiss m tabor and g carnevale j math phys 24 522 1983 10 1063 1 525721 j weiss m tabor and g carnevale j math phys 25 13 1984 10 1063 1 526009 designed for studying the integrability properties of nonlinear partial differential equations we investigate the singularity structure of a 2 1 dimensional wave equation describing the propagation of polariton solitary waves in a ferromagnetic slab as a result we show that out of any damping instability the system above is integrable looking forward to unveiling its complete integrability we derive its backlund transformation and hirota s bilinearization useful in generating a set of soliton solutions in the wake of such results using the arbitrary functions to enter into the laurent series of solutions to the above system we discuss some typical class of excitations generated from the previous solutions in account of a classification based upon the different expressions of a gene

on strongly α preinvex functions in this paper by means of a series of counterexamples we study in a systematic way the relationships among pseudo quasi preinvexity strict strong pseudo quasi invexity and strict strong pseudo quasi monotonicity results obtained in this paper can be viewed as a refinement and improvement of the results of noor and noor m a noor k i noor some characterizations of strongly preinvex functions j math anal appl 316 2006 697 706