galerkin projected residual method applied to diffusion reaction problems a stabilized finite element method is presented for scalar and linear second order boundary value problems the method is obtained by adding to the galerkin formulation multiple projections of the residual of the differential equation at element level these multiple projections allow the generation of appropriate number of free stabilization parameters in the element matrix depending on the local space of approximation and on the differential operator the free parameters can be determined imposing some convergence and or stability criteria or by postulating the element matrix with the desired stability properties the element matrix of most stabilized methods such as gls and ggls methods can be obtained using this new method with appropriate choices of the stabilization parameters we applied this formulation to diffusion reaction problems optimal rates of convergency are numerically observed for regular solutions

some nondifferentiable multiobjective programming under generalized d v type i univexity in this paper we introduce new classes of functions called d v type i univex by extending the definition of d v type i functions and consider a multiobjective optimization problem involving generalized d v type i univex functions a number of karush kuhn tucker type sufficient optimality conditions are obtained for a feasible solution to be a weak pareto efficient solution the mond weir type duality results are also presented the results obtained in this paper generalize and extend the previously known result in this area

interpolation error based a posteriori error estimation for two point boundary value problems and parabolic equations in one space dimension i derive a posteriori error estimates for two point boundary value problems and parabolic equations in one dimension based on interpolation error estimates the interpolation error estimates are obtained from an extension of the error formula for the lagrange interpolating polynomial in the case of symmetrically spaced interpolation points from this formula pointwise and h 1 seminorm a priori estimates of the interpolation error are derived the interpolant in conjunction with the a priori estimates is used to obtain asymptotically exact a posteriori error estimates of the interpolation error these a posteriori error estimates are extended to linear two point boundary problems and parabolic equations computational results demonstrate the convergence of a posteriori error estimates and their effectiveness when combined with an hp adaptive code for solving parabolic systems

new optimality conditions and duality results of g type in differentiable mathematical programming abstract in this paper a new class of differentiable functions called g invex functions with respect to is introduced by extending the definition of invex functions new necessary optimality conditions of g f john and g karush kuhn tucker type are obtained for differentiable constrained mathematical programming problems the g invexity concept introduced is used to prove the sufficiency of these necessary optimality conditions further a so called g mond weir type dual is formulated and various duality results are also established by assuming the functions involved to be g invex with respect to the same function

aperiodic virasoro algebra an aperiodic analog to the virasoro algebra is introduced and its representation theory is investigated in particular highest and lowest weight representations are constructed an analog to the kac determinant formula is derived and the implications for unitarity are discussed

a posteriori error estimation with finite element semi and fully discrete methods for nonlinear parabolic equations in one space dimension a posteriors error estimates for semi and fully discrete finite element methods using a pth degree polynomial basis are considered for nonlinear parabolic equations the error estimates are obtained by solving local parabolic or elliptic equations for corrections to the solution on each element using a p 1 st degree polynomial which is zero at the nodes singly implicit runge kutta sirk and backward difference formula bdf methods are considered in the fully discrete case local errors are defined in an analogous manner to the respective methods for ordinary differential equations the a posteriors error estimates are shown to converge to the local errors even in case the local correction is missing from the nonlinear term computational examples compare and verify the theoretical results

applications of lobatto polynomials to an adaptive finite element method a posteriori error estimates for hp adaptivity and grid to grid interpolation hp adaptive finite element codes require methods for estimating the error at several spatial orders and for interpolating solutions between grids lobatto polynomial based techniques are presented for both an interpolation error based error estimation strategy for a posteriori error estimates is generalized to yield asymptotically exact error estimates one order higher than the computed solution the estimates involve high order derivatives of the solution that must be approximated from the computed solution differentiating a taylor like series for error in the lobatto interpolant and using the weak form of the equations yields the correct derivative approximations this leads to a more robust order selection strategy interpolation between grids is done over each element using the lobatto interpolating polynomial explicit formulas for the inverse of the resulting lobatto interpolation matrices are given computational results illustrate the theory

optimality and duality for nonsmooth multiobjective programming using g type i functions abstract in this paper generalized g type i functions are defined for a nonlinear multiobjective programming problem where the functions involved are assumed to be locally lipschitz this new class of functions is a generalization of g invex functions defined in kang et al 2012 20 examples are given to show the existence of these functions g type kuhn tucker necessary conditions are established for a nondifferentiable multiobjective programming problem gmp by using suitable g type i functions sufficient optimality conditions are derived for the problem gmp further a mond weir type dual gmwd is formulated and using these newly defined functions various duality results are established

implicit interpolation error based error estimation for reaction diffusion equations in two space dimensions several authors have proposed an error estimation strategy for the finite element method applied to linear reaction diffusion equations in two space dimensions based on an odd even order dichotomy principle for odd order approximations the estimates are computed directly for even order approximations a second solution is computed although both estimators are asymptotically exact the latter are more robust than the former herein the even order method is extended to all orders greater than one thereby recovering robustness for odd orders proofs of asymptotic exactness are extended to nonlinear reaction diffusion equations computational results demonstrating their effectiveness are presented

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

a posteriori finite element error estimation for diffusion problems adjerid babuska and flaherty math models methods appl sci 9 1999 pp 261 286 and yu math numer sinica 13 1991 pp 89 101 and math numer sinica 13 1991 pp 307 314 show that a posteriori estimates of spatial discretization errors of piecewise bi p polynomial finite element solutions of elliptic and parabolic problems on meshes of square elements may be obtained from jumps in solution gradients at element vertices when p is odd and from local elliptic or parabolic problems when p is even we show that these simple error estimates are asymptotically correct for other finite element spaces the key requirement is that the trial space contain all monomial terms of degree p 1 except for x 1 p 1 and x 2 p 1 in a cartesian x1 x2 frame computational results show that the error estimates are accurate robust and efficient for a wide range of problems including some that are not supported by the present theory these involve quadrilateral element meshes problems with singularities and nonlinear problems

necessary and sufficient conditions in constrained optimization additional conditions are attached to the kuhn tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization under appropriate constraint qualifications necessary and sufficient conditions are also given for optimality of the dual problem duality and converse duality are treated accordingly

on quasicrystal lie algebras we realize the aperiodic witt and virasoro algebras as well as other quasicrystal lie algebras as factor algebras of some subalgebras of the higher rank virasoro algebras this realization allows us to generalize the notion of quasicrystal lie algebras in the case when the constructed algebra admits a conjugation we compute the kac determinant for the shapovalov form on the corresponding verma modules in the case of the aperiodic virasoro algebra this proves the conjecture of r twarock

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

validation of a posteriori error estimators by numerical approach abstract a numerical methodology which determines the quality or robustness of a posteriori error estimators is described the methodology accounts precisely for the factors which affect the quality of error estimators for finite element solutions of linear elliptic problems namely the local geometry of the grid and the structure of the solution the methodology can be employed to check the robustness of any estimator for the complex grids which are used in engineering computations

symmetries of quasicrystals we consider tiling models of round quasicrystals which would have diffraction patterns which are fully rotation invariant rings instead of bragg peaks they can be distinguished from glasses by self similarity of the pattern of radii of the rings

quasicrystals atomic coverings and windows are dual projects in the window approach to quasicrystals the atomic position space e is embedded into a space en e e windows are attached to points of a lattice en for standard fivefold and icosahedral tiling models the windows are perpendicular projections of dual voronoi and delone cells from their cuts by the position space e mark tiles and atomic positions in the alternative covering approach the position space is covered by overlapping copies of a quasi unit cell which carries a fixed atomic configuration the covering and window approach to quasicrystals are shown to be dual projects d and v clusters are defined as projections to position space e of delone or voronoi cells decagonal v clusters in the penrose tiling related to the decagon covering and two types of pentagonal d clusters in the triangle tiling of fivefold point symmetry with their windows are analysed they are linked cover position space and have definite windows for functions compatible with the tilings they form domains of definition for icosahedral tilings the v clusters are kepler triacontahedra the d clusters are two icosahedra and one dodecahedron

on sufficiency and duality for nonsmooth multiobjective programming problems involving generalized v r invex functions abstract in this paper a class of nonsmooth multiobjective programming problems with inequality constraints is considered we introduce the concepts of v r pseudo invex strictly v r pseudo invex and v r quasi invex functions in which the involved functions are locally lipschitz based upon these generalized v r invex functions sufficient optimality conditions for a feasible point to be an efficient or a weakly efficient solution are derived appropriate duality theorems are proved for a mond weir type dual program of a nonsmooth multiobjective programming under the aforesaid functions

virasoro type algebras associated with a penrose tiling a family of infinite dimensional lie algebras with generators in a one to one correspondence with the points of a penrose tiling is introduced central extensions leading to virasoro type algebras are constructed and highest weight representations for these algebras are considered furthermore extensions to a super symmetric setting and thus aperiodic analogues to virasoro super algebras are discussed

the relationship of some a posteriori estimators we present analytical and numerical investigation in the relationship of the recovery error estimator and the implicit residual error estimator it is shown that analytically both error estimators are equivalent for one dimensional problems numerical study indicates that such equivalence also exist for two dimensional problems

using krylov methods in the solution of large scale differential algebraic systems in this paper a new algorithm for the solution of large scale systems of differential algebraic equations is described it is based on the integration methods in the solver dassl but instead of a direct method for the associated linear systems which arise at each time step we apply the preconditioned gmres iteration in combination with an inexact newton method the algorithm along with those in dassl is implemented in a new solver called daspk we outline the algorithms and strategies used and discuss the use of the solver we develop and analyze some preconditioners for a certain class of dae stems and finally demonstrate the application of daspk on two example problems

optimality and duality in nonsmooth multiobjective optimization involving generalized type i functions abstract a nonsmooth multiobjective optimization problem involving generalized type i vectorvalued functions is considered karush kuhn tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be an efficient or properly efficient solution duality theorems are proved for wolfe type and mond weir type duals under the generalized type i assumptions

a posteriori error estimation with finite element methods of lines for one dimensional parabolic systems consider the solution of one dimensional linear initial boundary value problems by a finite element method of lines using a piecewisep th degree polynomial basis a posteriori estimates of the discretization error are obtained as the solutions of either local parabolic or local elliptic finite element problems using piecewise polynomial corrections of degreep 1 that vanish at element ends error estimates computed in this manner are shown to converge in energy under mesh refinement to the exact finite element discretization error computational results indicate that the error estimates are robust over a wide range of mesh spacings and polynomial degrees and are furthermore applicable in situations that are not supported by the analysis

a posteriori error estimation with the finite element method of lines for a nonlinear parabolic equation in one space dimension convergence of a posteriori error estimates to the true error for the semidiscrete finite element method of lines is shown for a nonlinear parabolic initial boundary value problem

a posteriori error estimation for hp adaptivity for fourth order equations a posteriori error estimates developed to drive hp adaptivity for second order reaction diffusion equations are extended to fourth order equations a c 1 hierarchical finite element basis is constructed from hermite lobatto polynomials a priori estimates of the error in several norms for both the interpolant and finite element solution are derived in the latter case this requires a generalization of the well known aubin nitsche technique to time dependent fourth order equations we show that the finite element solution and corresponding hermite lobatto interpolant are asymptotically equivalent a posteriori error estimators based on this equivalence for solutions at two orders are presented both are shown to be asymptotically exact on grids of uniform order these estimators can be used to control various adaptive strategies computational results for linear steady state and time dependent equations corroborate the theory and demonstrate the effectiveness of the estimators in adaptive settings