saddle points criteria in nondifferentiable multiobjective programming with v invex functions via an η approximation method the h approximation method is used to a characterization of solvability of nonconvex nondifferentiable multiobjective programming problems a family of h approximated vector optimization problems is constructed in this approach for the original nondifferentiable multiobjective programming problem the definitions of a vector valued h lagrange function and of an h saddle point for this family of h approximated vector optimization problems are introduced thus the equivalence between a weak pareto optimum of the original multiobjective programming problems and an h saddle point of the h lagrange function in its associated h approximated vector optimization problems is established under v invexity

globally convergent algorithms for convex programming we consider solving a minimization convex program by sequentially solving a minimization convex approximating subproblem and then executing a line search on an exact penalty function each subproblem is constructed from the current estimate of a solution of the given problem possibly together with other information under mild conditions solving the current subproblem generates a descent direction for the exact penalty function minimizing the exact penalty function along the current descent direction provides a new estimate of a solution and a new subproblem is formed for any arbitrary starting estimate this scheme generates a sequence of estimates that converges to a solution of the given problem moreover the functions defining the given problem and each subproblem need not be differentiable

very weak generalized and strong solutions to the stokes system in the half space abstract in this paper we study the stokes system in the half space r n with n 2 we give existence and uniqueness results in weighted sobolev spaces after the central case of the generalized solutions we are interested in strong solutions and symmetrically in very weak solutions by means of a duality argument

decay rate for the incompressible flows in half spaces we show that the time decay rate of l 2 norm of weak solution for the stokes equations and for the navier stokes equations on the half spaces are t frac n 2 frac 1 r frac 1 2 frac 1 2 if the initial data u 0 in l 2 cap l r and int mathbb r n y n u 0 y r dy infty for 1 r 2 we also show that the decay rate is determined by the linear part of the weak solution we use the heat kernel and ukai s solution formula for the stokes equations it has been known up to now that the decay rate on the half space was t frac n 2 frac 1 r frac 1 2 which was obtained by borchers and miyakawa 1 and ukai 9

on the inviscid limit problem of the vorticity equations for viscous incompressible flows in the half plane we consider the navier stokes equations for viscous incompressible flows in the half plane under the no slip boundary condition by using the vorticity formulation we prove the local in time convergence of the navier stokes flows to the euler flows outside a boundary layer and to the prandtl flows in the boundary layer in the inviscid limit when the initial vorticity is located away from the boundary 2014 wiley periodicals inc

saddle point criteria for multi dimensional control optimisation problem involving first order pde constraints in this paper the multi dimensional control optimisation problem involving first order pde constraints is considered the absolute value penalty function method is used to solve the considered pro

efficiency and approachability of nonconvex bicriteria programs abstract in this paper we investigate equivalences between an efficient solution of a bicriteria program and a lower envelope point of a certain image set of the bicriteria program we also employ various kinds of approachabilities to characterize efficiency and proper efficiency for nonconvex bicriteria programs in particular nonlinear lagranian functions are applied to construct dual problems and to study stability for the corresponding constrained scalar optimization problems under certain conditions we show that the finite approachability proper efficiency stability and exact penalization of the relevant constrained scalar optimization problems are equivalent

weakly singular initial values for the stokes equation on a half space we study the extension of ukai s formula to the case of singular initial values for the stokes problem on the half space

consistency of multi time dirac equations with general interaction potentials in 1932 dirac proposed a formulation in terms of multi time wave functions as candidate for relativistic many particle quantum mechanics a well known consistency condition that is necessary for existence of solutions strongly restricts the possible interaction types between the particles it was conjectured by petrat and tumulka that interactions described by multiplication operators are generally excluded by this condition and they gave a proof of this claim for potentials without spin coupling under suitable assumptions on the differentiability of possible solutions we show that there are potentials which are admissible give an explicit example however show that none of them fulfills the physically desirable poincare invariance we conclude that in this sense dirac s multi time formalism does not allow to model interaction by multiplication operators and briefly point out several promising approaches to interacting models one can instead pursue

lower bound of l2 decay of the navier stokes flow in the half space r n and its asymptotic behavior in the frequency space abstract we consider the asymptotic behavior of weak solutions of the navier stokes equations in the half space r n we obtain the lower bound of the energy decay of the navier stokes flow by means of the profile of the initial data indeed we construct a class of the initial data which causes the slow decay of the navier stokes flow with an explicit rate furthermore we investigate the asymptotic behavior of concentration in the frequency space

generalized convexity in fuzzy vector optimization through a linear ordering in this article we study efficiency and weakly efficiency in fuzzy vector optimization after formulating the problem we introduce two new concepts of generalized convexity for fuzzy vector mappings based on the generalized hukuhara differentiability pseudoinvexity i and pseudoinvexity ii we prove that pseudoinvexity is the necessary and sufficient condition for a stationary point to be a solution of a fuzzy vector optimization problem we give conditions to insure that a fuzzy vector mapping is invex and pseudoinvex i and ii moreover we present some examples to illustrate the results lastly we use these results to study the class of problems which have uncertainty and inaccuracies in the objective function coefficients of mathematical programming models

a sequential quadratic programming algorithm for nonconvex nonsmooth constrained optimization we consider optimization problems with objective and constraint functions that may be nonconvex and nonsmooth problems of this type arise in important applications many having solutions at points of nondifferentiability of the problem functions we present a line search algorithm for situations when the objective and constraint functions are locally lipschitz and continuously differentiable on open dense subsets of mathbb r n our method is based on a sequential quadratic programming sqp algorithm that uses an ell 1 penalty to regularize the constraints a process of gradient sampling gs is employed to make the search direction computation effective in nonsmooth regions we prove that our sqp gs method is globally convergent to stationary points with probability one and illustrate its performance with a matlab implementation

existence and regularity of a class of weak solutions to the navier stokes equations abstract we construct a class of weak solutions to the navier stokes equations which have second order spatial derivatives and one order time derivatives of p power summability for 1 p 5 4 meanwhile we show that u l s 0 t w 2 r with 1 s 3 2 r 2 for 1 r 5 4 r can be relaxed not to exceed 3 2 if we consider only in the interior of in the end we extend the classical regularity theorem our results show that u is a regular solution if u l s 0 t l r with 1 s 3 2 r 1 for satisfying 1 3 with 1 s 1 r 5 6 for arbitrary domain in r 3 and 1 s 2 for r n with n 3 this result was previously obtained byh beirao da veiga chinese ann math ser b 16 1995 407 412

new efficiency conditions for multiobjective interval valued programming problems abstract in this paper we focus on necessary and sufficient efficiency conditions for optimization problems with multiple objectives and a feasible set defined by interval valued functions a new concept of fritz john and karush kuhn tucker type points is introduced for this mathematical programming problem based on the gh derivative concept the innovation and importance of these concepts are presented from a practical and computational point of view the problem is approached directly without transforming it into a real valued programming problem thereby attaining theoretical results that are more powerful and computationally more efficient under weaker hypotheses we also provide necessary conditions for efficiency which have been inexistent in the relevant literature to date the identification of necessary conditions is important for the development of future computational optimization techniques in an interval valued environment we introduce new generalized convexity notions for gh differentiable interval valued problems which are a generalization of previous concepts and we prove a sufficient efficiency condition based on these concepts finally the efficiency conditions for deterministic programming problems are shown to be particular instances of the results proved in this paper the theoretical developments are illustrated and justified through several numerical examples

on the navier stokes equations in the half space with initial and boundary rough data in morrey spaces abstract we consider the initial boundary value problem for the navier stokes equations in the half space with data in morrey spaces existence of small global solutions is proved in spaces with the right homogeneity to allow self similar solutions moreover we analyze the long time behavior of the solutions and obtain a class of asymptotically self similar ones

on a larger class of stable solutions to the navier stokes equations in exterior domains where w w x w1 x wn x and x denote the unknown velocity vector and the unknown pressure of the fluid at point x respectively while f f x f i j x i j 1 n is the given tensor with div f n j 1 f 1 j xj nj 1 f n j xj denoting the external force in our previous paper 23 we established the theory of existence uniqueness and regularity for solutions to n s0 in the class w ln

duality and sufficiency in control problems with invexity recently mond chandra and husain 3 established duality results for a variational problem under more general convexity conditions called invex than mond and hanson 4 in a similar fashion the results of mond and hanson s for duality in control problems are extended to more general convex or invex functions it is also shown that for invex functions the necessary conditions for optimality in the control problem are also sufficient

asymptotic stability of large solutions with large perturbation to the navier stokes equations abstract consider weak solutions w of the navier stokes equations in serrin s class w l 0 l q for 2 3 q 1 with 3 q where is a general unbounded domain in r 3 we shall show that although the initial and external disturbances from w are large every perturbed flow v with the energy inequality converges asymptotically to w as v t w t l 2 0 v t w t l 2 o t 1 2 as t

upper bounds on nusselt number at finite prandtl number abstract we study rayleigh benard convection based on the boussinesq approximation we are interested in upper bounds on the nusselt number nu the upwards heat transport in terms of the rayleigh number ra that characterizes the relative strength of the driving mechanism and the prandtl number pr that characterizes the strength of the inertial effects we show that up to logarithmic corrections the upper bound nu ra 1 3 from 1 persists as long as pr ra 1 3 and then crosses over to nu pr 1 2 ra 1 2 this result improves the one of wang 2 by going beyond the perturbative regime pr ra the proof uses a new way to estimate the transport nonlinearity in the navier stokes equations capitalizing on the no slip boundary condition it relies on a new calderon zygmund estimate for the non stationary stokes equations in l 1 with a borderline muckenhoupt weight

graphical exploratory data analysis 1 the role of graphics in data exploration 1 introduction 2 historical background 3 content of the book 4 central data sets 5 different types of data 6 computer programs 2 graphics for univariate and bivariate data 1 introduction 2 graphics for univariate data 3 stem and leaf plots 4 graphics for bivariate data 5 graphical perception 3 graphics for selecting a probability model 1 introduction 2 discrete models 3 continuous models 4 general 4 visual representation of multivariate data 1 introduction 2 scatterplots in more than two dimensions 3 profiles 4 star representations 5 glyphs 6 boxes 7 andrews curves 8 chernoff faces 9 general 5 cluster analysis 1 introduction 2 the probability approach 3 measures of distance and similarity 4 hierarchical cluster analysis 5 computer programs for hierarchical cluster analysis 6 digraphs 7 spanning trees 8 cluster analysis of variables 9 application of cluster analysis to fitness cholesterol data 10 other graphical techniques of cluster analysis 11 general 6 multidimensional scaling 1 introduction 2 the biplot 3 principal component analysis 4 correspondence analysis 5 classical metric scaling 6 non metric scaling 7 three way multidimensional scaling indscal 8 guttman s techniques 9 facet theory 10 partial order scalogram analysis 11 general 7 graphical representations in regression analysis 1 introduction 2 the scatterplot 3 residual plots 4 mallows q statistic 5 confidence and forecast bands 6 the ridge trace 7 general 8 chaid and xaid exploratory techniques for analyzing extensive data sets 1 introduction 2 chaid an exploratory technique for analyzing categorical data 3 applying a chaid analysis 4 xaid an exploratory technique for analyzing a quantitative dependent variable with categorical predictors 5 application of xaid analysis 6 general 9 control charts 1 introduction 2 process capability 3 control charts for items with quantitative characteristics 4 control charts for dichotomous measurements p chart 5 cumulative sum charts 6 cumulative sine charts 7 general 10 time series representations 1 representations in the time domain 2 representations in the frequency domain 11 further useful graphics 1 graphics for the two sample problem 2 graphical techniques in analysis of variance 3 four fold circular display of 2 x 2 contingency tables references inde

nonlinear lagrangian for multiobjective optimization and applications to duality and exact penalization duality and penalty methods are popular in optimization the study on duality and penalty methods for nonconvex multiobjective optimization problems is very limited in this paper we introduce vector valued nonlinear lagrangian and penalty functions and formulate nonlinear lagrangian dual problems and nonlinear penalty problems for multiobjective constrained optimization problems we establish strong duality and exact penalization results the strong duality is an inclusion between the set of infimum points of the original multiobjective constrained optimization problem and that of the nonlinear lagrangian dual problem exact penalization is established via a generalized calmness type condition

solutions for semilinear parabolic equations in lp and regularity of weak solutions of the navier stokes system abstract we construct a unique local regular solution in l q 0 t l p for a class of semilinear parabolic equations which includes the semilinear heat equation u t u u u 0 and the navier stokes system here p and q are so chosen that the norm of l q 0 t l p is dimensionless or scaling invariant the main relation between p and q for the semilinear heat equation is 1 q 1 p 1 q n 2 provided that initial data are in l r with r n 2 1 where n is the space dimension applying our regular solutions to the navier stokes system we show that the k 2 dimensional hausdorff measure of possible time singularities of a turbulent solution is zero if the turbulent solution is in l q 0 t l p where k 2 q nq p p n 1 q we show moreover that a turbulent solution is regular if it is in c 0 t l n

liouville theorems in unbounded domains for the time dependent stokes system in this paper we characterize bounded ancient solutions to the time dependent stokes system with zero boundary value in various domains including the half space

asymptotic behavior of solutions of the compressible navier stokes equations on the half space asymptotic behavior of solutions of the compressible navier stokes equations on the half space r n n 2 is considered around a given constant equilibrium a solution formula for the linearized problem is derived and l p estimates for solutions of the linearized problem are obtained for 2 p it is shown that as in the case of the cauchy problem the leading part of the solution of the linearized problem is decomposed into two parts one that behaves like diffusion waves and the other one purely diffusively there however are some aspects different from the cauchy problem especially in considering spatial derivatives it is also shown that the solution of the linearized problem approaches for large times the solution of the nonstationary stokes problem in some l p spaces and as a result a solution formula for the nonstationary stokes problem is obtained large time behavior of solutions of the nonlinear problem is then investigated in l p spaces for 2 p by applying the results on the linearized analysis and the weighted energy method the results indicate that there may be some nonlinear interaction phenomena not appearing in the cauchy problem

scalarization in vector optimization in this paper some scalar optimization problems are presented whose optimal solutions are also solutions of a general vector optimization problem this will be done for weakly minimal and minimal solutions respectively finally the results will be applied to a certain class of approximation problems

commuting hamiltonians and hamilton jacobi multi time equations the aim of this paper is twofold first of all we show that the c 0 limit of a pair of commuting hamiltonians commute this means on one hand that if the limit of the hamiltonians is smooth the poisson bracket of their limit still vanishes and on the other hand that we may define commutation for c 0 functions the second part of the paper deals with solving multi time hamilton jacobi equations using variational solutions this extends the work of barles and tourin in the viscosity case to include the case of c 0 hamiltonians and removes their convexity assumption provided we are in the framework of variational solutions

on the uniqueness of time periodic solutions to the navier stokes equations in unbounded domains we present a uniqueness theorem for time periodic solutions to the navier stokes equations in unbounded domains thus far results on the uniqueness of time periodic solutions to the navier stokes equations in unbounded domain roughly speaking have only found that a small time periodic ln solution is unique within the class of solutions which have sufficiently small l ln norm in this paper we show that a small time periodic ln solution is unique within the class of all time periodic ln solutions which contains large solutions we also consider the uniqueness of solutions in weak ln space the proof of the present uniqueness theorem is based on the method of dual equations

higher order hamilton dynamics and hamilton jacobi divergence pde abstract this paper using a non standard legendrian duality investigates the hamiltonian dynamics and formulates a hamilton jacobi type divergence pde governed by higher order lagrangians

l2 decay for the navier stokes flow in halfspaces on etudie le comportement asymptotique dans l 2 des solutions faibles des equations de navier stokes dans des demi espaces

well posedness for the navier stokes equations where u is the velocity and p is the pressure it is well known that the navierstokes equations are locally well posed for smooth enough initial data as long as one imposes appropriate boundary conditions on the pressure at for instance it is easy to see see 9 for much more general results that if s n 2 then for any h initial data there exists a unique c 0 t h r local solution with a pressure p c 0 t h r in the sequel we consider solutions for less regular initial data this has to be understood in the sense that the map from the initial data to the solution extends continuously to rougher function spaces the question we are interested in is the global well posedness for small data and local well posedness for large data with respect to a certain space of

a review of the development and application of recursive residuals in linear models abstract recursive residuals have been shown to be useful in a variety of applications in linear models unlike the more familiar ordinary least squares residuals or studentized residuals recursive residuals are independent as well as homoscedastic under the model their independence is particularly appealing for use in developing test statistics they are not uniquely defined their values depend on the order in which they are calculated although their properties do not in some applications one can exploit this order dependence coupled with the fact that they are in clear one to one correspondence with the observations for which they are calculated uses for recursive residuals have been suggested in almost all areas of regression model validation regression diagnostics have been constructed from recursive residuals for detecting serial correlation heteroscedasticity functional misspecification and structural change other statistics based on recursive residuals have focused on detection of outli

a critical functional framework for the inhomogeneous navier stokes equations in the half space abstract this paper is devoted to solving globally the boundary value problem for the incompressible inhomogeneous navier stokes equations in the half space in the case of small data with critical regularity in dimension n 3 we state that if the initial density 0 is close to a positive constant in l w n 1 r n and the initial velocity u 0 is small with respect to the viscosity in the homogeneous besov space b n 1 0 r n then the equations have a unique global solution the proof strongly relies on new maximal regularity estimates for the stokes system in the half space in l 1 0 t b p 1 0 r n interesting for their own sake

global ln solution and its decay property for the navier stokes equations in half space r n soit r n x 1 x 2 x n 1 x n x n 0 n 2 dans q r n 0 on considere les equations de navier stokes u t u u u 0 dans q divu 0 dans q u x u n 0 0 u 0 a on demontre l existence et l unicite d une l n solution globale forte pour des donnees initiales petites

initial and boundary values for lαq lp solution of the navier stokes equations in the half space abstract in this paper we study the initial and boundary value problem of the navier stokes equations in the half space we prove the existence of weak solution u l q 0 l p r n 1 2 1 n p 2 q 0 n p with u l loc q 2 0 l loc p 2 r n for the solenoidal initial data h b p q 1 n p r n and the boundary data g l q 0 b p p 1 p r n 1 when h b p q 1 n p r n g l q 0 b p p 1 p r n 1 is small enough moreover the solution is unique in the class l q 0 t l p r n for any t if 0 and for some t if 0

a general sufficiency theorem for nonsmooth nonlinear programming second order conditions are given which are sufficient to guarantee that a given point be a local minimizer for a real valued locally lipschitzian function over a closed set in dimensional real euclidean space these conditions are expressed in terms of the generalized gradients of clarke the conditions provide a very general and unified framework into which many previous first and second order theorems fit 1 introduction let s be a closed subset of dimensional space r and let w be an open set in r suppose that the point x belongs to s d w and let be a real valued locally lipschitzian function on w we consider here the problem p minimize x over x in s d w we shall present a general theorem which gives second order conditions that are sufficient to guarantee that x be a local solution to problem p this theorem both unifies and extends separate earlier results presented for this problem by the author 2 specific remarks on this point are made below the theorems in 2 have already been shown to yield both the classical theorem for problems with a finite number of functional constraints and ioffe s theorem in finite dimensions it can be shown that they yield other results such as the sufficiency theorem of fletcher and watson 8 for certain nondifferentiable problems containing norms and a theorem proved by the author 1 for a certain class of nonsmooth problems the second order sufficiency conditions given here are formulated in terms of the generalized gradients of clarke the generalized gradients of at x are the members of the clarke subdifferential 3 x of at x the clarke subdifferential reduces to the subdifferential of convex analysis when is convex and it contains only the gradient vector v x when is c1 near x we shall give below a brief summary of those basic properties of generalized gradients which we shall use for more information about generalized gradients one should examine such earlier papers of clarke as 4 5 6 the work by rockafellar 23 20 21 or the forthcoming book by

exact penalty functions and stability in locally lipschitz programming in this paper we extend the theory of exact penalty functions for nonlinear programs whose objective functions and equality and inequality constraints are locally lipschitz arbitrary simple constraints are also allowed assuming a weak stability condition we show that for all sufficiently large penalty parameter values an isolated local minimum of the nonlinear program is also an isolated local minimum of the exact penalty function a tight lower bound on the parameter value is provided when certain first order sufficiency conditions are satisfied we apply these results to unify and extend some results for convex programming since several effective algorithms for solving nonlinear programs with differentiable functions rely on exact penalty functions our results provide a framework for extending these algorithms to problems with locally lipschitz functions

zero viscosity limit for analytic solutions of the navier stokes equation on a half space ii construction of the navier stokes solution this is the second of two papers on the zero viscosity limit for the incompressible navier stokes equations in a half space in either 2d or 3d under the assumption of analytic initial data we construct solutions of navier stokes for a short time which is independent of the viscosity the navier stokes solution is constructed through a composite asymptotic expansion involving the solutions of the euler and prandtl equations which were constructed in the first paper plus an error term this shows that the navier stokes solution goes to an euler solution outside a boundary layer and to a solution of the prandtl equations within the boundary layer the error term is written as a sum of first order euler and prandtl corrections plus a further error term the equation for the error term is weakly nonlinear its linear part is the time dependent stokes equation this error equation is solved by inversion of the stokes equation through expressing the solution as a regular euler like part plus a boundary layer prandtl like part the main technical tool in this analysis is the abstract cauchy kowalewski theorem

exact penalty functions in constrained optimization in this paper formal definitions of exactness for penalty functions are introduced and sufficient conditions for a penalty function to be exact according to these definitions are stated thus providing a unified framework for the study of both nondifferentiable and continuously differentiable penalty functions in this framework the best known classes of exact penalty functions are analyzed and new results are established concerning the correspondence between the solutions of the constrained problem and the unconstrained minimizers of the penalty functions

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

an η approximation method in nonlinear vector optimization abstract in this paper a new approach for a solution of a nonlinear multiobjective programming problem is introduced an equivalent approximated vector optimization problem is constructed by a modification of the objective and the constraint functions in the original multiobjective programming problem the connection between weak efficient points in the original multiobjective programming problem and its equivalent approximated vector optimization problem is proved in this way optimality conditions for nonlinear constrained multiobjective programming problems having invex and or generalized invex objective and constraint functions with respect to the same functions are obtained

e optimality criteria for convex programming problems via exact penalty functions in this paper we presente optimality criteria for convex programming problems associated with exact penalty functions several authors have given various criteria under the assumption that such convex problems and the associated dual problems can be solved we assume the solvability of neither the convex problem nor the dual problem to derive our criteria we estimate the size of the penalty parameter in terms of ane solution for the dual problem

on the extension of constrained optimization algorithms from differentiable to nondifferentiable problems this paper presents three general schemes for extending differentiable optimization algorithms to nondifferentiable problems it is shown that the armijo gradient method phase i phase ii methods of feasible directions and exact penalty function methods have conceptual analogs for problems with locally lipschitz functions and implementable analogs for problems with semismooth functions the exact penalty method has required the development of a new optimality condition

a maximal regularity estimate for the non stationary stokes equation in the strip in a d dimensional strip with d 2 we study the non stationary stokes equation with no slip boundary condition in the lower and upper plates and periodic boundary condition in the horizontal directions in this paper we establish a new maximal regularity estimate in the real interpolation norm f 0 1 inff f0 f1 sup0 z 1 f0 01 f1 dz 1 z z where the brackets denote the horizontal space and time average the norms involved in the definition of 0 1 are critical for two reasons the exponents are borderline for the calderon zygmund theory and the weight 1 z just fails to be muckenhoupt therefore the estimate is only true under horizontal bandedness condition i e a restriction to a packet of wave numbers in fourier space the motivation to express the maximal regularity in such a norm comes from an application to the rayleigh benard problem see 5

the vector exact l1 penalty method for nondifferentiable convex multiobjective programming problems abstract in this paper the vector exact l 1 penalty function method for nondifferentiable convex multiobjective programming problems is analyzed the vector penalized optimization problem with the vector exact l 1 penalty function is defined conditions are given guaranteeing the equivalence of the sets of weak pareto optimal solutions of the considered nondifferentiable multiobjective programming problem and of the associated vector penealized optimization problem with the vector exact l 1 penalty function this equivalence is established for nondifferentiable vector optimization problems with convex functions

energy decay for a weak solution of the navier stokes equation with slowly varying external forces we consider the navier stokes system with slowly decaying external forces formula we show that the energy norm of a weak solution has non uniform decay u t 2 0 t under suitable conditions on the data f and a which make the energy of solution bounded in time also we show the exact rate of the decay uniform decay of the energy u t 2 c 1 t e for external forces with a given explicit decay rate

efficient solutions in v kt pseudoinvex multiobjective control problems a characterization in this paper we introduce a new condition on functionals involved in a multiobjective control problem for which we define the v kt pseudoinvex control problem we prove that a v kt pseudoinvex control problem is characterized so that a kuhn tucker point is an efficient solution we generalize recently obtained optimality results of known mathematical programming problems and control problems we illustrate these results with an example

long time behavior for the nonstationary navier stokes flows in l1 r n the large time decay for the navier stokes flows in l1 r n is a long standing unsolved question the main difficulties are that usual lq lr estimates for the stokes flow fail in this case and the projection operator p l1 r n l 1 r n becomes unbounded using the stokes solution formula we find a crucial and new estimate for the stokes flow in l1 r n which plays a fundamental role in studying the time l1 behavior for the navier stokes equations in addition we decompose the operator p into two parts and reduce its unboundedness to establish an l1 estimate for an elliptic problem with neumann boundary condition which is overcome by using the weighted estimates of the gaussian kernel s convolution the main results in this article are motivated by bae s works 2006 2008 1 2 and brandolese s work 2001 11

a dual differentiable exact penalty function a new penalty function is associated with an inequality constrained nonlinear programming problem via its dual this penalty function is globally differentiable if the functions defining the original problem are twice globally differentiable in addition the penalty parameter remains finite this approach reduces the original problem to a simple problem of maximizing a globally differentiable function on the product space of a euclidean space and the nonnegative orthant of another euclidean space many efficient algorithms exist for solving this problem for the case of quadratic programming the penalty function problem can be solved effectively by successive overrelaxation sor methods which can handle huge problems while preserving sparsity features

a new graphical tool to detect non normality a new graphical tool for checking normality of independently and identically distributed observations based on the third derivative t 3 of the logarithm of the empirical moment generating function is proposed a significant departure of this function from the horizontal zero line is indicative of non normality behaviour in the neighbourhood of 0 indicates the type of departure from the normal distribution examples show that the t 3 method when used in conjunction with the classical probability plot can provide valuable insight into the data and be a powerful graphical tool

the navier stokes equations in the weak l n space with time dependent external force abstract we consider the navier stokes equations with time dependent external force either in the whole time or in positive time with initial data with domain either the whole space the half space or an exterior domain of dimension n ge 3 we give conditions on the external force sufficient for the unique existence of small solutions in the weak l n space bounded for all time in particular this result gives sufficient conditions for the unique existence and the stability of small time periodic solutions or almost periodic solutions this result generalizes the previous result on the unique existence and the stability of small stationary solutions in the weak l n space with time independent external force

efficiency in generalised v kt pseudoinvex control problems abstractin this paper strongly b v kt pseudoinvex multidimensional control problems are considered concretely we introduce a generalised condition on the functionals involved in a multidimensi

on a local energy decay estimate of solutions to the hyperbolic type stokes equations abstract in this paper we discuss a local energy decay estimate of solutions to the initial boundary value problem for the hyperbolic type stokes equations of incompressible fluid flow in an exterior domain and a perturbed half space the equations are linearized version of the hyperbolic navier stokes equations introduced by racke and saal 15 which are obtained as a delayed case for the deformation tensor in the incompressible navier stokes equations our proof of the local energy decay estimate is based on dan and shibata 2 in 2 they treated the dissipative wave equations in an exterior domain and discussed the local energy decay estimate our approach uses the fact that applying the helmholtz projection to the hyperbolic type stokes equations we obtain equations similar to the dissipative wave ones

sufficiency of exact penalty minimization by employing a recently obtained error bound for differentiable convex inequalities it is shown that under appropriate constraint qualifications a minimum solution of an exact penalty function for a single value of the penalty parameter which exceeds a certain threshold is also a solution of the convex program associated with the penalty function no a priori assumption is made regarding the solvability of the convex program if such a solvability assumption is made then we show that a threshold value of the penalty parameter can be used which is smaller than both the above mentioned value and that of zangwill these various threshold values of the penalty parameter also apply to the well known big m method of linear programming

pre invex functions in multiple objective optimization and called such functions convexlike if s is a convex set and if f is a convex function then clearly f is convexlike elster and nehse obtained a saddlepoint optimality condition for convexlike mathematical programs hayashi and komiya 9 also considered convexlike functions and developed a gordan type theorem of the alternative involving convexlike functions and in addition considered lagrangian duality for convexlike programs hanson 7 considered differentiable functions f s r for which there exists an n dimensional vector function q q u such that for all x u e s

rotating navier stokes equations in mathbb r 3 _ with initial data nondecreasing at infinity the ekman boundary layer problem we prove time local existence and uniqueness of solutions to a boundary layer problem in a rotating frame around the stationary solution called the ekman spiral we choose initial data in the vector valued homogeneous besov space dot mathcal b infty 1 sigma 0 mathbb r 2 l p mathbb r for 2 p here the l p integrability is imposed in the normal direction while we may have no decay in tangential components since the besov space dot mathcal b infty 1 0 contains nondecaying functions such as almost periodic functions a crucial ingredient is theory for vector valued homogeneous besov spaces for instance we provide and apply an operator valued bounded h calculus for the laplacian in dot mathcal b infty 1 0 mathbb r n mathsf e for a general banach space mathsf e

liouville theorems for the stokes equations with applications to large time estimates abstract we study liouville theorems for the non stationary stokes equations in exterior domains in r n under decay conditions for spatial variables as applications we prove that the stokes semigroup is a bounded analytic semigroup on l of angle 2 for n 3 we also prove large time estimates for n 2 with zero net force

weighted decay properties for the incompressible stokes flow and navier stokes equations in a half space abstract using the stokes solution formula and l q l r estimates of the stokes operator semigroup we establish the weighted decay properties for the stokes flow and navier stokes equations including their spatial derivatives in half spaces in addition the unboundedness of the projection operator p l r n l r n is overcome by employing a decomposition for the nonlinear term and l asymptotic behavior for the second derivatives of navier stokes flows in half spaces is given

kt invex control problem abstract in this paper we introduce a new condition on functions of a control problem for which we define a kt invex control problem we prove that a kt invex control problem is characterized in order that a kuhn tucker point is an optimal solution we generalize optimality results of known mathematical programming problems we illustrate these results with examples

using recursive residuals calculated on adaptively ordered observations to identify outliers in linear regression a new procedure for identifying outliers or influential observations is proposed the procedure uses recursive residuals calculated on observations that have been ordered according to their studentized residuals values of cook s d or another regression diagnostic of the user s choice under the model these recursive residuals appropriately standardized have approximate student s t distributions thus convenient critical values are available for deciding which observations merit scrutiny and perhaps special treatment the power of the test procedure to identify one or more outliers is investigated through simulation and its dependence on the number and configuration of the outliers that is their placement with respect to the main body of the data explored the proposed procedure and two variations of it also based on these recursive residuals are compared with alternatives based on internally or externally studentized residuals the use of recursive residuals calculated on adaptively ordered observations increases power and helps to combat the masking of one outlier by another when multiple outliers are present in configurations that create masking

optimality conditions for generalized differentiable interval valued functions in this paper we study the optimal solutions set for a generalized differentiable interval valued function necessary and sufficient optimality conditions are established for gh differentiable functions convexity assumptions that are necessary or required to ensure the characterization of the optimal solutions are weaker or less strict than those presented in previous works these convexity assumptions are the weakest to characterize the optimal solutions set known results for classical non interval valued optimization are particular cases of the ones proved here