extensions of frechet ϵ subdifferential calculus and applications abstract in this paper we establish some calculus rules for the limiting frechet subdifferentials of marginal functions and composite functions necessary conditions for approximate solutions of a constrained optimization problem are derived

on symmetric cauchy riemann manifolds the riemannian symmetric spaces play an important role in different branches of mathematics by definition a connected riemannian manifold m is called symmetric if to every a m there exists an involutory isometric diffeomorphism sa m m having a as isolated fixed point in m or equivalently if the differential dasa is the negative identity on the the tangent space ta tam of m at a in case such a transformation sa exists for a m it is uniquely determined and is the geodesic reflection of m about the point a as a consequence for every riemannian symmetric space m the group g gm generated by all symmetries sa a m is a lie group acting transitively on m in particular m can be identified with the homogeneous space g k for some compact subgroup k g using the elaborate theory of lie groups and lie algebras e cartan classified all riemannian symmetric spaces

investigation of a boundary integral equation mbi n times mbi h mbi j _ s on torus shaped perfect conductors we have found that a boundary integral equation n times h js results in an inaccurate solution on torus shaped perfect conducting surfaces although constraining a boundary condition n times h js automatically satisfies e x n 0 on a closed polyhedron shaped conductor there exists a solution which only satisfies the boundary condition n times h js but not the other boundary condition e times n 0 on a torus shaped conductor we have introduced a virtual magnetic current ms in the system equation as another degree of freedom and employed e times n 0 at one point on the perfect conducting surface so as to obtain the accurate solution to verify the proposed discussion we have formulated an axially symmetric method of moments based on n times h js and compared with other electromagnetic field solvers

contractions of low dimensional lie algebras theoretical background of continuous contractions of finite dimensional lie algebras is rigorously formulated and developed in particular known necessary criteria of contractions are collected and new criteria are proposed a number of requisite invariant and semi invariant quantities are calculated for wide classes of lie algebras including all low dimensional lie algebras an algorithm that allows one to handle one parametric contractions is presented and applied to low dimensional lie algebras as a result all one parametric continuous contractions for both the complex and real lie algebras of dimensions not greater than 4 are constructed with intensive usage of necessary criteria of contractions and with studying correspondence between real and complex cases levels and colevels of low dimensional lie algebras are discussed in detail properties of multiparametric and repeated contractions are also investigated

on second order optimality conditions in constrained multiobjective optimization abstract in this paper we study a multiobjective optimization problem with inequality constraints on finite dimensional spaces a second order necessary condition for local weak efficiency is proved under strict differentiability assumptions we also establish a second order sufficient condition for local firm efficiency of order 2 under l stability assumptions in this way we generalize some corresponding results obtained by p q khanh and n d tuan and by the authors

realizations of real low dimensional lie algebras using a new powerful technique based on the notion of megaideal we construct a complete set of inequivalent realizations of real lie algebras of dimension no greater than four in vector fields on a space of an arbitrary finite number of variables our classification amends and essentially generalizes earlier works on the subject

numerical analysis of low frequency electromagnetic scattering from three dimensional arbitrarily shaped conducting bodies using an inductance matrix we have proposed a numerical method for calculating low frequency electromagnetic scattering from three dimensional arbitrarily shaped perfectly conducting bodies using an inductance matrix the surface of the perfectly conducting scatterer and its apertures are modeled by a set of triangular patches the current on each patch is computed by solving a coupled inductance matrix equation scattering from various conducting bodies with apertures is calculated to compare with the other methods the proposed method well agrees with finite element method in electromagnetic field distribution

classification of homogeneous cr manifolds in dimension 4 locally homogeneous cr manifolds in dimension 3 were classified up to local cr equivalence by e cartan we classify up to local cr equivalence all locally homogeneous cr manifolds in dimension 4 the classification theorem enables us also to classify all symmetric cr manifolds in dimension 4 up to local cr equivalence

topological properties of the approximate subdifferential abstract the approximate subdifferential introduced by mordukhovich has attracted much attention in recent works on nonsmooth optimization potential advantages over other concepts of subdifferentiability might be related to its nonconvexity this is motivation to study some topological properties more in detail as the main result it is shown that any weakly compact subset of any hilbert space may be obtained as the kuratowski painleve limit of approximate subdifferentials from a one parametric family of lipschitzian functions sharper characterizations are possible for strongly compact subsets as a consequence in any hilbert space the approximate subdifferential of a suitable lipschitzian function may be homeomorphic both in the strong and weak topology to the cantor set further results relate the approximate subdifferential to specific topological types to the one dimensional case which is extraordinary in some sense and to the value function of a c 1 optimization problem

second order optimality conditions with the envelope like effect for nonsmooth vector optimization in infinite dimensions abstract second order necessary conditions and sufficient conditions with the envelope like effect for optimality in nonsmooth vector optimization are established we use approximations as generalized derivatives imposing strict differentiability for necessary conditions and differentiability for sufficient conditions and avoiding continuous differentiability convexity conditions are not imposed explicitly the results make it clear when the envelope like effect occurs and improve or include several recent existing ones examples are provided to show advantages of our theorems over some known ones in the literature

chern moser operators and polynomial models in cr geometry we consider the fundamental invariant of a real hypersurface in c n its holomorphic symmetry group and analyze its structure at a point of degenerate levi form generalizing the chern moser operator to hypersurfaces of finite multitype we compute the lie algebra of infinitesimal symmetries of the model and provide explicit description for each graded component compared with a hyperquadric it may contain additional components consisting of nonlinear vector fields defined in terms of complex tangential variables as a consequence we obtain exact results on jet determination for hypersurfaces with such models the results generalize directly the fundamental result of chern and moser from quadratic models to polynomials of higher degree c 2014 elsevier inc all rights reserved

a generalized second order derivative in nonsmooth optimization in this work a new notion of generalized second order directional derivative and generalized hessian for nonsmooth real valued functions is studied the general properties of these mathematical objects are investigated together with some calculus rules that may facilitate their practical computation two applications of these derivatives in optimization theory are considered first to obtaining necessary and sufficient second order optimality conditions for problems with or without constraints and second to extending the newton method for the minimization of a mathcal c 1 1 function

second order optimality conditions with the envelope like effect in nonsmooth multiobjective mathematical programming ii optimality conditions second order necessary conditions and sufficient conditions with the envelope like effect for optimality in nonsmooth multiobjective mathematical programming are established we use set valued second order directional derivatives and impose strict differentiability for necessary conditions and l stability for sufficient conditions avoiding continuous differentiability the results improve and sharpen several recent existing ones examples are provided to show advantages of our theorems over some known ones in the literature in part i we consider l stability and second order set valued directional derivatives of vector functions part ii is devoted to second order necessary optimality conditions and sufficient ones

second order optimality conditions for the extremal problem under inclusion constraints in this paper we establish second order optimality conditions for the problem of minimizing a function f on the solution set of an inclusion 0 f x where f and the support function of set valued map f have compact second order approximations at x

second order optimality conditions with the envelope like effect in nonsmooth multiobjective mathematical programming i l stability and set valued directional derivatives abstract second order necessary conditions and sufficient conditions with the envelope like effect for optimality in nonsmooth multiobjective mathematical programming are established we use set valued second order directional derivatives and impose strict differentiability for necessary conditions and l stability for sufficient conditions avoiding continuous differentiability the results improve and sharpen several recent existing ones examples are provided to show advantages of our theorems over some known ones in the literature in part i we consider l stability and second order set valued directional derivatives of vector functions part ii is devoted to second order necessary optimality conditions and sufficient ones

approximate jacobian matrices for nonsmooth continuous maps and c 1 optimization the notion of approximate jacobian matrices is introduced for a continuous vector valued map it is shown for instance that the clarke generalized jacobian is an approximate jacobian for a locally lipschitz map the approach is based on the idea of convexificators of real valued functions mean value conditions for continuous vector valued maps and taylor s expansions for continuously g teaux differentiable functions i e c1 functions are presented in terms of approximate jacobians and approximate hessians respectively second order necessary and sufficient conditions for optimality and convexity of c1 functions are also given

approximations and metric regularity in mathematical programming in banach space this paper establishes verifiable conditions ensuring the important notion of metric regularity for general nondifferentiable programming problems in banach spaces these conditions are used to obtain lagrange kuhn tucker multipliers for minimization problems with infinitely many inequality and equality constraints

second order optimality conditions using approximations for nonsmooth vector optimization problems under inclusion constraints abstract second order necessary conditions and sufficient conditions for optimality in nonsmooth vector optimization problems with inclusion constraints are established we use approximations as generalized derivatives and avoid even continuity assumptions convexity conditions are not imposed explicitly not all approximations in use are required to be bounded the results improve or include several recent existing ones examples are provided to show that our theorems are easily applied in situations where several known results do not work

on the existence of branch points in the eigenvalues of the electric field integral equation operator in the complex frequency plane it is demonstrated by specific examples that eigenvalues of the electric field integral equation efie operator for finite extent objects in lossless media can have branch points in the complex frequency s plane specifically it is shown from the analysis of the spheroidal wave equation in the s plane that branch points are present in the eigenvalues of the integral operator associated with the scalar scattering problem from a perfectly conducting spheroid similarly it is concluded from the analysis of the mathieu s differential equation that branch points besides that associated with the infinite extent of the object exist in the s plane behavior of the eigenvalues of the efie operator for a perfectly conducting infinite elliptic cylinder a proof is given that branch point singularities cannot occur in the eigenvalues of efie operators for structures in which geometrical symmetry completely determines the eigenfunctions and hence they are frequency independent it is conjectured that branch points may always be present when sufficient object symmetry is lacking this conjecture is supported by the fact that branch points appear when a sphere is deformed into a spheroid or when a circular cylinder is deformed into an elliptic one an analogous phenomenon has been observed in circuit and transmission line problems for example it is shown that when the taper parameter of an exponential transmission line goes to zero the line becomes uniform and thus a symmetrical structure the branch points in the eigenvalues of the impedance matrix move away to infinity