nondifferentiable multiobjective symmetric duality with f convexity over cones abstract in the present paper a pair of wolfe type nondifferentiable multiobjective second order symmetric dual programs over arbitrary cones are formulated using the concept of weak efficiency with respect to a convex cone weak strong and converse duality theorems are studied under second order k f convexity assumptions self duality is also discussed

optimum accelerated overrelaxation method in a special case absbact in this paper we give the optimum parameters for the accelerated overrelaxation aor method in the special case where the matrix coefficient of the linear system which is solved is consistently ordered with nonvanishing diagonal elements under certain assumptions concerning the eigenvalues of the corresponding jacobi matrix it is shown that the optimum aor method gives better convergence rates than the optimum sor does while in the remaining cases the optimum aor method coincides with the optimum sor one

conformal operators on forms and detour complexes on einstein manifolds for even dimensional conformal manifolds several new conformally invariant objects were found recently invariant differential complexes related to but distinct from the de rham complex these are elliptic in the case of riemannian signature the cohomology spaces of these conformally stable form spaces that we may view as spaces of conformal harmonics operators that generalise branson s q curvature global pairings between differential form bundles that descend to cohomology pairings here we show that these operators spaces and the theory underlying them simplify significantly on conformally einstein manifolds we give explicit formulae for all the operators concerned the null spaces for these the conformal harmonics and the cohomology spaces are expressed explicitly in terms of direct sums of subspaces of eigenspaces of the form laplacian for the case of non ricci flat spaces this applies in all signatures and without topological restrictions in the case of riemannian signature and compact manifolds this leads to new results on the global invariant pairings including for the integral of q curvature against the null space of the dimensional order conformal laplacian of graham et al

on conformal powers of the dirac operator on einstein manifolds we determine the structure of conformal powers of the dirac operator on einstein spin manifolds in terms of the product formula for shifted dirac operators the result is based on the techniques of higher variations for the dirac operator on einstein manifolds and spectral analysis of the dirac operator on the associated poincare einstein metric and relies on combinatorial recurrence identities related to the dual hahn polynomials

conformal theory of curves with tractors abstract we present the general theory of curves in conformal geometry using tractor calculus this primarily involves a specification of distinguished parametrizations and relative and absolute conformal invariants of generic curves the absolute conformal invariants are defined via a tractor analogue of the classical frenet frame construction and then expressed in terms of relative ones our approach applies likewise to conformal structures of any signature in the case of indefinite signature we focus especially on the null curves it also provides a conceptual tool for handling distinguished families of curves conformal circles and conformal null helices and conserved quantities along them

a note on higher order symmetric duality in this paper a pair of wolfe type higher order symmetric dual multiobjective programs is formulated strong and converse duality theorems are established under invexity assumptions duality relations for mond weir type dual models have also been obtained under pseudoinvexity assumptions

on higher spin partition functions we observe that the partition function of the set of all free massless higher spins s 0 1 2 3 in flat space is equal to one the ghost determinants cancel against the physical ones or equivalently the regularized total number of degrees of freedom vanishes this reflects large underlying gauge symmetry and suggests analogy with supersymmetric or topological theory the z 1 property extends also to the ads background i e the 1 loop vacuum partition function of vasiliev theory is equal to 1 assuming a particular regularization of the sum over spins this was noticed earlier as a consistency requirement for the vectorial ads cft duality we find that z 1 is true also in the conformal higher spin theory with higher derivative kinetic terms expanded near flat or conformally flat s4 background we also consider the partition function of free conformal theory of symmetric traceless rank s tensor field which has 2 derivative kinetic term but only scalar gauge invariance in flat 4d space this non unitary theory has weyl invariant action in curved background and it corresponds to partially massless field in ads5 we discuss in detail the special case of s 2 or conformal graviton compute the corresponding conformal anomaly coefficients and compare them with previously found expressions for generic representations of conformal group in 4 dimensions

multiobjective symmetric duality involving cones abstract in this paper a pair of multiobjective symmetric dual programs over arbitrary cones are formulated for cone convex functions weak strong converse and self duality theorems are proved for these programs

a note on multiobjective second order symmetric duality abstract in this paper we establish a strong duality theorem for a pair of multiobjective second order symmetric dual programs this removes an omission in an earlier result by yang et al x m yang x q yang k l teo s h hou multiobjective second order symmetric duality with f convexity euro j oper res 165 2005 585 591

minimax and symmetric duality for a class of multiobjective variational mixed integer programming problems abstract in this paper we formulate a pair of multiobjective variational mixed integer programs for arbitrary cones under the separability and partial invexity assumptions on the functions involved we establish the weak strong converse and self duality theorems related to efficient solution

minimax mixed integer symmetric duality for multiobjective variational problems abstract a mond weir type multiobjective variational mixed integer symmetric dual program over arbitrary cones is formulated applying the separability and generalized f convexity on the functions involved weak strong and converse duality theorems are established self duality theorem is proved a close relationship between these variational problems and static symmetric dual minimax mixed integer multiobjective programming problems is also presented

tractor calculi for parabolic geometries parabolic geometries may be considered as curved analogues of the homogeneous spaces g p where g is a semisimple lie group and p c g a parabolic subgroup conformal geometries and cr geometries are examples of such structures we present a uniform description of a calculus called tractor calculus based on natural bundles with canonical linear connections for all parabolic geometries it is shown that from these bundles and connections one can recover the cartan bundle and the cartan connection in particular we characterize the normal cartan connection from this induced bundle connection perspective we construct explicitly a family of fundamental first order differential operators which are analogous to a covariant derivative iterable and defined on all natural vector bundles on parabolic geometries for an important subclass of parabolic geometries we explicitly and directly construct the tractor bundles their canonical linear connections and the machinery for explicitly calculating via the tractor calculus

ambient constructions for sasakian η einstein manifolds abstract the theory of ambient spaces is useful to define cr invariant objects such as cr invariant powers of the sub laplacian the p prime operator and q prime curvature however in general it is difficult to write down these objects in terms of the tanaka webster connection in this paper we give those explicit formulas for cr manifolds satisfying an einstein condition called sasakian einstein manifolds as an application we study properties of the first and the second variation of the total q prime curvature at sasakian einstein manifolds

second order symmetric duality in multiobjective programming involving generalized cone invex functions abstract in this paper cone second order pseudo invex and strongly cone second order pseudo invex functions are defined a pair of mond weir type second order symmetric dual multiobjective programs is formulated over arbitrary cones weak strong and converse duality theorems are established under aforesaid generalized invexity assumptions a second self duality theorem is also given by assuming the functions involved to be skew symmetric

higher order symmetric duality under cone invexity and other related concepts in this paper we establish weak strong and converse duality results for a pair of wolfe type higher order symmetric dual problems over cones under the assumption of higher order cone invexity we also introduce the concepts of higher order strictly and strongly cone pseudoinvexity and use them to obtain weak strong and converse duality results for the pair of mond weir type higher order symmetric dual problems

multiobjective nonlinear second order symmetric duality with k f pseudoconvexity abstract the purpose of this paper is to introduce a new class of generalized cone pseudoconvex functions and strongly cone pseudoconvex functions called second order k f pseudoconvex functions and strongly second order k f pseudoconvex functions a pair of second order symmetric dual multiobjective nonlinear programs is formulated over arbitrary generalized cone pseudoconvex functions for these second order symmetric dual programs the weak strong and converse duality theorems are established using the above generalization of cone pseudoconvex functions a self duality theorem is also given by assuming the functions involved to be skew symmetric

the accelerated saor method for large linear systems abstract the paper is concerned with the chebyshev acceleration or semi iteration si and the conjugate gradient cg acceleration procedures for the saor method moreover in order to obtain more effective iteration the adaptive procedures which determine automatically the parameters required for each iteration are applied numerical results for the proposed algorithms are given and their characteristics are cleared the effectiveness and superiority to other algorithms are also considered

symmetric duality for minimax mixed integer programming problems with pseudo invexity in this paper we consider the pair of symmetric dual multiobjective variational mixed integer programs proposed by chen and yang x chen j yang symmetric duality for minimax multiobjective variational mixed integer programming problems with partial invexity european journal of operational research 181 2007 76 85 and extend some of their results under the assumptions of partial pseudo invexity and separability on the functions involved these results include several results available in literature as special cases

symmetric duality for a class of nonlinear fractional programming problems abstract a pair of symmetric dual nonlinear fractional programming problems is presented and duality theorems are established under pseudoinvexity pseudoincavity and invexity incavity respectively type assumptions on the kernel function special cases are particularly discussed to show that this paper extends some work appeared in this area

multiobjective second order symmetric duality with f convexity we suggest a pair of second order symmetric dual programs in multiobjective nonlinear programming for these second order symmetric dual programs we prove the weak strong and converse duality theorems under f convexity conditions

multiobjective second order symmetric duality with cone constraints abstract we formulate a pair of multiobjective symmetric dual programs for arbitrary cones our model unifies the wolfe and the mond weir type second order vector symmetric dual models we establish second order weak strong converse and self duality theorems for our pair of dual models devi s results european journal of operational resarch 104 1998 615 621 are obtained as special cases

higher symmetries of the conformal powers of the laplacian on conformally flat manifolds a r g gratefully acknowledges support from the royal society of new zealand via marsden grant nos 06 uoa 029 and 10 uoa 113 j s was supported by the max planck institute fur math ematik in bonn and by the grant agency of the czech republic under the grant no p201 12 g028

nondifferentiable multiobjective symmetric dual programs over cones abstract wolfe and mond weir type nondifferentiable multiobjective symmetric dual programs are formulated over arbitrary cones and appropriate duality theorems are established under k preinvexity k convexity pseudoinvexity assumptions

second order multiobjective symmetric duality with cone constraints abstract in this paper we formulate wolfe and mond weir type second order multiobjective symmetric dual problems over arbitrary cones weak strong and converse duality theorems are established under bonvexity pseudobonvexity assumptions this work also removes several omissions in definitions models and proofs for wolfe type problems studied in mishra 9 moreover self duality theorems for these pairs are obtained assuming the function involved to be skew symmetric

conformally invariant powers of the laplacian q curvature and tractor calculus we describe an elementary algorithm for expressing as explicit formulae in tractor calculus the conformally invariant gjms operators due to c r graham et alia these differential operators have leading part a power of the laplacian conformal tractor calculus is the natural induced bundle calculus associated to the conformal cartan connection applications discussed include standard formulae for these operators in terms of the levi civita connection and its curvature and a direct definition and formula for t branson s so called q curvature which integrates to a global conformal invariant as well as generalisations of the operators and the q curvature among examples the operators of order 4 6 and 8 and the related q curvatures are treated explicitly the algorithm exploits the ambient metric construction of fefferman and graham and includes a procedure for converting the ambient curvature and its covariant derivatives into tractor calculus expressions this is partly based on 12 where the relationship of the normal standard tractor bundle to the ambient construction is described

on the chern gauss bonnet integral for conformal metrics on r4 where m is the euler number ofm later huber hu extended this inequality to metrics with much weaker regularity more importantly he proved that such a surface m is conformally equivalent to a closed surface with finitely many punctures the deficit in formula 1 1 has an interpretation as an isoperimetric constant on a complete and open surface with gaussian curvature absolutely integrable one may represent each end conformally as r2 k for some compact set k we consider the isoperimetric ratio

multiobjective mixed symmetric duality involving cones a pair of multiobjective mixed symmetric dual programs is formulated over arbitrary cones weak strong converse and self duality theorems are proved for these programs under k preinvexity and k pseudoinvexity assumptions this mixed symmetric dual formulation unifies the symmetric dual formulations of suneja et al 2002 14 and khurana 2005 15

second order symmetric duality for nonlinear multiobjective mixed integer programming we formulate two pairs of second order symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones by using the concepts of efficiency and second order invexity we establish weak strong converse and self duality theorems for the dual models several known results are obtained as special cases

symmetric duality in multiobjective programming involving generalized cone invex functions abstract in this paper cone pseudoinvex and strongly cone pseudoinvex functions are defined a pair of mond weir type symmetric dual multiobjective programs is formulated over arbitrary cones weak duality strong duality and converse duality theorems are established using the above defined functions a self duality theorem is also given by assuming the functions involved to be skew symmetric

a note on pseudo invexity and symmetric duality a pair of symmetric dual nonlinear programming problems is presented and duality theorems are established under pseudoinvexity type assumptions on the kernel function this formulation removes certain inconsistencies in a recently introduced primal dual pair and gives the correct proof of various duality theorems

symmetric duality for the multiobjective fractional variational problem with partial invexity a symmetric dual problem for a class of multiobjective fractional variational problems is first formulated under partial invexity assumptions on the functions involved dual theorems are proved through a parametric approach to related properly efficient solutions of the primal and dual problems finally self dual and related problems are considered

pseudo invexity and duality in nonlinear programming abstract the purpose of this paper is to study various duality results in nonlinear programming for pseudo invex functions such results were known in the literature for invex functions

second order symmetric duality in multiobjective programming abstract a pair of mond weir type multiobjective second order symmetric dual programs are formulated without non negativity constraints weak duality strong duality and converse duality theorems are established under bonvexity and pseudobonvexity assumptions a second order self duality theorem is given by assuming the functions involved to be skew symmetric

minimax and symmetric duality for nonlinear multiobjective mixed integer programming abstract we formulate two pairs of symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones by using the concept of efficiency we establish the weak strong converse and self duality theorems for our symmetric models several known results are obtained as special cases

higher order f α ρ d convexity and symmetric duality in multiobjective programming a pair of higher order wolfe type and mond weir type multiobjective symmetric dual programs over arbitrary cones is formulated weak strong and converse duality theorems are then established using the notion of higher order f a r d convexity pseudoconvexity assumptions special cases are also discussed to show that this paper extends some known results of the literature

symmetric duality for nonlinear programming problem involving η bonvex functions a pair of second order symmetric dual is formulated and corresponding duality results are established for nonlinear programming problems involving bonvex functions

second order symmetric duality for nonlinear minimax mixed integer programs abstract wolfe type second order minimax mixed integer dual programs are formulated and a symmetric duality theorem is e established under separability and bonvexity boncavity of the kernel function k x y mond weir type symmetric duality is also discussed under weaker bonvexity assumptions moreover self duality theorems for these pairs are obtained assuming k x y to be skew symmetric

conformally invariant powers of the laplacian a complete nonexistence theorem conformally invariant operators and the equations they determine play a central role in the study of manifolds with pseudo riemannian riemannian conformai and related structures this observation dates back to at least the very early part of the last century when it was shown that the equations of massless particles on curved space time exhibit conformai invariance in this setting a key operator is the con formally invariant wave operator which has leading term a pseudo laplacian the riemannian signature variant of this operator is a fundamental tool in the yam abe problem on compact manifolds here one seeks to find a metric from a given conformai class that has constant scalar curvature recently it has become clear that higher order analogues of these operators viz conformally invariant operators on weighted functions i e conformai densities with leading term a power of the laplacian have a central role in generating and solving other curvature prescription problems as well as other problems in geometric spectral theory and mathematical physics 2 5 15 in the flat setting the existence of such operators dates back to 16 where it is shown that on 4 dimensional minkowski space for k g n 1 2 the kth power of the flat wave operator ak acting on densities of the appropriate weight is invariant under the action of the conformai group more generally if w denotes the space of conformai densities of weight uigl then on a flat conformai manifold of dimension n 3 and any signature there exists for each k e n a unique conformally invariant operator

second order symmetric duality with cone constraints wolfe and mond weir type second order symmetric duals are formulated and appropriate duality theorems are established under h bonvexity h pseudobonvexity assumptions this formulation removes several omissions in an earlier second order primal dual pair introduced by devi symmetric duality for nonlinear programming problems involving h bonvex functions european j oper res 104 1998 615 621

converse duality in nonlinear programming with cone constraints abstract the purpose of this paper is to establish various converse duality results for nonlinear programming with cone constraints and its four dual models introduced by chandra and abha s chandra abha a note on pseudo invex and duality in nonlinear programming european journal of operational research 122 2000 161 165

yang mills detour complexes and conformal geometry working over a pseudo riemannian manifold for each vector bundle with connection we construct a sequence of three differential operators which is a complex termed a yang mills detour complex if and only if the connection satisfies the full yang mills equations a special case is a complex controlling the deformation theory of yang mills connections in the case of riemannian signature the complex is elliptic if the connection respects a metric on the bundle then the complex is formally self adjoint in dimension 4 the complex is conformally invariant and generalises to the full yang mills setting the composition of two operator yang mills complexes for anti self dual yang mills connections via a prolonged system and tractor connection a diagram of differential operators is constructed which when commutative generates differential complexes of natural operators from the yang mills detour complex in dimension 4 this construction is conformally invariant and is used to yield two new sequences of conformal operators which are complexes if and only if the bach tensor vanishes everywhere in riemannian signature these complexes are elliptic in one case the first operator is the twistor operator and in the other sequence it is the operator for einstein scales the sequences are detour sequences associated to certain bernstein gelfand gelfand sequences

symmetric duality for multiobjective fractional variational problems involving cones in this paper a pair of multiobjective fractional variational symmetric dual problems over cones is formulated weak strong and converse duality theorems are established under generalized f convexity assumptions moreover self duality theorem is also discussed

existence of conformal metrics with constant q curvature given a compact four dimensional manifold we prove existence of conformal metrics with constant q curvature under generic assumptions the problem amounts to solving a fourth order nonlinear elliptic equation with variational structure since the corresponding euler functional is in general unbounded from above and from below we employ topological methods and min max schemes jointly with the compactness result of 35

pseudo invexity and symmetric duality in nonlinear fractional programming abstract the purpose of this paper is to study the symmetric dual fractional programming problem for pseudo invex functions and arbitrary cones several known results are obtained as special cases

non differentiable symmetric duality for multiobjective programming with cone constraints abstract two pairs of non differentiable multiobjective symmetric dual problems with cone constraints over arbitrary cones which are wolfe type and mond weir type are considered on the basis of weak efficiency with respect to a convex cone we obtain symmetric duality results for the two pairs of problems under cone invexity and cone pseudoinvexity assumptions on the involved functions our results extend the results in khurana s khurana symmetric duality in multiobjective programming involving generalized cone invex functions european journal of operational research 165 2005 592 597 to the non differentiable multiobjective symmetric dual problem

on multiobjective second order symmetric duality with cone constraints abstract a pair of wolfe type multiobjective second order symmetric dual programs with cone constraints is formulated and usual duality results are established under second order invexity assumptions these results are then used to investigate symmetric duality for minimax version of multiobjective second order symmetric dual programs wherein some of the primal and dual variables are constrained to belong to some arbitrary sets i e the sets of integers this paper points out certain omissions and inconsistencies in the earlier work of mishra s k mishra multiobjective second order symmetric duality with cone constraints european journal of operational research 126 2000 675 682 and mishra and wang s k mishra s y wang second order symmetric duality for nonlinear multiobjective mixed integer programming european journal of operational research 161 2005 673 682

an equation of monge ampere type in conformal geometry and four manifolds of positive ricci curvature we formulate natural conformally invariant conditions on a 4 manifold for the existence of a metric whose schouten tensor satisfies a quadratic inequality this inequality implies that the eigenvalues of the ricci tensor are positively pinched

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

second order symmetric duality in mathematical programming with f convexity abstract under second order f convexity f concavity and second order f pseudoconvexity f pseudoconcavity appropriate second order duality results for pair of wolfe and mond weir type second order symmetric dual nonlinear programming problems are established these second order duality results are then used to formulate wolfe type and mond weir type second order minimax mixed integer dual programs and symmetric duality theorem is established under separability and second order f convexity f concavity of the kernel function f x y second order symmetric dual fractional mixed integer programs are studied using the above programs moreover second order self duality theorems for the above pairs are obtained assuming f x y to be skew symmetric

symmetric duality for multiobjective variational problems with invexity abstract we formulate a pair of multiobjective nonlinear symmetric dual variational problems for the single objective problems our problems become the symmetric dual pair of i smart and b mond j math anal appl 152 1990 536 545 under invexity assumptions we establish the weak strong converse and self duality theorems for our variational problems by using the concept of efficiency also we give the static case of our symmetric duality results

mond weir type second order symmetric duality in non differentiable minimax mixed integer programming problems abstract a pair of mond weir type non differentiable second order symmetric minimax mixed integer primal and dual problems in mathematical programming is formulated symmetric and self duality theorems are then established under second order f pseudo convexity assumptions several known results including that of gulati and ahmad eur j oper res 101 1997 122 hou and yang j math anal appl 255 2001 491 and mond and schechter bull aust math soc 53 1996 177 as well as others are obtained as special cases

on a pair of nonlinear mixed integer programming problems abstract we consider maximin and minimax nonlinear mixed integer programming problems which are nonsymmetric in duality sense under weaker pseudo convex pseudo concave assumptions we show that the supremum infimum of the maximin problem is greater than or equal to the infimum supremum of the minimax problem as a particular case this result reduces to the weak duality theorem for minimax and symmetric dual nonlinear mixed integer programming problems further this is used to generalize available results on minimax and symmetric duality in nonlinear mixed integer programming

optimum accelerated overrelaxation aor method for systems with positive definite coefficient matrix given a linear system with a hermitian positive definite coefficient matrix a a splitting of it of varga s type 18 is considered and the corresponding generalized accelerated overrelaxation aor scheme is formed under certain assumptions concerning one of the components of a and the convergence domains of the two parameters of the aor method an analysis analogous to that by varga enables one to determine optimum values for the parameters involved as both theory and numerical examples show the optimum aor method obtained in this way is faster than the corresponding sor one

symmetric duality for minimax nonlinear mixed integer programming abstract a pair of symmetric dual minimax integer programming problems is formulated and an appropriate duality theorem is established under the pseudoconvexity pseudoconcavity assumption on the kernel function k x y this model removes certain inconsistencies in an earlier model and helps to study self duality as well

technical note on symmetric duality in multiobjective programming some remarks on recent results abstract certain shortcomings are pointed out in some recent works of das and nanda european journal of operational research 97 1997 167 171 and kim et al european journal of operational research 107 1998 686 691 which show that these studies are highly restricted

non adaptive and adaptive saor cg algorithms abstract the paper is concerned with an improvement over the symmetric accelerated overrelaxation saor method for an iterative solution of large linear systems at first the conjugate gradient cg acceleration procedure is introduced to the saor method and the non adaptive saor cg algorithm is developed next the adaptive procedure to determine automatically the cg parameters n n and the saor parameters is constructed based on the adaptive procedure the adaptive saor cg algorithm is proposed and its characteristics are shown with numerical experiments a comparison with the optimum sor algorithm and the adaptive ssor algorithm is also given it is finally proved that the proposed adaptive saor cg algorithm is feasible and very efficient for the iterative solution

mixed symmetric duality in non differentiable multiobjective mathematical programming two mixed symmetric dual models for a class of non differentiable multiobjective nonlinear programming problems with multiple arguments are introduced in this paper these two mixed symmetric dual models unify the four existing multiobjective symmetric dual models in the literature weak and strong duality theorems are established for these models under some mild assumptions of generalized convexity several special cases are also obtained

multiobjective symmetric duality with cone constraints we formulate a pair of multiobjective symmetric dual programs for pseudo invex functions and arbitrary cones our model is unifying the wolfe vector symmetric dual and the mond weir vector symmetric dual models we establish the weak strong converse and self duality theorems for our pair of dual models nanda and das results optimization 28 1994 267 eur j oper res 88 1996 572 are obtained as special cases

multiobjective higher order symmetric duality involving generalized cone invex functions in this paper a pair of mond weir type multiobjective higher order symmetric dual programs over arbitrary cones is formulated and usual duality results are established under higher order k preinvexity k pseudoinvexity assumptions symmetric minimax mixed integer primal and dual problems are also discussed

semiholonomic verma modules abstract verma modules arise geometrically through the jets of homogeneous vector bundles we consider in this article the modules that arise from the semiholonomic jets of a homogeneous vector bundle we are particularly concerned with the case of a sphere under mobius transformations in this case there are immediate applications in the theory of conformally invariant differential operators

symmetric duality for minimax multiobjective variational mixed integer programming problems with partial invexity a pair of symmetric dual multiobjective variational mixed integer programs for the polars of arbitrary cones are formulated which some primal and dual variables are constrained to belong to the set of integers under the separability with respect to integer variables and partial invexity assumptions on the functions involved we prove the weak strong converse and self duality theorems to related minimax efficient solution these results include some of available results

optimality criteria in nonlinear programming involving nonconvex functions abstract in this paper a new class of functions called convex quasiconvex and pseudoconvex are defined and a number of sufficient optimality criteria are obtained for nonlinear programming problems involving these functions

conformally invariant differential operators on minkowski space and their curved analogues this article describes the construction of a natural family of conformally invariant differential operators on a four dimensional pseudo riemannian manifold included in this family are the usual massless field equations for arbitrary helicity but there are many more besides the article begins by classifying the invariant operators on flat space this is a fairly straightforward task in representation theory best solved through the theory of verma modules the method generates conformally invariant operators in the curved case by means of penrose s local twistor transport

sharp weighted sobolev trace inequalities and fractional powers of the laplacian abstract we establish a family of sharp sobolev trace inequalities involving the w k 2 r n 1 y a norm these inequalities are closely related to the realization of fractional powers of the laplacian on r n r n 1 as generalized dirichlet to neumann operators associated to powers of the weighted laplacian in upper half space generalizing observations of caffarelli silvestre and of yang

a note on pseudo invexity and duality in nonlinear programming abstract certain shortcomings are pointed out in the recent work of s nanda l n das european journal of operational research 88 1996 572 577 and appropriate modifications are suggested for studying duality under pseudo invexity assumptions

laplacian operators and q curvature on conformally einstein manifolds a new definition of canonical conformal differential operators p k k 1 2 with leading term a kth power of the laplacian is given for conformally einstein manifolds of any signature these act between density bundles and more generally between weighted tractor bundles of any rank by construction these factor into a power of a fundamental laplacian associated to einstein metrics there are natural conformal laplacian operators on density bundles due to graham jenne mason sparling gjms it is shown that on conformally einstein manifolds these agree with the p k operators and hence on einstein manifolds the gjms operators factor into a product of second order laplacian type operators in even dimension n the gjms operators are defined only for 1 k n 2 and so on conformally einstein manifolds the p k give an extension of this family of operators to operators of all even orders for n even and k n 2 the operators p k are each given by a natural formula in terms of an einstein metric but they are not natural conformally invariant operators in the usual sense they are shown to be nevertheless canonical objects on conformally einstein structures there are generalisations of these results to operators between weighted tractor bundles it is shown that on einstein manifolds the branson q curvature is constant and an explicit formula for the constant is given in terms of the scalar curvature as part of development conformally invariant tractor equations equivalent to the conformal killing equation are presented

heat kernel expansions ambient metrics and conformal invariants abstract the conformal powers of the laplacian of a riemannian metric which are known as the gjms operators admit a combinatorial description in terms of the taylor coefficients of a natural second order one parameter family h r g of self adjoint elliptic differential operators h r g is a non laplace type perturbation of the conformal laplacian p 2 g h 0 g it is defined in terms of the metric g and covariant derivatives of the curvature of g we study the heat kernel coefficients a 2 k r g of h r g on closed manifolds we prove general structural results for the heat kernel coefficients a 2 k r g and derive explicit formulas for a 0 r g and a 2 r g in terms of renormalized volume coefficients the taylor coefficients of a 2 k r g as functions of r interpolate between the renormalized volume coefficients of a metric g k 0 and the heat kernel coefficients of the conformal laplacian of g r 0 although h r g is not conformally covariant there is a beautiful formula for the conformal variation of the trace of its heat kernel its proof rests on the combinatorial relations between taylor coefficients of h r g and gjms operators as a consequence we give a heat equation proof of the conformal transformation law of the integrated renormalized volume coefficients by refining these arguments we also give a heat equation proof of the conformal transformation law of the renormalized volume coefficients itself the taylor coefficients of a 2 r define a sequence of higher order riemannian curvature functionals with extremal properties at einstein metrics which are analogous to those of integrated renormalized volume coefficients among the various additional results the reader finds a polyakov type formula for the renormalized volume of a poincare einstein metric in terms of q curvature of its conformal infinity and additional holographic terms the present study of relations between spectral theoretic heat kernel coefficients and geometric quantities like renormalized volume coefficients is stimulated by the holographic perspective of the ads cft duality proposing relations between functional determinants and renormalized volumes

on fractional gjms operators we describe a new interpretation of the fractional gjms operators as generalized dirichlet to neumann operators associated to weighted gjms operators on naturally associated smooth metric measure spaces this gives a geometric interpretation of the caffarelli silvestre extension for when 0 1 and both a geometric interpretation and a curved analogue of the higher order extension found by r yang for when 1 we give three applications of this correspondence first we exhibit some energy identities for the fractional gjms operators in terms of energies in the compactified poincare einstein manifold including an interpretation as a renormalized energy second for 1 2 we show that if the scalar curvature and the fractional q curvature q2 of the boundary are nonnegative then the fractional gjms operator p2 is nonnegative third by assuming additionally that q2 is not identically zero we show that p2 satisfies a strong maximum principle 2014 wiley periodicals inc

determinants and conformal anomalies of gjms operators on spheres the conformal anomalies and functional determinants of the branson gjms operators p2k on the d dimensional sphere are evaluated in explicit terms for any d and k such that k d 2 if d is even the determinants are given in terms of multiple gamma functions and a rational multiplicative anomaly which vanishes for odd d taking the mode system on the sphere as the union of neumann and dirichlet ones on the hemisphere is a basic part of the method and leads to a heuristic explanation of the non existence of super critical operators 2k d for even d significant use is made of the barnes zeta function the results are given in terms of ratios of determinants of operators on a d 1 dimensional bulk dual sphere for odd dimensions the log determinant is written in terms of multiple sine functions and agreement is found with holographic computations yielding an integral over a plancherel measure the n d determinant ratio is also found explicitly for even dimensions ehrhart polynomials are encountered