sufficiency and duality in nonsmooth multiobjective optimization involving generalized f α π d type i functions in this paper new classes of generalized f a p d type i functions are introduced for a nonsmooth multiobjective programming problem based upon these generalized functions sufficient optimality conditions are established weak strong and strict converse duality theorems are also derived for wolfe and mond weir type multiobjective dual programs in order to relate the efficient and weak efficient solutions of primal and dual problems

design parametrization and pole placement of stabilizing output feedback compensators via injective cogenerator quotient signal modules control design belongs to the most important and difficult tasks of control engineering and has therefore been treated by many prominent researchers and in many textbooks the systems being generally described by their transfer matrices or by rosenbrock equations and more recently also as behaviors our approach to controller design uses in addition to the ideas of our predecessors on coprime factorizations of transfer matrices and on the parametrization of stabilizing compensators a new mathematical technique which enables simpler design and also new theorems in spite of the many outstanding results of the literature 1 we use an injective cogenerator signal module f over the polynomial algebra d f s f an infinite field a saturated multiplicatively closed set t of stable polynomials and its quotient ring dt of stable rational functions this enables the simultaneous treatment of continuous and discrete systems and of all notions of stability called t stability we investigate stabilizing control design by output feedback of input output io behaviors and study the full feedback io behavior especially its autonomous part and not only its transfer matrix 2 the new technique is characterized by the permanent application of the injective cogenerator quotient signal module dtft and of quotient behaviors bt of df behaviors b 3 for the control tasks of tracking disturbance rejection model matching and decoupling and not necessarily proper plants we derive necessary and sufficient conditions for the existence of proper stabilizing compensators with proper and stable closed loop behaviors parametrize all such compensators as io behaviors and not only their transfer matrices and give new algorithms for their construction moreover we solve the problem of pole placement or spectral assignability for the complete feedback behavior the properness of the full feedback behavior ensures the absence of impulsive solutions in the continuous case and that of the compensator enables its realization by kalman state space equations or elementary building blocks we note that every behavior admits an io decomposition with proper transfer matrix but that most of these decompositions do not have this property and therefore we do not assume the properness of the plant 4 the new technique can also be applied to more general control interconnections according to willems in particular to two parameter feedback compensators and to the recent tracking framework of fiaz takaba trentelman in contrast to these authors however we pay special attention to the properness of all constructed transfer matrices which requires more subtle algorithms

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

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

weak exponential stability of linear time varying differential behaviors abstract we develop a new approach to exponential stability of linear time varying ltv differential behaviors that is analogous to that in our paper on exponential stability of discrete ltv behaviors h bourles et al 2015 5 stability theory for differential state space systems with smooth coefficients is an important subject in the literature for differential ltv behaviors with arbitrary smooth coefficients there is no reasonable stability theory therefore we restrict the smooth varying coefficients to functions that are defined by means of locally convergent puiseux series all rational functions are of this type we introduce a new kind of behaviors and prove a module behavior duality for these we define a new notion of weak exponential stability w e s of a behavior b and its associated finitely generated f g module m and show that the w e s modules and behaviors are closed under isomorphisms subobjects factor objects and extensions the standard uniform exponential stability of state space equations is not preserved under behavior isomorphisms and unsuitable for a behavioral theory in the main result we assume a nonzero f g torsion module m and its associated autonomous behavior b such a module may be regular or irregular singular according to the galois theory of differential equations if it is nonzero and regular singular it is never w e s for irregular singular m we characterize w e s of most b algebraically and constructively

optimality and duality in multiobjective fractional programming involving ρ semilocally type i preinvex and related functions abstract optimality conditions are obtained for a nonlinear fractional multiobjective programming problem involving semidifferentiable functions also a general dual is formulated and a duality result is proved using concepts of generalized semilocally type i preinvex functions

free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule the generalized differential quadrature rule proposed recently by these authors is applied here to the free vibration analyses of solid circular plates with radially varying thickness and elastic restraints the thickness can vary radially in any given continuous form and it varies exponentially and linearly in this work two regularity conditions corresponding to the plate center are expressed in explicit formulae since they have been inexactly or even wrongly expressed in the literature such errors are pointed out in the application of the differential quadrature techniques and in the expression of the regularity conditions at the plate center numerical results are presented for a number of plates illustrating the versatility and accuracy of the approach

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

generalized mixed quasi variational like inequalities in this paper we use the auxiliary principle technique to suggest and analyze some iterative methods for solving generalized mixed quasi variational like inequalities we show that the convergence of the proposed method requires either pseudomonotonicity or partially relaxed strongly monotonicity under some mild condition as special cases one can obtain a number of new and known algorithms for solving variational inequalities and complementarity problems our results represent significant and important refinements of the previously known results

on the relationships between g preinvex functions and semistrictly g preinvex functions a new class of functions termed semistrictly g preinvex functions is introduced in this paper the relationships between semistrictly g preinvex functions and g preinvex functions are investigated under mild assumptions our results improve and extend the existing ones in the literature

continuous varying linear systems abstract we discuss implicit systems of ordinary linear differential equations with time variable coefficients their solutions in the signal space of hyperfunctions according to sato and their solution spaces called time varying linear systems or behaviours from the system theoretic point of view the basic result inspired by an analogous one for multidimensional constant linear systems is a duality theorem which establishes a categorical one one correspondence between time varying linear systems or behaviours and finitely generated modules over a suitable skew polynomial ring of differential operators this theorem is false for the signal spaces of infinitely often differentiable functions or of meromorphic hyper functions or of distributions on r it is used to obtain various results on key notions of linear system theory several new algorithms for modules over rings of differential operators and in particular new grobner basis algorithms due to insa and pauer make the system theoretic results effective

some basic structural properties of generalized linear systems abstract this paper shows how to give a kalman state variable realization to generalized linear systems simple characterizations of controllability observability of their duality and of a minimal realization are proposed our techniques based on elementary module theory are applicable to time varying systems as well as constant systems the note ends with a brief discussion of asymptotic observers in the constant case

on optimality conditions for multiobjective optimization problems in topological vector space abstract in this paper we are concerned with a differentiable multiobjective programming problem in topological vector spaces an alternative theorem for generalized k subconvexlike mappings is given this permits the establishment of optimality conditions in this context several generalized fritz john conditions in line to those in hu and ling y hu c ling the generalized optimality conditions of multiobjective programming problem in topological vector space j math anal appl 290 2004 363 372 are obtained and in the presence of the generalized slater s constraint qualification the karush kuhn tucker necessary optimality conditions

transverse vibrations of circular plates and membranes with intermediate supports the present paper deals with an approximate solution of the title problem in the case of a a concentric circular support and b a secant support fundamental frequency coefficients are determined by means of the rayleigh minimization procedure the modal shapes been approximated by simple polynomial co ordinate functions in the case of a circular plate with a secant support an independent solution is obtained by means of a finite element code and very good agreement is shown to exist

hemiequilibrium like problems abstract in this paper we introduce and consider a new class of equilibrium problems known as hemiequilibrium like problems this new class includes hemiequilibrium equilibrium like problems and several classes of variational inequalities as special cases a number of iterative methods for solving hemiequilibrium like problems are suggested and analyzed by using the auxiliary principle technique we also study the convergence analysis of these iterative methods under some mild conditions the results obtained in this paper can be considered as a novel application of the auxiliary principle technique

stabilisation and control design by partial output feedback and by partial interconnection we study stabilisation and control design by partial output feedback on the one hand and by partial interconnection according to willems on the other hand this article is based on the paper design parametrization and pole placement of stabilizing output feedback compensators via injective cogenerator quotient signal modules by i blumthaler and u oberst and the same technique is used both discrete and continuous behaviours and various notions of stability are treated simultaneously in the case of partial output feedback we require that both the compensator and the feedback behaviour have proper transfer matrices without presuming properness of the plant we obtain conditions ensuring the existence of such stabilising compensators which perform additional control tasks like for instance tracking and an algorithm for constructing a large class of such compensators in the case of stabilisation by interconnection no input output structures of plant or compensator are assumed but the controlled be

relationships between pre invex concepts abstract it is well known that some properties of convex optimization problems especially sufficient conditions for optimality and duality conditions are preserved when convexity is weakened to pre invexity however there are several distinct pre invex concepts b vex b pre invex pre univex p r pre invex and these are not equivalent the pre invexity concepts mentioned above have also some properties which are characteristic and invariant for functions belonging to these classes of functions

stabilising compensators for linear time varying differential systems abstractin this paper we describe a constructive test to decide whether a given linear time varying ltv differential system admits a stabilising compensator for the control tasks of tracking disturbance rejection or model matching and construct and parametrise all of them if at least one exists in analogy to the linear time invariant lti case the ring of stable rational functions noncommutative in the ltv situation and the kucera youla parametrisation play prominent parts in the theory we transfer blumthaler s thesis from the lti to the ltv case and sharpen complete and simplify the corresponding results in the book linear time varying systems by bourles and marinescu

on minimax fractional optimality conditions with invexity abstract under different forms of invexity conditions sufficient kuhn tucker conditions and three dual models are presented for the minimax fractional programming

non differentiable minimax fractional programming with generalized α univexity in this paper we study a non differentiable minimax fractional programming problem under the assumption of generalized a univex function in this paper we extend the concept of a invexity m a noor on generalized preinvex functions and monotonicities j inequalities pure appl math 5 2004 1 9 and pseudo a invexity s k mishra m a noor on vector variational like inequality problems j math anal appl 311 2005 69 75 to a univexity and pseudo a univexity from a view point of generalized convexity we also introduce the concept of strict pseudo a univex and quasi a univex functions we derive karush kuhn tucker type sufficient optimality conditions and establish weak strong and converse duality theorems for the problem and its three different form of dual problems the results in this paper extend a few known results in the literature

hemivariational like inequalities in this paper we introduce and consider a new class of variational inequalities known as the hemivariational like inequalities it is shown that the hemivariational like inequalities include hemivariational inequalities variational like inequalities and the classical variational inequalities as special cases the auxiliary principle is used to suggest and analyze some iterative methods for solving hemivariational like inequalities under mild conditions the results obtained in this paper can be considered as a novel application of the auxiliary principle technique

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

a characterization of pseudoinvexity for the efficiency in non differentiable multiobjective problems duality abstract we prove that in order for the kuhn tucker or fritz john points to be efficient solutions it is necessary and sufficient that the non differentiable multiobjective problem functions belong to new classes of functions that we introduce here kt pseudoinvex ii or fj pseudoinvex ii respectively we illustrate it by examples these characterizations generalize recent results given for the differentiable case we study the dual problem and establish weak strong and converse duality results

factoring and decomposing a class of linear functional systems abstract within a constructive homological algebra approach we study the factorization and decomposition problems for a class of linear functional determined over determined under determined systems using the concept of ore algebras of functional operators e g ordinary partial differential operators shift operators time delay operators we first concentrate on the computation of morphisms from a finitely presented left module m over an ore algebra to another one m where m resp m is a module intrinsically associated with the linear functional system ry 0 resp r z 0 these morphisms define applications sending solutions of the system r z 0 to solutions of r y 0 we explicitly characterize the kernel image cokernel and coimage of a general morphism we then show that the existence of a non injective endomorphism of the module m is equivalent to the existence of a non trivial factorization r r 2 r 1 of the system matrix r the corresponding system can then be integrated in cascade under certain conditions we also show that the system ry 0 is equivalent to a system r z 0 where r is a block triangular matrix of the same size as r we show that the existence of idempotents of the endomorphism ring of the module m allows us to reduce the integration of the system ry 0 to the integration of two independent systems r 1 y 1 0 and r 2 y 2 0 furthermore we prove that under certain conditions idempotents provide decompositions of the system ry 0 i e they allow us to compute an equivalent system r z 0 where r is a block diagonal matrix of the same size as r applications of these results in mathematical physics and control theory are given finally the different algorithms of the paper are implemented in the maple package m orphisms based on the library oremodules

a note on invex problems with nonnegative variable we provide sufficient optimality conditions involving invexity for mathematical programming problems with nonnegative variable we also show that upon certain assumptions on the scaling function these problems are convex transformable hence certain associated convex problems should be solved some applications are shown

on variational problems characterization of solutions and duality in this paper we introduce a new class of pseudoinvex functions for variational problems using this new concept we obtain a necessary and sufficient condition for a critical point of the variational problem to be an optimal solution illustrated with an example also weak strong and converse duality are established

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

multiple objective fractional programming involving semilocally type i preinvex and related functions abstract sufficient optimality conditions are obtained for a nonlinear multiple objective fractional programming problem involving semidifferentiable type i preinvex and related functions furthermore a general dual is formulated and duality results are proved under the assumptions of generalized semilocally type i preinvex and related functions our result generalize the results of preda v preda optimality and duality in fractional multiple objective programming involving semilocally preinvex and related functions j math anal appl 288 2003 365 382 and stancu minasian i m stancu minasian optimality and duality in fractional programming involving semilocally preinvex and related functions j inform optim sci 23 2002 185 201

exact vibration solutions for circular mindlin plates with multiple concentric ring supports this paper presents an analytical approach to investigate the vibration behaviour of circular mindlin plates with multiple concentric ring supports a circular plate is first divided into multiple annular segments and a circular segment at the locations of the ring supports the governing differential equations and the solutions of these equations for the annular and circular segments based on the mindlin plate theory are presented a homogenous equation system governing the vibration of circular mindlin plates with ring supports is derived by imposing the essential and natural boundary and segment interface conditions the first known exact vibration frequencies for circular mindlin plates with multiple concentric ring supports are obtained and the modal shapes of displacement fields and stress resultants for several selected cases are presented the influence of the ring support locations plate boundary conditions and plate thickness ratios on the vibration behaviour of circular plates is discussed

existence and iterative approximations of solutions for mixed quasi variational like inequalities in banach spaces abstract in this paper we introduce and investigate a new class of mixed quasi variational like inequalities in reflexive banach spaces by applying a minimax inequality due to ding tan and a lemma due to chang we establish some existence and uniqueness results of solution for the mixed quasi variational like inequality next by using a kkm theorem due to fan and an auxiliary principle technique due to cohen we suggest two iterative algorithms and study the convergence criteria of iterative sequences generated by the iterative algorithms our results extend improve and unify several known results in the literature

sufficiency and duality in nondifferentiable multiobjective programming involving generalized type i functions abstract recently hachimi and aghezzaf defined generalized f d type i functions a new class of functions that unifies several concepts of generalized type i functions in this paper the generalized f d type i functions are extended to nondifferentiable functions by utilizing the new concepts we obtain several sufficient optimality conditions and prove mixed type and mond weir type duality results for the nondifferentiable multiobjective programming problem

two invariants for weak exponential stability of linear time varying differential behaviors abstract in the paper h bourles b marinescu u oberst weak exponential stability w e s of linear time varying ltv differential behaviors linear algebra appl 486 2015 523 571 we studied the problem of the title if a finitely generated torsion module over an appropriate ring of differential operators and its associated autonomous system are regular singular the system is never w e s in contrast we computed a square complex matrix for each irregular singular module and showed that the system is w e s resp not stable if all eigenvalues of the matrix have positive real parts resp if at least one eigenvalue has negative real part in this supplement of the quoted paper we show that the spectrum of the matrix and the decay exponent are isomorphy invariants of the module the proofs make essential use of results exposed in p maisonobe c sabbah d module coherents et holonomes hermann paris 1993 we also complement the main w e s result of our quoted paper by the case where at least one eigenvalue of the matrix is purely imaginary

time varying polynomial matrix systems abstract differential polynomial matrices with coefficients meromorphic on an open interval i r are studied first the subclass of full matrices p having the properties p is non singular antl every local solution of pf 0 extends analytically to i forms a sublattice with respect to right division of square matrices which is anti isomorphic to the lattice of the corresponding solution spaces this and further properties are then exploited in the study of time varying systems in differential operator representation results on equivalence state space models controllability observability and transfer functions are derived

nonsmooth invex functions and sufficient optimality conditions in this paper the various definitions of nonsmooth invex functions are gathered in a general scheme by means of the concept of k directional derivative characterizations of nonsmooth k invexity are derived as well as results concerning constrained optimization without any assumption of convexity of the k directional derivatives

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

a behavioral approach to time varying linear systems part 2 descriptor systems in the sequel to a ilchmann and v mehrmann em siam j control optim 44 2005 pp 1725 1747 we discuss a behavioral approach for linear time varying differential algebraic descriptor systems with real analytic coefficients the analysis is almost global in the sense that the analysis is not restricted to an interval i subset r but is allowed for the time axis r setminus t where t is a discrete set of critical points at which the solution may exhibit a finite escape time controllable observable and autonomous behavior for linear time varying descriptor systems is characterized

stabilizability of linear time varying systems abstract for linear time varying systems with bounded system matrices we discuss the problem of stabilizability by linear state feedback for example it is shown that complete controllability implies the existence of a feedback so that the closed loop system is asymptotically stable we also show that the system is completely controllable if and only if the lyapunov exponent is arbitrarily assignable by a suitable feedback for uniform exponential stabilizability and the assignability of the bohl exponent this property is known also dynamic feedback does not provide more freedom to address the stabilization problem the unifying tools for our results are two finite l 2 cost conditions the distinction of exponential and uniform exponential stabilizability is then a question of whether the finite cost condition is uniform in the initial time or not

optimality and duality for generalized fractional programming involving nonsmooth f ρ convex functions using a parametric approach we establish necessary and sufficient conditions and derive duality theorems for a class of nonsmooth generalized minimax fractional programming problems containing f r convex functions

optimality and duality in fractional multiple objective programming involving semilocally preinvex and related functions necessary and sufficient optimality conditions are obtained for a nonlinear fractional multiple objective programming problem involving semidifferentiable functions also a general dual is formulated and duality results are proved using concepts of generalized semilocally preinvex functions

nondifferentiable multiobjective programming under generalized d univexity abstract in this paper we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints we introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex strong pseudoinvex weak quasi invex weak pseudoinvex and strong quasi invex functions in aghezzaf and hachimi numer funct anal optim 22 2001 775 d invex functions in antczak europ j oper res 137 2002 28 and univex functions in bector et al univex functions and univex nonlinear programming proc admin sci assoc canada 1992 p 115 by utilizing the new concepts we derive a karush kuhn tucker sufficient optimality condition and establish mond weir type and general mond weir type duality results for the nondifferentiable multiobjective programming problem

multi objective infinite programming using the theory of abstract optimization problems in infinite dimensional spaces we provide necessary optimality conditions of first and second order for weakly efficient solutions of the multi objective infinite programming problem sufficient conditions are given under invexity assumptions we generalize the notion of kkt invexity for the multi objective infinite problem and show that this notion is a necessary and sufficient condition for every vector kkt solution to be a weakly efficient solution moreover we develop a theorem of the alternative useful for proving some of our results

a behavioral approach to time varying linear systems part 1 general theory we develop a behavioral approach to linear time varying differential algebraic systems the analysis is almost everywhere in the sense that the statements hold on mathbb r setminus mathbb t where mathbb t is a discrete set controllability observability and autonomy are introduced and related to the behavior of the system classical results on the behavior of time invariant systems are studied in the context of time varying systems

generalized proper efficiency and duality for a class of nondifferentiable multiobjective variational problems withv invexity abstract a mond weir type dual for a class of nondifferentiable multiobjective variational problems in which every component of the objective function contains a term involving the square root of a certain positive semidefinite quadratic form is considered and various duality results viz weak strong and converse duality theorems are developed for conditionally properly efficient solutions these results are obtained under v invexity assumptions and its generalizations on objective and constraint functions this work extends many results on variational problems established earlier

multiobjective programming under d invexity abstract in this paper a generalization of convexity is considered in the case of nonlinear multiobjective programming problem where the functions involved are nondifferentiable by considering the concept of pareto optimal solution and substituting d invexity for convexity the fritz john type and karush kuhn tucker type necessary optimality conditions and duality in the sense of mond weir and wolfe for nondifferentiable multiobjective programming are given

on invex sets and preinvex functions abstract in this paper we consider the class of the invex function introduced by hanson we show that under certain condition an invex function defined on an invex set a is preinvex on a similarly a quasiinvex function defined on an invex set a is pre quasiinvex

optimality and duality in nondifferentiable multiobjective optimization involvingd type i and related functions abstract in this paper new classes of functions namely d type i d quasitype i and d pseudo type i are defined for a multiobjective nondifferentiable programming problem kuhn tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be a weak minimum for this problem two duals are formulated and various duality results are given by using the above defined classes of functions considering the concept of a weak minimum

free vibration analysis of circular plates using generalized differential quadrature rule the free vibration of solid circular plates has been studied using the generalized differential quadrature rule gdqr the effects such as stepped thickness intermediate concentric ring supports and elastic restraints have been considered discrete system equations for natural frequency analysis were derived based on the gdqr issues related to the implementation of the boundary and compatibility conditions were addressed two regularity conditions at the solid circular plate center were formularized since they were not quite clear in the present literature some wrong applications in the implementation of both differential quadrature methods and regularity conditions at the solid circular plate center have been pointed out excellent results have been obtained with the presented examples

minimax fractional programming under nonsmooth generalized f ρ θ d univexity abstract in this paper we are concerned with a nondifferentiable minimax fractional problem with inequality constraints we introduce a new class of generalized convex function that is nonsmooth generalized f d univex function in the framework of the new concept we derive kuhn tucker type sufficient optimality conditions and establish weak strong and converse duality theorems for the problem and its three different types of dual problems

on ratio invexity in mathematical programming abstract the nonlinear fractional programming problem is considered the functions involved in the objective function and constraints are assumed to be invex and differentiable it is shown that the ratio of invex functions is invex sufficient optimality and duality theorems are presented for an invex fractional programming problem

semistrictly preinvex functions a new class of functions termed semistrictly preinvex functions is introduced in this paper some properties of semistrictly preinvex functions are discussed in particular the relationship between semistrictly preinvex functions and preinvex functions is investigated some characterization properties of semistrictly preinvex functions are derived under a lower semicontinuous condition and a gradient property of semistrictly preinvex functions is obtained

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

vibration of eccentric ring and line supported circular plates carrying concentrated masses abstract the vibration of circular plates supported by combinations of ring and line supports and which are carrying concentrated masses is investigated for the first time to the author s knowledge by using the newly developed pb 2 rayleigh ritz method a set of ritz functions consisting of the product of the boundary expressions is used as the admissible displacement function this set of pb 2 ritz functions can accurately approximate the mode shapes of these circular plates with any prescribed boundary conditions and interior supports such as eccentric annular and or line supports to validate the present method numerical calculations have been carried out for several simplified plate problems and these are compared with those results available in the literature excellent agreement is achieved in all cases

exponentially stable linear time varying discrete behaviors we study implicit systems of linear time varying ltv difference equations with rational coefficients of arbitrary order and their solution spaces called discrete ltv behaviors the signals are sequences i e functions from the discrete time set of natural numbers into the complex numbers the difference field of rational functions with complex coefficients gives rise to a noncommutative skew polynomial algebra of difference operators that act on sequences via left shift for this paper it is decisive that the ring of operators is a principal ideal domain and that nonzero rational functions have only finitely many poles and zeros and grow at most polynomially due to the poles a new definition of behaviors is required for the latter we derive the important categorical duality between finitely generated left modules over the ring of operators and behaviors the duality theorem implies the usual consequences for willems elimination the fundamental principle input output decompositions and controlla

on properties of preinvex functions abstract we consider in this paper the class of preinvex functions introduced by t weir and co workers 1988 j math anal appl 136 29 38 1988 bull austral math soc 38 177 189 under semi continuity conditions a determination of the satisfaction of preinvexity for a function can be achieved via an intermediate point preinvexity check a characterization of a preinvex function in terms of its relationship with an intermediate point preinvexity and prequasi invexity is provided

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

normalized coprime factorizations for linear time varying systems abstract in this paper we show that a finite dimensional linear time varying continuous time system admits normalized coprime factorizations if and only if it admits a stabilizable and detectable realization we construct state space formulas for these factorizations using the stabilizing solutions to standard riccati differential equations in the process we give a simple proof that stabilizability and detectability are sufficient to ensure the existence of such solutions based on these results and on recent advances in the theory of h optimization we present an algorithm to compute the distance between two systems in the gap metric