new approximation schemes for general variational inequalities in this paper we suggest and consider a class of new three step approximation schemes for general variational inequalities our results include ishikawa and mann iterations as special cases we also study the convergence criteria of these schemes

a modified predictor corrector algorithm for solving nonconvex generalized variational inequality in this paper we suggest and analyze a new modified predictor corrector algorithm for solving a nonconvex generalized variational inequality using the auxiliary principle technique the convergence of the algorithm requires the partially relaxed strong monotonicity of the operator

an explicit projection method for a system of nonlinear variational inequalities with different cocoercive mappings in this paper we introduce and consider a new system of variational inequalities involving two different operators using the projection technique we suggest and analyze new explicit iterative methods for this system of variational inequalities we also study the convergence analysis of the new iterative method under certain mild conditions since this new system includes the system of variational inequalities involving the single operator variational inequalities and related optimization problems as special cases results obtained in this paper continue to hold for these problems our results can be viewed as a refinement and improvement of the previously known results for variational inequalities

equivalence and optimization of relational transactions a large class of relational database update transactions is investigated with respect to equivalence and optimization the transactions are straight line programs with inserts deletes and modifications using simple selection conditions several basic results are obtained it is shown that transaction equivalence can be decided in polynomial time a number of optimality criteria for transactions are then proposed as well as two normal forms polynomial time algorithms for transaction optimization and normalization are exhibited also an intuitively appealing system of axioms for proving transaction equivalence is introduced finally a simple natural subclass of transactions called strongly acyclic is shown to have particularly desirable properties

l2 regularity for parabolic partial integrodifferential equations with delay in the highest order derivatives abstract a partial integrodifferential equation is studied in which the derivatives of highest order also contain a discrete and a distributed delay by means of abstract regularity results global existence and uniqueness of a strict solution are obtained moreover a characterization of the infinitesimal generator of the solution operator is given

on a class of retarded partial differential equations on developpe des resultats recents sur des equations d evolution abstraites afin de les appliquer a un type d equations dans des espaces de banach avec un retard discret et continu ces equations peuvent etre considerees comme la version abstraite d equations integrodifferentielles partielles a retard

feedback control of second order evolution equations with damping feedback control is developed for a class of distributed systems described by second order evolution equations with slight damping in order to increase the degree of stability of the system a dynamic compensator is designed on the basis of a finite dimensional model of the system and a feedback control system is constructed by using sensor outputs it is shown that the degree of stability of the whole system including the compensator is improved by modal control based on a finite dimensional modal model this proves the mathematical validity of the modal control of distributed systems

controllability for semilinear functional differential equations with unbounded delays in this paper the approximate controllability of the semilinear functional differential equations with unbounded delays is first investigated then the regularity of solutions of the given system is addressed finally a simple example to which our main result can be applied is given

projection methods for a generalized system of nonconvex variational inequalities with different nonlinear operators abstract in this paper we introduce and consider a new generalized system of nonconvex variational inequalities with different nonlinear operators we establish the equivalence between the generalized system of nonconvex variational inequalities and the fixed point problems using the projection technique this equivalent alternative formulation is used to suggest and analyze a general explicit projection method for solving the generalized system of nonconvex variational inequalities our results can be viewed as a refinement and improvement of the previously known results for variational inequalities

dynamic functional dependencies and database aging a simple extension of the relational model is introduced to study the effects of dynamic constraints on database evolution both static and dynamic constraints are used in conjunction with the model the static constraints considered here are functional dependencies fds the dynamic constraints involve global updates and are restricted to certain analogs of fds called dynamic fds the results concern the effect of the dynamic constraints on the static constraints satisfied by the database in the course of time the effect of the past history of the database on the static constraints is investigated using the notions of age and age closure the connection between the static constraints and the potential future evolution of the database is briefly discussed using the notions of survivability and survivability closure

dynamic constraints and object migration a role set is the set of classes in a class hierarchy where an object may reside simultaneously a migration pattern is a sequence of role sets that an object can migrate through we define a migration inventory which is a set of migration patterns as a dynamic integrity constraint on object migration we consider three update languages sl which has five operators csl which extends sl with positive conditionals and csl which allows both positive and negative conditionals three subclasses of migration patterns of transactions are studied which are immediate start proper and lazy patterns it is shown that the family of all immediatestart proper or lazy migration patterns of every set of sl transactions is a regular set and the converse also holds in particular testing satisfiability of an inventory by a set of transactions is decidable for the extended languages we give a weaker characterization the family of all immediate start proper or lazy migration patterns of every set of csl csl transactions is recursively enumerable r e however every r e inventory can be the family of all migration patterns of some set of csl csl transactions and be a left quotient of the family of immediate start migration patterns of another set of csl csl transactions by a regular set although the exact characterizations of immediate start proper lazy migration patterns of csl csl transactions are still open it is proved that every context free inventory can be the family of proper and immediate start migration patterns of some csl csl transactions testing satisfiability of an inventory by a set of csl csl transactions is unfortunately undecidable

direct strain feedback control of flexible robot arms new theoretical and experimental results this paper addresses control problems for flexible robot arms by using direct strain feedback the purpose is to make clear why direct strain feedback can damp out vibration of flexible arms satisfactorily we concentrate on one link flexible robot arms whose dynamic models can be represented by linear partial differential equations with appropriate boundary conditions which have been well examined in a number of papers a key contribution of this paper is the introduction of the concept of strict a dependent operators which allows us to prove rigorously the closed loop stability of direct strain feedback and the existence and uniqueness of nonstandard second order abstract differential equations in hilbert spaces several control experiments are performed verifying the main theoretical points of this paper demonstrating satisfactory control results of direct strain feedback and leading to potential application of this simple control method for flexible robot control

nonautonomous retarded wave equations in this work we study the well posedness of a class of retarded integrodifferential volterra equations the proofs are based on the nonautonomous version of desch schappacher s perturbation result and extrapolation theory as an application we get c2 solutions of the nonautonomous retarded wave equation with memory effectswtt t x wxx t x x wx t x r0k1 t x wxx t x d r0k2 t x wx t x d f t x 0 t x 0 l with dirichlet boundary conditions

approximate controllability for semilinear retarded control equations using surjectivity results abstract sufficient conditions for approximate controllability of semilinear retarded functional control equations are obtained under general conditions on nonlinear terms to get the main result we transform the controllability problem into surjectivity results similar to fredholm alternative for nonlinear operators under restrictive assumptions finally a simple example to which our main result can be applied is given

finitely specifiable implicational dependency families une famille de dependance d implication id est une famille d exemples de base de donnees relationnelles composee de tous les cas qui satisfont un ensemble donne d ids dans cet article on montre que la collection de familles de dependances d implication specifiable de maniere finie n est pas bloquee sous les dependances de jointure ou de projection

necessary conditions for partial differential equations with delay to generate c0 semigroups on etudie l existence des solutions ou le caractere bien pose d equations aux derivees partielles a retard du type du t dt f u t ou f est un operateur d un espace de fonction 7b f r 0 y dans l espace de banach y dans lequel l equation evolue

some developments in general variational inequalities general variational inequalities provide us with a unified natural novel and simple framework to study a wide class of equilibrium problems arising in pure and applied sciences in this paper we present a number of new and known numerical techniques for solving general variational inequalities using various techniques including projection wiener hopf equations updating the solution auxiliary principle inertial proximal penalty function dynamical system and well posedness we also consider the local and global uniqueness of the solution and sensitivity analysis of the general variational inequalities as well as the finite convergence of the projection type algorithms our proofs of convergence are very simple as compared with other methods our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems since the general variational inequalities include quasi variational inequalities and quasi implicit complementarity problems as special cases results presented here continue to hold for these problems several open problems have been suggested for further research in these areas

differentiable non convex functions and general variational inequalities abstract in this paper we introduce a new class of non convex functions which is called the g convex functions we prove that the minimum of the differentiable non convex functions on the non convex sets can be characterized by a class of variational inequalities which is called the general variational inequality essentially using the projection technique we establish the equivalence between the general variational inequalities and the fixed point problems as well as with the wiener hopf equations this equivalent formulation is used to suggest and analyze some iterative algorithms for solving the general variational inequalities we also discuss the convergence analysis of these iterative methods several special cases are also discussed

on existence and uniqueness of solutions of a class of perturbed second order evolution equations abstract in this paper properties of operators of the kind a are investigated where a is a selfadjoint positive definite differential operator with compact inverse on a hilbert space and is assumed to be a bounded a symmetric and a positive semidefinite a general theory on the existence and uniqueness of solutions of second order evolution equations involving the operator a is developed the new findings obtained in this paper have potential applications in modeling and control of flexible structures

projection algorithms for solving a system of general variational inequalities a b s t r a c t in this paper we introduce and consider a new system of general variational inequalities involving four different operators using the projection operator technique we suggest and analyze some new explicit iterative methods for this system of variational inequalities we also study the convergence analysis of the new iterative method under certain mild conditions since this new system includes the system of variational inequalities involving three operators variational inequalities and related optimization problems as special cases results obtained in this paper continue to hold for these problems our results can be viewed as a refinement and improvement of the previously known results for variational inequalities

characterizations for functional dependency and boyce codd normal form families abstract a functional dependency fd family was recently defined 20 as the set of all instances satisfying some set of functional dependencies a boyce codd normal form abbreviated bcnf family is defined here as an fd family specified by some bcnf set of functional dependencies the purpose of this paper is to present set theoretic algebraic characterizations relating to both types of families two characterizations of f i the smallest fd family containing the family i of instances are established the first involves the notion of agreement a concept related to that of a closed set of attributes the second describes f i as the smallest family of instances containing i and closed under four specific operations on instances companion results are also given for bcnf families the remaining results concern characterizations involving the well known operations of projection join and union two characterizations for when the projection of an fd family is again an fd family are given several corollaries are obtained including the effective decidability of whether a projection of an fd family is an fd family the problem for bcnf families disappears since it is shown that the projection of a bcnf family is always a bcnf family analogous to results for fd families presented in 20 characterizations of when the join and union of bcnf families are bcnf families are given finally the collections of all fd families and all bcnf families are characterized in terms of inverse projection operations and intersection

solvability of the cauchy problem for infinite delay equations abstract in this paper we study the solvability of the cauchy problem for functional differential equations with infinite delay in a banach space x which are more general than those in many previous publications we undertake our study under suitable hypotheses based on noncompactness measures and kamke type functions and in a general setting of admissible phase space p including the space lp 0 x therefore our results extend and unify many existing results for finite and infinite delay equations as a sample of possible applications we analyze the solvability of the cauchy problem for a schrodinger type partial functional integro differential equation in l1 r

local differentiability of distance functions recently clarke stern and wolenski characterized in a hilbert space the closed subsets c for which the distance function dc is continuously differentiable everywhere on an open tube of uniform thickness around c here a corresponding local theory is developed for the property of dc being continuously differentiable outside of c on some neighborhood of a point x c this is shown to be equivalent to the prox regularity of c at x which is a condition on normal vectors that is commonly fulfilled in variational analysis and has the advantage of being verifiable by calculation additional characterizations are provided in terms of dc being locally of class c 1 or such that dc 2 is convex around x for some 0 prox regularity of c at x corresponds further to the normal cone mapping nc having a hypomonotone truncation around x and leads to a formula for pc by way of nc the local theory also yields new insights on the global level of the clarke stern wolenski results and on a property of sets introduced by shapiro as well as on the concept of sets with positive reach considered by federer in the finite dimensional setting

on the structure of armstrong relations for functional dependencies an armstrong relation for a set of functional dependencies fds is a relation that satisfies each fd implied by the set but no fd that is not implied by it the structure and size number of tuples of armstrong relatsons are investigated upper and lower bounds on the size of minimal sized armstrong relations are derived and upper and lower bounds on the number of distinct entries that must appear m an armstrong relation are given it is shown that the time complexity of finding an armstrong relation gwen a set of functional dependencies is precisely exponential in the number of attributes also shown s the falsity of a natural conjecture which says that almost all relations obeying a given set of fds are armstrong relations for that set of fds finally armstrong relations are used to generahze a result obtained by demetrovics using quite complicated methods about the possible sets of keys for a relauon