presymplectic geometry and fermat s principle for anisotropic media the tools of presymplectic geometry are used to study light ray trajectories in anisotropic media

new perturbed finite step iterative algorithms for a system of extended generalized nonlinear mixed quasi variational inclusions this paper introduces a new system of extended generalized nonlinear mixed quasi variational inclusions involving a maximal m relaxed h accretive so called a h accretive lan et al 2006 37 mappings in q uniformly smooth banach spaces by using the resolvent operator technique for a maximal m relaxed h accretive mappings due to lan et al we establish the existence and uniqueness of solution for this system of extended generalized nonlinear mixed quasi variational inclusions and construct a new perturbed n step iterative algorithm with mixed errors for solving the mentioned system we also prove the convergence of the sequences generated by our algorithms in q uniformly smooth banach spaces the results presented in this paper extend and improve some known results in the literature

a class of global fractional order projective dynamical systems involving set valued perturbations this paper studies a class of global fractional order projective dynamical systems involving set valued perturbations in real separable hilbert spaces we prove that the set of solutions for this type of systems is nonempty and closed under some suitable conditions furthermore we show that the set of solutions is continuous with respect to initial value in the sense of hausdorff metric finally an interesting numerical example is given to illustrate the validity of the main theorem presented in this paper

predictor corrector iterative algorithms for solving generalized mixed variational like inequalities the concept of partially relaxed h strong monotonicity of set valued mappings is introduced by applying the auxiliary variational inequality technique some new predictor corrector iterative algorithms for solving generalized mixed variational like inequalities are suggested and analyzed the convergence of the algorithms only need the continuity and the partially relaxed h strongly monotonicity of set valued mappings the algorithm and convergence result are new and generalize some known results in literatures

three step iterative algorithm for a system of set valued variational inclusions with h η monotone operators abstract in this paper we introduce and study a new system of set valued variational inclusions with h monotone operators we prove the convergence of a new three step iterative algorithm for this system of set valued variational inclusions the results in this paper extend and improve some known results from the literature

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

discrete vakonomic mechanics discretizations of vakonomic mechanics are developed by using the methodology of variational integrators the resulting algorithms are symplectic in some sense that we will explain and preserve the momentum map associated with a lie group of symmetries a specific example illustrating the theory is tested numerically

auxiliary principle and iterative algorithms for generalized set valued strongly nonlinear mixed variational like inequalities in this paper we extend the auxiliary principle technique to study a class of generalized set valued strongly nonlinear mixed variational like inequalities we prove the existence of a solution of the auxiliary problem for the generalized set valued strongly nonlinear mixed variational like inequalities construct the iterative algorithm for the generalized set valued strongly nonlinear mixed variational like inequalities and show the existence of a solution of the generalized set valued strongly nonlinear mixed variational like inequality by using the auxiliary principle technique we also prove the convergence of iterative sequences generated by the algorithm

algorithm for generalized multivalued variational inequalities in hilbert spaces abstract we introduce a new class of generalized multivalued variational inequality problems 1 1 which contain several existing variational inequality problems as special cases an iterative algorithm for finding approximate solutions of problem 1 1 is considered several convergence results for this algorithm are derived and in particular several existence results of problems 1 1 are obtained we also introduce a new class of generalized multivalued complementarity problems 5 1 which also contain several known complementarity problems as special cases it is shown that problem 5 1 is equivalent to problem 1 1 of special type from which several existence results of problem 5 1 are obtained

on quiver theoretic description for quasitriangularity of hopf algebras abstract this paper is devoted to the study of the quasitriangularity of hopf algebras via hopf quiver approaches we give a combinatorial description of the hopf quivers whose path coalgebras give rise to coquasitriangular hopf algebras with a help of the quiver setting we study general coquasitriangular pointed hopf algebras and obtain a complete classification of the finite dimensional ones over an algebraically closed field of characteristic 0

gap function and global error bounds for generalized mixed quasi variational inequalities in this paper we obtain some gap functions for generalized mixed quasi variational inequality problems in terms of regularized gap function and d gap function further by using these gap functions we obtain global error bounds for the solution of generalized mixed quasi variational inequality problems in hilbert spaces the results obtained in this paper generalize and improve some corresponding known results in literatures

a new method for a class of linear variational inequalities in this paper we introduce a new iterative scheme for the numerical solution of a class of linear variational inequalities each iteration of the method consists essentially only of a projection to a closed convex set and two matrix vector multiplications both the method and the convergence proof are very simple

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

predictor corrector iterative algorithms for solving generalized mixed quasi variational like inclusion by applying the concept of partially relaxed h strong monotonicity of set valued mappings due to author and the auxiliary variational inequality technique some new predictor corrector iterative algorithms for solving generalized mixed quasi variational like inclusions are suggested and analyzed the convergence of the algorithms only need the continuity and the partially relaxed h strongly monotonicity of set valued mappings the algorithm and convergence result are new and generalize some recent known results in literatures

basic hopf algebras and quantum groups this paper investigates the structure of basic finite dimensional hopf algebras h over an algebraically closed field k the algebra h is basic provided h modulo its jacobson radical is a product of the field k in this case h is isomorphic to a path algebra given by a finite quiver with relations necessary conditions on the quiver and on the coalgebra structure are found in particular it is shown that only the quivers gamma g w given in terms of a finite group g and sequence w w 1 w 2 ldots w r of elements of g in the following way can occur the quiver gamma g w has vertices v g g in g and arrows a i g colon v g 1 to v w ig 1 mid g in g w i in w where the set w 1 w 2 ldots w r is closed under conjugation with elements in g and for each g in g the sequences w and gw 1g 1 gw 2g 1 ldots gw rg 1 are the same up to a permutation we show how k gamma g w is a kg bimodule and study properties of the left and right actions of g on the path algebra furthermore it is shown that the conditions we find can be used to give the path algebras k gamma g w themselves a hopf algebra structure for an arbitrary field k the results are also translated into the language of coverings finally a new class of finite dimensional basic hopf algebras are constructed over a not necessarily algebraically closed field most of which are quantum groups the construction is not characteristic free all the quivers gamma g w where the elements of w generates an abelian subgroup of g are shown to occur for finite dimensional hopf algebras the existence of such algebras is shown by explicit construction for closely related results of cibils and rosso see ci r

projection methods algorithms and a new system of nonlinear variational inequalities abstract the convergence of projection methods is based on a new iterative algorithm for the approximation solvability of the following system of nonlinear variational inequalities snvi determine elements x y k such that t y x y x x 0 for all x k and for 0 and t x y x x y 0 for all x k and for 0 where t k h is a mapping from a nonempty closed convex subset k of a real hilbert space h into h this new class of generalized nonlinear variational inequalities reduces to standard class of nonlinear variational inequalities which are widely studied and applied to various problems arising from mathematical sciences optimization and control theory and other related fields

algorithm of solutions for mixed implicit quasi variational inequalities with fuzzy mappings abstract in this paper by applying the auxiliary variational principle technique some existence theorems of solutions for a class of mixed implicit quasi variational inequalities with fuzzy mappings are proved in hilbert spaces a novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed the convergence criteria is also given as special cases of these results the open problem put forward by noor is answered positively our results are new and generalize a number of known results to mixed implicity quasi variational inequalities with fuzzy mappings

three step iterative algorithms for solving the system of generalized mixed quasi variational like inclusions in this paper we consider the system of generalized mixed quasi variational like inclusions in hilbert spaces we extend the auxiliary principle technique to develop a three step iterative algorithm for solving the system of generalized mixed quasi variational like inclusions under the assumptions of the continuity and partially relaxed h strong monotonicity of set valued mappings we establish the convergence for our algorithm our algorithm and its convergence results are new and generalize ding s predictor corrector iterative algorithms moreover our results unify some known results in the literature as well

lagrangian systems with constraints a geometric approach to the method of lagrange multipliers a geometric approach to the method of lagrange multipliers is presented using the framework of the tangent bundle geometry the nonholonomic systems with constraint functions linear in the velocities are studied in the first place and then and using this study of the nonholonomic mechanical systems as a previous result the holonomic systems are considered the lagrangian inverse problem is also analysed and finally the theory is illustrated with several examples

time dependent lagrangian systems a geometric approach to the theory of systems with constraints a geometric approach to the theory of time dependent regular lagrangian systems with constraints is presented using the framework of the exact contact manifold tq r l the main subject of the article concerns the properties of the time dependent nonholonomic constraints and the geometric approach to the method of the lagrange multipliers it is shown that every constraint determines a contact one form a vertical vector field and a nonvertical vector field the explicit form of the vector field representing the constrained dynamics is obtained and finally the properties of all these one forms and vector fields are discussed

asymmetric variational inequality problems over product sets applications and iterative methods in this paper we i describe how several equilibrium problems can be uniformly modelled by a finite dimensional asymmetric variational inequality defined over a cartesian product of sets and ii investigate the local and global convergence of various iterative methods for solving such a variational inequality problem because of the special cartesian product structure these iterative methods decompose the original variational inequality problem into a sequence of simpler variational inequality subproblems in lower dimensions the resulting decomposition schemes often have a natural interpretation as some adjustment processes

auxiliary principle for generalized mixed variational like inequalities abstract in this paper we use the auxiliary principle technique to prove the existence of a solution of some new classes of variational inequalities which are called the generalized mixed variational like inequalities this technique is used to analyze an iterative algorithm several special cases which can be obtained from our main result are also discussed

a class of gap functions for variational inequalities recently auchmuty 1989 has introduced a new class of merit functions or optimization formulations for variational inequalities in finite dimensional space we develop and generalize auchmuty s results and relate his class of merit functions to other works done in this field especially we investigate differentiability and convexity properties and present characterizations of the set of solutions to variational inequalities we then present new descent algorithms for variational inequalities within this framework including approximate solutions of the direction finding and line search problems the new class of merit functions include the primal and dual gap functions introduced by zuhovickii et al 1969a 1969b and the differentiable merit function recently presented by fukushima 1992 also the descent algorithm proposed by fukushima is a special case from the class of descent methods developed in this paper through a generalization of auchmuty s class of merit functions we extend those inherent in the works of dafermos 1983 cohen 1988 and wu et al 1991 new algorithmic equivalence results relating these algorithm classes to each other and to auchmuty s framework are also given

the auxiliary principle and an algorithm for a system of generalized set valued mixed variational like inequality problems in banach spaces in this paper we introduce and study a new system of generalized set valued mixed variational like inequality problems sgsmvlip and its related auxiliary problems in reflexive banach spaces the auxiliary principle technique is applied to study the existence and an iterative algorithm of solutions for the system of generalized set valued mixed variational like inequality problems at first the existence and uniqueness of solutions of the auxiliary problems for sgsmvlip is shown next an iterative algorithm for solving sgsmvlip is constructed by using the existence and uniqueness result finally we prove the existence of solutions of sgsmvlip and discuss the convergence analysis of the algorithm these results improve unify and generalize many corresponding known results given in the literature

on the geometry of non holonomic lagrangian systems we present a geometric framework for non holonomic lagrangian systems in terms of distributions on the configuration manifold if the constrained system is regular an almost product structure on the phase space of velocities is constructed such that the constrained dynamics is obtained by projecting the free dynamics if the constrained system is singular we develop a constraint algorithm which is very similar to that developed by dirac and bergmann and later globalized by gotay and nester special attention to the case of constrained systems given by connections is paid in particular we extend the results of koiller for caplygin systems an application to the so called non holonomic geometry is given

set valued resolvent equations and mixed variational inequalities in this paper we introduce and study a new class of variational inequalities which is called the generalized set valued mixed variational inequality the resolvent operator technique is used to establish the equivalence among generalized set valued variational inequalities fixed point problems and the generalized set valued resolvent equations this equivalence is used to study the existence of a solution of set valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems the results proved in this paper represent a significant refinement and improvement of the previously known results in this area

a quiver quantum group we construct quantum groups at a root of unity and we describe their monoidal module category using techniques from the representation theory of finite dimensional associative algebras

the extragradient method for finding a common solution of a finite family of variational inequalities and a finite family of fixed point problems in the presence of computational errors abstract in a hilbert space we study the convergence of the subgradient method to a common solution of a finite family of variational inequalities and of a finite family of fixed point problems under the presence of computational errors most results known in the literature establish the convergence of algorithms when computational errors are summable in the present paper the convergence of the subgradient method is established for nonsummable computational errors we show that the subgradient method generates a good approximate solution if the sequence of computational errors is bounded from above by a constant

constructing quantum groups and hopf algebras from coverings abstract given a group graded free associative algebra we show that in many cases the path algebra associated to the covering coming from the grading has a hopf algebra structure our structure on the path algebra is that of a quantum group far most of these constructions adding more restrictions we create some finite dimensional quotients which inherit the structure of a hoof algebra usually a quantum group from the path algebra

generalized multivalued variational inequalities ii abstract in this paper we prove that the generalized multivalued variational inequalities are equivalent to the generalized multivalued wiener hopf equations this equivalence is used to suggest a number of iterative algorithms for solving generalized multivalued variational inequalities we also discuss the convergence of these algorithms

set valued variational inclusions in banach spaces the purpose of this paper is to introduce and study a class of set valued variational inclusions without compactness condition in banach spaces by using michael s selection theorem and nadler s theorem an existence theorem and an iterative algorithm for solving this kind of set valued variational inclusions in banach spaces are established and suggested

algorithms for general monotone mixed variational inequalities abstract in this paper we suggest and analyze some new iterative methods for solving general monotone mixed variational inequalities which are being used to study odd order and nonsymmetric boundary value problems arising in pure and applied sciences these new methods can be viewed as generalizations and extensions of the methods of he solodov and tseng and noor for solving monotone mixed variational inequalities

on the structure of tame graded basic hopf algebras ii abstract in this paper firstly we give a complete list of tame local graded frobenius algebras then by the method of bosonization and this list we determine the structure of tame radically graded basic hopf algebras completely

iterative algorithms for solving generalized nonlinear mixed variational inequalities a new concept of g partially relaxed strong monotonicity of mappings is introduced by applying the auxiliary variational inequality technique some new predictor corrector iterative algorithms for solving generalized nonlinear mixed variational inequalities are suggested and analyzed the convergence of the algorithms only need the continuity and the g partially relaxed strongly monotonicity of mappings these algorithms and convergence result are new and generalize some known results in literature

sensitivity analysis for parametric completely generalized strongly nonlinear implicit quasi variational inclusions in this paper by using a resolvent operator technique of maximal monotone mappings and the property of a fixed point set of set valued contractive mappings we study the behavior and sensitivity of the solutions of the parametric completely generalized strongly nonlinear implicit quasi variational inclusion in hilbert space our results extend improve and unify the previously many results in this field

on a new system of generalized mixed quasi variational like inclusions involving a η m accretive operators with applications in this paper we introduce a new and interesting system of generalized mixed quasi variational like inclusions with a h m accretive operators and relaxed cocoercive mappings which contains variational inequalities variational inclusions systems of variational inequalities systems of variational like inequalities and systems of variational inclusions in the literature as special cases by using the resolvent technique for the a h m accretive operators we prove the existence of solutions and the convergence of a new p step iterative algorithm for this system of generalized mixed quasi variational like inclusions in real q uniformly smooth banach spaces the results in this paper unifies extends and improves some known results in the literature

a new system of variational inclusions involving h accretive operator in banach spaces in this paper we introduced and study a new class of system of variational inclusions involving h accretive operator in banach spaces by using the resolvent operator technique associated with h accretive operator we prove the existence of the solution for the system of inclusions and develop a step controlled iterative algorithm to approach the unique solution

geometric theory of the equivalence of lagrangians for constrained systems the lagrangian description of a system is analysed from a geometric viewpoint in order to find a concept for equivalence of singular lagrangians generalising that of the regular case geometric and gauge equivalence of singular lagrangians are studied and the authors also give some conditions in which second order differential equations exist satisfying the dynamical equation on the final constraint submanifold

solving a class of linear projection equations many interesting and important constrained optimization problems in mathematical programming can be translated into an equivalent linear projection equation u p omega u mu q here p omega cdot is the orthogonal projection on some convex set omega e g omega bbb r n and m is a positive semidefinite matrix this paper presents some new methods for solving a class of linear projection equations the search directions of these methods are straighforward extensions of the directions in traditional methods for unconstrained optimization based on the idea of a projection and contraction method 7 we get a simple step length rule and are able to obtain global linear convergence

lifting of quantum linear spaces and pointed hopf algebras of orderp3 abstract we propose the following principle to study pointed hopf algebras or more generally hopf algebras whose coradical is a hopf subalgebra given such a hopf algebraa consider its coradical filtration and the associated graded coalgebra gr a then gr ais a graded hopf algebra since the coradicala0ofais a hopf subalgebra in addition there is a projection gr a a0 letrbe the algebra of coinvariants of then by a result of radford and majid ris a braided hopf algebra and gr ais the bosonization or biproduct ofranda0 gr a r a0 the principle we propose to studyais first to studyr then to transfer the information to gr avia bosonization and finally to lift toa in this article we apply this principle to the situation whenris the simplest braided hopf algebra a quantum linear space as consequences of our technique we obtain the classification of pointed hopf algebras of orderp3 pan odd prime over an algebraically closed field of characteristic zero with the same hypothesis the characterization of the pointed hopf algebras whose coradical is abelian and has indexporp2 and an infinite family of pointed nonisomorphic hopf algebras of the same dimension this last result gives a negative answer to a conjecture of i kaplansky

geometric lagrangian approach to first order systems and applications the geometric theory of presymplectic systems is developed to study both the lagrangian and hamiltonian formulations of a system described by a lagrangian linear in the velocities the results are used to study some related problems for second order differential equations and regular lagrangians

on the classification of finite dimensional pointed hopf algebras we classify finite dimensional complex hopf algebras a which are pointed that is all of whose irreducible comodules are one dimensional and whose group of group like elementsg a is abelian such that all prime divisors of the order of g a are 7 since these hopf algebras turn out to be deformations of a natural class of generalized small quantum groups our result can be read as an axiomatic description of generalized small quantum groups

existence of solutions for lower semicontinuous quasi equilibrium problems in this paper we deal with the following quasi equilibrium problem given a nonempty subset c of a topological vector space x a nonempty set d two functions t c d f x d r and a multifunction s c 2x find x x such that x c x s x and f x tx f x tx for all x s x such a problem recently introduced in 1 extends and unifies several variational inequality problems generalized complementarity problems and nash equilibrium problems we prove several existence results in which the upper semicontinuity of the multifunction s is not assumed

general nonlinear variational inequalities abstract the fixed point technique is used to prove the existence of a unique solution of a new unified and general class of nonlinear variational inequalities several special cases which can be obtained from our main result are also discussed

generalized quasi variational like inequality problem this paper gives some very general results on the generalized quasi variational like inequality problem since the problem includes all the existing extensions of the classical variational inequality problem as special cases our existence theorems extend the previous results in the literature by relaxing both continuity and concavity of the functional the approach adopted in this paper is based on continuous selection type arguments and thus is quite different from the berge maximum theorem or hahn banach theorem approach used in the literature

generalized set valued variational inclusions and resolvent equations in this paper we establish the equivalence between the generalized set valued variational inclusions the resolvent equations and the fixed point problem using the resolvent operator technique this equivalence is used to suggest and analyze some iterative algorithms for solving the generalized set valued variational inclusions and related optimization problems

exchange price equilibria and variational inequalities the aim of this paper is to show the relevance of the concept and the theory of variational inequalities in the study of economic equilibria

projection methods for a system of nonconvex variational inequalities relying on the prox regularity notion we introduce and establish the convergence of two step projection methods for a system of nonconvex variational inequality problems we obtain as a particular case some known results in this field

iterative methods for variational and complementarity problems in this paper we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems included among such methods are the newton and several successive overrelaxation algorithms for the most part the study is concerned with the family of linear approximation methods these are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches the paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria finally several convergence results are obtained for some nonlinear approximation methods

comments on the presymplectic formalism and the theory of regular lagrangians with constraints the lagrangian formalism for systems with constraints is developed using a singular lagrangian defined in the extended tangent bundle t q r the dynamics defined by the new extended lagrangian that incorporates the constraints is studied using the formalism of the presymplectic geometry a comparative study with other geometric approaches is presented

finite quantum groups and cartan matrices abstract we consider a class of hopf algebras having as an invariant a generalized cartan matrix for a hopf algebra of this kind we prove that it is finite dimensional if and only if its generalized cartan matrix is actually a finite cartan matrix under some mild hypothesis these results allow us to classify all the finite dimensional coradically graded pointed hopf algebras whose coradical has odd prime dimension p we also characterize coradically graded pointed hopf algebras of order p 4

auxiliary problems and algorithm for a system of generalized variational like inequality problems in this paper we consider a system of generalized variational like inequality problems sgvlip involving nondifferentiable terms and its related auxiliary problems in real hilbert spaces an existence theorem for auxiliary problems is established further by exploiting this theorem an algorithm for the sgvlip is constructed furthermore we prove the existence of a unique solution of sgvlip and discuss the convergence analysis of the algorithm the technique and results presented in this paper generalize and unify the corresponding techniques and results given in m a noor general nonlinear variational inequalities j math anal appl 126 1987 78 84 m a noor general variational inequalities appl math lett 1 1988 119 122 m a noor mixed variational like inequalities commun appl nonlinear anal 1 4 1994 63 75

iterative algorithm for a system of nonlinear variational like inclusions in this paper we consider a system of nonlinear variational like inclusions snvli in hilbert spaces in particular snvli reduces to a variational inclusion an extension of variational inclusion studied by h a s s o u n i a n d m o u d a f i 1 using fixed point method we suggest an iterative algorithm for finding an approximate solution to snvli further we prove the existence of solution and discuss convergence criteria for the approximate solution of snvli the theorems presented in this paper improve and unify many known results of variational inclusions and variational inequalities see for example 1 3

iterative algorithms for a new system of nonlinear variational inclusions with a η accretive mappings in banach spaces in this paper we introduce and study a new system of nonlinear variational inclusions with a h accretive mappings in banach spaces by using the resolvent operator associated with a h accretive mappings we construct some new iterative algorithms for approximating the solution of this system of variational inclusions we also prove the existence of solutions and the convergence of the sequences generated by the algorithm in banach spaces the results presented in this paper extend and improve some known results in the literature

monomial hopf algebras abstract let k be a field of characteristic 0 containing all roots of unity we classified all the hopf structures on monomial k coalgebras or in dual version on monomial k algebras

some aspects of variational inequalities abstract in this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence uniqueness computational properties various generalizations sensitivity analysis and their applications we also propose some open problems with sufficient information and references so that someone may attempt solution s in his her area of special interest we also include some new results which we have recently obtained

a geometric approach to the gibbs appell equations in lagrangian mechanics we present a geometrical derivation of the gibbs appell equations in constrained lagrangian mechanics using the affine structures existing in the spaces of velocities and accelerations the theoretical basis is the gauss principle of least constraint and the necessary conditions for the minimum expressed in terms of the gibbs function give rise to the gibbs appell equations we give a second order formulation of the constraint equation and using the concept of moore penrose inverse we provide an explicit intrinsic construction of the projector on the space of the effective or non ideal forces the gibbs appell equations are expressed in an intrinsic way in terms of the fibre derivative of the gibbs function and the effective part of the applied force

a constraint algorithm for singular lagrangians subjected to nonholonomic constraints we construct a constraint algorithm for singular lagrangian systems subjected to nonholonomic constraints which generalizes that of dirac for constrained hamiltonian systems

the generalized quasi variational inequality problem with applications a new problem called the generalized quasi variational inequality problem is introduced this new problem extends all the existing variational inequality problems in finite dimensional spaces and enlarges the class of problems that can be approached by the variational inequality theory some existence results without convexity assumptions are presented applications to mathematical and equilibrium programming are given

auxiliary principle and iterative algorithm for a new system of generalized mixed equilibrium problems in banach spaces abstract in this paper we study a new system of generalized mixed equilibrium problems involving skew symmetric bifunctions sgmep in reflexive banach spaces a system of auxiliary mixed equilibrium problems samep for solving the sgmep is introduced and the existence and uniqueness of the solutions of the samep is first proved next by using the auxiliary principle technique a new iterative algorithm to compute the approximate solutions of the sgmep is suggested and analyzed finally the strong convergence of the iterative sequences generated by the algorithm is also proved under quite mild conditions these results improve unify and generalize some known results in recent literature

reduction of some classical non holonomic systems with symmetry two types of nonholonomic systems with symmetry are treated i the configuration space is a total space of a g principal bundle and the constraints are given by a connection ii the configuration space is g itself and the constraints are given by left invariant forms the proofs are based on the method of quasicoordinates in passing a derivation of the maurer cartan equations for lie groups is obtained simple examples are given to illustrate the algorithmical character of the main results

a parallel projection method for a system of nonlinear variational inequalities in this paper we introduce and consider a new system of nonlinear variational inequalities involving two different operators using the parallel projection technique we suggest and analyze an iterative method for this system of variational inequalities we establish a convergence result for the proposed method under certain conditions our results can be viewed as a refinement and improvement of the previously known results for variational inequalities

the geometrical theory of constraints applied to the dynamics of vakonomic mechanical systems the vakonomic bracket a vakonomic mechanical system can be alternatively described by an extended lagrangian using the lagrange multipliers as new variables since this extended lagrangian is singular the constraint algorithm can be applied and a dirac bracket giving the evolution of the observables can be constructed

non holonomic lagrangian systems in jet manifolds a geometrical setting in terms of jet manifolds is developed for time dependent non holonomic lagrangian systems an almost product structure on the evolution space is constructed in such a way that the constrained dynamics is obtained by projection of the free dynamics a constrained poincare cartan 2 form is defined if the non holonomic system is singular a constraint algorithm is constructed special attention is devoted to caplygin systems and a reduction theorem is proved

quiver hopf algebras abstract in this paper we study subhopfalgebras of graded hopf algebra structures on a path coalgebra k q c we prove that a hopf structure on some subhopfquivers can be lifted to a hopf structure on the whole hopf quiver if q is a schurian hopf quiver then we classified all simple pointed subhopfalgebras of a graded hopf structure on k q c we also prove a dual gabriel theorem for pointed hopf algebras

existence and algorithm of solutions for generalized mixed implicit quasi variational inequalities1this project was supported by the national science foundation of people s republic china 1 in this paper by applying the auxiliary variational principle technique some existence theorems of solutions for a class of generalized mixed implicit quasi variational inequalities are proved in hilbert spaces a novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed the convergence criteria are also given as special cases of these results the open problem put forward by noor is answered positively and some results of existence and algorithm of solutions for generalized implicit quasi complementarity problems are also obtained our results are new and generalize a number of known results of mixed variational inequalities mixed quasi variational inequalities and quasi complementary problems involving single valued and set valued mappings in recent literatures