on the structural stability of the euler voigt and navier stokes voigt models abstract we consider the euler voigt equations and the navier stokes voigt equations which are obtained by an inviscid regularization from the corresponding equations the main result we show is the structural stability of the system in terms of the variations of both viscosity and regularization parameters

the study of existence of equilibria for generalized games without lower semicontinuity in locally topological vector spaces the aim of this paper is to establish general existence results of maximal elements for l majorized mappings which are in turn used to establish the general existence theorems of equilibria for generalized games resp abstract economics without lower semicontinuity for both constraint and preference mappings correspondences and in which strategic resp commodity spaces may not be compact the set of players resp agents may not be countable and underlying spaces are either finite or infinite dimensional locally topological vector spaces our results unify or improve corresponding results in the literature

generalized surface quasi geostrophic equations with singular velocities this paper establishes several existence and uniqueness results for two families of active scalar equations with velocity fields determined by the scalars through very singular integrals the first family is a generalized surface quasigeostrophic sqg equation with the velocity field u related to the scalar by where and is the zygmund operator the borderline case 1 corresponds to the sqg equation and the situation is more singular for 1 we obtain the local existence and uniqueness of classical solutions the global existence of weak solutions and the local existence of patch type solutions the second family is a dissipative active scalar equation with which is at least logarithmically more singular than the velocity in the first family we prove that this family with any fractional dissipation possesses a unique local smooth solution for any given smooth data this result for the second family constitutes a first step towards resolving the global regularity issue recently proposed by k ohkitani 2012 wiley periodicals inc

generalizations of the fkkm theorem and the ky fan minimax inequality with applications to maximal elements price equilibrium and complementarity abstract this paper generalizes the fan knaster kuratowski mazurkiewicz fkkm theorem of ky fan game theory and related topics pp 151 156 north holland amsterdam 1979 and math ann 266 1984 519 537 and the ky fan minimax inequality by introducing a class of the generalized closedness and continuity conditions which are called the transfer closedness and transfer continuities we then apply these results to prove the existence of maximal elements of binary relations under very weak assumptions we also prove the existence of price equilibrium and the complementarity problem without the continuity assumptions thus our results generalize many of the existence theorems in the literature

on equilibrium problem of abstract economy generalized quasi variational inequality and an optimization problem in locally h convex spaces in this paper the equilibrium existence problem for abstract economies the existence problem for solution of generalized quasi variational inequality and an optimization problem in locally h convex spaces are researched

remarks on generalized quasi equilibrium problems our main aim in this paper is to obtain fundamental existence theorems of quasi equilibrium problems and generalized quasi equilibrium problems of multivalued functions we use a continuous selection theorem to show that the existence theorems of generalized quasi equilibrium problems are simple consequences of the corresponding quasi equilibrium problems we use a generalization of himmelberg s theorem due to the third author for not necessary locally convex topological vector spaces to prove the existence theorems of quasi equilibrium problems for multivalued functions

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

existence of equilibrium for generalized abstract fuzzy economies in this paper we introduce and study a new class of generalized abstract fuzzy economies we prove some new existence theorems of equilibrium and maximal element for generalized abstract fuzzy economies with uncountable number of agents and qualitative fuzzy games respectively

the ziegler spectrum for derived discrete algebras let be a derived discrete algebra we show that the krull gabriel dimension of the homotopy category of projective modules and therefore the cantor bendixson rank of its ziegler spectrum is 2 thus extending a result of bobinski and krause 8 we also describe all the indecomposable pure injective complexes and hence the ziegler spectrum for derived discrete algebras extending a result of z han 17 using this we are able to prove that all indecomposable complexes in the homotopy category of projective modules are pure injective so obtaining a class of algebras for which every indecomposable complex is pure injective but which are not derived pure semisimple

an intersection theorem formultivalued maps and applications a new intersection theorem for multivalued maps is obtained this new theorem requires the maps involved to satisfy a weaker compactness condition and generalizes known results applications of this new theorem are given to the existence of maximal and greatest elements for strict and weak relations and to minimax inequalities

some problems and results in the study of nonlinear analysis this paper is presented as a survey of the latest and new results on some topics in the study of nonlinear analysis which were obtained by the author and some chinese mathematicians

some deterministic and random vector equilibrium problems in this paper some generalized concepts about semicontinuity and convexity for vector valued bifunctions are introduced a new existence theorem for vector equilibrium problems is proved further a random version of this result is considered applications to cone saddle points random vector optimization random vector variational inequalities and random vector best approximation problems are finally given

on generalized equilibrium points generalizations of the usual definition of saddle point and equilibrium point are introduced in this paper the existence of these points is shown to be related to a class of functions that we call perturbed convex functions first and second order conditions regarding the existence of these points are also proved

quasi variational inequalities without the concavity assumption this paper generalizes a foundational quasi variationalinequality by relaxing the 0 diagonal concavity condition the approach adopted in this paper is based on continuous selection type arguments and hence it is quite different from the approach used in the literature thus it enables us to prose the existence of equilibrium of the constrained noncooperative games without assuming the quasi convexity of loss functions

thick subcategories of discrete derived categories abstract we classify the thick subcategories of discrete derived categories to do this we introduce certain generating sets called es collections which correspond to configurations of non crossing arcs on a geometric model we show that every thick subcategory is generated by an es collection and we describe a version of mutation which acts transitively on the set of es collections generating a given thick subcategory

new generalizations of browder s variational inequalities and the ky fan minimax inequality abstract in the present paper some new generalized versions of browder s theorems for variational inequalities and the ky fan minimax inequality are obtained

root categories and simple lie algebras abstract by using the t 2 orbit category of the derived category of a hereditary algebra which is proved to be a triangulated category too we give a complete realization of a simple lie algebra this is a global version of ringel s work for the positive parts of simple lie algebras in this realization the grothendieck group provides the cartan subalgebra the indecomposable objects correspond to the chevalley basis and the structure constants are given by the evaluations of hall polynomials

derived hall algebras of one cycle gentle algebras the infinite global dimension case abstract we describe in terms of generators and relations the derived hall algebras associated to the one cycle gentle algebras of infinite global dimension

new fixed point theorems for two maps and applications to problems on sets with convex sections and minimax inequalities abstract new fixed point theorems for two maps defined on product spaces are obtained these new results only require one of them to satisfy a noncompactness condition previous results required each map to satisfy a noncompactness condition applications of our results are given to intersection problems for transfer closed maps to problems on sets with convex sections and to minimax inequalities of sion type our results generalize many well known results

the graded centers of derived discrete algebras abstract we describe in the paper the graded centers of the bounded derived categories of the derived discrete algebras in particular we prove that if a is a derived discrete algebra then the reduced part of the graded center of the bounded derived category of a is nontrivial if and only if a has infinite global dimension moreover we show that the nilpotent part of the graded center is controlled by the objects for which the auslander reiten translation coincides with a power of the suspension functor

existence theorems of solutions for a kind of quasi variational inequalities with monotone type multivalued mapping abstract in this paper two existence theorems of solutions for a kind of quasi variational inequalities with monotone type multivalued mapping are obtained

existence of pareto equilibria for constrained multiobjective games in h space abstract in this paper we introduce and study a new class of constrained multiobjective games in h spaces without linear structure an existence theorem of solutions for quasi equilibrium problems is first proved in noncompact h spaces then as applications of the quasi equilibrium existence theorem several existence theorems of weighted nash equilibria and pareto equilibria for the constrained multiobjective games are established in noncompact h spaces these theorem improve unify and generalize the corresponding results of the multiobjective games in recent literature

approximate selection theorems and their applications abstract we prove three approximate selection theorems and give an improved version of the michael selection theorem as their applications new fixed point theorems and equilibrium theorems for generalized games are established

global regularity and convergence of a birkhoff rott α approximation of the dynamics of vortex sheets of the two dimensional euler equations we present an regularization of the birkhoff rott equation br equation induced by the two dimensional euler equations for the vortex sheet dynamics we show the convergence of the solutions of euler equations to a weak solution of the euler equations for initial vorticity being a finite radon measure of fixed sign which includes the vortex sheets case we also show that provided the initial density of vorticity is an integrable function over the curve with respect to the arc length measure i an initially lipschitz chord arc vortex sheet curve evolving under the br equation remains lipschitz for all times ii an initially holder c1 0 1 chord arc curve remains in c1 for all times and finally iii an initially holder cn n 1 0 1 closed chord arc curve remains so for all times in all these cases the weak euler and the br descriptions of the vortex sheet motion are equivalent 2009 wiley periodicals inc

nonexistence of simple hyperbolic blow up for the quasi geostrophic equation the problem we are concerned with is whether singularities form in finite time in incompressible fluid flows it is well known that the answer is no in the case of euler and navier stokes equations in dimension two in dimension three it is still an open problem for these equations in this paper we focus on a two dimensional active scalar model for the 3d euler vorticity equation constantin majda and tabak 7 suggested by studying rigorous theorems and detailed numerical experiments a general principle if the level set topology in the temperature field for the 2d quasi geostrophic active scalar in the region of strong scalar gradients does not contain a hyperbolic saddle then no finite time singularity is possible numerical simulations showed evidence of singular behavior when the geometry of the level sets of the active scalar contain a hyperbolic saddle there is a naturally associated notion of simple hyperbolic saddle breakdown the main theorem we present in this paper shows that such breakdown cannot occur in finite time we also show that the angle of the saddle cannot close in finite time and it cannot be faster than a double exponential in time using the same techniques we see that analogous results hold for incompressible 2d and 3d euler these results were announced in 9 but with a slight difference in the definition of a simple hyperbolic saddle the definition given in section 4 generalizes the one given in the announcement see also constantin 4 discussed in section 7 remark 5 below the whole work described in this paper is basically part of the author s thesis i am particularly grateful to my thesis advisor charles fefferman for his attention support guidance and advice i am indebted to d christodoulou and p constantin for helpful corrections and suggestions i wish to thank a majda for suggesting the subject and e tabak for discussions and com

some applications of variational inequalities in nonsmooth analysis abstract in this paper we apply some results on variational inequalities to the clarke generalized gradient and the generalized second order directional derivative f x u v and obtain some variational inequalities of them

constrained multiobjective games in general topological space abstract in this paper we introduce and study a new class of constrained multiobjective games in general noncompact topological space by employing an existence theorem of quasi equilibrium problems due to this author several existence theorems of weighted nash equilibria and pareto equilibria for the constrained multiobjective games are established in noncompact topological spaces these theorems improve unify and generalize the corresponding results of the multiobjective games in recent literature

on ky fan s section theorem abstract in this paper we first give a new section theorem of ky fan type and its equivalent theorem in an h space and next as their applications we obtain some minimax theorems and a coincidence theorem

fixed points coincidence points and maximal elements with applications to generalized equilibrium problems and minimax theory abstract in this paper using a generalization of the fan browder fixed point theorem we obtain a new fixed point theorem for multivalued maps in generalized convex spaces from which we derive several coincidence theorems and existence theorems for maximal elements applications of these results to generalized equilibrium problems and minimax theory will be given in the last sections of the paper

on the existence of maximal elements fixed points and equilibria of generalized games in a fuzzy environment we give new sufficient conditions for the existence of fuzzy maximal elements fuzzy fixed points and equilibria of generalized fuzzy games in our results a key role is played by the existence of upper semicontinuous selection maps of set valued functions that we obtain for the class of generalized transfer open lower sections maps

on generalized vector equilibrium problems an existence result for a generalized vector equilibrium problem is proved in a general topological vector space as applications existence results are derived for vector equilibrium problems and vector variational like inequalities with set valued mappings under monotonicity condition and maximal monotonicity condition these results extend and unify a number of existence results for vector variational inequalities in the previous literature

equilibria and fixed points of set valued maps with nonconvex and noncompact domains and ranges abstract let c be a nonempty subset of a topological vector space e we state and prove new various fixed point theorems of fan browder type for set valued maps f c 2 e such that c f c called expansive without assuming that the sets c and f c are convex or compact or equal and e is hausdorff let k be a convex subset of e and let c be a nonempty subset of k our proofs use a technique based on the investigations of the images of maps and restated for maps f c k r of g x z yuan s results concerning the existence of equilibrium points and minimax inequalities for maps f k k r examples are provided

the algebras with discrete derived category abstract we classify the finite dimensional algebras over an algebraically closed field whose bounded derived category does not admit an infinite continuous family of pairwise non isomorphic indecomposable complexes

existence of solutions for quasi equilibrium problems in noncompact topological spaces abstract in this paper a new fan browder type fixed point theorem is proved under noncompact setting of general topological spaces by applying the fixed point theorem several new existence theorems of solutions for quasi equilibrium problems are proved under noncompact setting of topological spaces these theorems improve and generalize a number of important known results in literature

on derived hall numbers for tame quivers abstract in the present paper we study the derived hall algebra for the bounded derived category of the finite dimensional nilpotent representations of a dynkin or tame quiver over a finite field we show that for any three given objects in the bounded derived category the associated derived hall numbers are given by a rational function in the cardinalities of ground fields

front formation in an active scalar equation we study the formation of thermal fronts in an active scalar equation that is similar to the euler equation for a particular initial condition an earlier candidate for finite time blowup the front forms in a generalized self similar way with constant hyperbolicity at the center the behavior belongs to a class of scenarios for which finite time blowup is impossible a systematic exploration of many different initial conditions reveals no evidence of singular solutions copyright ital 1999 ital the american physical society

a further generalization of yannelis prabhakar s continuous selection theorem and its applications abstract in this article we first prove one improved version of the yannelis prabhakar continuous selection theorem and next as its applications a fixed point theorem in noncompact product spaces a nonempty intersection theorem some existence theorems of solutions for the generalized quasi variational inequalities and some equilibrium existence theorems for the abstract economies are given

continuous selection and fixed point theorems in this paper we obtain continuous selection theorems with range in a g convex space or in a space related to a g convex space and noncompact domain some applications to fixed point theorems and coincidence theorems are given we obtain some new results as well as generalizations of many known results

a generalization of h space and some results on multivalued mappings without convexity in this paper we introduce the concept of g h space which is a generalization of h space and a g h kkm map which unifies h kkm maps and generalized kkm maps and obtain intersection and fixed point theorems in g h space we also give applications to the existence of greatest and maximal elements for preference relations in topological spaces

a two dimensional model for quasigeostrophic flow comparison with the two dimensional euler flow abstract a simple two dimensional model for quasigeostrophic flow is contrasted with the two dimensional incompressible euler equations the model arises under the assumptions of fast rotation uniform stratification and uniform potential vorticity it is found that the more loca feed back of the quasigeostrophic model gives rise to strongly nonlinear front formation as opposed to two dimensional euler where the steepening process of mature fronts obeys a nonlocal nearly linear mechanism

system of coincidence theorems with applications in this paper we establish systems of coincidence theorems from which solution of system of inequalities and system of minimax theorems was established in this paper

interaction of four rarefaction waves in the bi symmetric class of the two dimensional euler equations the global existence and structures of solutions to multi dimensional unsteady compressible euler equations are interesting and important open problems in this paper we construct global classical solutions to the interaction of four orthogonal planar rarefaction waves with two axes of symmetry for the euler equations in two space dimensions in the case where the initial rarefaction waves are large the bi symmetric initial data is a basic type of four wave two dimensional riemann problems the solutions in this case are continuous bounded and self similar and we characterize how large the rarefaction waves must be we use the methods of hodograph transformation characteristic decomposition and phase space analysis we resolve binary interactions of simple waves in the process

on the generalized quasi variational inequality problems the purpose of this paper is to study the existence problem of solutions for some kinds of abstract generalized quasi variational inequality problems by using a new kind of fixed point approach

global well posedness of the velocity vorticity voigt model of the 3d navier stokes equations abstract the velocity vorticity formulation of the 3d navier stokes equations was recently found to give excellent numerical results for flows with strong rotation in this work we propose a new regularization of the 3d navier stokes equations which we call the 3d velocity vorticity voigt vvv model with a voigt regularization term added to momentum equation in velocity vorticity form but with no regularizing term in the vorticity equation we prove global well posedness and regularity of this model under periodic boundary conditions we prove convergence of the model s velocity and vorticity to their counterparts in the 3d navier stokes equations as the voigt modeling parameter tends to zero we prove that the curl of the model s velocity converges to the model vorticity which is solved for directly as the voigt modeling parameter tends to zero finally we provide a criterion for finite time blow up of the 3d navier stokes equations based on this inviscid regularization

on existence and essential components of the solution set for the system of vector quasi equilibrium problems abstract in this paper we study the existence and essential components of the solution set for the system of vector quasi equilibrium problems and establish some new results by defining the best reply map

fixed point and maximal element theorems with applications to abstract economies and minimax inequalities in this paper we establish some fixed point theorems for a family of multivalued maps under mild conditions by using our fixed point theorems we derive some maximal element theorems for a particular family of multivalued maps namely the condensing multivalued maps as applications of our results we prove some general equilibrium existence theorems in the generalized abstract economies with preference correspondences further applications of our results are also given to minimax inequalities for a family of functions

coincidence and maximal element theorems and their applications to generalized equilibrium problems and minimax inequalities abstract in this paper we obtain first a very general coincidence theorem from this we derive a new coincidence theorem and two alternative theorems concerning existence of maximal elements applications of these results to generalized equilibrium problems and minimax inequalities are given in the last sections

equilibria with discontinuous preferences new fixed point theorems abstract we prove new equilibrium existence results for games and economies with discontinuous and non ordered preferences to do so we introduce the notion of continuous inclusion property and prove new fixed point theorems which extend and generalize the results of fan 17 glicksberg 20 browder 7 and gale and mas colell 19 our results also extend the previous work of yannelis 47 and wu and shen 46

an inviscid regularization for the surface quasi geostrophic equation inspired by recent developments in berdina like models for turbulence we propose an inviscid regularization for the surface quasi geostrophic sqg equations we are particularly interested in the celebrated question of blowup in finite time of the solution gradient of the sqg equations the new regularization yields a necessary and sufficient condition satisfied by the regularized solution when a regularization parameter tends to 0 for the solution of the original sqg equations to develop a singularity in finite time as opposed to the commonly used viscous regularization the inviscid equations derived here conserve a modified energy therefore the new regularization provides an attractive numerical procedure for finite time blowup testing in particular we prove that if the initial condition is smooth then the regularized solution remains as smooth as the initial data for all times 2007 wiley periodicals inc

a generalization of browder s fixed point theorem with applications abstract in this paper the concept of c compact mapping is introduced a generalization of browder s fixed point theorem and some equivalence forms are given as applications the existence of solutions for some variational inequalities and monotone operator equations is discussed

generalized quasi variational inequalities in locally convex topological vector spaces abstract let e be a hausdorff topological vector space and x e an arbitrary nonempty set denote by e the dual space of e and the pairing between e and e by w x for w e and x e given a point to set map s x 2x and a point to set map t x 2e the generalized quasi variational inequality problem gqvi is to find a point y s y and a point u t y such that re u y x 0 for all x s y by using the ky fan minimax principle or its generalized version as a tool some general theorems on solutions of the gqvi in locally convex hausdorff topological vector spaces are obtained which include a fixed point theorem due to ky fan and i l glicksberg and two different multivalued versions of the hartman stampacchia variational inequality

fixed points theorems for mappings with non compact and non convex domains this note gives some fixed point theorems for lower and upper semi continuous mappings and mappings with open lower sections defined on non compact and non convex sets it will be noted that the conditions of our theorems are not only sufficient but also necessary also our theorems generalize some well known fixed point theorems such as the kakutani fixed point theorem and the brouwer schauder fixed point theorem by relaxing the compactness and convexity conditions

selecting families and their applications deguire and lassonde p deguire m lassonde familles selectantes topol methods nonlinear anal 5 1995 261 269 extend the concept of continuous selection and introduce the notion of selecting family for a family of set valued mappings in this paper we first establish a new existence theorem of selecting families the existence of the selecting families will be then used in order to obtain several fixed component theorems of fan browder type an intersection result a maximal element theorem for a family of set valued mappings and a minimax inequality

kkm and nash equilibria type theorems in topological ordered spaces abstract in this paper we obatin a generalized kkm theorem a generalized fan browder fixed theorem and an existence theorem of nash equilibria in topological ordered spaces

discrete derived categories i homomorphisms autoequivalences and t structures discrete derived categories were studied initially by vossieck j algebra 243 168 176 2001 and later by bobinski et al cent eur j math 2 19 49 2004 in this article we describe the homomorphism hammocks and autoequivalences on these categories we classify silting objects and bounded t structures

hall algebras associated to triangulated categories by counting triangles and applying the octahedral axiom we find a direct way to prove the formula of toen in t section 5 1 for a triangulated category satisfying the left homological finiteness condition

derived hall algebras the purpose of this work is to define a derived hall algebra mathcal dh t associated to any dg category t under some finiteness conditions our main theorem states that mathcal dh t is associative and unital it is shown that mathcal dh t contains the usual hall algebra mathcal h t when t is an abelian category we will also prove an explicit formula for the derived hall numbers purely in terms of invariants of the triangulated category associated to t as an example we describe the derived hall algebra of an hereditary abelian category