on fuzzy linear representations of finite groups abstract a linear representation of a finite group g in a finite dimensional vector space v induces through zadeh s extension principle a function 9 from igto into igl v where gl v is the group of all linear automorphisms of v if w is a fuzzy subspace of v the group of all fuzzy linear automorphisms of w gl w is a subgroup of gl v w is said to be stable under the action of a fuzzy subgroup a of g if 9 a is a subset of gl w i e 9 a is zero at every f inside gl v and outside gl q if w is stable under the action of a then its support subspace is stable under the action of the support subgroup of a in the crisp sense finally we show that if there are two stable fuzzy subspaces one of them is contained in the other then the smaller one has a fuzzy direct summand in the bigger which is also a stable fuzzy subspace

cauchy problems for fractional differential equations with riemann liouville fractional derivatives abstract in this paper we are concerned with cauchy problems of fractional differential equations with riemann liouville fractional derivatives in infinite dimensional banach spaces we introduce the notion of fractional resolvent obtain some its properties and present a generation theorem for exponentially bounded fractional resolvents moreover we prove that a homogeneous order cauchy problem is well posed if and only if its coefficient operator is the generator of an order fractional resolvent and we give sufficient conditions to guarantee the existence and uniqueness of weak solutions and strong solutions of an inhomogeneous order cauchy problem

boundary feedback stabilization for an unstable time fractional reaction diffusion equation in this paper we consider boundary feedback stabilization for unstable time fractional reaction diffusion equations new state feedback controls with actuation on one end are designed by the backstepping method for both dirichlet and neumann boundary controls by the riesz basis approach and the fractional lyapunov method we prove the existence and uniqueness and the mittag leffler stability for the closed loop systems for both cases the observers and the observer based output feedback are designed to stabilize the systems

relaxation in nonconvex optimal control problems described by fractional differential equations abstract we consider the minimization problem of an integral functional with integrand that is not convex in the control on solutions of a control system described by fractional differential equation with mixed nonconvex constraints on the control a relaxation problem is treated along with the original problem it is proved that under general assumptions the relaxation problem has an optimal solution and that for each optimal solution there is a minimizing sequence of the original problem that converges to the optimal solution with respect to the trajectory the control and the functional in appropriate topologies simultaneously

approximate controllability of fractional nonlocal delay semilinear systems in hilbert spaces we study the existence and approximate controllability of a class of fractional nonlocal delay semilinear differential systems in a hilbert space the results are obtained by using semigroup theory fractional calculus and schauder s fixed point theorem multi delay controls and a fractional nonlocal condition are introduced furthermore we present an appropriate set of sufficient conditions for the considered fractional nonlocal multi delay control system to be approximately controllable an example to illustrate the abstract results is given

finsler metrics and kobayashi hyperbolicity of the moduli spaces of canonically polarized manifolds we show that the base complex manifold of an eectively parametrized holomorphic family of compact canonically polarized complex manifolds admits a smooth invariant finsler metric whose holomorphic sectional curvature is bounded above by a negative constant as a consequence we show that such a base manifold is kobayashi hyperbolic

generating properties of fuzzy algebraic structures abstract an axiomatic approach is taken to the concept of fuzzy generators for fuzzy subspaces fuzzy field extensions and fuzzy subgroups the fundamental generating properties necessary to yield fuzzy bases and uniqueness of their cardinalities for these structures are given

approximate controllability of fractional evolution systems with riemann liouville fractional derivatives in this paper we deal with the control systems governed by fractional evolution differential equations involving riemann liouville fractional derivatives in banach spaces our main purpose in this article is to establish suitable assumptions to guarantee the existence and uniqueness results of mild solutions under these conditions the approximate controllability of the associated fractional evolution systems involving riemann liouville fractional derivatives is formulated and proved

existence theorems of global solutions for nonlinear volterra type integral equations in banach spaces in this paper first a new fixed point theorem is established and then by the use of it the existence theorems of global solutions for nonlinear volterra type integral equations in banach spaces are investigated the results obtained in this paper generalize and improve the results corresponding to those obtained by others

a fractional differential equation for a mems viscometer used in the oil industry a mathematical model is developed for a micro electro mechanical system mems instrument that has been designed primarily to measure the viscosity of fluids that are encountered during oil well exploration it is shown that in one mode of operation the displacement of the device satisfies a fractional differential equation fde the theory of fdes is used to solve the governing equation in closed form and numerical solutions are also determined using a simple but efficient central difference scheme it is shown how knowledge of the exact and numerical solutions enables the design of the device to be optimised it is also shown that the numerical scheme may be extended to encompass the case of a nonlinear spring where the resulting fde is nonlinear

bases of fuzzy algebraic substructures abstract an axiomatic approach is developed concerning the existence of a basis for certain fuzzy algebraic substructures let the set of truth values be a complete brouwerian lattice l let g be an abelian group we show that there exists an l subgroup of g which does not have a p basis even if g is finite let f be a field of characteristic p 0 and let a b be l subfields of f such that a b we show there exists an intermediate l subfield of a b which does not have a relative p basis over b even if f has finite relative imperfection degree over the support of b when l 0 1 we show that every fuzzy subgroup of g with the sup property has a p basis and that every intermediate fuzzy subfield of a b with the sup property has a relative p basis if certain compatibility conditions hold

existence results for fractional order semilinear functional differential equations with nondense domain abstract in this paper we establish sufficient conditions for existence and uniqueness of solutions for some nondensely defined semilinear functional differential equations involving the riemann liouville derivative our approach is based on integrated semigroup theory the banach contraction principle and the nonlinear alternative of leray schauder type

mild solutions to the time fractional navier stokes equations in r n abstract this paper addresses the existence and uniqueness of mild solutions to the navier stokes equations with time fractional differential operator of order 0 1 several interesting properties about the solution are also highlighted like regularity and decay rate in lebesgue spaces which will depend on the fractional exponent moreover it is shown that the l p exponent range which the solution belongs to is different from the range for the solution of the classical problem with 1

approximate controllability of fractional order semilinear systems with bounded delay abstract in this paper sufficient conditions are established for the approximate controllability of a class of semilinear delay control systems of fractional order the existence and uniqueness of mild solution of the system is also proved the results are obtained by using contraction principle and the schauder fixed point theorem some examples are given to illustrate the theory

on a solution to fractional order integrodifferential equations with analytic semigroups abstract in this paper we study a class of fractional order integrodifferential equations considered in an arbitrary banach space using the theory of analytic semigroups we establish the existence uniqueness and regularity of a mild solution to these fractional order integrodifferential equations

existence of mild solutions for fractional neutral evolution equations abstract in this paper by using the fractional power of operators and some fixed point theorems we discuss a class of fractional neutral evolution equations with nonlocal conditions and obtain various criteria on the existence and uniqueness of mild solutions in the end we give an example to illustrate the applications of the abstract results

approximate controllability of second order distributed implicit functional systems abstract in this paper we study the approximate controllability of control systems with states and controls in hilbert spaces and described by a second order semilinear abstract functional differential equation with infinite delay initially we establish a characterization for the approximate controllability of a second order abstract linear system and in the last section we compare the approximate controllability of a semilinear abstract functional system with the approximate controllability of the associated linear system

nonexistence results for a class of fractional elliptic boundary value problems abstract in this paper we study a class of fractional elliptic problems of the form s u f x u in u 0 in r n where s 0 1 we prove nonexistence of positive solutions when is star shaped and f is supercritical we also derive a nonexistence result for subcritical f in some unbounded domains the argument relies on the method of moving spheres applied to a reformulated problem using the caffarelli silvestre extension caffarelli and silvestre 2007 11 of a solution of the above problem

fuzzy ideals and fuzzy subalgebras of lie algebras abstract a fuzzy idea l of a lie algebra l factors it into a lie algebra l l called a fuzzy quotient lie algebra this fuzzy algebra lie algebra is always a fuzzy partition of l and a fuzzy partition of l will be a fuzzy quotient lie algebra if and only if its associated fuzzy similarity relation is compatible with the lie algebra operations relationship between the operations of the lie algebras l i t and zadeh s extension principle are studied we also study homomorphisms of lie algebras and the relationship between them and fuzzy ideals and fuzzy subalgebras of the domains and the co domains of these homomorphisms finally solvability of fuzzy ideals and studied in defining these solvable fuzzy ideals we use zadeh s extension principle

fuzzy linear and affine spaces abstract elementary properties of fuzzy linear and affine spaces are studied the concept of a basis for a fuzzy linear space is defined and an algorithm for computing a basis when the underlying space is finite dimensional is given

the adjoint representation of fuzzy lie algebras the commutator of a lie algebra l is extended by zadeh s extension principle to a product of fuzzy subsets a fuzzy subspace generated by the product of two fuzzy ideals is also a fuzzy ideal this notion of product of fuzzy ideals is used to define the descending central series of a fuzzy ideal nilpotency of fuzzy ideals is introduced using this descending central series fuzzification of the adjoint representation of lie algebras is introduced and some relations between this representation and nilpotent fuzzy ideals are proved finally the killing form in the fuzzy case is defined and some of its properties are studied

kodaira dimension and zeros of holomorphic one forms we show that every holomorphic one form on a smooth complex projective variety of general type must vanish at some point the proof uses generic vanishing theory for hodge modules on abelian varieties

approximate controllability of fractional nonlinear differential inclusions fractional differential equations have wide applications in both physical and social sciences this paper addresses the issue of approximate controllability for a class of fractional nonlinear differential inclusions in banach spaces a new set of sufficient conditions are formulated and proved for the approximate controllability of fractional nonlinear differential inclusions in particular the results are established with the assumption that the associated linear part of system is approximately controllable further the result is extended to obtain the conditions for the solvability of controllability results for fractional inclusions with nonlocal conditions finally an example is presented to illustrate the theory of the obtained result

controllability of a backward fractional semilinear differential equation abstract in this paper we study the approximate controllability of a fractional semilinear differential equation involving the right fractional caputo derivative more precisely we construct by means of tikhonov type regularization method the controllability operator then under certain condition on this operator we obtain that the associate backward fractional linear system can be steered to an arbitrary small neighborhood of the state at initial time this allows us to prove the approximate controllability of the semilinear system

existence of the mild solution for fractional semilinear initial value problems abstract in this paper we will study the existence and uniqueness of mild solution for the semilinear initial value problem of non integer order u t a u t f t u t g u t s u t where 0 1 and f t u t g u t s u t is a given function

the existence of mild solutions for impulsive fractional partial differential equations abstract this paper is concerned with the existence of mild solutions for a class of impulsive fractional partial semilinear differential equations some errors in mophou 2010 2 are corrected and some previous results are generalized

fuzzy daniell integral ii abstract in our earlier paper we introduced the concept of a fuzzy daniell functional in this paper integrable class of fuzzy points are studied it is also proved that can be extended to the class of all fuzzy integrable fuzzy points and that the integrable class of fuzzy points is a vector lattice

fractional cauchy problems with almost sectorial operators this paper concerns the abstract cauchy problem of fractional evolution equations with almost sectorial operators the suitable mild solutions of evolution equations with riemann liouville derivative and caputo derivative are introduced respectively the existence theorems of mild solutions of cauchy problems are established the results obtained here improve and generalize some known results finally an example is given for demonstration

degenerate type fractional evolution hemivariational inequalities and optimal controls via fractional resolvent operators in this paper we mainly investigate controlled fractional evolution hemivariational inequalities of degenerate type in caputo and riemann liouville fractional derivatives of order in 1 2 respect

families over a base with a birationally nef tangent bundle mathematicssubjectclassi cation 1991 14j10 14d99itisawell knownconsequenceofthetorellitheoremthatasmoothprojec tivefamilyofcurvesofgenusatleast2overaprojectiverationalorellipticcurveisisotrivial thatis the bresofthefamilyareisomorphic sincetheautomorphismgroupofacurveofgenusatleast2is nite thisalsoimpliesthatthefamilybecomestrivialaftera nitebasechange the above statement was generalized for smooth projective families ofminimalsurfacesofgeneraltypein migliorini95 andforsmoothprojec tivefamiliesofvarieties ofarbitrarydimension withamplecanonicalbundlein kov acs96 botharticlesstudiedfamiliesovercurves theaimofthisarticleistopresentafurthergeneralization namelyletthebaseofthefamilyhavearbitrarydimension 0 1theorem 4 2theorem letf x s beasmoothmorphismofpro jectivealgebraicvarietiessuchthatthecanonicalbundleofevery breoffisample assumethats isbirationaltoans

analytical fuzzy plane geometry iii in this study we attempt to construct fuzzy circles in a fuzzy geometrical plane we provide a comprehensive study where we find a fuzzy number with a predetermined fuzzy distance from a given fuzzy number we formulate fuzzy circles using the conventional basic definitions of crisp circles two different formulations of fuzzy circles are proposed which depend on the information known about a fuzzy circle the interrelations between the evaluated fuzzy circles are investigated we show that the center of a fuzzy circle may not be a fuzzy point however the radius of a fuzzy circle that passes through three given fuzzy points is always a fuzzy number the concepts of same and inverse points and a fuzzy number along a line are used to define and analyze the proposed ideas our discussions and studies are supported by suitable numerical and pictorial examples

on recent developments in the theory of abstract differential equations with fractional derivatives abstract this note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives we show that the existence results in agarwal et al 2009 1 belmekki and benchohra 2010 2 darwish et al 2009 3 hu et al 2009 4 mophou and n guerekata 2009 6 7 mophou 2010 8 9 muslim 2009 10 pandey et al 2009 11 rashid and el qaderi 2009 12 and tai and wang 2009 13 are incorrect since the considered variation of constant formulas is not appropriate in this note we also consider a different approach to treat a general class of abstract fractional differential equations

families of canonically polarized varieties over surfaces shafarevich s hyperbolicity conjecture asserts that a family of curves over a quasi projective 1 dimensional base is isotrivial unless the logarithmic kodaira dimension of the base is positive more generally it has been conjectured by viehweg that the base of a smooth family of canonically polarized varieties is of log general type if the family is of maximal variation in this paper we relate the variation of a family to the logarithmic kodaira dimension of the base and give an affirmative answer to viehweg s conjecture for families parametrized by surfaces

approximate controllability of a delayed semilinear control system with growing nonlinear term abstract this paper deals with the approximate controllability of a semilinear control system with delay where the nonlinear term satisfies the linear growth condition sufficient conditions for the approximate controllability of a semilinear control system have been established by assuming that the corresponding linear control system with delay is approximately controllable to prove our results the schauder fixed point theorem is applied and instead of a co semigroup associated with the mild solution of the system we use the so called fundamental solution

existence and uniqueness of mild solutions to impulsive fractional differential equations this paper is concerned with the existence and uniqueness of a mild solution to impulsive fractional semilinear differential equations the results are obtained by means of fixed point methods we also give an example of such problems

the set of fuzzy points of a fuzzy vector lattice is not a vector lattice abstract samuel introduced the notions of fuzzy vector lattices and fuzzy points of fuzzy vector lattices he considered unique extensions of fuzzy daniell integrals i e positive linear order continuous maps defined on sets of fuzzy points to spaces that behave like l 1 spaces his arguments hinge on the fact that sets of fuzzy points of a fuzzy vector lattice form vector lattices we show by means of a counter example that the set of fuzzy points of a fuzzy vector lattice does not form a vector lattice consequently samuel s fuzzy daniell integrals need not be linear

controllability of fractional evolution nonlocal impulsive quasilinear delay integro differential systems in this work the controllability result of a class of fractional evolution nonlocal impulsive quasilinear delay integro differential systems in a banach space has been established by using the theory of fractional calculus fixed point technique and also we introduced a new concept called a u resolvent family as an application that illustrates the abstract results an example is given

on the approximate controllability of semilinear fractional differential systems fractional differential equations have wide applications in science and engineering in this paper we consider a class of control systems governed by the semilinear fractional differential equations in hilbert spaces by using the semigroup theory the fractional power theory and fixed point strategy a new set of sufficient conditions are formulated which guarantees the approximate controllability of semilinear fractional differential systems the results are established under the assumption that the associated linear system is approximately controllable further we extend the result to study the approximate controllability of fractional systems with nonlocal conditions an example is provided to illustrate the application of the obtained theory

fuzzy topological vector spaces ii abstract some of the properties of fuzzy topological vector spaces are investigated also there are given necessary and sufficient conditions for a family of fuzzy sets in a vector space e to be the family of all neighborhoods of zero for a fuzzy linear topology

abstract fractional cauchy problems with almost sectorial operators abstract of concern are the cauchy problems for linear and semilinear time fractional evolution equations involving in the linear part a linear operator a whose resolvent satisfies the estimate of growth 1 0 in a sector of the complex plane which occurs when one considers for instance the partial differential operators in the limit domain of dumb bell with a thin handle or in the space of holder continuous functions by constructing a pair of families of operators in terms of the generalized mittag leffler type functions and the resolvent operators associated with a for the first time and a deep analysis on the properties for these families we obtain the existence and uniqueness of mild solutions and classical solutions to the cauchy problems moreover we present three examples to illustrate the feasibility of our results

on the brody hyperbolicity of moduli spaces for canonically polarized manifolds we show that the moduli stack mh of canonically polarized complex manifolds with hilbert polynomial h is brody hyperbolic hence if mh denotes the corresponding coarse moduli scheme and if u mh is a quasi finite morphism induced by a family then there are no nonconstant holomorphic maps c u

semilinear fractional integro differential equations with compact semigroup abstract in this paper we study the local and global existence of mild solutions to a class of fractional integro differential equations in an arbitrary banach space associated with operators generating compact semigroup on the banach space

free fuzzy modules and their bases abstract the notions of a basis for fuzzy modules and of a free fuzzy module are defined and the elementary properties of both are studied it is shown that a fuzzy module possesses a basis if and only if it is free results on the existence of a basis are obtained

bases of fuzzy vector spaces abstract let v be a vector space over a field f let a be a fuzzy subspace of v over f we give sufficient conditions for a to have a basis over a fuzzy subfield k of f we also show that if a has the sup property then a has a fully free basis over f but not necessarily a fully free basis over k

nonlocal initial value problems for differential equations with hilfer fractional derivative in this paper we discuss the existence of solutions to nonlocal initial value problem for differential equations with hilfer fractional derivative to begin with we establish an equivalent mixed type integral equation for our problem then we utilize basic properties of hilfer fractional calculus and fixed point methods to derive three fundamental existence results in the weighted space of continuous functions some examples are given to illustrate our results

controllability of semilinear control systems dominated by the linear part while various equivalent conditions for controllability have been obtained in the case of linear control systems controllability problems of semilinear control systems usually require some complicated and limited assumptions in this paper we show the approximate controllability of an abstract semilinear control system under the assumption which has a simple form and can be easily checked in many examples

on fuzzy bases of vector spaces abstract in this paper the concept of fuzzy basis of fuzzy vector space is studied the criterion for existence of fuzzy basis is proved any countable dimensional space has a fuzzy basis there are spaces without fuzzy basis

on pseudo fuzzy linear mappings in this paper we study a more general class of linear maps on fuzzy subsets of vector spaces than those on fuzzy subspaces we obtain a version of the fundamental theorem of homomorphisms which applies to these pseudo fuzzy linear maps in the case of fuzzy subspaces the results become those for fuzzy linear maps we introduce the notion of magnification of pseudo fuzzy linear mappings it is shown that this notion behaves well with respect to the fundamental theorem and with respect to the composition of mapping we note that the class of distribution functions of random variables naturally produces pseudo fuzzy linear mappings which are not fuzzy linear mappings we observe that pseudo fuzzy linear mappings are examples of gain relations we consider general properties of these relations as well as many other examples from these results additional properties of pseudo fuzzy linear mappings are obtained