calculus for interval valued functions using generalized hukuhara derivative and applications this paper is devoted to studying differential calculus for interval valued functions by using the generalized hukuhara differentiability which is the most general concept of differentiability for interval valued functions conditions examples and counterexamples for limit continuity integrability and differentiability are given special emphasis is set to the class f t c g t where c is an interval and g is a real function of a real variable here the emphasis is placed on the fact that f and g do not necessarily share their properties underlying the extra care that must be taken into account when dealing with interval valued functions two applications of the obtained results are presented the first one determines a delta method for interval valued random elements in the second application a new procedure to obtain solutions to an interval differential equation is introduced our results are relevant to fuzzy set theory because the usual fuzzy arithmetic extension functions and mathematical analysis are done on a cuts which are intervals

differentiability of multivalued functions on time scales and applications to multivalued dynamic equations abstract in this paper a class of new derivatives of multivalued functions on a time scale called the hukuhara hilger derivative suited to our study of multivalued dynamic equations is developed moreover some corresponding properties of the hukuhara hilger derivative are discussed the proposed approach forms the appropriate environment within which the study of multivalued dynamic inclusions on time scales can be developed a first example of multivalued dynamic equations is included

weak solutions of set valued stochastic differential equations abstract the paper is devoted to the existence of weak solutions of set valued stochastic differential equations such equations were considered in the authors paper 22 where existence and uniqueness of strong solutions have been investigated now apart from the existence of weak solutions the weak compactness in distribution of the set of all weak solutions of set valued stochastic differential equations is considered

set valued functions in frechet spaces continuity hukuhara differentiability and applications to set differential equations abstract the set k c f of compact convex subsets of a frechet space f is studied in detail and is realized as a projective limit of metric spaces the notion of hausdorff metric on it is replaced by a family of corresponding semi metrics which provide the necessary background for the support of continuity and lipschitz continuity finally the notion of hukuhara derivative suited to our study is developed the proposed approach forms the appropriate environment within which the study of set differential equations for frechet spaces can be developed a first example on r is included

coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces abstract we introduce the concept of a mixed g monotone mapping and prove coupled coincidence and coupled common fixed point theorems for such nonlinear contractive mappings in partially ordered complete metric spaces presented theorems are generalizations of the recent fixed point theorems due to bhaskar and lakshmikantham t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal tma 65 2006 1379 1393 and include several recent developments

two dimensional gauge theories of the symmetric group s n in the large n limit we study the two dimensional gauge theory of the symmetric group s n describing the statistics of branched n coverings of riemann surfaces we consider the theory defined on the disc and on the sphere in the large n limit a non trivial phase structure emerges with various phases corresponding to different connectivity properties of the covering surface we show that any gauge theory on a two dimensional surface of genus zero is equivalent to a random walk on the gauge group manifold in the case of s n one of the phase transitions we find can be interpreted as a cutoff phenomenon in the corresponding random walk a connection with the theory of phase transitions in random graphs is also pointed out finally we discuss how our results may be related to the known phase transitions in yang mills theory we discover that a cutoff transition occurs also in two dimensional yang mills theory on a sphere in a large n limit where the coupling constant is scaled with n with an extra log n compared to the standard t hooft scaling

the interrelation between stochastic differential inclusions and set valued stochastic differential equations abstract in this paper we connect the well established theory of stochastic differential inclusions with a new theory of set valued stochastic differential equations solutions to the latter equations are understood as continuous mappings taking on their values in the hyperspace of nonempty bounded convex and closed subsets of the space l 2 consisting of square integrable random vectors we show that for the solution x to a set valued stochastic differential equation corresponding to a stochastic differential inclusion there exists a solution x for this inclusion that is a l 2 continuous selection of x this result enables us to draw inferences about the reachable sets of solutions for stochastic differential inclusions as well as to consider the viability problem for stochastic differential inclusions

martingale problem to stratonovich stochastic inclusion abstract in the paper we consider a martingale problem approach to stratonovich stochastic inclusion the proposed method enables us to investigate both the existence and topological properties of the set of weak solutions to such inclusions

second type hukuhara differentiable solutions to the delay set valued differential equations abstract in this paper we consider the delay set valued differential equations with a recently introduced notion of a second type hukuhara derivative under condition that the right hand side of the equation is lipschitzian in the functional variable we obtain the existence and uniqueness of the solution to such the equations some properties of the solutions are established existence of at least one solution is also proved application of the second type hukuhara differentiability concept to the problems of set valued differential equations implies that the diameter of the solution values is a function nonincreasing in time

properties of set valued integrals and set valued stochastic equations driven by two parameter martingales abstract in the paper we study properties of aumann s stochastic integral driven by a two parameter increasing process and set valued ito s integral with respect to the two parameter martingale both types of integrals are understood as set valued processes next the existence uniqueness and convergence properties of solutions to set valued stochastic integral equations with respect to such integrators are investigated we present new types of such equations that generalize those studied earlier the results obtained in the paper present a set valued counterpart dealing with this topic known both in single valued deterministic and stochastic cases

some results on sheaf solutions of sheaf set control problems abstract in this paper we study the existence and some properties of solutions of the so called set control differential equations scde and sheaf solutions of sheaf set control problems

stability criteria for set dynamic equations on time scales very recently a new theory known as set dynamic equations on time scales has been built in this paper notions of stability for the solutions of set dynamic equations on time scales using lyapunov like functions are considered criteria for the equistability equiasymptotic stability uniform and uniform asymptotic stability are developed

complex matrix models and statistics of branched coverings of 2d surfaces we present a complex matrix gauge model defined on an arbitrary two dimensional orientable lattice we rewrite the model s partition function in terms of a sum over representations of the group u n the model solves the general combinatorial problem of counting branched covers of orientable riemann surfaces with any given fixed branch point structure we then define an appropriate continuum limit allowing the branch points to freely float over the surface the simplest such limit reproduces two dimensional chiral u n yang mills theory and its string description due to gross and taylor

the enestrom kakeya theorem encounters the theory of orthogonal polynomials on the unit circle abstract a classical result due to enestrom and kakeya gives some bounds for the moduli of the zeros of polynomials having a monotone sequence of non negative real coefficients the main subject of the present paper is a study of this fact with a view to the recurrence relations fulfilled by systems of orthogonal polynomials on the unit circle in particular we will be interested in the special case where the zeros of the polynomials in question are not located on the boundary of the estimate which occurs in the enestrom kakeya theorem among other things we will give characterizations of this case in terms of orthogonal polynomials and present an alternative approach to a well known characterization due to hurwitz furthermore we will give some insight how one can apply the main results of this paper in the context of positive hermitian toeplitz matrices

nonlinear variation of parameters formula for set differential equations in a metric space nonlinear variation of parameters formula for set differential equations in a metric space is developed investigating necessary tools such as differentiability of solutions relative to initial values other needed results are also proven

set valued stochastic integral equations driven by martingales abstract we consider a notion of set valued stochastic lebesgue stieltjes trajectory integral and a notion of set valued stochastic trajectory integral with respect to martingale then we use these integrals in a formulation of set valued stochastic integral equations the existence and uniqueness of the solution to such the equations is proven as a generalization of set valued case results we consider the fuzzy stochastic trajectory integrals and investigate the fuzzy stochastic integral equations driven by bounded variation processes and martingales

on set differential equations in banach spaces a second type hukuhara differentiability approach in this paper we consider set differential equations in banach spaces and with the second type hukuhara derivative we show that a sequence of successive approximations converges uniformly to a unique local solution of a cauchy problem some comparison results are formulated and a continuity of solution with respect to equation data is shown the existence of a global solution is also established

on the enestrom kakeya theorem abstract a classical result of enestrom and kakeya if a n a n 1 a 0 0 then for z 1 n k 0 a k z k 0 is extended to polynomials whose coefficients satisfy the condition t n a n t n 1 a n 1 t 1 a 1 t a t 1 a 1 ta 1 a 0 for some t 0 and 0 n

phase spaces and periodic solutions of set functional dynamic equations with infinite delay abstract very recently a new theory known as set dynamic equations on time scales has been built in this paper a phase space is built for set functional dynamic equations with infinite delay on time scales and sufficient criteria are established for the existence of periodic solutions of such equations which generalize and incorporate as special cases some known results for set differential equations and for set difference equations when the time scale is the real number set or the integer set respectively moreover for differential inclusions and difference inclusions if the variable under consideration is a single valued mapping our results show that one can unify the study of some continuous or discrete problems in the sense of set dynamic equations on general time scales

inverse problems for positive hermitian block toeplitz matrices and nondegenerate schur sequences abstract using the concrete structure of the arov krein resolvent matrices connected with the matricial versions of the classical interpolation problems of schur and caratheodory several inverse problems are treated in this way former results of gohberg and lerer who studied the problem of determining a positive hermitian block toeplitz matrix given the first block column or the last block row of its inverse are extended in various directions moreover a new type of inverse problems for nondegenerate schur sequences is considered

on connections between stochastic differential inclusions and set valued stochastic differential equations driven by semimartingales abstract in the paper we study properties of solutions to stochastic differential inclusions and set valued stochastic differential equations with respect to semimartingale integrators we present new connections between their solutions in particular we show that attainable sets of solutions to stochastic inclusions are subsets of values of multivalued solutions of certain set valued stochastic equations we also show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set valued stochastic equation the results obtained in the paper generalize results dealing with this topic known both in deterministic and stochastic cases

interval cauchy problem with a second type hukuhara derivative in this paper we consider interval differential equations such the equations can be appropriate in modeling of dynamical systems under presence of uncertainty of parameters we study an interval initial value problem with a second type hukuhara derivative by an example of real world application we indicate the advantages of the usage of such a kind of interval valued derivative a continuous dependence of the solution on initial value and right hand side of the equation is shown the existence of approximate local solutions is proven and then it is used in the derivation of existence of at least one local solution to interval cauchy problem with second type hukuhara derivative the compactness of solutions set is also stated finally the explicit formulae for local solutions to linear interval differential equations are provided

set valued and fuzzy stochastic differential equations driven by semimartingales abstract in the paper we present set valued and fuzzy stochastic integrals with respect to semimartingale integrators as well as their main properties then we study the existence of solutions to set valued and fuzzy set valued stochastic differential equations driven by semimartingales the stability of solutions is also established

differentiable selections of multifunctions and their applications abstract in the paper we present some selection properties of differentiable multifunctions next we introduce the definition of a set valued stratonovich stochastic integral finally using selection properties of differentiable multifunctions we discuss the existence of weak solutions to stochastic inclusions with respect to such an integral

general change of variable formulas for semimartingales in one and finite dimensions a general one dimensional change of variables formula is established for continuous semimartingales which extends the famous meyer tanaka formula the inspiration comes from an application arising in stochastic finance theory for functions mapping n to a general change of variables formula is established for arbitrary semimartingales where the usualc2 hypothesis is relaxed

fixed point theorems in partially ordered metric spaces and applications abstract we prove a fixed point theorem for a mixed monotone mapping in a metric space endowed with partial order using a weak contractivity type of assumption besides including several recent developments our theorem can be used to investigate a large class of problems as an application we discuss the existence and uniqueness of solution for a periodic boundary value problem