For a continuous complex-valued function g on the real line without zeros, several notions of a mean winding number are introduced. We give necessary conditions for a Toeplitz operator with matrix-valued symbol G to be semi-Fredholm in terms of mean winding numbers of detG. The matrix function G is assumed to be continuous on the real line, and no other apriori assumptions on it are made.

We show the existence result of viable solutions to the differential inclusion ẋ(t) ∈ G(x(t)) + F (t, x(t)) x(t) ∈ S on [0, T ], where F : [0, T ] × H → H (T > 0) is a continuous set-valued mapping, G : H → H is a Hausdorff upper semi-continuous set-valued mapping such that G(x) ⊂ ∂g(x), where g : H → R is a regular and locally Lipschitz function and S is a ball, compact subset in a separable H...

In this paper, we study stability and linearization of multivalued nonlinear feedback shift registers which are considered as logic networks. First, the linearization of multi-valued nonlinear feedback shift registers (NFSRs) is discussed, which is to find their state transition matrices by considering it as a logical network via a semi-tensor product approach. For a multi-valued NFSR, the new ...

We associate a 3-manifold to a multiple valued semi-conformal mapping on the 3-sphere and study the branching set of the corresponding covering projection. Some remarkable geometric structures occur.

In this paper, we define Some domination parameters on IVIFG and derive some relations and then verify by using Interval valued intuitionistic fuzzy graphs and discussed some properties. Also, we introduced Immoderate semi-complete IVIFG and its properties.

We use graph convergence of set valued maps to show the existence of an equilibrium for an abstract economy without assuming the lower semi continuity of the constraint maps.

In this paper‎, ‎we introduce and study some new single-valued gap functions for non-differentiable semi-infinite multiobjective optimization problems with locally Lipschitz data‎. ‎Since one of the fundamental properties of gap function for optimization problems is its abilities in characterizing the solutions of the problem in question‎, ‎then the essential properties of the newly introduced ...

In this paper we introduce a new method for manufacturing complex valued harmonic morphisms from semi-Riemannian manifolds. This is employed to yield a variety of new examples from the compact Riemannian Lie groups SO(n), SU(n), Sp(n). We then develop a duality principle and show how this can be used to construct the first known examples of harmonic mor-phisms from the non-compact semi-Riemanni...

Let us introduce n pairs of random variables (Xi, Yi)i=1,...,n that we suppose drawn from the pair (X,Y ), valued in F × IR, where F is a semi-metric space. Let d denotes the semi-metric. Assume that there exists a regular version of the conditional probability of Y given X , which is absolutely continuous with respect to Lebesgue measure on IR and has bounded density. Assume that for a corresp...