By exploiting his recent results, the author further investigates the extent to which variation in the coefficients of a unitary convex decomposition of a vector in a unital JB∗-algebra permits the vector decomposable as convex combination of fewer unitaries; certain C∗-algebra results due to M. Rørdam have been extended to the general setting of JB∗-algebras.

It is proved that every doubly stochastic quantum channel that is properly averaged with the completely depolarizing channel can be written as a convex combination of unitary channels. As a consequence, we find that the collection of channels expressible as convex combinations of unitary channels has non-zero Borel measure within the space of doubly stochastic channels.

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

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In this paper we analyze the nature of Shafer’s belief functions as geometric entities. We focus on the geometric behavior of Dempster’s rule of combination in the context of the belief space, i.e. the set of all the admissible belief functions defined over a given finite domain. After showing how convex closure and orthogonal sum commute in the belief space and introducing the concept of condi...

the aim of this paper is to prove some inequalities for p-valent meromorphic functions in thepunctured unit disk δ* and find important corollaries.

this paper undertakes the synthesis of a logic-based switching h2/h∞ state-feedback controller for continuous-time lti singular perturbation systems. our solution achieves a minimum bound on the h2 performance level, while also satisfying the h∞ performance requirements. the proposed hybrid control scheme is based on a fuzzy supervisor managing the combination of two controllers. a convex lmi-b...

This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the average of an exponential function of the codeword length and the average redundancy. This framework encompasses as a special case several criteria previousl...

The Tensor Product (TP) model transformation is a recently proposed technique for transforming given Linear Parameter Varying (LPV) models into polytopic model form, namely, to parameter varying convex combination of Linear Time Invariant (LTI) models. The main advantage of the TP model transformation is that the Linear Matrix Inequality (LMI) based control design frameworks can immediately be ...

A fundamental problem in geometry processing is that of expressing a point inside a convex polyhedron as a combination of the vertices of the polyhedron. Instances of this problem arise often in mesh parameterization and 3D deformation. A related problem is to express a vector lying in a convex cone as a non-negative combination of edge rays of this cone. This problem also arises in many applic...