We develop two generalizations of contraction theory, namely, semi-contraction and weak-contraction theory. First, using the notion seminorm, we propose a geometric framework for introduce matrix semimeasures characterize their properties. show that spectral abscissa is infimum over weighted semimeasures. For dynamical systems, use semimeasure Jacobian to contractivity properties trajectories. ...

This paper will propose modifications to the current ISO C++ Memory Model [ISOMM] to efficiently support a wider group of machine architectures, in particular those that support relaxed memory consistency models. Our model provides three forms of standalone memory fences which, when combined with unordered atomic operations, allow the programmer to represent arbitrarily complex ordered atomic o...

The main aim of this paper is to introduce and study some fixed point results for rational multivalued G-contraction F-Khan-type contraction mappings on a metric space with graph. At the end, we give an illustrative example.

In this paper, a concept of monotone generalized contraction in partially ordered metric spaces is introduced and some fixed point and common fixed point theorems for the so-called weak contractions are proved. The concept of weak contraction was introduced by Kada, Suzuki and Takahashi [Math. Japonica, 44 (1996), 381-391], in connection to the concept of w-distance on a metric space. The resul...

Given a row contraction of operators on Hilbert space and a family of projections on the space which stabilize the operators, we show there is a unique minimal joint dilation to a row contraction of partial isometries which satisfy natural relations. For a fixed row contraction the set of all dilations forms a partially ordered set with a largest and smallest element. A key technical device in ...

Let M = 〈M,<,+, . . .〉 be a weakly o-minimal expansion of an ordered group. This paper has two parts. In the rst part, we introduce the notion of M having no external limits and use it to prove that a large collection of non-valuational structures M do not admit de nable Skolem functions. In the second part, we provide an alternative characterization of the canonical o-minimal completion from [...

We report a novel transient instability upon temperature quench in weakly ordered block copolymer microphases possessing a soft direction or directions, such as the lamellar and hexagonal cylinder ~HEX! phases. We show that reequilibration of the order parameter is accompanied by transient long wavelength undulation of the layers or cylinders—with an initial wavelength that depends on the depth...