We prove that a homogeneous Banach space B on the unit circle T can be embedded as a closed subspace of a dual space ΞB contained in the space of bounded Borel measures on T in such a way that the map B → ΞB defines a bijective correspondence between the class of homogeneous Banach spaces on T and the class of prehomogeneous Banach spaces on T. We apply our results to show that the algebra of a...

Networks have been extensively used to model various complex systems such as online social networks, co-authorship and citation networks and gene networks. Due to different kinds of variations such as temporal, spatial, topic and phenotypic variations, several variants of the same network may exist. For several practical problems, identifying the nodes that are changing between the networks pro...

We develop our general machinery of the Campbell-Hausdorff invariants of links, in the case of pure links, with emphasis on the connections with the lower central series of the pure braid groups. We present a complete simple set of rules for the Artin calculus of longitudes modulo the central series. We prove that if two pure links differ by an order k pure braid commutator, then their order k ...

Abstract—In this paper an unsupervised color image segmentation method is suggested. Color image segmentation is an important but still open problem in image processing. At first, FCM is applied to the image and the cluster centers are obtained. Quite similar to the famous TSK fuzzy control model, we form several rules (IF-THEN like) for pixel classification. The results obtained from the rules...

This paper presents a novel method for real-time homogenous translucent material editing under fixed illumination. We consider the complete analytic BSSRDF model proposed by Jensen et al. [JMLH01], including both multiple scattering and single scattering. Our method allows the user to adjust the analytic parameters of BSSRDF and provides high-quality, real-time rendering feedback. Inspired by r...

The contract is described and market examples given. Essential theoretical developments are introduced and cited chronologically. The principles and techniques of hedging and unique pricing are illustrated for the two simplest nontrivial examples: the classical Black-Scholes/Merton/Margrabe exchange option model brought somewhat upto-date from its form three decades ago, and a lesser exponentia...

In this paper, the interface crack of two non-homogenous functionally graded materials is studied. Subsequently, with employing the displacement method for fracture of mixed-mode stress intensity factors, the continuous variation of material properties are calculated. In this investigation, the displacements are derived with employing of the functional graded material programming and analysis o...