Minimal realizations for finite sets in categorial automata theory
Physical analysis of phase transformation of materials consisting from several (both substitutional and interstitial) components, coming from the Onsager extremal thermodynamic principle, leads, from the mathematical point of view, to a system of partial differential equations of evolution type, including certain integral term, with substantial differences in particular phases (, ) and in moving interface of finite thickness (), in whose center the ideal liquid material behaviour can be detected....
This paper deals with calculus which is an extension of finite operator calculus due to Rota, and leading results of Rota’s calculus are easily -extendable. The particular case is known to be relevant for quantum group investigations. It is shown here that such umbral calculus leads to infinitely many new -deformed quantum like oscillator algebra representations. The authors point to several references dealing with new applications of umbral and calculus in which new families of extensions...
Multi-scale modeling plays an important role in understanding the structure and biological functionalities of large biomolecular complexes. In this paper, we present an efficient computational framework to construct multi-scale models from atomic resolution data in the Protein Data Bank (PDB), which is accelerated by multi-core CPU and programmable Graphics Processing Units (GPU). A multi-level summation of Gaussian kernel functions is employed to generate implicit models for biomolecules. The coefficients...