This paper presents the generalized multipole, local and translation operators for three dimensional static potentials of the form r, where λ is any real number. Addition theorems are developed using Gegenbauer polynomials. Multipole expansions and error bounds are presented in a manner similar to those for truncated classical multipole expansions. Numerical results showing error behavior versu...

It is well known that the generalized translation operator T associated with the Bessel function of the first kind is positive in the sense if f > 0, then Tf > 0. This property is easily seen when we write Tf as an integral representation with a kernel involving the area of some triangle ([1],[9]) and has several applications in many mathematical fields such that hypergroup structure, heat equa...

We develop and test new machine learning methods for the prediction of topological representations of protein structures in the form of coarse-or ne-grained contact or distance maps that are translation and rotation invariant. The methods are based on generalized input-output hidden Markov models (GIOHMMs) and generalized recursive neural networks (GRNNs). The methods are used to predict topolo...

We present a construction of a wavelet-type orthonormal basis for the space of radial L-functions in R via the concept of a radial multiresolution analysis. The elements of the basis are obtained from a single radial wavelet by usual dilations and generalized translations. Hereby the generalized translation reveals the group convolution of radial functions in R. We provide a simple way to const...

in this paper, we introduce and study the notion of precompacttopological generalized groups and some new results are given.

given a mapping $f:xto x$ we naturally associate to it a monotonic map $gg_f:exp xto exp x$ from the power set of $x$ into itself, thus inducing a generalized topology on $x$. in this paper we investigate some properties of generalized topologies which are defined by such a procedure.

A non-clausal connection calculus for classical first-order logic is presented that does not require the translation of input formulae into any clausal form. The definition of clauses is generalized, which may now also contain (sub-) matrices. Copying of appropriate (sub-)clauses in a dynamic way, i.e. during the actual proof search, is realized by a generalized extension rule. Thus, the calcul...

In this paper, non-Hamiltonian systems with holonomic constraints are treated by a generalization of Dirac's formalism. Non-Hamiltonian phase space flows can be described by generalized antisymmetric brackets or by general Liouville operators which cannot be derived from brackets. Both situations are treated. In the first case, a Nosé-Dirac bracket is introduced as an example. In the second one...

in this article the possible effects of the translation technologies on the critical thinking and translation ability of the students of the translation studies would be studied through a pre-experimental method of research. the participants of this research were thirty one iranian senior translation studies students at the age group of 20-26 who were selected based on their age, educational le...

We present a tool that transforms nondeterministic ω-automata to semi-deterministic ω-automata. The tool Seminator accepts transition-based generalized Büchi automata (TGBA) as an input and produces automata with two kinds of semi-determinism. The implemented procedure performs degeneralization and semi-determinization simultaneously and employs several other optimizations. We experimentally ev...