We propose a nite diierence scheme to approximate the Fokker-Planck collision operator in 3 velocity dimensions. The principal feature of this scheme is to provide a decay of the numerical entropy. As a consequence, it preserves the collisional invariants and its stationary solutions are the discrete Maxwellians. We consider both the whole velocity-space problem and the bounded velocity problem...

Let G be a connected graph of order n with Laplacian eigenvalues [Formula: see text]. The Laplacian-energy-like invariant of G, is defined as [Formula: see text]. In this paper, we investigate the asymptotic behavior of the 3.6.24 lattice in terms of Laplacian-energy-like invariant as m, n approach infinity. Additionally, we derive that [Formula: see text], [Formula: see text] and [Formula: see...

Due to the increasing interest in 3D models in various applications there is a growing need to support e.g. the automatic search or the classification in such databases. As the description of 3D objects is not canonical it is attractive to use invariants for their representation. We recently published a methodology to calculate invariants for continuous 3D objects defined in the real domain R b...

Given a quiver algebra A with relations defined by a superpotential, this paper defines a set of invariants of A counting framed cyclic A-modules, analogous to rank-1 Donaldson–Thomas invariants of Calabi–Yau threefolds. For the special case when A is the non-commutative crepant resolution of the threefold ordinary double point, it is proved using torus localization that the invariants count ce...

This paper is concerned with the relations between the differential invariants of a smooth manifold embedded in the Euclidean space and the square of the distance function from the manifold. In particular, we are interested in curvature invariants like the mean curvature vector and the second fundamental form. We find that these invariants can be computed in a very simple way using the third or...

The study of mutual entropy (information) and capacity in classical system was extensively done after Shannon by several authors like Kolmogorov [12] and Gelfand [7]. In quantum systems, there have been several definitions of the mutual entropy for classical input and quantum output [5, 8, 9, 14]. In 1983, the author defined [21] the fully quantum mechanical mutual entropy by means of the relat...

We propose an immune system inspired Artificial Immune System (AIS) algorithm for the purposes of automated program verification. It is proposed to use this AIS algorithm for a specific automated program verification task: that of predicting shape of program invariants. It is shown that the algorithm correctly predicts program invariant shape for a variety of benchmarked programs. Program invar...