In this paper we classify all finite solvable groups satisfying the following property P5: their orders of representatives are set-wise relatively prime for any 5 distinct non-central conjugacy classes.

This work aims to build a semantic framework for automated debugging. A debugging process consists of tracing, locating, and fixing processes consecutively. The first two processes are accomplished by a tracing procedure and a locating procedure, respectively. The tracing procedure reproduces the execution of a failed test case with well-designed data structures and saves necessary information ...

Spin coherent states play a crucial role in defining QESM (quasi-exactly solvable models) establishing a strict correspondence between energy spectra of spin systems and low-lying quantum states for a particle moving in a potential field of a certain form. Spin coherent states are also used for finding the Wigner-Kirkwood expansion and quantum corrections to energy quantization rules. The close...

The Onsager algebra is one of the cornerstones exactly solvable models in statistical mechanics. Starting from generalised Clifford algebra, we demonstrate its relations to graph Temperley--Lieb and a generalisation algebra. We present series quantum lattice as representations possessing structure special type [1]. integrability those presented, analogous free fermionic eight-vertex model. also...

Consider an undirected graph modeling a social network, where the vertices represent users, and the edges do connections among them. In the competitive diffusion game, each of a number of players chooses a vertex as a seed to propagate his/her opinion, and then it spreads along the edges in the graphs. The objective of every player is to maximize the number of vertices the opinion infects. In t...

This paper investigates single-machine scheduling with a deteriorating maintenance activity, where the processing time of job depends on whether it is handled before or after activity. Under common and slack due date assignments, aim to find optimal schedule, position value (flow-allowance) so that linear weighted sum earliness, tardiness minimized, weights are location-dependent (position-depe...

Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ODEs by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries. In fact, under regularity assumptions, any given ODE always admits solvable structures even though finding them in general could be a very difficult task. In ...

Let m be a positive integer and let ? finite set. The m-closure of G?Sym(?) is the largest permutation group on having same orbits as G in its induced action Cartesian product ?m. 1-closure 2-closure solvable need not solvable. We prove that always for m?3.