New solutions for the elliptic Darboux equation are obtained as particular cases of constructed Heun's general equation. We consider two groups power series expansions and new in Gauss hypergeometric functions. The convergence one group is determined by means ratio tests infinite series, while other designed to solve problems which admit finite-series solutions. Actually, we envisage periodic q...

We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G ∼= H. The n barrier for group isomorphism has withstood all attacks — even for the special cases of p-groups and solvable groups — ever since the n generator-enumeration algorithm. Following a framework due to Wagner, we present the first significant improvement over ...

We investigate the analyticity property of the partially resummed series expansion(PRSE) of the partition function for the eight-vertex model. Developing a graphical technique, we have obtained a first few terms of the PRSE and found that these terms have a pole only at one point in the complex plane of the coupling constant. This result supports the conjecture proposed by Guttmann and Enting c...

Every finite solvable group G has a normal series with nilpotent factors. The smallest possible number of factors in such is called the Fitting height h(G). In present paper, we derive an upper bound for h(G) terms exponent G. Our constitutes considerable improvement earlier obtained Shalev (Proc Am Math Soc 126(12):3495–3499, 1998).

Abstract The Yukawa interaction is considered in 0+1 dimensions as a pedagogical example to illustrate quantum field theory methods. From the mechanical point of view system trivially exactly solvable, but this can be difficult see from path integral perspective. It shown how despite initial appearances perturbation series terms Feynman diagrams consistent with picture for finite temperature.

The topic in the PI’s current grant1 is: Given a linear homogeneous linear differential equation with polynomial coefficients, decide if it can be solved in terms of special functions, and if so, find such solutions. Much progress on his topic has been made by the PI and his graduate students (Sections 2 and 6). Numerous algorithms were developed that turned out to be very effective. The PI tes...

We define an obstruction for a knot to be ?[?]-homology ribbon, and use this provide restrictions on the integers that can occur as triple linking numbers of derivative links knots are either homotopy ribbon or doubly slice. Our main application finds new non-doubly slice knots. In particular, gives information solvable filtration Taehee Kim: algebraically need not (1)-solvable, (0.5, 1)-solvab...

Limits to consistent on-line forecasting for ergodic time series. Abstract This study concerns problems of time-series forecasting under the weakest of assumptions. Related results are surveyed and are points of departure for the developments here, some of which are new and others are new derivations of previous findings. The contributions in this study are all negative, showing that various pl...