‎Suppose G is a group of order p^2q^2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, ‎respectively‎. ‎In this paper‎, ‎we show that up to isomorphism‎, ‎there are four groups of order p^2q^2 when Q and P are cyclic‎, ‎three groups when Q is a cyclic and P is an elementary ablian group‎, ‎p^2+3p/2+7 groups when Q is an elementary ablian group an...

Here dz denotes Lebesgue measure on R. More precisely, if f lies in L(R), then P (f) is defined almost everywhere on R if 1 ≤ q < n, it is defined almost everywhere modulo constants when q = n, and it is defined modulo constants everywhere if n < q < ∞. (If q = ∞, then one can take it to be defined modulo affine functions.) We shall review the reasons behind these statements in a moment. The ca...

We investigate the local integrability in C3 of some three-dimensional Lotka–Volterra equations at the origin with (p : q : r)-resonance, ẋ = P = x(p+ ax+ by + cz), ẏ = Q = y(q + dx+ ey + fz), ż = R = z(r + gx+ hy + kz). Recent work on this problem has centered on the case where the resonance is of “rank-2”. That is, there are two independent linear dependencies of p, q and r over Q. Here, we c...

We define the (q, r)-Whitney numbers of the first and second kinds in terms of the q-Boson operators, and obtain several fundamental properties such as recurrence formulas, orthogonality and inverse relations, and other interesting identities. As a special case, we obtain a q-analogue of the r-Stirling numbers of the first and second kinds. Finally, we define the (q, r)-Dowling polynomials in t...

lexicographic ordering by spectral moments ($s$-order) among all trees is discussed in this‎ ‎paper‎. ‎for two given positive integers $p$ and $q$ with $pleqslant q$‎, ‎we denote $mathscr{t}_n^{p‎, ‎q}={t‎: ‎t$ is a tree of order $n$ with a $(p‎, ‎q)$-bipartition}‎. furthermore, ‎the last four trees‎, ‎in the $s$-order‎, ‎among $mathscr{t}_n^{p‎, ‎q},(4leqslant pleqslant q)$ are characterized‎.

In this paper, two vector control systems for investigating the performance of Static Synchronous Series Compensators (SSSC) in steady state conditions are presented that are based on famous d-q axis theory. The workability of proposed method to simplify the SSSC mathematical expressions is shown. The performance of SSSC with two different vector controllers, first based on d-q line current...

Given an odd prime q and integer m ≤ q, a binary mq × q2 quasi-cyclic parity-check matrix H(m, q) can be constructed for array low-density (LDPC) code C(m, q). In this letter, we investigate the first separating redundancy of We prove that is 1-separating any pair (m, q), from which conclude upper bounded by mq. Then show our bound on tighter than general deterministic constructive bounds in li...

OBJECTIVE Imbalances of pulmonary to systemic blood flow ratio (Q(p)/Q(s)) compounded with inadequate systemic oxygen delivery correlate with mortality after first-stage Norwood palliation of hypoplastic left heart syndrome. Mathematical models suggest that maximal systemic oxygen delivery occurs with Q(p)/Q(s) of less than 1. Whether this applies to clinical practice is unclear. This study eva...

The core of a category (first defined in “Core algebra revisited” Theoretical Computer Science, Vol 375, Issues 1–3 pp 193–200) has the structure of an abstract core algebra (first defined in the same place). A question was left open: is there more structure yet to be defined? The answer is no: it is shown that any operation on an object arising from the fact that the object is the core of its ...