in this paper‎, ‎we determine the simple groups $g=ab$‎, ‎where $b$ is isomorphic to $l_{3}(4)$ and $a$ isomorphic to an alternating or a symmetric group on $ngeq5$‎, ‎letters‎.

‎The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$‎, ‎to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$‎. ‎If there exists an $ntimes n$ symmetric doubly stochastic ...

In 1963, Shrikhande and Raghavarao [5] published a recursive construction for designs that starts with a resolvable design (the “master design”) and then uses a second design (“the indexing design”) to take certain unions of blocks in each parallel class of the master design. Several variations of this construction have been studied by different authors. We revisit this construction, concentrat...

To meet the demands of different high bandwidth service, OFDM-PON has been considered as one of the candidates for NG-PON2. In this paper, downstream transmission performance based on LDPC-OFDM coding PON system is studied. The simulation results show that employing the LDPC-OFDM coding in PON system can achieve 10 Gb/s downstream transmission. The transmission performance of the LDPC-OFDM syst...

Let H be a normal subgroup of a finite group G. We show that: If a GBRD(v, k, A.; G IH) exists and a GBRD(k,j, JA.; H) exists then a GBRD(v,j, AJA.; G) exists. We apply this result to show that: i) If k does not exceed the least prime factor of IG I, then a GBRD(k, k, A; G) exists for all A EO (mod IG I); ii) If G is of order IG Ie lor 5 (mod 6) then a GBRD(v, 3, A = t IG I; G), v>3, exists if ...

Commutative properties of four-dimensional generalized symmetric pseudo-Riemannian manifolds were considered. Specially, in this paper, we studied Skew-Tsankov and Jacobi-Tsankov conditions in 4-dimensional pseudo-Riemannian generalized symmetric manifolds.

In this paper we introduce a special form of symmetric matrices that is called central symmetric $X$-form matrix and study some properties, the inverse eigenvalue problem and inverse singular value problem for these matrices.

In this note we use matrices to construct group divisible designs (GDDs). The constructions of GDDs of the form A 0 D + A ® D will be carried out in two cases. The first case uses the incidence matrix D of a GDD with a certain (0,1) matrix A. The second case uses the incidence matrix D of a BIBD with A as in the first case. In both cases necessary and sufficient conditions in terms of parameter...