Sorghum (Sorghum bicolor (L.) Moench) presents a suitable source of green fodder in the livestock sector. However, its use as feed is limited by high concentration lignocellulose. A study was conducted to evaluate influence environment and developmental stage harvesting on lignin, cellulose, hemicellulose selected sorghum cultivars. field experiment laid randomized complete block design replica...

For a prime polynomial f(T ) ∈ Z[T ], a classical conjecture predicts how often f has prime values. For a finite field κ and a prime polynomial f(T ) ∈ κ[u][T ], the natural analogue of this conjecture (a prediction for how often f takes prime values on κ[u]) is not generally true when f(T ) is a polynomial in T p (p the characteristic of κ). The explanation rests on a new global obstruction wh...

Let $R$ be a commutative ring and $M$ be an $R$-module. In this paper, we investigate some properties of 2-absorbing submodules of $M$. It is shown that $N$ is a 2-absorbing submodule of $M$ if and only if whenever $IJLsubseteq N$ for some ideals $I,J$ of R and a submodule $L$ of $M$, then $ILsubseteq N$ or $JLsubseteq N$ or $IJsubseteq N:_RM$. Also, if $N$ is a 2-absorbing submodule of ...

here we consider all finite non-abelian 2-generator $p$-groups ($p$ an odd prime) of nilpotency class two and study the probability of having $n^{th}$-roots of them. also we find integers $n$ for which, these groups are $n$-central.

Let Km,n be a complete bipartite graph with two partite sets having m and n vertices, respectively. A K1,k-factorization of Km,n is a set of edge-disjoint K1,k-factors of Km,n which partition the set of edges of Km,n. When k is a prime number p, Wang [Discrete Math. 126 (1994)] investigated the K1,p-factorization of Km,n and gave a sufficient condition for such a factorization to exist. Du [Dis...

Let C be the image of a canonical embedding φ of the Atkin-Lehner quotient X + 0 (N) associated to the Fricke involution w N. Suppose φ is defined over the rationals. In this note we give some collinearity relations among rational points of C, for each X + 0 (N) of genus 3 and the first X + 0 (N) of genus 4, for N prime.

We examine n×nmatrices over Zm, with 0’s in the diagonal and nonzeros elsewhere. If m is a prime, then such matrices have large rank (i.e., n1/(p−1) − O(1) ). If m is a non-prime-power integer, then we show that their rank can be much smaller. For m = 6 we construct a matrix of rank exp(c √ log n log log n). We also show, that explicit constructions of such low rank matrices imply explicit cons...

In this paper we study mixed sums of primes and linear recurrences. We show that if m ≡ 2 (mod 4) and m+1 is a prime then (m2n−1−1)/(m−1) 6= m+p for any n = 3, 4, . . . and prime power p. We also prove that if a > 1 is an integer, u0 = 0, u1 = 1 and ui+1 = aui + ui−1 for i = 1, 2, 3, . . ., then all the sums um + aun (m, n = 1, 2, 3, . . .) are distinct. One of our conjectures states that any i...

For relatively prime positive integers u0 and r, we consider the least common multiple Ln := lcm(u0, u1, . . . , un) of the finite arithmetic progression {uk := u0 + kr}k=0. We derive new lower bounds on Ln which improve upon those obtained previously when either u0 or n is large. When r is prime, our best bound is sharp up to a factor of n + 1 for u0 properly chosen, and is also nearly sharp a...