Plants depend on light signals to modulate many aspects of their development and optimize their photosynthetic capacity. Phytochromes (phys), a family of photoreceptors, initiate a signal transduction pathway that alters expression of a large number of genes to induce these responses. Recently, phyA and phyB were shown to bind members of a basic helix-loop-helix family of transcription factors ...

let $g$ be a finite group and let $text{cd}(g)$ be the set of all‎ ‎complex irreducible character degrees of $g$‎. ‎b‎. ‎huppert conjectured‎ ‎that if $h$ is a finite nonabelian simple group such that‎ ‎$text{cd}(g) =text{cd}(h)$‎, ‎then $gcong h times a$‎, ‎where $a$ is‎ ‎an abelian group‎. ‎in this paper‎, ‎we verify the conjecture for‎ ${f_4(2)}.$‎

let $gamma(s_n)$ be the minimum number of proper subgroups‎ ‎$h_i, i=1‎, ‎dots‎, ‎l $ of the symmetric group $s_n$ such that each element in $s_n$‎ ‎lies in some conjugate of one of the $h_i.$ in this paper we‎ ‎conjecture that $$gamma(s_n)=frac{n}{2}left(1-frac{1}{p_1}right)‎ ‎left(1-frac{1}{p_2}right)+2,$$ where $p_1,p_2$ are the two smallest primes‎ ‎in the factorization of $ninmathbb{n}$ an...

‎we obtain the porc formulae for the number of non-associative algebras‎ ‎of dimension 2‎, ‎3 and 4 over the finite field gf$(q)$‎. ‎we also give some‎ ‎asymptotic bounds for the number of algebras of dimension $n$ over gf$(q)$‎.

 In this paper, we prove Frankl's Conjecture for an upper semimodular lattice $L$ such that $|J(L)setminus A(L)| leq 3$, where $J(L)$ and $A(L)$ are the set of join-irreducible elements and the set of atoms respectively. It is known that the class of planar lattices is contained in the class of dismantlable lattices and the class of dismantlable lattices is contained in the class of lattices ha...

in this paper, we mainly investigate the uniqueness of the entire function sharing a small entire function with its high difference operators. we obtain one results, which can give a negative answer to an uniqueness question relate to the bruck conjecture dealt by liu and yang. meanwhile, we also establish a difference analogue of the bruck conjecture for entire functions of order less than 2, ...

We present previously unpublished elementary proofs by Dekker and Ottens (1991) and Boyce (private communication) of a special case of the Dinitz conjecture. We prove a special case of a related basis conjecture by Rota, and give a reformulation of Rota's conjecture using the Nullstellensatz. Finally we give an asymptotic result on a related Latin square conjecture.

Abstract We compute the number of points over finite fields character stack associated to a compact surface group and reductive with connected centre. find that answer is polynomial on residue classes (PORC). The key ingredients in proof are Lusztig’s Jordan decomposition complex characters groups Deriziotis’s results their genus numbers. As consequence our main theorem, we obtain an expression...