In this paper, we prove that there exist infmitely many positive integers n satisfying S(Z(n»> Z(S(n» or S(Z(n» < Z(S(n».

In this paper, the Fischer matrices of maximal subgroup G = 21+8+ : (U4(2):2) U6(2):2 will be derived from quotient group Q G/Z(21+8+) 28 (U4(2):2), where Z(21+8+) denotes center extra-special 2-group 21+8+. Using approach, and associated ordinary character table are computed in an elegantly simple manner. This approach can used to compute any split extension form 21+2n+ :G, n ∈ N, provided irr...

Single crystals of the low (t-) and high (h-) temperature form of Z n 0Z n 3(A s 0 4)2 have been prepared by flux and by C 0 2-LASER techniques respectively. Both compounds crystal­ lizes monoclinic, space group C2h-P2;/n with the lattice parameters t-Z n0Z n3(A s 0 4)2: a = 9.807(3), b = 8.180(2), c = 9.967(2) A , ß = 116.53(2)°, Z = 4 and h-Z n0Z n3(A s 0 4)2: a = 9.743(3), b = 8.163(8), c = ...

let $f$ be a locally univalent function on the unit disk $u$. we consider the normalized extensions of $f$ to the euclidean unit ball $b^nsubseteqmathbb{c}^n$ given by$$phi_{n,gamma}(f)(z)=left(f(z_1),(f'(z_1))^gammahat{z}right),$$ where $gammain[0,1/2]$, $z=(z_1,hat{z})in b^n$ and$$psi_{n,beta}(f)(z)=left(f(z_1),(frac{f(z_1)}{z_1})^betahat{z}right),$$in which $betain[0,1]$, $f(z_1)neq 0$ and $...

The title compound, C(8)H(18)N(4)O(2) (2+)·2Cl(-), contains two oxime groups. The methyl oxime group has a Z configuration, and the ethyl oxime group is disordered, with both Z and E configurations in occupancies of 0.840 (8) and 0.160 (8), respectively. In the crystal structure, there are a number of N-H⋯Cl hydrogen bonds.

let $p$ be a complex polynomial of the form $p(z)=zdisplaystyleprod_{k=1}^{n-1}(z-z_{k})$,where $|z_k|ge 1,1le kle n-1$ then $ p^prime(z)ne 0$. if $|z|