Prime reciprocals have applications in coding and cryptography and for generation of random sequences. This paper investigates the structural redundancy of prime reciprocals in base 10 in a manner that parallels an earlier study for binary prime reciprocals. Several different kinds of structural relationships amongst the digits in reciprocal sequences are classified with respect to the digit in...

illustration, the prime reciprocal of 1/7 is , and the prime reciprocal sequence is considered to be 142857. The period of this sequence is 6. Since the maximum length of the period can be (p-1), this is an example of a maximum-length d-sequence. But a prime reciprocal sequence that is maximum length in one base need not be maximum length in another base. Thus the binary prime reciprocal sequen...

The Atacama Large Millimeter/submillimeter Array (ALMA) serendipitously detected H$_2$O $J_{Ka, Kc} = 10_{2,9} - 9_{3,6}$ emission at 321 GHz in NGC 1052. This is the first submillimeter maser detection a radio galaxy and most luminous 321-GHz known to date with isotropic luminosity of 1090 $L_{\odot}$. line profile consists broad velocity component FWHM $= 208 \pm 12$ km s$^{-1}$ straddling sy...

Let $A$ be a Banach algebra and $E$ be a Banach $A$-bimodule then $S = A oplus E$, the $l^1$-direct sum of $A$ and $E$ becomes a module extension Banach algebra when equipped with the algebras product $(a,x).(a^prime,x^prime)= (aa^prime, a.x^prime+ x.a^prime)$. In this paper, we investigate $triangle$-amenability for these Banach algebras and we show that for discrete inverse semigroup $S$ with...

In this paper we construct a cover {as(mod ns)}s=1 of Z with odd moduli such that there are distinct primes p1, . . . , pk dividing 2 n1 − 1, . . . , 2k − 1 respectively. Using this cover we show that for any positive integer m relatively prime to 15015 there exists an infinite arithmetic progression of positive odd integers the mth powers of whose terms are never of the form 2±p with a, n ∈ {0...

The logarithmic coefficients play an important role for different estimates in the theory of univalent functions.Due to significance recent studies about coefficients, problem obtaining sharp bounds second Hankel determinant these that is $H_{2,1}(F_f/2)$ was paid attention. We recall if $f$ and $F$ are two analytic functions $\mathbb{D}$, function subordinate $F$, written $f(z)\prec F(z)$, the...

let r be a commutative ring with identity. let n and k be two submodules of a multiplication r-module m. thenn=im and k=jm for some ideals i and j of r. the product of n and k denoted by nk is defined by nk=ijm. inthis paper we characterize some particular cases of multiplication modules by using the product of submodules.

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

a gyrogroup is a nonassociative group-like structure modelled on the space of relativistically admissible velocities with a binary operation given by einstein's velocity addition law. in this article, we present a few of groups sitting inside a gyrogroup $g$, including the commutator subgyrogroup, the left nucleus, and the radical of $g$. the normal closure of the commutator subgyrogroup, ...