Topic
Divisor
About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.
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Posted Content•
15 Mar 2017
TL;DR: An infinite family of two-weight codes which meet the Griesmer bound are constructed and can be used in authentication codes and secret sharing schemes.
Abstract: Let $p$ be a prime number, $q=p^s$ for a positive integer $s$. For any positive divisor $e$ of $q-1$, we construct an infinite family codes of size $q^{2m}$ with few Lee-weight. These codes are defined as trace codes over the ring $R=\mathbb{F}_q + u\mathbb{F}_q$, $u^2 = 0$. Using Gauss sums, their Lee weight distributions are provided. When $\gcd(e,m)=1$, we obtain an infinite family of two-weight codes over the finite field $\mathbb{F}_q$ which meet the Griesmer bound. Moreover, when $\gcd(e,m)=2, 3$ or $4$ we construct new infinite family codes with at most five-weight.
1 citations
TL;DR: In this paper, the authors predict that large moments placed into a crystal field with the cubic point symmetry group, differ by their spectrum and magnetic properties, e.g., properties of the odd-integer moments are different from those of the even-integer ones.
Abstract: We predict that large moments $J$, placed into a crystal field with the cubic point symmetry group, differ by their spectrum and magnetic properties. E. g., properties of the odd-integer moments are different from those of the even-integer. The effect is due to Berry's phases gained by the moment, when it tunnels between minima of the external field. Two cases of the group $O$ are classified, namely, 6- and 8-fold coordinations. The spectrum and degeneration of energy levels depend on a remainder $\{J/n\}$, where the divisor $n=4$ and 3 for 6-fold and 8-fold coordination respectively. %High symmetry results in a finite magnetic moment for half-integer %and some integer moments, for example odd $J$ at 6-fold coordination. Large moments in the cubic environment can be realized by diluted alloys ${R}_{1-x}{R}_{x}'$Sb, where R=Lu, La, and R$'$=Tb, Dy, Ho, Er.
1 citations
Posted Content•
TL;DR: In this article, the authors gave explicit relations between absolute and relative Gromov-Witten invariants and proved that a symplectic manifold is symplectic rationally connected if it contains a positive divisor symplectomorphic to $P^n.
Abstract: In this paper, we gave some explicit relations between absolute and relative Gromov-Witten invariants. We proved that a symplectic manifold is symplectic rationally connected if it contains a positive divisor symplectomorphic to $P^n$.
1 citations
Posted Content•
14 Mar 2001
TL;DR: In this article, the additive properties of a Boolean lattice of mutiplication mod m_k have been studied, and it is shown that each complementary pair in BL adds to 1 mod m-k and each even idempotent e in BL has successor e+1 in G_1, so each even residue is the sum of two roots of unity.
Abstract: The product m_k of the first k primes (2..p_k) has neighbours m_k +/- 1 with all prime divisors beyond p_k, implying there are infinitely many primes [Euclid]. All primes between p_k and m_k are in the group G_1 of units in semigroup Z_{m_k}(.) of mutiplication mod m_k. Due to the squarefree modulus Z_{m_k} is a disjoint union of 2^k groups, with as many idempotents - one per divisor of m_k, which form a Boolean lattice BL. The generators of Z_{m_k} and the additive properties of its lattice are studied. It is shown that each complementary pair in BL adds to 1 mod m_k and each even idempotent e in BL has successor e+1 in G_1. It follows that G_1+G_1 \equiv E, the set of even residues in Z_{m_k}, so each even residue is the sum of two roots of unity, proving "Goldbach for Residues" mod m_k ("GR"). . . . Induction on k by extending residues mod m_k with "carry" a 1) successive 2n are in overlapping intervals, while the smallest composite unit in G_1 mod m_k is p_{k+1}^2, yielding "GC": Each 2n > 4 is the sum of two odd primes.
1 citations
Patent•
15 Oct 1992
TL;DR: In this article, a pre-processor of a division circuit of a high radix division system consists of a 1st zero counter 1 which counts (n) bits in a single units among those 0 bits which are continuous at the heads of an input divisor and an input dividend.
Abstract: PURPOSE:To perform the pre-processing of division of the high radixes at high speed in regard of the pre-processing of a division circuit. CONSTITUTION:A pre-processor of a division circuit of a high radix division system consists of a 1st zero counter 1 which counts (n) bits in a single units among those 0 bits which are continuous at the heads of an input divisor and an input dividend, a 1st shifter 2 which shifts the (unit number X n bits) obtained from the divisor end the dividend by the counter 1, a 2nd counter 3 which counts continuously the 0 bits at the shifted divisor, a latch 4 which stores the value of the counter 3, and a 2nd shifter 5 which shifts the divisor by the count value of the counter 3 and the dividend by the count value outputted from the latch 4 respectively.
1 citations