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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Patent•
31 Jan 2008
TL;DR: In this article, the problem of performing division processing at high speed with a small hardware scale is addressed, where an input control part outputs the result of a plus or minus judgement of a divisor to an output control part 5, and also converts the divisors into an SB (straight binary) code to output the resultant.
Abstract: PROBLEM TO BE SOLVED: To perform division processing at high speed with a small hardware scale. SOLUTION: An input control part 1 outputs the result of a plus or minus judgement of a divisor to an output control part 5, and also converts the divisor into an SB (straight binary) code to output the resultant. An effective number of bits judgement part 2 inputs the SB coded divisor, judges the number of bits, and outputs the result to an arithmetic table part 3 and an arithmetic processing part 4. The arithmetic table part 3 inputs the SB coded divisor and the effective number of bits, refers to the arithmetic table when the effective number of bits is within the predetermined effective number of bits, and outputs the quotient and the table use flag corresponding to the value of the SB coded divisor. The arithmetic processing part 4 inputs the SB coded divisor and the effective number of bits, and when the effective number of bits is judged as not within the predetermined effective number of bits, performs division processing. The output control part 5 outputs the table read result from the arithmetic table part 3 or the arithmetic processing result from the arithmetic processing part 4 as the quotient based on the table use flag from the arithmetic table part 3. COPYRIGHT: (C)2008,JPO&INPIT
1 citations
TL;DR: The main result of as mentioned in this paper is that for any fixed constant σ ≥ 0, the relation holds that σ ≤ σ 3 σ 1/6 + σ 2/6+α /6 + \varepsilon.
Abstract: The main result of this paper is the following theorem. Suppose thatτ(n) = ∑
d|n
l and the arithmetical functionF satisfies the following conditions:
Then there exist constantsA
1,A
2, andA
3 such that for any fixed \g3\s>0 the following relation holds:
$$\sum\limits_{n \leqslant x} {r(n)} r(n + 1)F(n) = A_1 xln^{\text{2}} x + A_{\text{2}} xlnx + A_{\text{3}} x + O(x^{5/6 + \varepsilon } + x^{1 - \alpha /6 + \varepsilon } ), x \to \infty .$$
. Moreover, if for any primep the inequality \vbf(p)\vb\s<1 holds and the functionF is strongly multiplicative, thenA
1\s>0.
1 citations
Patent•
09 Nov 2016
TL;DR: In this article, a split-divisor frequency divider module is used to generate a clock signal and an output signal based on a first divisor and two second divisors.
Abstract: A frequency divider system and method includes a split-divisor frequency divider module. The split-divisor frequency divider module receives a clock signal and generates an output signal based on a first divisor and a second divisor. The clock signal and output signal each have rectangular waveforms characterized by a respective frequency and pulse width. The frequency of the output signal is a selectable integer fraction of the frequency of the clock signal, the frequency of the output signal being selected based on a sum of the first and second divisors. The pulse width of the output signal is a selectable integer number of clock cycles, the pulse width of the output signal being selected based on at least one of the first divisor and the second divisor.
1 citations
TL;DR: In this paper, the exact number of fixed-point-free automorphisms of the group Zpa⊕Zpb was shown to be θ(G,d), where d is a divisor of the order of G.
Abstract: Let G=Zp⊕Zp2, where p is a prime number. Suppose that d is a divisor of the order of G. In this paper, we find the number of automorphisms of G fixing d elements of G and denote it by θ(G,d). As a consequence, we prove a conjecture of Checco-Darling-Longfield-Wisdom. We also find the exact number of fixed-point-free automorphisms of the group Zpa⊕Zpb, where a and b are positive integers with a
1 citations
TL;DR: In this article, it was shown that every prime divisor of the order of the finite abelian group with complex character values of a finite group G is a proper divisors of G unless G = 1.
Abstract: Let $K:=\mathbb{Q}(G)$ be the number field generated by the complex character values of a finite group $G$. Let $\mathbb{Z}_K$ be the ring of integers of $K$. In this paper we investigate the suborder $\mathbb{Z}[G]$ of $\mathbb{Z}_K$ generated by the character values of $G$. We prove that every prime divisor of the order of the finite abelian group $\mathbb{Z}_K/\mathbb{Z}[G]$ divides $|G|$. Moreover, if $G$ is nilpotent, we show that the exponent of $\mathbb{Z}_K/\mathbb{Z}[G]$ is a proper divisor of $|G|$ unless $G=1$. We conjecture that this holds for arbitrary finite groups $G$.
1 citations