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•
09 May 1973
TL;DR: In this article, a serial bit digit word format with the least significant bit of the digit word being supplied first both to and from the circuit is presented. But the circuit operates in a normal long division process of examining the magnitude of each partial remainder in the division process, subtracting if the remainder is larger than the divisor, inserting a digit in the quotient upon each subtraction and increasing the value of the remainder for the next examination.
Abstract: A circuit using standardized components and providing a given word length quotient from the same length dividend and divisor. The circuit checks the input dividend and divisor for polarity and uses logic circuitry to determine if the quotient would be an improper fraction of either polarity. If an improper fraction did result, a given limit output of one polarity or the other is provided. Otherwise, the circuit operates in a normal long division process of examining the magnitude of each partial remainder in the division process, subtracting if the remainder is larger than the divisor, inserting a digit in the quotient upon each subtraction and increasing the value of the remainder for the next examination. The circuit operates with serial bit digit word format with the least significant bit of the digit word being supplied first both to and from the circuit.
6 citations
TL;DR: In this article, the existence of α ∈ F q ⁎ such that D m ( α ) = D m( α − 1 ) = 0 was studied and connections of this question to an open question by Wiedemann and a game called "Button Madness" were explored.
6 citations
TL;DR: In this article, it was shown that the group of units O(X) in the coordinate ring of a normal affine variety X over an algebraically closed field k is equal to k, the nonzero scalars, if X is a sufficiently general affine hyperelliptic curve.
Abstract: The object of study is the group of units O^\ast(X) in the coordinate ring of a normal affine variety X over an algebraically closed field k. Methods of Galois cohomology are applied to those varieties that can be presented as a finite cyclic cover of a rational variety. On a cyclic cover X \rightarrow A^m of affine m-space over k such that the ramification divisor is irreducible and the degree is prime, it is shown that O^\ast(X) is equal to k^\ast, the nonzero scalars. The same conclusion holds, if X is a sufficiently general affine hyperelliptic curve. If X has a projective completion such that the divisor at infinity has r components, then sufficient conditions are given for O^\ast(X)/k^\ast to be isomorphic to Z^(r-1).
6 citations
01 Sep 2017
TL;DR: In this paper, the authors presented a slightly simplified proof for the hyperbolicity conjecture of Campana and P\u{a}un: if some ε-tensor power of the bundle of the complex numbers contains a subsheaf with a big determinant, then the bundle is of log general type.
Abstract: Let $X$ be a smooth projective variety over the complex numbers, and $\Delta
\subseteq X$ a reduced divisor with normal crossings. We present a slightly
simplified proof for the following theorem of Campana and P\u{a}un: If some
tensor power of the bundle $\Omega_X^1(\log \Delta)$ contains a subsheaf with
big determinant, then $(X, \Delta)$ is of log general type. This result is a
key step in the recent proof of Viehweg's hyperbolicity conjecture.
6 citations
01 Jan 2009
TL;DR: In this article, it was shown that the largest divisor of a composite number n x with n j n 1 is at most x 1 = 2 =(logx) 1=2+o(1) as x! 1.
Abstract: Let ’ denote Euler’s function. Clearly ’(n) j n 1 if n = 1 or if n is a prime. In 1932, Lehmer asked if any composite numbers n have this property. Improving on some earlier results, we show that the number of composite integers n x with ’(n) j n 1 is at most x 1=2 =(logx) 1=2+o(1) as x ! 1. Key to the proof are some uniform estimates of the distribution of integers n where the largest divisor of ’(n) supported on primes from a xed set is abnormally small. 1
6 citations