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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21 Jan 1999
TL;DR: In this article, a polynominal comprising powers of the basic unit of computer operation is used to determine integer remainders, and no shift operation is required as opposed to the conventional method, which can be determined simply by addition and subtraction.
Abstract: An integer Z101 is divided by another integer I102 to determine the remainder R109 The integer I102 is expressed by a polynominal comprising powers of the basic unit of computer operation By limiting the divisor according to the basic unit of computer operation, no shift operation is required as opposed to the conventional method, and remainders can thus be determined simply by addition and subtraction This allows code size to be compact, resulting in high-speed determination of integer remainders
2 citations
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TL;DR: In this article, the branch divisor of a normal triple cover over an elliptic curve or a normal cubic surface was shown to be a branch diviser of a regular triple cover.
Abstract: Let $S$ and $T$ be reduced divisors on $\mathbb{P}^2$ which have no common components, and $\Delta=S+2\,T.$ We assume $°\Delta=6.$ Let $\pi:X\to\mathbb{P}^2$ be a normal triple cover with branch divisor $\Delta,$ i.e. $\pi$ is ramified along $S$ (resp. $T$) with the index 2 (resp. 3). In this note, we show that $X$ is either a $\mathbb{P}^1$-bundle over an elliptic curve or a normal cubic surface in $\mathbb{P}^3.$ Consequently, we give a necessary and sufficient condition for $\Delta$ to be the branch divisor of a normal triple cover over $\mathbb{P}^2.$
2 citations
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10 Jul 2016TL;DR: This paper attacks a particular version of this problem, where the divisor is small and the circuit outputs a quotient and remainder, and proposes a fast yet area-efficient combinational circuit topology, which is called Binary Tree based Constant Division (BTCD).
Abstract: Division of an integer by an integer constant is a widely used operation and hence justifies a customized efficient implementation. There are various versions of this operation. This paper attacks a particular version of this problem, where the divisor is small and the circuit outputs a quotient and remainder. We propose a fast (low-latency) yet area-efficient combinational circuit topology, which we call Binary Tree based Constant Division (BTCD). BTCD uses a collection of small LUTs wired to each other to form a binary tree. The circuit also has bunch of adders, whose latencies are almost hidden as they operate in parallel with the binary tree. We wrote RTL code generators for BTCD and two previous works in the literature, then generated circuits for dividends of up to 128 bits and divisors of 3, 5, 11, and 23. We synthesized the generated RTL designs using a commercial ASIC synthesis tool. BTCD strikes a good balance between timing (latency) and area. It is up to 3.3 times better in Area-Timing Product (ATP) compared to the best alternative. ATP has a good correlation with energy consumption.
2 citations
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TL;DR: In particular, this article constructed ALE Calabi-Yau metrics with cone singularities along the exceptional set of resolutions of C n / ε with non-positive discrepancies for any finite subgroup U(2) acting freely on the three-sphere, hence generalizing Kronheimer's construction of smooth ALE gravitational instantons.
Abstract: We construct ALE Calabi-Yau metrics with cone singularities along the exceptional set of resolutions of $\mathbb{C}^n / \Gamma$ with non-positive discrepancies. In particular, this includes the case of the minimal resolution of two dimensional quotient singularities for any finite subgroup $\Gamma \subset U(2)$ acting freely on the three-sphere, hence generalizing Kronheimer's construction of smooth ALE gravitational instantons. Finally, we show how our results extend to the more general asymptotically conical setting.
2 citations
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TL;DR: In this article, the real inflection points of the associated complete real linear series on real plane curves are studied, using Viro's patchworking of real plane curve, recast in the context of some Berkovich spaces studied by M. Jonsson.
Abstract: Given a real hyperelliptic algebraic curve $X$ with non-empty real part and a real effective divisor $\mc{D}$ arising via pullback from $\mathbb{P}^1$ under the hyperelliptic structure map, we study the real inflection points of the associated complete real linear series $|\mc{D}|$ on $X$.
To do so we use Viro's patchworking of real plane curves, recast in the context of some Berkovich spaces studied by M. Jonsson. Our method gives a simpler and more explicit alternative to limit linear series on metrized complexes of curves, as developed by O. Amini and M. Baker, for curves embedded in toric surfaces.
2 citations