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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TL;DR: In this paper, the number of partitions of n into k different parts by constructing a generating function was studied and the congruence property of the overpartition function was investigated by using a convolution sum of two divisor functions modulo 8.
13 citations
TL;DR: In this article, the authors investigated the birational geometry inspired by L. They proved that |mL| and |K_X+mL| can give birational maps for all threefold X with |mL | and |k_X +mL|, under the assumption that L is big and has no stable base components.
Abstract: For a minimal threefold X with $$K_X\equiv 0$$
and a nef and big Weil divisor L on X, we investigate the birational geometry inspired by L. We prove that |mL| and $$|K_X+mL|$$
give birational maps for all $$m\ge 17$$
. The result remains true under weaker assumption that L is big and has no stable base components.
13 citations
TL;DR: For an effective divisor with support in a compact Kahler manifold, the following properties are antinomic: 1) the normal bundle is topologically trivial; 2) the Levi form has pointwise at least 3 positive eigenvalues outside a compact subset of the manifold as mentioned in this paper.
Abstract: For an effective divisor $A$ with support $B$ in a compact Kahler manifold $M$ of dimension $\geq 3$, the following are antinomic. a) $M\backslash B$ has a $C^{\infty}$ plurisubharmonic exhaustion function whose Levi form has pointwise at least 3 positive eigenvalues outside a compact subset of $M\backslash B$. b) $[A]|B$, the normal bundle of $A$, is topologically trivial.
13 citations
Patent•
14 Nov 2000
TL;DR: In this article, the authors presented an SRT division algorithm using a radix r and the number of iterations needed to determine all quotient-digits is N, such that N=54/k for a 64 bit floating point value.
Abstract: An SRT division unit for performing a novel SRT division algorithm is presented. The novel SRT division algorithm comprises a method for performing SRT division using a radix r. As one skilled in the art will appreciate, the radix r dictates the number of quotient-bits k generated during a single iteration. The relationship between radix r and the number of quotient-bits k generated in a single iteration is r=2 k . The number of iterations needed to determine all quotient-digits is N, such that N=54/k for a 64 bit floating point value. In accordance with one embodiment of the present invention, the SRT division unit generates a scaling factor M, which comprises scaling sub-factors M1 and M2 according to the relationship M=r*M1+M2. Next, the division unit generates a scaled divisor Y by multiplying a divisor DR by scaling factor M, such that said scaled divisor Y=DR*M=r(DR*M1)+DR*M2. In addition, the division unit generates partial remainder values w[00] and w[0] by muliplying a dividend DD by scaling sub-factor M1 and scaling factor M, respectively. Partial remainder value w[00]=DD*M1, and partial remainder value w[0]=DD*M=r(DD*M1)+DD*M2. Scaled divisor Y and partial remainders w[0] and w[00] then are used to generate quotient-digits and additional partial remainders. Accordingly, the division unit performs iterations j which generate quotient-digits according to the formula q[j]=SEL(r 2 *w msb [j−2], q[j−1]). Also, the iterations generate additional partial remainders w[j] according to the formula w[j]=rw[j−1]−q[j−1]*Y. N iterations are performed, generating all quotient-digits for the division operation.
13 citations
TL;DR: In this article, the existence of an integer H t (m, n ; s, k ) when s and k are both even was proved. But the existence was not proved when k and s were both even.
13 citations