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.

The dimension of automorphism groups of algebraic varieties with pseudo-effective log canonical divisors

Abstract: Let $(X,D)$ be a log smooth pair of dimension $n$, where $D$ is a reduced effective divisor such that the log canonical divisor $K_X + D$ is pseudo-effective. Let $G$ be a connected algebraic subgroup of $\mathrm{Aut}(X,D)$. We show that $G$ is a semi-abelian variety of dimension $\le \min\{n-\bar{\kappa}(V), n\}$ with $V := X\setminus D$. In the dimension two, Shigeru Iitaka claimed in his 1979 Osaka J. Math. paper that $\dim G\le \bar{q}(V)$ for a log smooth surface pair with $\bar{\kappa}(V) = 0$ and $\bar{p}_g(V) = 1$. We (re)prove and generalize this classical result for all surfaces with $\bar{\kappa}=0$ without assuming Iitaka's classification of logarithmic Iitaka surfaces or logarithmic $K3$ surfaces.

Encoding method, encoding device, decoding method, decoding device and system using them

Abstract: PROBLEM TO BE SOLVED: To use the specified use of a padding bit in a turbo code SOLUTION: A first padding operation (508) filling an original system (u) so that the system (u) after filling can be divided by a first divisor polynomial is performed for encoding the original system (u) of binary data A first recursive convolution encoding operation (508) for encoding the original system (u) after filling is performed by using the first divisor polynomial An interleaving operation (506) for substituting binary data of the original system (u) by specified substitution is preformed so that an interleaving system (u*) is obtained A second padding operation (510) for filling the interleaving system (u*) is performed so that the interleaving system (u*) after filling can be divided by a second divisor polynomial (g2) A second recursive convolution encoding operation (510) for encoding the interleaving system (u*) after filling is performed by using the second divisor polynomial

Low latency floating-point divider

Abstract: An improved method and apparatus for performing floating-point division is disclosed. In a particular embodiment, fractional operands are pre-scaled and an estimate of a reciprocal of the pre-scaled fractional divisor is obtained from a lookup table using a portion of the bits of the pre-scaled fractional divisor. This value is used to scale the fractional operands and a multiply-add operation is used based on principles of series expansion to compute a final result with an acceptable degree of accuracy.

Characteristic of Bipolar Fuzzy and Bipolar Fuzzy Divisor of Zero of a Ring

Abstract: During this paper, we present the documentation of characteristic of bipolar fuzzy and bipolar fuzzy divisor of zero of a ring, and study essential properties. We concentrate fundamental operation on characteristic of bipolar fuzzy and bipolar fuzzy divisor of a ring and explore a few properties of these ideas in association with bipolar fuzzy perfect of a ring.

Central units of integral group rings of monomial groups

Abstract: In this paper, it is proved that the group generated by Bass units contains a subgroup of finite index in the group of central units $\mathcal{Z}(\mathcal{U}(\mathbb{Z}G))$ of the integral group ring $\mathbb{Z}G$ for a subgroup closed monomial group $G$ with the property that every cyclic subgroup of order not a divisor of $4$ or $6$ is subnormal in $G$. If $G$ is a generalized strongly monomial group, then it is shown that the group generated by generalized Bass units contains a subgroup of finite index in $\mathcal{Z}(\mathcal{U}(\mathbb{Z}G))$. Furthermore, for a generalized strongly monomial group $G$, the rank of $\mathcal{Z}(\mathcal{U}(\mathbb{Z}G))$ is determined. The formula so obtained is in terms of generalized strong Shoda pairs of $G$.