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.

Divider using interpolation approximation

Abstract: PURPOSE:To decrease the division execution time by providing a table information storage unit storing the difference between adjacent approximated reciprocals and an interpolation approximation circuit dividing proportionally the difference and applying the result in a way of approximated reciprocal CONSTITUTION:A divisor set to a divisor register 13 is normalized by a normalizing circuit 14, an approximated reciprocal M is read from a table information storage unit 17 by using a high-order bit of the divisor and the normalized divisor D0 is set to a mutliplicand selection circuit and register 15 After the precision of the approximated reciprocal is improved by an interpolation approximation circuit 18, a -M is outputted, the -M is selected by a multiplier selecting circuit 16 and the calculation of D0X(-M) is conducted by a multiplier 19 The produce is set to a multiplication result register 23 in this case Then after the dividened set to a dividened register 12 is normalized by the circuit 14, the dividened register 12 is set to the register 15 and also the calculation of N0XM is executed The D0X(-M) is set to the register 15 at the same time The calculation above is repeated The check and correction of the quotient are conducted during the repeated calculation

The module $D f^s$ for locally quasi-homogeneous free divisors

Abstract: We find explicit free resolutions for the $\scr D$-modules ${\scr D} f^s$ and ${\scr D}[s] f^s/{\scr D}[s] f^{s+1}$, where $f$ is a reduced equation of a locally quasi-homogeneous free divisor. These results are based on the fact that every locally quasi-homogeneous free divisor is Koszul free, which is also proved in this paper

Semistable reduction of a normal crossing \(\mathbb {Q}\)-divisor

Abstract: In a previous work, we have introduced the notion of embedded \(\mathbb {Q}\)-resolution, which allows the final ambient space to contain abelian quotient singularities, and A’Campo’s formula was calculated in this setting. Here, we study the semistable reduction associated with an embedded \(\mathbb {Q}\)-resolution and compute the mixed Hodge structure on the cohomology of the Milnor fiber in the isolated case using a generalization of Steenbrink’s spectral sequence. Examples of Yomdin-Le surface singularities are presented as an application.

A bogomolov unobstructedness theorem for log-symplectic manifolds in general position

Abstract: We consider compact Kahlerian manifolds $X$ of even dimension 4 or more, endowed with a log-symplectic holomorphic Poisson structure $\Pi$ which is sufficiently general, in a precise linear sense, with respect to its (normal-crossing) degeneracy divisor $D(\Pi)$. We prove that $(X, \Pi)$ has unobsrtuced deformations, that the tangent space to its deformation space can be identified in terms of the mixed Hodge structure on $H^2$ of the open symplectic manifold $X\setminus D(\Pi)$, and in fact coincides with this $H^2$ provided the Hodge number $h^{2,0}_X=0$, and finally that the degeneracy locus $D(\Pi)$ deforms locally trivially under deformations of $(X, \Pi)$. \