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.

Coadjoint Orbits, Spectral Curves and Darboux Coordinates

Abstract: For generic rational coadjoint orbits in the dual \(\tilde gl(r)^{ + *}\) of the positive half of the loop algebra \(\tilde gl(r)^{ + *}\), the natural divisor coordinates associated to the eigenvector line bundles over the spectral curves project to Darboux coordinates on the Gl(r)-reduced space. The geometry of the embedding of these curves in an ambient ruled surface suggests an intrinsic definition of symplectic structure on the space of pairs (spectral curves, duals of eigenvector line bundles) based on Serre duality. It is shown that this coincides with the reduced Kostant-Kirillov structure. For all Hamiltonians generating isospectral flows, these Darboux coordinates allow one to deduce a completely separated Liouville generating function, with the corresponding canonical transformation to linearizing variables identified as the Abel map.

An Energy-Efficient, Yet Highly-Accurate, Approximate Non-Iterative Divider

Abstract: In1 this paper, we present a highly accurate and energy efficient non-iterative divider, which uses multiplication as its main building block In this structure, the division operation is performed by first reforming both dividend and divisor inputs, and then multiplying the rounded value of the scaled dividend by the reciprocal of the rounded value of the scaled divisor Precisely, the interval representing the fractional value of the scaled divisor is partitioned into non-overlapping sub-intervals, and the reciprocal of the scaled divisor is then approximated with a linear function in each of these sub-intervals The efficacy of the proposed divider structure is assessed by comparing its design parameters and accuracy with state-of-the-art, non-iterative approximate dividers as well as exact dividers in 45nm digital CMOS technology Circuit simulation results show that the mean absolute relative error of the proposed structure for doing 1 32-bit division is less than 02%, while the proposed structure has significantly lower energy consumption than the exact divider Finally, the effectiveness of the proposed divider in one image processing application is reported and discussed

Low latency integer divider and integration with floating point divider and method

Abstract: A method and device divides a dividend by a divisor, the dividend and the divisor both being integers. The method and device determine a maximum possible number of quotient digits (NDQ) based on a number of significant digits of the divisor and the dividend, normalizes the dividend and divisor, and calculates NDQ number of quotient digits from the normalized divisor and dividend.

Existence of Curves with Prescribed Topological Singularities

Abstract: Throughout this paper we study the existence of irreducible curves C on smooth projective surfaces S with singular points of prescribed topological types S_1,...,S_r. There are necessary conditions for the existence of the type \sum_{i=1}^r \mu(S_i) < aC^2+bC.K+c+1 for some fixed divisor K on S and suitable coefficients a, b and c, and the main sufficient condition that we find is of the same type, saying it is asymptotically optimal. Even for the case where S is the projective plane, ten years ago general results of this quality have not been known. An important ingredient for the proof is a vanishing theorem for invertible sheaves on the blown up S of the form O_{S'}(\pi^*D-\sum_{i=1}^r m_iE_i), deduced from the Kawamata-Vieweg Vanishing Theorem. Its proof covers the first part of the paper, while the middle part is devoted to the existence theorems. In the last part we investigate our conditions on ruled surfaces, products of elliptic curves, surfaces in projective 3-space, and K3-surfaces.