Topic
Division (mathematics)
About: Division (mathematics) is a research topic. Over the lifetime, 12717 publications have been published within this topic receiving 87814 citations.
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12 Sep 2005
TL;DR: In this paper, a new type of monomial division called Janet-like is introduced, which preserves all algorithmic merits of Janet division, including Noetherianity, continuity and constructivity, and the algorithm for constructing Grobner bases based on the new division is more efficient than its Janet division counterpart.
Abstract: In this paper we introduce a new type of monomial division called Janet-like, since its properties are similar to those of Janet division. We show that the former division improves the latter one. This means that a Janet divisor is always a Janet-like divisor but the converse is generally not true. Though Janet-like division is not involutive, it preserves all algorithmic merits of Janet division, including Noetherianity, continuity and constructivity. Due to superiority of Janet-like division over Janet division, the algorithm for constructing Grobner bases based on the new division is more efficient than its Janet division counterpart.
19 citations
Patent•
31 May 2018
TL;DR: In this article, a wafer processing method is described, which includes a first laser processing step of forming a first modified layer inside the wafer by applying a laser beam at a wavelength which transmits the wafers along first projected division lines, a second laser process step of formulating a second modified layer outside the wofers, and a grinding step of grinding a reverse side of the walfers to thin the reverse side to a predetermined thickness and at the same time dividing the wofters into a plurality of chips starting from the first and second modified layers.
Abstract: A wafer processing method is provided. The wafer processing method includes a first laser processing step of forming a first modified layer inside the wafer by applying a laser beam at a wavelength which transmits the wafer along first projected division lines, a second laser processing step of forming a second modified layer inside the wafer excluding non-processed regions in intersecting regions where the first and second projected division lines intersect each other by applying a laser beam at a wavelength which transmits the wafer along the second projected division lines, and a grinding step of grinding a reverse side of the wafer to thin the wafer to a predetermined thickness and at the same time dividing the wafer into a plurality of chips starting from the first and second modified layers. In the second laser processing step, no second modified layers are formed in the non-processed regions.
19 citations
01 Sep 2006
TL;DR: A low-power, area-efficient four-way 32-bit multifunction arithmetic unit has been developed for programmable shaders for handheld 3D graphics systems and unified into a single arithmetic platform with maximum four-cycle latency and single-cycle throughput.
Abstract: A low-power, area-efficient 128-bit multifunction arithmetic unit has been developed for programmable shaders for handheld 3-D graphics systems. It adopts the logarithmic number system (LNS) at the arithmetic core for the single cycle throughput and the small-size low-power unification of various complex arithmetic operations such as power, logarithm, trigonometric functions, vector multiplication, division, square root and inner product. An uneven 24-piecewise logarithmic conversion scheme is proposed with 0.8% of maximum conversion error. A 93K gate test chip is fabricated with 0.18-?m CMOS technology. It operates at 210MHz with 15.3mW power consumption at 1.8V.
19 citations
Patent•
09 Nov 1965
19 citations