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.

Image processing apparatus, image processing method, and storage medium

Abstract: An image processing apparatus that generates an output image by deforming an input image by coordinate transformation, comprises a divisor calculation unit calculates a minimum value and a maximum value of a divisor, used in division operation of coordinate transformation; a coefficient calculation unit obtains a range of the divisor in a way that a result of the division operation becomes equal to or smaller than an allowable error, and calculates a normalization parameter by dividing a minimum value of the range by the minimum value of the divisor; a parameter adjustment unit calculates an adjustment parameter used in the coordinate transformation, and outputs the adjustment parameter; and an image deformation processing unit performs transformation processing of the coordinate information using the adjustment parameter, and outputs a result of the transformation processing.

On Eckl's pseudo-effective reduction map

Abstract: Suppose that X is a complex projective variety and L is a pseudo-effective divisor. A numerical reduction map is a quotient of X by all subvarieties along which L is numerically trivial. We construct two variants: the L-trivial reduction map and the pseudo-effective reduction map of [Eckl05]. We show that these maps capture interesting geometric properties of L and use them to analyze abundant divisors.

Digital filters for semiconductor devices

Abstract: A memory device that, in certain embodiments, includes a memory element and a digital filter. The digital filter may include a counter and a divider, where the divider is configured to divide a count from the counter by a divisor.

Divisors computing the minimal log discrepancy on a smooth surface

Abstract: We study a divisor computing the minimal log discrepancy on a smooth surface. Such a divisor is obtained by a weighted blow-up. There exists an example of a pair such that any divisor computing the minimal log discrepancy computes no log canonical thresholds.

Length functions in commutative rings with zero divisors

Abstract: Let R be a commutative ring. We investigate several functions which measure the length of factorizations of an element of R. Some of these functions are l,lU:R→ℕ0 (for R atomic) and L,LU:R→ℕ0∪{∞} where l(x)=lU(x)=L(x)=LU(x)=0 for x a unit, and for x not a unit l(x)=inf{n|x=x1⋯xn,xi irreducible}, lU(x)=inf{n|x=y1⋯ym⌈x1⋯xn⌉, a U-decomposition}, L(x)=sup{n|x=x1⋯xn,xi a nonunit}, and LU(x)=sup{n|x=y1⋯ym⌈x1⋯xn⌉ a U-factorization}. For R satisfying the ascending chain condition on principal ideals, we consider the ordinal-valued function L obtained by recursively defining L(x) to be the least ordinal strictly greater than L(y) for each proper divisor y of x.