We introduce concepts of “recursive polynomial remainder sequence (PRS)” and “recursive subresultant,” and investigate their properties. In calculating PRS, if there exists the GCD (greatest common divisor) of initial polynomials, we calculate “recursively” with new PRS for the GCD and its derivative, until a constant is derived. We call such a PRS a recursive PRS. We define recursive subresult...

WITHINTHE CONFINES OF SPECIAL COLLECTIONS in libraries, an established practice of preservation for film and video collections is largely nonexistent. By comparison, the scale of resources needed to achieve meaningful programmatic efforts to preserve them is far greater than the resources libraries have assembled for traditional paper-based preservation. Management of moving image collections r...

We consider the distribution of spacings between consecutive elements in subsets of Z/qZ, where q is highly composite and the subsets are defined via the Chinese Remainder Theorem. We give a sufficient criterion for the spacing distribution to be Poissonian as the number of prime factors of q tends to infinity, and as an application we show that the value set of a generic polynomial modulo q ha...

A unique decoder for the Chinese remainder codes was stated in [1] in 2000. In this paper, we present a decoder which gives the same error correction radius by introducing syndromes of the Chinese remainder codes. The error positions can be found using a so–called error–locator integer Λ which appears in the proposed key equation. To find Λ, this key equation can be solved by the extended Eucli...

Nitrogen balance (NB) experiments allow calculation of N retention in the body by subtracting excreted feces (NF), urine (NU) and milk (NM) from intake (NI). In a previous study, we found that NB data with lactating dairy cows were generally high and, current meta-analysis, update our earlier study last 2 decades investigate probable causes error. A total 83 publications, 86 307 dietary treatme...

In this paper we will propose a high quality image steganography technique which can hide secret data within an image in such a way so that it is imperceptible to human eye. This method solves the overlapping problem of remainder and use modulo operator efficiently for hiding purpose. First, we calculate the base eight equivalent of target string. That increases the hiding capacity as well as r...

Player ONE chooses a meager set and player TWO, a nowhere dense set per inning. They play ω many innings. ONE's consecutive choices must form a (weakly) increasing sequence. TWO wins if the union of the chosen nowhere dense sets covers the union of the chosen meager sets. A strategy of TWO which depends on knowing only the uncovered part of the most recently chosen meager set is said to be a re...

Levinson’s Theorem in asymptotic integration of linear differential systems is strengthened in a quantitative way. It is shown that any decay in excess of absolute integrability appears with the remainder.

The time efficiency of many storage systems rely critically on the ability to perform a large number of evaluations of certain hashing functions fast enough. The remainder function B mod P , generally applied with a large prime number P , is often used as a building block of such hashing functions, which leads to the need of accelerating remainder evaluations, possibly using parallel processors...