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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Patent•
19 Jan 1955
TL;DR: In this article, a material handling device for transferring coal from railway cars to vessels is described, and the present application is a division of my copending application Serial No. 207,776 filed May 13, 1938, granted as Patent No. 2,216,742.
Abstract: This invention relates to material handling devices for transferring material such as coal from railway cars to vessels, and the present application is a division of my copending application Serial No. 207,776 filed May 13, 1938, granted as Patent No. 2,216,742. One form of device that is suitable...
32 citations
TL;DR: This paper defines the concepts of interval-valued intuitionistic fuzzy function (IVIFF) and develops two kinds of derivatives of IVIFFs and gives an equivalent condition for the existence of the derivative of an IVIFF.
Abstract: The interval-valued intuitionistic fuzzy set (IVIFS) generalizes Atanassov's intuitionistic fuzzy set (A-IFS) with the membership and non-membership degrees being intervals instead of real numbers, so it can contain more information. In this paper, we study the derivatives and differentials under interval-valued intuitionistic fuzzy environment. Firstly, we discuss the four change directions (the addition, subtraction, multiplication and division directions) of the interval-valued intuitionistic fuzzy values (IVIFVs); Secondly, we propose four kinds of limits (the addition, subtraction, multiplication and division limits) for different sequences of IVIFVs, and then we define the concepts of interval-valued intuitionistic fuzzy function (IVIFF) and study the continuities of IVIFFs; Thirdly, we develop two kinds of derivatives (the subtraction and division derivatives) of IVIFFs and give an equivalent condition for the existence of the derivative of an IVIFF. At last, we define the concepts of two k...
32 citations
TL;DR: The approach to steady-state size distribution is studied for a growing population of cells and incorporates cell growth at a linear rate and division into two equal daughters after a random time composed of an exponentially distributed phase and a constant deterministic phase.
Abstract: The approach to steady-state size distribution is studied for a growing population of cells. The model incorporates cell growth at a linear rate and division into two equal daughters after a random time composed of an exponentially distributed phase and a constant deterministic phase.
32 citations
TL;DR: Methods for selecting constant and linear approximations which minimize the maximum absolute error of the final result are developed.
Abstract: Newton-Raphson iteration provides a high-speed method for performing division. The Newton-Raphson division algorithm begins with an initial approximation to the reciprocal of the divisor. This value is iteratively refined until a specified accuracy is achieved. In this paper, we develop methods for selecting constant and linear approximations which minimize the maximum absolute error of the final result. These approximations are compared with previous methods which minimize the maximum relative error in the final result or the maximum absolute error in the initial value.
32 citations
TL;DR: This paper investigates a variant of intermediate power, limiting membrane nesting hence membrane division to constant depth, and proves that the resulting P systems can solve all problems in the counting hierarchy CH, which is located between PPP and PSPACE.
Abstract: Polynomial-time P systems with active membranes characterise PSPACE by exploiting membranes nested to a polynomial depth, which may be subject to membrane division rules. When only elementary leaf membrane division rules are allowed, the computing power decreases to PPP = P#P, the class of problems solvable in polynomial time by deterministic Turing machines equipped with oracles for counting or majority problems. In this paper we investigate a variant of intermediate power, limiting membrane nesting hence membrane division to constant depth, and we prove that the resulting P systems can solve all problems in the counting hierarchy CH, which is located between PPP and PSPACE. In particular, for each integer k ≥ 0 we provide a lower bound to the computing power of P systems of depth k.
32 citations