Division (mathematics)

About: Division (mathematics) is a research topic. Over the lifetime, 12717 publications have been published within this topic receiving 87814 citations.

Electric control system

Abstract: My invention relates to electric control systems and more particularly to electric valve control systems for dynamo-electric machines. This application Is a division of my copending application Serial No. 176,281, filed May 24, 1937, now Patent No. 2,229,448, Jan. 21, 1941, and which is assigned...

Estimating the Locations of Multiple Change Points in the Mean

Abstract: Detecting and estimating the number and locations of multiple change points is difficult. Sometimes a single-change method can locate multiple shifts by recursively dividing the data at the most likely location of a single shift. However, a single-change method may not detect the presence of multiple changes and may not accurately estimate a division point when multiple changes are present. The Schwarz information criterion offers a direct way to estimate the number of shifts, but the locations maximizing the likelihood function must be known for each possible number of shifts. The latter task is computationally infeasible for a realistic amount of data. This paper proposes a general algorithm for estimating the likelihood-maximizing locations and gives an example in which multiple changes are detected. The performance is evaluated using simulation and the proposed method is shown to be superior to the recursive application of a single shift procedure.

Division algebras with infinite genus

Abstract: To what extent does the maximal subfield spectrum of a division algebra determine the isomorphism class of that algebra? It has been shown that over some fields a quaternion division algebra's isomorphism class is largely if not entirely determined by its maximal subfield spectrum. However in this paper, we show that there are fields for which the maximal subfield spectrum says little to nothing about a quaternion division algebra's isomorphism class. We give an explicit construction of a division algebra with infinite genus. Along the way we introduce the notion of a "linking field extension," which we hope will be of independent interest. We go on to show that there exists a field K for which (1) there are infinitely many nonisomorphic quaternion division algebras with center K, and (2) any two quaternion division algebra with center K are pairwise weakly isomorphic. In fact we show that there are infinitely many nonisomorphic fields satisfying these two conditions.