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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Book•
12 Mar 1991
TL;DR: This work presents a general model of the Bacterial Division Cycle and the Conservation Laws of the Division Cycle, which describes the growth and division of bacteria in the Eukaryotic Division Cycle.
Abstract: Prologue. Bacterial Growth. A General Model of the Bacterial Division Cycle. Experimental Analysis of the Bacterial Division Cycle. Cytoplasm Synthesis during the Division Cycle. DNA Replication during the Bacterial Division Cycle. Synthesis of the Cell Surface during the Division Cycle. Density and Turgor during the Division Cycle. Variability of the Division Cycle. The Segregation of DNA and the Cell Surface. Transitions and the Bacterial Life Cycle. The Division Cycle of Caulobacter crescentus. Growth and Division of Streptococcus. Growth and Division of Bacillus. The Growth Law and Other Topics. The Eukaryotic Division Cycle. Conservation Laws of the Division Cycle. Epilogue. Bibliography. Author Index. Subject Index.
128 citations
Posted Content•
TL;DR: MILP method is extended to search integral distinguishers of block ciphers based on division property with block size larger than 32 to solve the challenge of solving bit-based division property of SIMON32.
Abstract: Division property is a generalized integral property proposed by Todo at EUROCRYPT 2015, and very recently, Todo et al. proposed bit-based division property and applied to SIMON32 at FSE 2016. However, this technique can only be applied to block ciphers with block size no larger than 32 due to its high time and memory complexity. In this paper, we extend Mixed Integer Linear Programming (MILP) method, which is used to search differential characteristics and linear trails of block ciphers, to search integral distinguishers of block ciphers based on division property with block size larger than 32.
127 citations
Patent•
17 Oct 1996
TL;DR: A flow-dividing and conversion arrangement is proposed in this paper, where a substance is guided to a series of openings from a total flow channel (K1) guiding the substance in a combined flow.
Abstract: The invention concerns a flow-dividing and conversion arrangement (1) comprising a dividing system in which a substance is guided to a series of openings (3) from a total flow channel (K1) guiding the substance in a combined flow. At a first division point (T1), the total flow (K1) is branched off into two channels. Each channel end in the preceding stage branches into two channels which divide the flow and deflect the divided flows in opposite directions along the length of the arrangement. In order to improve the dividing function, the total flow channel (K1) merges at the first division point (T1) into two parallel, adjacent sections of partial flow channels (K2a, K2b) which guide the substance in the same direction. In the regions before, at and after the division point (T1) the flow is rectilinear or at least approximately rectilinear.
122 citations
TL;DR: The error of approximation for repeated use of the multiplication operand is examined and it is shown it can be sufficiently large in simple circumstances to produce erroneous results.
120 citations