Division (mathematics)

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

Operation support device of field work vehicle

Abstract: PROBLEM TO BE SOLVED: To provide operation support information such as the field position, travel tracks, work tracks, etc., of a field work vehicle, such as a tractor, moving about in an arbitrary division of a field on the work of the field work vehicle. SOLUTION: Field information and work information such as field division lines 1, a mark 2 for displaying a work vehicle, travel tracks 3 and work tracks 4 up to now, work divisions, work contents, and word widths, and a recommended work route 5 for improving the efficiency and accuracy of works in response to the present position of the work vehicle are displayed on the display section of a display device. Grid lines 6 parallel to standard lines such as the short and long sides of a field division are displayed through spaces in the display section of the display device.

Division cryptanalysis of block ciphers with a binary diffusion layer

Abstract: In this study, the authors propose an accurate approach to model the propagation of the division property of linear layers by the smallest amount of inequalities. The solutions of the inequalities are exactly the division trails of a linear transformation. Therefore, the description is compact and optimal. As applications of their results, they present a 7-round integral distinguisher for both Midori64 and Midori128. The designers of Midori only obtained a 3.5-round integral characteristic. For Skinny64, they find a 10-round integral distinguisher which was previously found by the designers. It is well to remind that their result proves that 7 rounds and 10 rounds are the upper bounds of Midori and Skinny64 correspondingly when searching for integral distinguishers based on division property. The significance of their result lies in that they shed light on how far division cryptanalysis can influence the security analysis of block ciphers with a binary diffusion layer, and their technique can be used to prove security against division cryptanalysis.

On the multiplicative structure of finite division rings

Abstract: All division ringsD of 16, 27, 32, 125 and 343 elements are shown to have aright primitive elementp such that $$\mathcal{D}* = \{ e,ep,(ep)p,...,(...(ep)p...)p\} .$$ That is, the multiplicative loop is the set of all right multiples of the identitye by the elementp. A construction of Dickson [5] is used to show that all commutative division algebras three-dimensional over a finite field not of characteristic 2 have a primitive element. Examples of division rings of 27, 29 and 211 elements with right primitive elements are given. Finally, a “pre-semifield” is exhibited that does not have a right primitive element.

Visual math teaching method

Abstract: A visual method of teaching arithmetic, in which graphical representations of familiar objects are used instead of numbers, is particularly well suited for children who are visually oriented and have difficulty with numbers. The shapes of the objects resemble the numerals zero through nine. The objects may appear in any visual medium. Students are first shown examples of multiplication, division, addition, and subtraction, in which objects replace numbers. Each object is then shown by itself. The numeral that corresponds to the number value of each object is then overlaid on top of each object. Students are also shown groups of colored dots or balls, in which the colors of the dots match the colors of the objects and the number of dots corresponds to the numerical value represented by its corresponding object.