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Tables
Published in William F. Ames, George Cain, Y.L. Tong, W. Glenn Steele, Hugh W. Coleman, Richard L. Kautz, Dan M. Frangopol, Paul Norton, Mathematics for Mechanical Engineers, 2022
A permutation is an ordered arrangement (sequence) of all or part of a set of objects. The number of permutations of n objects taken r at a time is p(n,r)=n(n−1)(n−2)⋯(n−r+1)=n!(n−r)!
Elementary Algebra and Geometry
Published in Richard C. Dorf, Ronald J. Tallarida, Pocket Book of Electrical Engineering Formulas, 2018
Richard C. Dorf, Ronald J. Tallarida
A permutation is an ordered arrangement (sequence) of all or part of a set of objects. The number of permutations of n objects taken r at a time is p(n,r)=n(n−1)(n−2)…(n−r+1)=n!(n−r)!
Probability and Statistics
Published in Paul J. Fortier, George R. Desrochers, Modeling and Analysis of Local Area Networks, 1990
Paul J. Fortier, George R. Desrochers
Permutations and combinations of elements in a sample space may take many different forms. Often, we can form probability measures about combinations of sample points, and the basic combinations and permutations discussed below are of use in this task. By definition, a combination is an unordered selection of items, whereas a permutation is an ordered selection of items. The most basic combination involves the occurrence of one of n1 events, followed by one of n2 events, and so on to one of nk events. Thus, for each path taken to get to the last event k, there are nk possible choices. Backing up one level, there were nk−1 choices at that level, thereby yielding nk−1n choices for the last two events. Following similar logic back up to the first level yields () n1n2…nk − 1nk=∏i=ikni
Structure of the w-solution set of the tensor complementarity problem
Published in Optimization, 2023
Sonali Sharma, K. Palpandi, Punit Kumar Yadav
Let in be a column adequate tensor and be a permutation matrix of order n. Since is a permutation matrix, there exists a bijection map such that Let . Then it is easy to check that Let satisfies . If we set , then we have From the above equation, we get . Since is column adequate, . This implies that from Equation (3). Hence is a column adequate tensor.The proof follows similarly as (a).
Accurate screw detection method based on faster R-CNN and rotation edge similarity for automatic screw disassembly
Published in International Journal of Computer Integrated Manufacturing, 2021
Xinyu Li, Ming Li, Yongfei Wu, Daoxiang Zhou, Tianyu Liu, Fang Hao, Junhong Yue, Qiyue Ma
Finite group is a rather mature discipline in Mathematics, the properties and derived methods of which are widely used for image processing. The symmetric group defined over any set forms the finite group, the elements of which are all bijections from the set to itself, and the group operation is the composition of functions. In particular, the finite symmetric group defined over a finite set of symbols, consists of permutation operations that can be performed on symbols. Because there are ( factorial) such permutation operations, the order (number of elements) of the symmetric group is . For regular polygons, the mapping invariance is mainly reflected in the equidistant transformations of their vertices, implying that they are entirely consistent, before and after a specific angle of rotation (Ledermann 1976).
Closures and openings of ternary relations
Published in International Journal of General Systems, 2020
Lemnaouar Zedam, Nourelhouda Bakri, Bernard De Baets
Next, we recall the ternary relations obtained by permuting a given ternary relation. A permutation σ of a 3-element set is a bijection from U to itself. We use the shorthand notation instead of . The six permutations of U are given by For a ternary relation T on X and any of the above six permutations σ, the ternary relation on X is defined as Zedam, Barkat, and De Baets (2018)