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20 hours ago · Similarly to what we said above, the quotient comes from stacking all the regions back on top of each other with the help of the Möbius transformations that relate them, merging the stack down, and then gluing the sides in a way given by two particular Möbius transformations that can be used to generate the whole group.
4 days ago · This chapter extends the Möbius function to the Soft Möbius function. The regular Möbius function, which is related to prime factorization, accepts three values: 1, 0, and − 1. Using Soft logic, we extend the function to the following five values: −1, − 0, 0, + 0, and 1.
4 days ago · TOPICS. Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld
2 days ago · The Möbius function \(μ(n)\) is a multiplicative function which is important in the study of Dirichlet convolution. It is an important multiplicative function in number theory and combinatorics. While the values of the function itself are not difficult to calculate, the function is the Dirichlet inverse of the unit function \({\bf ...
1 day ago · Bent functions are maximally nonlinear Boolean functions with an even number of variables, which include a subclass of functions, the so-called hyper-bent functions whose properties are stronger than bent functions and a complete classification of hyper-bent functions is elusive and inavailable.~In this paper,~we solve an open problem of Mesnager that describes hyper-bentness of hyper-bent ...
5 days ago · In contrast, Möbius Transformations highlight changes in polarization and do not require interval selection. Instead of using a single set of stringent criteria, this method generates an ensemble of transformations, requires several transformations generated from variations in parameter values.
4 days ago · example, the Möbius band is a well-known topological structure discovered independently by the German mathematicians and astronomers Möbius and Johanlestein in 1858,4 and macrocycles with the Möbius ring structure have been successfully synthesized recently.5 Besides, infinity-shaped or
