181 research outputs found
A note on factorization of the Fermat numbers and their factors of the form 3h2\sp n+1
summary:We show that any factorization of any composite Fermat number into two nontrivial factors can be expressed in the form for some odd and , and integer . We prove that the greatest common divisor of and is 1, , and either or , i.e., for an integer . Factorizations of into more than two factors are investigated as well. In particular, we prove that if then and
There are only two nonobtuse binary triangulations of the unit -cube
Triangulations of the cube into a minimal number of simplices without
additional vertices have been studied by several authors over the past decades.
For this so-called simplexity of the unit cube is now
known to be , respectively. In this paper, we study
triangulations of with simplices that only have nonobtuse dihedral
angles. A trivial example is the standard triangulation into simplices. In
this paper we show that, surprisingly, for each there is essentially
only one other nonobtuse triangulation of , and give its explicit
construction. The number of nonobtuse simplices in this triangulation is equal
to the smallest integer larger than .Comment: 17 pages, 7 figure
Generalization of the Zlámal condition for simplicial finite elements in
summary:The famous Zlámal's minimum angle condition has been widely used for construction of a regular family of triangulations (containing nondegenerating triangles) as well as in convergence proofs for the finite element method in . In this paper we present and discuss its generalization to simplicial partitions in any space dimension
Kleinova čtyřgrupa
summary:The article deals with properties of the Klein Four-Group and its occurrences not only in mathematics
Wireless Power Transmission System for Powering Rotating Parts of Automatic Machineries
This paper deals with the analysis of a suitable compensation topology of a wireless power transmission system for powering the rotating parts of modern automatic machine tools. It summarizes the important properties of the serio-parallel compensation topology suitable for this application and demonstrates a detailed mathematical derivation using the first harmonic approximation. The paper details the industrial implementation of the system in a specific automatic machine tool application and demonstrates the strong technical advantages of the proposed design. Important theoretical conclusions and technical assumptions made when considering the system layout are verified by experimental laboratory measurements and the final deployment of the technology in the professional tool DMU 40 eVo linea
The maximum angle condition is not necessary for convergence of the finite element method
We show that the famous maximum angle condition in the finite element analysis is not necessary to achieve the optimal convergence rate when simplicial finite elements are used to solve elliptic problems. This condition is only sufficient. In fact, finite element approximations may converge even though some dihedral angles of simplicial elements tend to π
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