Results 1 to 10 of about 606 (166)
A new Euler's formula for DNA polyhedra. [PDF]
PLoS ONE, 2011 DNA polyhedra are cage-like architectures based on interlocked and interlinked DNA strands. We propose a formula which unites the basic features of these entangled structures.
Guang Hu, Wen-Yuan Qiu, Arnout Ceulemans
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Euler's Polyhedron Formula [PDF]
Formalized Mathematics, 2008 where V , E, and F are, respectively, the number of vertices, edges, and faces of p. The formula was first stated in print by Euler in 1758 [11]. The proof given here is based on Poincare’s linear algebraic proof, stated in [17] (with a corrected proof in [18]), as adapted by Imre Lakatos in the latter’s Proofs and Refutations [15].
Jesse Alama
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A theorized new class of polyhedral hydrocarbons of molecular formula CnHn and their bottom-up scaffold expansions into hyperstructures [PDF]
Scientific Reports, 2021 We address the use of Euler's theorem and topological algorithms to design 18 polyhedral hydrocarbons of general formula CnHn that exist up to 28 vertexes containing four- and six-membered rings only; compounds we call “nuggets”.
Camila M. B. Machado +3 more
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Euler's Formula and De Moivre's Formula for Quaternions
Missouri Journal of Mathematical Sciences, 1999 Natural generalizations of Euler's formula and De Moivre's formula for quaternions are derived.
Eungchun Cho
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An Automatic Proof of Euler's Formula [PDF]
Computer Science Journal of Moldova, 2005 In this information age, everything is digitalized. The encoding of functions and the automatic proof of functions are important. This paper will discuss the automatic calculation for Taylor expansion coefficients, as an example, it can be applied to
Jun Zhang
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De Moivre's Formula and Euler's Formula for Octonions
, 2014 In this paper, we generalized De Moivre's formula and Euler's formula to octonions and find the roots of generalized octonions using these formulae.
Cristina Flaut, Vitalii Shpakivskyi
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K-regular decomposable incidence structure of maximum degree [PDF]
Mathematica Moravica, 2023 This paper discusses incidence structures and their rank. The aim of this paper is to prove that there exists a regular decomposable incidence structure J = (P, B) of maximum degree depending on the size of the set and a predetermined rank.
Stošović Dejan +2 more
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Euler's totient function applied to complete hypergroups
AIMS Mathematics, 2023 We study the Euler's totient function (called also the Euler's phi function) in the framework of finite complete hypergroups. These are algebraic hypercompositional structures constructed with the help of groups, and endowed with a multivalued operation,
Andromeda Sonea, Irina Cristea
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The completion of Euler's factoring formula
Rocky Mountain Journal of Mathematics, 2013 Richard Blecksmith +2 more
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Euler-Maclaurin formulae [PDF]
Mathematical Inequalities & Applications, 2003 A number of inequalities, for functions whose derivatives are either functions of bounded variation or Lipschitzian functions or functions in L_p-spaces, is proved by applying the Euler-Maclaurin formulae. The results are applied to obtain some error estimates for the Maclaurin quadrature rules.
Marko Matić +2 more
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