Results 1 to 10 of about 6,793 (328)
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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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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Euler?s Exponential Formula for Semigroups [PDF]
Semigroup Forum, 2004 In this paper, the author presents several generalizations of Euler's exponential formula for some semigroups, which are not \(C_0\)-semigroups.
Cachia, Vincent
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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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An elementary proof of Euler's formula using Cauchy's method
, 2021 The use of Cauchy's method to prove Euler's well-known formula is an object of many controversies. The purpose of this paper is to prove that Cauchy's method applies for convex polyhedra and not only for them, but also for surfaces such as the torus, the
Jean‐Paul Brasselet +1 more
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EULER'S FORMULA VIA POTENTIAL FUNCTIONS
Journal of the Operations Research Society of Japan, 1994 Summary: A new proof of Euler's formula for polytopes is presented via an approach using potential functions. In particular, a connection between Euler's formula and the Morse relation from differential topology is established.
Ryuichi Hirabayashi +2 more
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Mathematics, 2021 In this paper, we find some inequalities which involve Euler’s function, extended Euler’s function, the function τ, and the generalized function τ in algebraic number fields.
Nicuşor Minculete, Diana Savin
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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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Applications of neutrosophic complex numbers in triangles [PDF]
Neutrosophic Sets and Systems, 2023 It may be difficult for researchers to memorize or remember the trigonometric ratios of any neutrosophic angle, and this is what prompted us to activate the role of the neutrosophic complex numbers for that.
Yaser Ahmad Alhasan +2 more
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The Derivation of the Riemann Analytic Continuation Formula from the Euler’s Quadratic Equation
Journal of Nigerian Society of Physical Sciences, 2022 The analysis of the derivation of the Riemann Analytic Continuation Formula from Euler’s Quadratic Equation is presented in this paper. The connections between the roots of Euler’s quadratic equation and the Analytic Continuation Formula of the Riemann ...
Opeyemi O. Enoch +2 more
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