Results 11 to 20 of about 1,194 (217)
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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A note on hyperbolic quaternions
Universal Journal of Mathematics and Applications, 2018 In this work, we introduce hyperbolic quaternions and their algebraic properties. Moreover, we express Euler's and De Moivre's formulas for hyperbolic quaternions.
İşıl Arda Kösal
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A simple proof of generalizations of number-theoretic sums [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2022 For positive integers 𝑘, 𝑚, and 𝑛, let 𝑆𝑘 𝑚(𝑛) be the sum of all elements in the finite set {𝑥 𝑘 : 1 ≤ 𝑥 ≤ 𝑛⁄𝑚 , (𝑥, 𝑛) = 1}. The formula for 𝑆𝑘 𝑚(𝑛) is established and simpler formulae for 𝑆𝑘 𝑚(𝑛) under some conditions on 𝑚 and 𝑛 are verified. The
Yanapat Tongron +1 more
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The Desymmetrized PSL(2, Z) Group; Its ‘Square-Box’ One-Cusp Congruence Subgroups
Computer Sciences & Mathematics Forum, 2023 In this paper, the desymmetrized PSL(2, Z) group is studied. The Fourier coefficients of the non-holomorphic one-cusp Eisenstein series expansion are summed, and as a further result, a new dependence on the Euler’s γ constant is found.
Orchidea Maria Lecian
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Unification Theories: Means and Generalized Euler Formulas
Axioms, 2020 The main concepts in this paper are the means and Euler type formulas; the generalized mean which incorporates the harmonic mean, the geometric mean, the arithmetic mean, and the quadratic mean can be further generalized.
Radu Iordanescu +2 more
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An Examination of Counterexamples in Proofs and Refutations
Philosophia Scientiæ, 2009 : Lakatos’s seminal work Proofs and Refutations introduced the methods of proofs and refutations by discussing the history and methodological development of Euler’s formula V — E+F = 2 for three dimensional polyhedra.
Samet Bağçe, Can Başkent
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On a generalization of Euler's constant [PDF]
Surveys in Mathematics and its Applications, 2021 A one parameter generalization of Euler's constant γ from [Numer. Algorithms 46(2) (2007) 141--151] is investigated, and additional expressions for γ are derived.
Stephen Kaczkowski
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Coccolith arrangement follows Eulerian mathematics in the coccolithophore Emiliania huxleyi [PDF]
PeerJ, 2018 Background The globally abundant coccolithophore, Emiliania huxleyi, plays an important ecological role in oceanic carbon biogeochemistry by forming a cellular covering of plate-like CaCO3 crystals (coccoliths) and fixing CO2. It is unknown how the cells
Kai Xu, David Hutchins, Kunshan Gao
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Complex Numbers Related to Semi-Antinorms, Ellipses or Matrix Homogeneous Functionals
Axioms, 2021 We generalize the property of complex numbers to be closely related to Euclidean circles by constructing new classes of complex numbers which in an analogous sense are closely related to semi-antinorm circles, ellipses, or functionals which are ...
Wolf-Dieter Richter
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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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