Note on the Lower Bound of Least Common Multiple by Shea-Ming Oon

“…Consider a sequence of positive integers in arithmetic progression with . Denote the least common multiple of by . …”
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The probabilistic number theory and continuum by Vilius Stakėnas

“…The conditions on bn are considered, which imply the regularity of distribution of B(n, α) in arithmetic prog­ressions for almost all α > 0. This allows to develop a piece of probabilistic number theory on sequences B(n, α) for almost all α > 0. …”
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Sequential Properties over Negative Pauli Pascal Table by Eunmi Choi, Jiin Jo

“…For polynomials x+yi and x+y−i satisfying the noncommutative multiplication yx=−xy, let C−1 and N−1 be the arithmetic tables, respectively. We investigate sequential properties of various diagonal sums over the tables C−1 and N−1 and prove that they are types of interlocked Fibonacci sequence and Padovan sequence.…”
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On Generalized Carleson Operators of Periodic Wavelet Packet Expansions by Shyam Lal, Manoj Kumar

“…An application of these theorems as convergence a.e. for the periodic Walsh-type wavelet packet expansion of block function with the help of summation by arithmetic means has been studied.…”
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New Modification on Heun’s Method Based on Contraharmonic Mean for Solving Initial Value Problems with High Efficiency by Abushet Hayalu Workie

“…In this paper, small modification on Improved Euler’s method (Heun’s method) is proposed to improve the efficiency so as to solve ordinary differential equations with initial condition by assuming the tangent slope as an average of the arithmetic mean and contra-harmonic mean. In order to validate the conclusion, the stability, consistency, and accuracy of the system were evaluated and numerical results were presented, and it was recognized that the proposed method is more stable, consistent, and accurate with high performance.…”
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Design of generic vedic ALU using reversible logic by Kanchan S. Tiwari

“…The proposed ALU architecture is optimized to perform fundamental arithmetic operations: addition, subtraction, multiplication, and division; as well as bitwise logical operations: AND, OR, and XOR. …”
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On a generalization of u-means by Francois Dubeau

“…When ϕ(x)=x, the (u,ϕ)-means are the u-means introduced by Bauer. The arithmetic, geometric and harmonic means are special cases.…”
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On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function by Tristan Guillaume

“…This paper provides explicit formulae for the probability that an arithmetic or a geometric Brownian motion will not cross an absorbing boundary defined as a step function during a finite time interval. …”
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Teaching of decimal positional number system and decimal fractions in the 5-th grade by Albertas Bakštys, Irena Šukienė, Albina Viliminė

“…This proves that acquaintance with such a complex concept as decimal fraction is must be started long before the arithmetic of decimal fractions is introduced. Teachers working experience using A. …”
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New Degree-Based Topological Indices of Toroidal Polyhex Graph by Means of M-Polynomial by Farkhanda Afzal, Mohammad Zeeshan, Deeba Afzal, Sufian Munawar, Dhan Kumari Thapa, Alina Mirza

“…Some new indices such as reduced reciprocal randic, arithmetic geometric, SK, SK1, SK2 indices, First Zagrab, the general sum-connectivity, SCIλ, and the forgotten index have been used. …”
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Equidistribution Modulo 1 by Wiem Gadri

“…The generalisation of questions of the classic arithmetic has long been of interest. One line of questioning, introduced by Car in 1995, inspired by the equidistribution of the sequence nαn∈N where 0<α<1, is the study of the sequence K1/l, where K is a polynomial having an l-th root in the field of formal power series. …”
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Topological Indices of Families of Bistar and Corona Product of Graphs by A. Khalid, N. Kausar, M. Munir, M. Gulistan, M. M. Al-Shamiri, T. Lamoudan

“…In this study, we study certain degree-based topological indices such as Randić index, Zagreb indices, multiplicative Zagreb indices, Narumi–Katayama index, atom-bond connectivity index, augmented Zagreb index, geometric-arithmetic index, harmonic index, and sum-connectivity index for the bistar graphs and the corona product KmoKn′, where Kn′ represents the complement of complete graph Kn.…”
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Computation of New Degree-Based Topological Indices of Graphene by V. S. Shigehalli, Rachanna Kanabur

“…Inspired by recent work on Graphene of computing topological indices, here we propose new topological indices, namely, Arithmetic-Geometric index (AG1 index), SK index, SK1 index, and SK2 index of a molecular graph G and obtain the explicit formulae of these indices for Graphene.…”
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Parallel features of the activities of mathematics professors in Gdansk, Vilnius and Kenigsberg in the middle of the XVIIth century by Evaldas Gečiauskas

“… In the middle of the XVIIth century professors of mathematics in Gdansk, Vilnius and Ke­nigsberg lectured on arithmetic, geometry, astronomy, calendar and determination of geographical coordinates. …”
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Polynomial effective equidistribution by Lindenstrauss, Elon, Mohammadi, Amir, Wang, Zhiren

“…We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of $\mathrm{SL}_2(\mathfrak{l})$ in arithmetic quotients of $\mathrm{SL}_2(\mathbb{C})$ and $\mathrm{SL}_2(\mathfrak{l})\times \mathrm{SL}_2(\mathfrak{l})$.The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.…”
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An Algorithm for Higher Order Hopf Normal Forms by A.Y.T. Leung, T. Ge

“…Illustrative examples include a cubic system, a quadratic system and a Duffing–Van der Pol system. We use exact arithmetic and find that the undamped Duffing equation can be represented by an exact polynomial differential amplitude equation in a finite number of terms.…”
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Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations by Xiaobin Guo, Dequan Shang

“…The fuzzy matrix systems is extended into three crisp systems of linear matrix equations according to arithmetic operations of LR fuzzy numbers. Based on pseudoinverse of matrix, the fuzzy approximate solution of original fuzzy systems is obtained by solving the crisp linear matrix systems. …”
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Schur m-Power Convexity of a Class of Multiplicatively Convex Functions and Applications by Wen Wang, Shiguo Yang

“…By applying the theory of majorization, several inequalities involving the pth power mean and the arithmetic, the geometric, or the harmonic means are presented.…”
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Some Improvements of Jensen’s Inequality via 4-Convexity and Applications by Hidayat Ullah, Muhammad Adil Khan, Tareq Saeed, Zaid Mohammed Mohammed Mahdi Sayed

“…We discuss some interesting relations for quasi-arithmetic and power means as consequences of main results. …”
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On Some Properties of Multiplicative Topological Indices in Silicon-Carbon by Abid Mahboob, Sajid Mahboob, Mohammed M. M. Jaradat, Nigait Nigar, Imran Siddique

“…In this paper, we compute the first and second multiplicative Zagreb indices (M1G and (M1G)), generalized multiplicative geometric arithmetic index (GAαIIG), and multiplicative sum connectivity and multiplicative product connectivity indices (SCIIG and PCIIG) of SiC4−Im,n and SiC4−IIm,n.…”
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