Arithmetic of the sound of silence by Robert Madoi Nasaba

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Some inequalities in the arithmetic semigroups by Gintautas Bareikis

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New Results on the Geometric-Arithmetic Index by Akbar Jahanbani, Maryam Atapour, Zhibin Du

“…Let du denote the degree of vertex u∈VG. The geometric-arithmetic index of G is defined as GAG=∑uv∈EG2dudv/du+dv. …”
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About the possibility of the extension of the additive arithmetic by Livija Maliaukienė

“… In this paper the sequential variant of the additive arithmetic with equality and the non-logical symbols o, t, P, + , = is investigated and the proovable properties of the additional function nit is ascertained. …”
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Arithmetic-Analytic Representation of Peano Curve by Guangjun Yang, Xiaoling Yang, Ping Wang

“…Applying the iteration method of fractal, we established a simple arithmetic-analytic representation of the Peano curve as a function of ternary numbers. …”
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Further Results on a Curious Arithmetic Function by Long Chen, Kaimin Cheng, Tingting Wang

“…In this paper, we introduce an arithmetic function fp:N∗⟶Q+ defined by fpn≔n/pvpn1−vpn for any positive integer n. …”
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Arithmetic functions associated with infinitary divisors of an integer by Graeme L. Cohen, Peter Hagis

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Summatory Multiplicative Arithmetic Functions: Scaling and Renormalization by Leonid G. Fel

“…We consider a wide class of summatory functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mfenced separators="" open="{" close="}"><mi>f</mi><mo>;</mo><mi>N</mi><mo>,</mo><msup><mi>p</mi><mi>m</mi></msup></mfenced><mo>=</mo><msub><mo>∑</mo><mrow><mi>k</mi><mo>≤</mo><mi>N</mi></mrow></msub><mi>f</mi><mfenced separators="" open="(" close=")"><msup><mi>p</mi><mi>m</mi></msup><mi>k</mi></mfenced></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>∈</mo><msub><mi mathvariant="double-struck">Z</mi><mo>+</mo></msub><mo>∪</mo><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow></mrow></semantics></math></inline-formula> associated with the multiplicative arithmetic functions <i>f</i> of a scaled variable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>∈</mo><msub><mi mathvariant="double-struck">Z</mi><mo>+</mo></msub></mrow></semantics></math></inline-formula>, where <i>p</i> is a prime number. …”
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Finite and Infinite Arithmetic Progressions Related to Beta-Expansion by Bing Li, Chao Ma

“…We consider the sets of points x such that Aβ(x) contains arbitrarily long arithmetic progressions and includes infinite arithmetic progressions, respectively. …”
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An identity for a class of arithmetical functions of several variables by Pentti Haukkanen

Subjects: “…arithmetical functions of several variables…”
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A Note on Cube-Full Numbers in Arithmetic Progression by Mingxuan Zhong, Yuankui Ma

“…We obtain an asymptotic formula for the cube-full numbers in an arithmetic progression n≡lmod q, where q,l=1. By extending the construction derived from Dirichlet’s hyperbola method and relying on Kloosterman-type exponential sum method, we improve the very recent error term with x118/4029<q.…”
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On the influence of the arithmetical character of the parameters for the Lerch zeta-function by Jolita Ignatavičiūtė

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A Dynamic Dual Fixed-Point Arithmetic Architecture for FPGAs by G. Alonzo Vera, Marios Pattichis, James Lyke

“…In this context, a designer is left with the task of implementing several arithmetic cores for parallel processing while supporting high numerical precision with finite logical resources. …”
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Arithmetically Fast Position Transformation for View Synthesis and Depth Estimation by Krzysztof Wegner, Tomasz Grajek, Krzysztof Klimaszewski

“…As a result, the number of necessary arithmetic operations is reduced and some of the calculations can be reused for consecutive pixel position transformations. …”
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On Reciprocal Series of Generalized Fibonacci Numbers with Subscripts in Arithmetic Progression by Neşe Ömür

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An Adaptive Parallel Arithmetic Optimization Algorithm for Robot Path Planning by Ruo-Bin Wang, Wei-Feng Wang, Lin Xu, Jeng-Shyang Pan, Shu-Chuan Chu

“…Aiming at the issue of robot path planning with the goal of finding a collision-free optimal motion path in an environment with barriers, this study proposes an adaptive parallel arithmetic optimization algorithm (APAOA) with a novel parallel communication strategy. …”
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Solving problems in the text as main way in teaching applying arithmetic by Bronius Balčytis

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