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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Hermite Polynomials and their Applications Associated with Bernoulli and Euler Numbers by Dae San Kim, Taekyun Kim, Seog-Hoon Rim, Sang Hun Lee

“…We derive some interesting identities and arithmetic properties of Bernoulli and Euler polynomials from the orthogonality of Hermite polynomials. …”
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Study of Vanadium Carbide Structures Based on Ve and Ev-Degree Topological Indices by Abdul Rauf, Saba Maqbool, Muhammad Naeem, Adnan Aslam, Hamideh Aram, Kraidi Anoh Yannick

“…In particular, we have computed the closed forms of Zagreb, Randic, geometric-arithmetic, and atom-bond connectivity (ABC) indices of vanadium carbide structure based on ev and ve degrees. …”
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Numerical Algorithm for Delta of Asian Option by Boxiang Zhang, Yang Yu, Weiguo Wang

“…In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. …”
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Approximate Solution of LR Fuzzy Sylvester Matrix Equations by Xiaobin Guo, Dequan Shang

“…Then we extend the fuzzy linear system into two systems of linear equations according to the arithmetic operations of LR fuzzy numbers. The fuzzy approximate solution of the original fuzzy matrix equation is obtained by solving the crisp linear systems. …”
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Conditioned secure access control model based on multi-weighted roles and rules in workflow system

“…A rule-based modeling method of separation of du- ties was discussed and its improved rule consistency check arithmetic was given.…”
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Solution of Linear and Quadratic Equations Based on Triangular Linear Diophantine Fuzzy Numbers by Naveed Khan, Naveed Yaqoob, Mudassir Shams, Yaé Ulrich Gaba, Muhammad Riaz

“…We first introduce the concept of TLDFNs and then study the arithmetic operations on these numbers. We find a method for the ranking of these TLDFNs. …”
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On Reverse Valency Based Topological Characterization of a Chemical Compound by Maria Singaraj Rosary, Samuel Asefa Fufa

“…In this paper, we give explicit expression of the reverse general Randic index, the reverse atom bond connectivity index, the reverse geometric arithmetic index, the reverse forgotten index, the reverse Balaban index, the reverse augmented index, and different types of reverse Zagreb indices of the metal-organic framework M1TPyP-M2 (TPyP = 5, 10, 15, 20-tetrakis (4-pyridyl) porphyrin and M1, M2 = Fe and Co). …”
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Symmetric Blind Decryption with Perfect Secrecy by Juha Partala

“…We also devise a symmetric blind decryption scheme based on modular arithmetic on a ring Zp2, where p is a prime, and show that it satisfies our notion of perfect secrecy.…”
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Changes in Potato Production and Consumption in Poland in 2001-2020 by Anna Kowalska, Klaudia Gurkowa

“…During the development of the data, the basic methods of statistical analysis were used, i.e. correlation, change dynamics, arithmetic mean and standard deviation.…”
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Note on the quadratic Gauss sums by George Danas

“…Let p be an odd prime and {χ(m)=(m/p)}, m=0,1,...,p−1 be a finite arithmetic sequence with elements the values of a Dirichlet character χ  modp which are defined in terms of the Legendre symbol (m/p), (m,p)=1. …”
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Indicadores ambientais de sustentabilidade para uma instituição federal de ensino superior by Andréia Castro de Paula Nunes, Leci Martins Menezes Reis, Robson Garcia da Silva

“…Among the universe of 50 indicators weighted by specialists, 6 obtained the highest simple arithmetic means of weights and, therefore, were considered the most relevant sustainability environmental indicators for the UFRN.…”
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On Accuracy of Testing Decryption Failure Rate for Encryption Schemes under the LWE Assumption by Lin Wang, Yang Wang, Huiwen Jia

“…We quantitatively analyze how the floating-point arithmetic and neglecting small probabilities impact the precision, and propose a new effective and efficient test of the failure probability. …”
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Study of Ge-Sb-Te Superlattice Structure Based on Topological Descriptors by Xiujun Zhang, Muhammad Naeem, Abdul Rauf, Adnan Aslam, Zafar Iqbal, Abudulai Issa

“…We have calculated the Zagreb, geometric-arithmetic, Randic, and atom-bond connectivity indices of the Ge-Sb-Te superlattice structure using the ev- and ve-degrees. …”
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On Omega Index and Average Degree of Graphs by Sadik Delen, Musa Demirci, Ahmet Sinan Cevik, Ismail Naci Cangul

“…Average degree of a graph is defined to be a graph invariant equal to the arithmetic mean of all vertex degrees and has many applications, especially in determining the irregularity degrees of networks and social sciences. …”
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Kinematics Singularity Solution and Simulation Analysis of Redundant Manipulator based on Screw Theory by Xinhong Feng

“…The analysis results reveals that there are four singular conditions of the seven axis cooperative KUKA robot within its workspace， and the simulation results verifies the correctness of the analysis， and it lays a foundation for subsequent manipulator singularity avoidance arithmetic research.…”
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On the Origins of Calculation Abilities by A. Ardila

“…Counting, starting with finger sequencing, has been observed in different ancient and contemporary cultures, whereas number representation and arithmetic abilities are found only during the last 5000–6000 years. …”
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AN IMPROVED ALGORITHM FOR TIME DOMAIN AVERAGING BASED ON FRACTIONAL DELAY FILTERING by ZOU JinChun, QU Lei, DAI GuangHao, WANG XiuFeng, SHEN YuDi

“…For reducing the influence of truncation error on the accuracy of time domain averaging（ TDA） induced by noninteger-period sampling,an improved algorithm of TDA based on fractional delay filtering（ FDF） is presented.On the basis of analyzing the disadvantages of current methods of TDA and the characteristics of FDF,a presently improved method of signal truncation was used in the method to avoid the accumulation of truncation error and obtain a delay factor on each of the truncated signals,the reconstruction and resample for the truncated signals were implemented with FDF,and finally the arithmetic mean were computed after all of the truncated signals were added.The theoretical analysis and experimental results demonstrate that the method which fully makes using of the advantages of FDF on the change of delay factor,apparently reduces the truncation error of signals with non-integer-period sampling,and could obviously improve the accuracy of TDA without key-phase signal.…”
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On Topological Indices of Fractal and Cayley Tree Type Dendrimers by Muhammad Imran, Abdul Qudair Baig, Waqas Khalid

“…These indices include atom bond connectivity index, geometric arithmetic index and their fourth and fifth versions, Sanskruti index, augmented Zagreb index, first and second Zagreb indices, and general Randic index for α={-1,1,1/2,-1/2}. …”
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Impact Response Prediction Method of Packaging Systems with a Key Component considering Different Excitations and Cushioning Materials by Heye Xiao, ChiZhen Xu, Focai Yuan, Xudong Zhang, Junqiang Bai, Jie Zhou

“…To solve the nonlinear dynamic equations of the models, Newmark method is combined with Newton-Arithmetic mean method to transfer nonlinear equations to the linear discretization equations. …”
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