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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Optimization of movement activity and the mental state of students by dance aerobics by Natalia Chuprun, Sergey Zakopaylo, Mykola Shulga, Alexander Gordienko

“…Unpaired test, applied in comparative statistics, was performed in order to compare the arithmetic means of two independent data sets (experimental and control groups). …”
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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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Study of a new packet marking scheme for DDoS attack source traceback by LI Jin-ming, WANG Ru-chuan

“…Meanwhile, a new safe verified packet marking scheme had been brought forward to countermeasure the information forged by routes which had been controlled by an attacker, and this forged information should disturb the arithmetic of rebuilding the attacking path. Lastly, this scheme’s performances were emulated and tested and the result shows that the performances are better than other packet marking schemes.…”
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STATISTICAL PROCESSING OF RESULTS OF TESTING OF STUDENTS by Yulia V. Gumennikova, Elena N. Ryabinova, Ruzilya N. Chernitsina

“…Built interval variation series calculated the most important numerical characteristics of random variable - the sample mean (arithmetic mean value of the flag of sample), the sample variance (the arithmetic average of the squared deviations of the observed values of the trait from their average values) and sample standard deviation was given the opportunity to build a histogram of relative frequencies - a stepped shape consisting of rectangles whose bases are partial intervals, and the height equal to the density of the relative frequency. …”
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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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Study of equivalent point-to-point transmission model for coded relay cooperations by Qiu-xia ZHANG, Feng-fan YANG, Shun-wai ZHANG, Lin LUO

“…LDPC-coded relay cooperation and its joint iterative decoding based on the bi-layer Tanner graph were investigated.The coded relay cooperation becomed an equivalent and relatively simple point-to-point transmission model by introducing the notation of average arithmetic/geometr SNR for the receiver in the destination,which could be employed to perform the further study on more complex coded relay cooperations.Both LDPC-coded relay cooperation and its equivalent point-to-point model have almost the same performance by theoretical analysis and ical simulation,which proves the validity of the introduced equivalent model and the joint iterative decoding based on bi-layer Tanner graph.…”
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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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Study of CABAC-based digital video encryption in the H.264/AVC standard by BAO Xian-yu1, JIANG Jian-guo1.2, YUAN Wei1, LI Yuan1

“…Several candidate domains were analyzed and summarized to apply encryption to the latest video coding standard H.264/AVC,and a novel digital video encryption scheme based on CABAC（context-based adaptive binary arithmetic coding） was proposed.During the CABAC encoding,two kinds of secure encryption operations including RCME（regular coding mode encryption） and BCME（bypass coding mode encryption） were utilized,in order to encrypt residual coefficient codeword,motion vector difference codeword and intra-prediction mode,respectively.The experimental results show that the scheme has significant advantages on security,coding efficiency,and errors robustness.…”
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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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Research on Radio Network Intelligent Frequency Selection Technology Based on an Adaptive Genetic Algorithm by Wenjun Wang

“…In order to solve the problem of selecting frequency more and more difficultly for radio network,an intelligent frequency selection technology based on an adaptive genetic algorithm was proposed.Frequencies were selected for whole radio network from the perspective of intelligent optimization.On the basis of the standard genetic algorithm,this novel method improved genetic operators,and the preservation of the optimal individual algorithm to ensure the diversity of the population was introduced.Therefore,the arithmetic which did well in avoiding some deficiencies of the traditional frequency selection algorithm prevented local optimization and ran into overall optimization ultimately.Theoretical analysis and simulation results show that the new algorithm in solving the problem of frequency selection for large-scale network has higher efficiency and precision than the traditional algorithm,and stability is significantly enhanced.…”
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