One Kind New Hybrid Power Mean and Its Computational Formulae by Li Wang, Xuexia Wang

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Explicit decomposition of a rational prime in a cubic field by Saban Alaca, Blair K. Spearman, Kenneth S. Williams

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Even perfect numbers and their Euler's function by Syed Asadulla

“…The results obtained are all straightforward deductions from well-known elementary number theory.…”
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Introductory remarks on complex multiplication by Harvey Cohn

“…In its advanced form it is a unifying motivation of classical mathematics from elliptic integrals to number theory; and it is still of active interest. This interrelation is explored in an introductory expository fashion with emphasis on a central historical problem, the modular equation between j(z) and j(2z).…”
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Solutions to All-Colors Problem on Graph Cellular Automata by Xiaoyan Zhang, Chao Wang

“…We also introduce a new kind of All-Colors Problem, k-Random Weak-All-Colors Problem, which is relevant to both combinatorial number theory and cellular automata theory.…”
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Series and Connections Among Central Factorial Numbers, Stirling Numbers, Inverse of Vandermonde Matrix, and Normalized Remainders of Maclaurin Series Expansions ^† by Feng Qi

“…This paper presents an extensive investigation into several interrelated topics in mathematical analysis and number theory. The author revisits and builds upon known results regarding the Maclaurin power series expansions for a variety of functions and their normalized remainders, explores connections among central factorial numbers, the Stirling numbers, and specific matrix inverses, and derives several closed-form formulas and inequalities. …”
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Analytic Erdös-Turán conjectures and Erdös-Fuchs theorem by L. Haddad, C. Helou, J. Pihko

“…The sequences of such coefficients have a lot of similarity with sequences of natural numbers considered in additive number theory. It is this analogy that we pursue, thus establishing many properties and giving equivalent statements to the well-known Erdös-Turán conjectures in terms of supported series and extending to them a version of Erdös-Fuchs theorem.…”
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Survey of code-based digital signatures by Yongcheng SONG, Xinyi HUANG, Wei WU, Haixia CHEN

“…The rapid development of quantum computing theory and practice brings great uncertainty to the security of cryptography based on hard problems in number theory.Code-based hard problem is recognized as NP-complete problem, the complexity increases exponentially, and there is currently no threat of quantum computing to code-based cryptographic algorithm.Therefore, code-based algorithm can resist the quantum algorithm attack, which is one of the main directions of quantum-resistant cryptography.It is still an open problem to design secure and efficient code-based signatures.For many years, international researchers use classical and new methods to construct code-based signatures, but existing constructions are weak in security or poor in performance.Code-based signatures were comprehensively summarized and analyzed, and future research directions were indicated.…”
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A new class of generalized polynomials associated with Milne-Thomson-based poly-Bernoulli polynomials by Waseem Ahmad Khan, Divesh Srivastava, Kottakkaran Sooppy Nisar

“…Motivated by their importance and potential for applications in certain problems in number theory, combinatorics, classical and numerical analysis, and other field of applied mathematics, a variety of polynomials and numbers with their variants and extensions have recently been introduced and investigated. …”
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Research on high security G function algorithm by Rui CHEN, Zan LI, Jia SHI, Lei GUAN

“…The differential frequency hopping (DFH) overcomes the limitation of frequency hopping and improves the ability to resist tracking interference.The G function determines the DFH sequence and directly affects the performance of DFH communication systems.However,with the complication of wireless communication system such as large capacity DFH network,which poses huge challenges to the use of the number theory based and chaos theory assisted sequence.As a result,in order to improve the security of the system,the novel G function construction was proposed with the aid of hybrid encryption algorithm and the security of hybrid algorithm was analyzed.Moreover,the equivalence principle of G function algorithm and the encryption algorithm was proved.The simulation results show that the DFH sequence generated by the new G function has excellent performance and the performance of the DFH systems is improved greatly.…”
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On the System of Diophantine Equations x2-6y2=-5 and x=az2-b by Silan Zhang, Jianhua Chen, Hao Hu

“…The proof utilizes algebraic number theory and p-adic analysis which successfully avoid discussing the class number and factoring the ideals.…”
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Homological dimension based on a class of Gorenstein flat modules by Dalezios, Georgios, Emmanouil, Ioannis

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Survey of digital signature technology based on error correcting codes by Fang REN, Dong ZHENG, Jiu-lun FAN

“…The emergence of quantum algorithms have threatened the security of digital signature algorithms widely used currently,most of which based on some hard problems in number theory.The digital signature algorithms based on error correcting codes,which can resist quantum attack,has been studied by many researchers in recent years and there have been many research results in different areas,such as normal digital signature,blind signature,ring signature,group signature.Because of the fast computation speed and high security,it has become one of the most promising digital signature technologies.A comprehensive introduction was given and digital signature technologies based on error correcting codes were summarized,the key technologies were analyzed and the possible research directions in the future were pointed out.…”
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Analytical Relations and Statistical Estimations for Sums of Powered Integers by Stan Lipovetsky

“…Finding analytical closed-form solutions for the sums of powers of the first <i>n</i> positive integers is a classical problem of number theory. Analytical methods of constructing such sums produce complicated formulae of polynomials of a higher order, but they can be presented via the first two power sums. …”
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An improved method to determine basic probability assignment with interval number and its application in classification by Bowen Qin, Fuyuan Xiao

“…In this article, a new method integrating interval number theory and k -means++ cluster method is proposed to determine basic probability assignment. …”
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The Principle of Mathematical Induction: Applications in Physical Optics by Joseph Ivin Thomas

“…In the contemporary university milieu, the demonstrative scheme is taught as part of a course in discrete mathematics, set theory, number theory, graph theory, group theory, game theory, linear algebra, logic, and combinatorics. …”
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An Extensive Review of the Literature Using the Diophantine Equations to Study Fuzzy Set Theory by K. M. Abirami, Narayanan Veena, R. Srikanth, P. Dhanasekaran

“…An interdisciplinary approach of fuzzy theory with number theory, especially Diophantine equations, needs to be accomplished to overcome this problem. …”
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A new proof of Nishioka’s theorem in Mahler’s method by Adamczewski, Boris, Faverjon, Colin

“…In a recent work [3], the authors established new results about general linear Mahler systems in several variables from the perspective of transcendental number theory, such as a multivariate extension of Nishioka’s theorem. …”
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Solving the Problem of Time, Cost, and Quality Trade-Off in Project Scheduling under Fuzzy Conditions Using Meta-Heuristic Algorithms by Hojjatullah Ghadir, Seyed Ahmad Shayannia, Mehdi Amir Miandargh

“…This means that by fuzzy number theory, the specifications and conditions of a project are included in the problem of balancing time, cost, and quality. …”
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Social network user geolocating method based on weighted least squares by Wenqi SHI, Xiangyang LUO, Jiashan GUO

“…When providing location-based dating and other location-based services, social networks will confuse the displayed user distance text to protect the user’s location privacy.In order to verify whether the current location confusion mechanism adopted by social networks can effectively protect user’s accurate location, a social network user geolocating method based on weighted least squares was proposed.The method constructed real-world tests to collect a large number of confused distance texts in location dating service, and identified the real distance boundary of reported distance combined with real distance data.Then, based on the discrimination of the quadrant of the coordinate system where the target user was located, the position of probes was optimally deployed, and multiple preliminary position estimations of the target user were obtained by using the trilateration model.The weights of the longest and the shortest distance of the target user were determined by the estimated position, and the related objective function was constructed.The optimal solution of the objective function was calculated based on the weighted least squares, which was the final geolocating result of the target user.The proposed method inferred the location of social network user based on the distance boundary constraint, which avoided the frequent query of location services and ensured the geolocating efficiency.The actual geolocating results based on 500 WeChat users showed that, the proposed method can accurately geolocate the “eople nearby” users of WeChat.Compared with the existing typical geolocating methods based on space partition and heuristic number theory, the proposed method have better performance in geolocating accuracy and efficiency.The average geolocating error is reduced by more than 10%, and the number of location service quarries in the geolocating process is reduced by more than 50%.…”
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