Graph Theory Algorithms of Hamiltonian Cycle from Quasi-Spanning Tree and Domination Based on Vizing Conjecture by T. Anuradha, T. Lakshmi Surekha, Praveena Nuthakki, Bullarao Domathoti, Ganesh Ghorai, Faria Ahmed Shami

“…As a result, when the Lemmas 1 and 2 theorems are compared, the greedy routing method of Hamiltonian cycle faces generates valuable output from a quasi-spanning tree. …”
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APPROXIMATELY SINGULAR WAVELET by V. M. Romanchak

“…In the approximation by the method of singular wavelets, summation of Nadaraya-Watson kernel regression estimates with the smoothing parameter takes place, which solves the problem of the optimal choice of this parameter.In the main part of the paper theorems are formulated that determine the properties of the regularized wavelet transform. …”
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A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings by Suwicha Imnang, Suthep Suantai

“…In this paper, weak and strong convergence theorems of the sequence {xn} to a common fixed point of a finite family of nonexpansive mappings Ti  (i=1,2,…,r) are established under some certain control conditions.…”
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On geometry of fixed figures via φ−interpolative contractions and application of activation functions in neural networks and machine learning models by Khairul Habib Alam, Yumnam Rohen, Anita Tomar, Mohammad Sajid

“…In this work, we introduce novel postulates to establish fixed figure theorems with a focus on their extension to the domain of mvb−metric spaces. …”
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Minimal operational theories: classical theories with quantum features by Davide Rolino, Marco Erba, Alessandro Tosini, Paolo Perinotti

“…We demonstrate that minimal theories with conditioning and a spanning set of non-separable states satisfy two quantum no-go theorems: no-information without disturbance and no-broadcasting. …”
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Extracting the symmetries of nonequilibrium quantum many-body systems by Aleksandr N. Mikheev, Viktoria Noel, Ido Siovitz, Helmut Strobel, Markus K. Oberthaler, Jürgen Berges

“…Symmetries play a pivotal role in our understanding of the properties of quantum many-body systems. While there are theorems and a well-established toolbox for systems in thermal equilibrium, much less is known about the role of symmetries and their connection to dynamics out of equilibrium. …”
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Effects of Self-Explanation on the Expansion and Indulgent of Mathematics Teaching: Case of the Students of the University of Wachemo by Abdela Atisso, Dawit Kachine, Dinku Feyissa

“…So that self-explanation has prominent effect in supporting students to achieve the intended objectives in proving theorems. Of these, two areas were measured quantitatively: student achievement in calculus and transformation geometry, and self-concept toward these courses. …”
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μ Robust Stable Extrapolation of a Stationary Random Process with Interval Limited Variance by Igor G. Sidorov

“…A robust and stable minimax extrapolation is shown in a constructive form of μ, both in terms of the result and the solution. The theorems of determinization and reduction on the existence and uniqueness of a consistent interval saddle point in the problem of extrapolation with small indistinct interval deviations in the right parts of the restrictions on the spectral power density of the perturbation of the measured signal in the form of a consistent interval Lagrange function are formulated and proved. …”
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Effect of Initial Cable Tension on Cable-Stayed Bridge Performance and a New Construction Method by Hamid Dehghani, Ehsan Dehghani, Mehdi Sharifi, Seyed Rohollah Hoseini Vaez

“…These results were theoretically validated using plastic analysis theorems. This paper presents a new construction method for cable-stayed bridges based on the finding that adjusting the cable tension to the design value is not necessary during construction and operation. …”
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A CDFT-Based Computational Peptidology (CDFT-CP) Study of the Chemical Reactivity and Bioactivity of the Marine-Derived Alternaramide Cyclopentadepsipeptide by Norma Flores-Holguín, Juan Frau, Daniel Glossman-Mitnik

“…The results represent a new confirmation of the superiority of the MN12SX density functional in the fulfilment of the Janak and ionization energy theorems through the proposed KID procedure. This has been useful for the accurate prediction of the CDFT reactivity descriptors that help in understanding the chemical reactivity. …”
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On a New Epidemic Model with Asymptomatic and Dead-Infective Subpopulations with Feedback Controls Useful for Ebola Disease by M. De la Sen, A. Ibeas, S. Alonso-Quesada, R. Nistal

“…The global stability is formally discussed by using tools of qualitative theory of differential equations by using Gauss-Stokes and Bendixson theorems so that neither Lyapunov equation candidates nor the explicit solutions are used. …”
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Large-scale S-box design and analysis of SPS structure by Lan ZHANG, Liangsheng HE, Bin YU

“…A class of optimal linear transformation P over a finite field<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <msup> <mrow> <mrow><mo>(</mo> <mrow> <msubsup> <mi>F</mi> <mn>2</mn> <mi>m</mi> </msubsup> </mrow> <mo>)</mo></mrow></mrow> <mn>4</mn> </msup> </mrow></math></inline-formula> was constructed based on cyclic shift and XOR operation.Using the idea of inverse proof of input-output relation of linear transformation for reference, a proof method was put forward that transformed the objective problem of optimal linear transformation into several theorems of progressive relation, which not only solved the proof of that kind of optimal linear transformation, but also was suitable for the proof of any linear transformation.By means of small-scale S-box and optimal cyclic shift-XOR linear transformation P, a large-scale S-box model with 2-round SPS structure was established, and a series of lightweight large-scale S-boxes with good cryptographic properties were designed.Only three kind of basic operations such as look-up table, cyclic shift and XOR were used in the proposed design scheme, which improved the linearity and difference uniformity of large-scale S-boxes.Theoretical proof and case analysis show that, compared with the existing large-scale S-box construction methods, the proposed large-scale S-box design scheme has lower computational cost and better cryptographic properties such as difference and linearity, which is suitable for the design of nonlinear permutation coding of lightweight cryptographic algorithms.…”
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Comparative Analysis of Mechanisms of Schumpeterian Evolution by Agnieszka Lipieta, Andrzej

“…Due to both the formal conceptual apparatus of the general equilibrium theory and Hurwicz’s approach to the problem of designing economic mechanisms, the paper takes the form of an axiomatc deductve system of mathematcal theorems interpreted in the language of economics.…”
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Theory of Robust Quantum Many-Body Scars in Long-Range Interacting Systems by Alessio Lerose, Tommaso Parolini, Rosario Fazio, Dmitry A. Abanin, Silvia Pappalardi

“…As a by-product, we find a predictive criterion for the presence or absence of heating under periodic driving for 0<α<d, beyond existing Floquet-prethermalization theorems.…”
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FEATURES OF ELECTROMECHANICAL ACOUSTIC ENERGY CONVERSION BY CYLINDRICAL PIEZOCERAMIC TRANSDUCERS WITH INTERNAL SCREENS IN COMPOSITION OF FLAT SYSTEMS by A. G. Leiko, I. V. Kandrachuk, A. O. Sviatnenko

“…The purpose of the work is to determine the peculiarities of the electromechanical acoustic transformation of energy by cylindrical piezoceramic radiators with internal screens in the composition of flat systems, taking into account all types of interaction.The research was carried out by the method of bound fields in multiply connected domains with the use of addition theorems for the cylindrical wave functions. The physical fields arising from the emission of sound by such a system are determined by the joint solution of the system of differential equations: the wave equation; equations of motion of thin piezoceramic shells with circular polarization in displacements; the equations of forced electrostatics for piezoceramics at given boundary conditions, the conditions of conjugation of fields at the boundaries of the division of domains and electric conditions.The solution of the problem is reduced to the solution of an infinite system of linear algebraic equations with respect to unknown coefficients of field expansions.An analysis of the results of numerical calculations, performed on the basis of the obtained analytical relations, called to establish a number of features in the electromechanical acoustic transformation of energy by emitters in the composition of flat systems. …”
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A New Topological Degree Theory for Perturbations of Demicontinuous Operators and Applications to Nonlinear Equations with Nonmonotone Nonlinearities by Teffera M. Asfaw

“…The theory improves the degree theory of Berkovits and Mustonen for L+C, where C is bounded demicontinuous pseudomonotone. New existence theorems are provided. In the case when L is monotone, a maximality result is included for L and L+T. …”
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Topology Unveiled: A New Horizon for Economic and Financial Modeling by Yicheng Wei, Junzo Watada, Zijin Wang

“…By collecting abundant literature indexed in SCOPUS/WoS and other famous databases, with a qualitative analysis to classify and summarize it, we found that topological methods were introduced to modern economics when dealing with dynamic optimization, functional analysis, and convex programming problems, including famous applications such as uncovering equilibrium with fixed-point theorems in Walrasian economics. Topology can help uncover and refine the topological properties of these function space transformations, thus finding unchangeable features. …”
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Factor Rings with Algebraic Identities via Generalized Derivations by Ali Yahya Hummdi, Zakia Z. Al-Amery, Radwan M. Al-omary

“…To emphasize the necessity of the primeness of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Π</mo></semantics></math></inline-formula> in the hypotheses of our various theorems, we provide a list of examples.…”
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Approximating Common Fixed Points for a Finite Family of Asymptotically Nonexpansive Mappings Using Iteration Process with Errors Terms by Seyit Temir, Adem Kiliçman

“…The purpose of this paper is to study the above iteration scheme for approximating common fixed points of a finite family of asymptotically nonexpansive mappings and to prove weak and some strong convergence theorems for such mappings in real Banach spaces. The results obtained in this paper extend and improve some results in the existing literature.…”
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Survey on the development of mimic defense in cyberspace:from mimic concept to “mimic+” ecology by Hailong MA, Liang WANG, Tao HU, Yiming JIANG, Yanze QU

“…Build upon the dynamic-heterogeneous-redundant architecture for multi-body execution, multi-mode ruling and multi-dimension reconstruction, cyberspace mimic defense (CMD) uses uncertain system to deal with the uncertain threat to cyberspace ubiquity.The evolution of CMD over the past 8 years were reviewed systematically from the vertical, horizontal, current, developing and future perspectives.From the vertical perspective, the development process of CMD from concept to theory and practice was summarized.From the horizontal view, it elaborated the core structure DHR (dynamical heterogeneous redundancy) of CMD, the principles based on CMD’s three major theorems, safety gains and performance costs.A comparison was conducted between CMD and five other active defense technologies, namely intrusion tolerance, moving target defense, zero trust architecture, trusted computing and computer immunology.From the current perspective, it reviewed the implementation elements, performance, system architecture, heterogeneous strategies, scheduling strategies, voting strategies and other common technology patterns and characteristics of 11 types of main existing mimic products including mimicry router, mimicry processor, mimicry DNS server and mimicry cloud platform.From the developing perspective, it explored the “mimic+” AICDS (Mimic + AI/IoT/Cloud/Data/SDN) symbiotic ecology with respect to 5 types of new technologies, namely artificial intelligence, Internet of things, cloud computing, big data and software-defined network, and proposed the corresponding technology junctions and cross research value.From the future perspective, it looked into the future mimicry baseline 2.0 product ecology, “mimic +5G/6G”, “mimic + edge computing”,“mimic + cloud” and “mimic + blockchain” application scenarios.Besides, 4 types of challenges faced by CMD in the future were analyzed and summarized, including escape space of multi-mode decision attack, mutual restriction of heterogeneous and synchronous, difficult balance between security and function, and limited transformation space of existing endogenous security components.…”
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