A New Family of Phase-Fitted and Amplification-Fitted Runge-Kutta Type Methods for Oscillators by Zhaoxia Chen, Xiong You, Xin Shu, Mei Zhang

“…New practical RK integrators are obtained with the phase-fitting and amplification-fitting conditions and algebraic order conditions. Two of the new methods have updates that are also phase-fitted and amplification-fitted. …”
Get full text

Analytic Solution for Nonlinear Multimode Beam Vibration Using a Modified Harmonic Balance Approach and Vieta’s Substitution by Y. Y. Lee

“…The aim of the modification in the solution procedures is to develop the analytic formulations, which are used to calculate the vibration amplitudes of a nonlinear multimode damped beam without the need of nonlinear equation solver for the nonlinear algebraic equations generated in the harmonic balance processes. …”
Get full text

Some Graph-Based Encryption Schemes by Baizhu Ni, Rabiha Qazi, Shafiq Ur Rehman, Ghulam Farid

“…This paper proposes some new encryption algorithms for secure transmission of messages using some special corona graphs and bipartite graph along with some algebraic properties. These proposed encryption schemes will lead to more secure communication of secret messages.…”
Get full text

Common Weak Linear Copositive Lyapunov Functions for Positive Switched Linear Systems by Yuangong Sun, Zhaorong Wu, Fanwei Meng

“…We not only establish necessary and sufficient conditions for the existence of CWCLFs but also clearly describe the algebraic structure of all CWCLFs. Numerical examples are also given to demonstrate the effectiveness of the obtained results.…”
Get full text

New Inner Product Quasilinear Spaces on Interval Numbers by Hacer Bozkurt, Yılmaz Yilmaz

“…Secondly, we present Is,Ic0,Il∞, and Il2 quasilinear spaces and we research some algebraic properties of these spaces. We obtain some new results and provide an important contribution to the improvement of quasilinear functional analysis.…”
Get full text

Trapezium-Type Inequalities for k-Fractional Integral via New Exponential-Type Convexity and Their Applications by Artion Kashuri, Sajid Iqbal, Saad Ihsan Butt, Jamshed Nasir, Kottakkaran Sooppy Nisar, Thabet Abdeljawad

“…In this paper, the authors investigated the concept of s,m-exponential-type convex functions and their algebraic properties. New generalizations of Hermite–Hadamard-type inequality for the s,m-exponential-type convex function ψ and for the products of two s,m-exponential-type convex functions ψ and ϕ are proved. …”
Get full text

Orthogonal Polynomials of Compact Simple Lie Groups by Maryna Nesterenko, Jiří Patera, Agnieszka Tereszkiewicz

“…Recursive algebraic construction of two infinite families of polynomials in n variables is proposed as a uniform method applicable to every semisimple Lie group of rank n. …”
Get full text

A Survey on Generalized Topological Indices for Silicon Carbide Structure by Sajid Mahboob Alam, Fahd Jarad, Abid Mahboob, Imran Siddique, Taner Altunok, Muhammad Waheed Rasheed

“…Topological indices facilitate the collection of beneficial information and provide an approach to understanding the properties of chemical structure by providing information about algebraic graphs. Let G be a graph with u-vertices and Ωu be the degree of uth vertex. …”
Get full text

Applications of a New q-Difference Operator in Janowski-Type Meromorphic Convex Functions by Bakhtiar Ahmad, Muhammad Ghaffar Khan, Mohamed Kamal Aouf, Wali Khan Mashwani, Zabidin Salleh, Huo Tang

“…Furthermore, we discuss a number of useful geometric properties for the functions belonging to this class such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity. Also, algebraic property of closure is discussed of functions belonging to this class. …”
Get full text

New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds by W. M. Abd-Elhameed, E. H. Doha, Y. H. Youssri

“…The principal idea for obtaining spectral numerical solutions for such equations is employing third- and fourth-kind Chebyshev wavelets along with the spectral collocation method to transform the differential equation with its boundary conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients which can be efficiently solved. …”
Get full text

Syntheses of differential games and pseudo-Riccati equations by Yuncheng You

“…For differential game problems of Mayer type, the existence of a regular solution to the pseudo-Riccati equation is proved under certain assumptions and a constructive expression of that solution can be found by solving an algebraic equation with time parameter.…”
Get full text

Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature by Yawei Chu, Dehe Li, Jundong Zhou

“…The arguments mainly rely on algebraic curvature estimates and several analysis tools on Mn,g,f, such as the property of f-parabolic and a Liouville type theorem.…”
Get full text

2-Prime Hyperideals of Multiplicative Hyperrings by Mahdi Anbarloei

“…Multiplicative hyperrings are an important class of algebraic hyperstructures which generalize rings further to allow multiple output values for the multiplication operation. …”
Get full text

Finite-part singular integral approximations in Hilbert spaces by E. G. Ladopoulos, G. Tsamasphyros, V. A. Zisis

“…Therefore, some existence theorems are proved for the solutions of the finite-part singular integral equations, approximated by several systems of linear algebraic equations. The method is further extended for the proof of the existence of solutions for systems of finite-part singular integral equations defined on Hilbert spaces, when their singularity consists of a system of diffeomorphisms of the integration interval, which is a unit circle, on itself.…”
Get full text

Bosonic sectorized strings and the (DF)2 theory by Thales Azevedo, Renann Lipinski Jusinskas, Matheus Lize

“…We also consider an extension of the bosonic model with current algebras. In that case, we compute the effective action and show that it is essentially the same as the action of the mass-deformed (DF )2 theory found by Johansson and Nohle. …”
Get full text

THE EFFICIENT USE OF HUMAN RESOURCES IN RUSSIA IN CONDITIONS OF CATCHING-UP DEVELOPMENT by G. Ryazanova, P. Tolkachev

“…On the basis of empirical data, the trends of productivity growth in comparison with the growth of other macroeconomic indicators algebraically and graphically have been shown. It has been concluded, that the development of human resources is necessary, since low productivity is a brake on the economic growth of the country in the conditions of catching-up development.…”
Get full text

Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method by Berna Bülbül, Mehmet Sezer

“…Duffing equation and conditions are transformed into the matrix equations, which corresponds to a system of nonlinear algebraic equations with the unknown coefficients, via collocation points. …”
Get full text

Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations by Fukang Yin, Junqiang Song, Xiaoqun Cao, Fengshun Lu

“…The main advantage of the new method is that it can avoid solving the nonlinear algebraic system and symbolic computation. Furthermore, the developed vector-matrix form makes it computationally efficient. …”
Get full text

On Hyperbolic 3-Manifolds Obtained by Dehn Surgery on Links by Soo Hwan Kim, Yangkok Kim

“…We study the algebraic and geometric structures for closed orientable 3-manifolds obtained by Dehn surgery along the family of hyperbolic links with certain surgery coefficients and moreover, the geometric presentations of the fundamental group of these manifolds. …”
Get full text

The Generalized Hermite Spectral Method Combined with Laplace Transform for Solution of the Time Fractional Fokker–Planck Equation by Lu-feng Yang

“…By the Laplace transform, the ordinary differential equation about the orthogonal expansion coefficient is transformed into a linear algebraic equation system, with the coefficient matrix being a tridiagonal lower triangular matrix. …”
Get full text