A Novel Approach towards Bipolar Soft Sets and Their Applications by Tahir Mahmood

“…In the end, we have deliberated the algebraic structures associated with T-bipolar soft sets and the applications of T-bipolar soft sets in decision-making problems.…”
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On the relationship of interior-point methods by Ruey-Lin Sheu, Shu-Cherng Fang

“…In this paper, we show that the moving directions of the primal-affine scaling method (with logarithmic barrier function), the dual-affine scaling method (with logarithmic barrier function), and the primal-dual interior point method are merely the Newton directions along three different algebraic paths that lead to a solution of the Karush-Kuhn-Tucker conditions of a given linear programming problem. …”
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On the System of Diophantine Equations x2-6y2=-5 and x=az2-b by Silan Zhang, Jianhua Chen, Hao Hu

“…In this paper, we extend this result and put forward a generalized method which can completely solve the family of systems of Diophantine equations x2-6y2=-5 and x=az2-b for each pair of integral parameters a,b. 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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A Pseudospectral Algorithm for Solving Multipantograph Delay Systems on a Semi-Infinite Interval Using Legendre Rational Functions by E. H. Doha, D. Baleanu, A. H. Bhrawy, R. M. Hafez

“…A Legendre rational collocation method based on Legendre rational-Gauss quadrature points is utilized to reduce the solution of such systems to systems of linear and nonlinear algebraic equations. In addition, accurate approximations are achieved by selecting few Legendre rational-Gauss collocation points. …”
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Singular LQ Problem for Irregular Singular Systems by Qingxiang Fang, Baolin Zhang, Jun-e Feng

“…The optimal control-state pair can be explicitly formulated via solving an algebraic Riccati equation and a Sylvester equation. …”
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Numerical Solutions for the Eighth-Order Initial and Boundary Value Problems Using the Second Kind Chebyshev Wavelets by Xiaoyong Xu, Fengying Zhou

“…The second kind Chebyshev wavelets operational matrix of integration is derived and used to transform the problem to a system of algebraic equations. The uniform convergence analysis and error estimation for the proposed method are given. …”
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A Theory Approach towards Tradable Rail Freight Option by Jingwei Guo, Lutian Li, Ji Zhang, Qi Shen, Zhongqi Xie, Qinglin Li

“…The most significant feature of this method is its simplicity in analyzing the optimal pricing decision using only the algebraic category and Ito’s lemma.…”
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Numerical solution of nonlinear complex integral equations using quasi- wavelets by Ahmed Ayad Khudhair, Saeed Sohrabi, Hamid Ranjbar

“…The combination of the standard collocation method with periodic quasi-wavelets, as well as their fundamental properties, was utilized to convert the solution of the newly formulated integral equation into a nonlinear complex system of algebraic equations. The convergence properties of the scheme were also presented. …”
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Sieve Method for Polynomial Linear Equivalence by Baocang Wang, Yupu Hu

“…Some cryptographic and algebraic properties of PLE are discussed, and from the properties we derive three sieves called multiplicative, differential, and additive sieves. …”
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A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain by Faezeh Toutounian, Emran Tohidi, Stanford Shateyi

“…This matrix equation corresponds to a system of linear algebraic equations. By solving this system, the unknown Bernoulli coefficients are determined and thus the approximate solutions are obtained. …”
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Radial Kernels Collocation Method for the Solution of Volterra Integro-Differential Equations by Stephen Mkegh Nengem, Friday Haruna, Shalom Danjuma Bitrus

“…This was achieved by simplifying the Volterra integral problem's solution to an algebraic system of equations. The impact of the shape parameter present in every kernel on the method's accuracy is examined and found to be significant. …”
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Lagrangians, Gauge Functions, and Lie Groups for Semigroup of Second-Order Differential Equations by Z. E. Musielak, N. Davachi, M. Rosario-Franco

“…A set of linear second-order differential equations is converted into a semigroup, whose algebraic structure is used to generate novel equations. …”
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Higher Order Compact Finite Difference Schemes for Unsteady Boundary Layer Flow Problems by P. G. Dlamini, S. S. Motsa, M. Khumalo

“…The CFDRM utilizes the Gauss-Seidel approach of decoupling algebraic equations to linearize the governing equations and solve the resulting system of ordinary differential equations using compact finite difference schemes. …”
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Numerical Solution of Piecewise Constant Delay Systems Based on a Hybrid Framework by H. R. Marzban, S. Hajiabdolrahmani

“…The operational matrices of integration, delay, and product are employed to transform the problem under consideration into a system of algebraic equations. It is shown that the developed approach is also applicable to a special class of nonlinear piecewise constant delay differential equations. …”
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DYNAMIC RESPONSE ANALYSES OF COLLINEAR BARS WITH CONCENTRATED MASSES by LIU XinQin

“…At first,the equations to be determined were written out,the linear algebraic equations of the unknown coefficients were obtained utilizing the supposed harmonic solutions with unknown coefficients,boundary conditions of the problem and the dynamic conditions of the concentrated masses. …”
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A Global Optimization Algorithm for Signomial Geometric Programming Problem by Xue-Ping Hou, Pei-Ping Shen, Yong-Qiang Chen

“…In the algorithm, by the straight forward algebraic manipulation of terms and by utilizing a transformation of variables, the initial nonconvex programming problem (SGP) is first converted into an equivalent monotonic optimization problem and then is reduced to a sequence of linear programming problems, based on the linearizing technique. …”
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Evaluation and analysis of the computation cost of linear network coding by PU Bao-xing1, WANG Wei-ping2

“…The complexity of algebraic operation methods on Galois fields was analyzed and the operation mechanism of linear network coding was anatomized.Based on deterministic network coding data transmission and random network coding data transmission for single-source multicast connection,the mathematic model had been created to estimate the computation cost of linear network coding and the relationship between operation cost and environmental parameters had been revealed.The key factors of affecting the operation cost were also analyzed.The analysis results indicate that computation cost can be decreased through properly choosing environment parameters.Numerical calculation and simulation results demonstrate the correctness of the proposed model and validate the theoretical analysis.…”
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Approximation Technique for Solving Linear Volterra Integro-Differential Equations with Boundary Conditions by Mohamed E. A. Alnair, Ahmed A. Khidir

“…The application of the proposed method leads the Volterra integro-differential equation to a system of algebraic equations that are easy to solve. Some examples are introduced and the obtained results are compared with exact solution as well as the methods that reported in the literature to illustrate the effectiveness and accuracy of the method. …”
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A New Technique for Solving Neutral Delay Differential Equations Based on Euler Wavelets by Mutaz Mohammad, Alexander Trounev

“…Based on the operational matrix, the neutral delay differential equations are reduced to a system of algebraic equations, which is solved through a numerical algorithm. …”
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Construction of a new class of (2k, k, 1) convolutional codes by Cheng-chang ZHENG, Wan-quan PENG, Bo WEI

“…The structural mechanism of the codes was revealed by defining a state transition matrix and using algebraic method as well as grille graph. This code structure was excellent in both proportionality and diversity, besides, the distance characteristics of it are also quite well. …”
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