Math-Phys-Chem Approaches to Life by Hitomi Kitaojima, Shigeru Kanemitsu

“…They correspond to three mathematical dsciplines—probability, linear algebra and free groups, respectively. We shall give some basics for the Rényi (𝛼)-entropy, Chebyshev polynomials and the notion of free groups inrespective places. …”
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Transfer functions of a time-varying control system by Volt Avdieiev

“…This makes it possible to transform differential equations into algebraic ones, as a result to use the developed apparatus of linear algebra to solve problems of analysis and synthesis. …”
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Extensions of Riordan Arrays and Their Applications by Paul Barry

“…The methods used include generating functions, linear algebra, weighted compositions, and linear recurrences. …”
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The Discriminative Lexicon: A Unified Computational Model for the Lexicon and Lexical Processing in Comprehension and Production Grounded Not in (De)Composition but in Linear Discr... by R. Harald Baayen, Yu-Ying Chuang, Elnaz Shafaei-Bajestan, James P. Blevins

“…This novel theory is inspired by word and paradigm morphology but operationalizes the concept of proportional analogy using the mathematics of linear algebra. It embraces the discriminative perspective on language, rejecting the idea that words’ meanings are compositional in the sense of Frege and Russell and arguing instead that the relation between form and meaning is fundamentally discriminative. …”
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Elastodynamic modeling and analysis of a 4SRRR overconstrained parallel robot by B. Wang, Y. Zhao, C. Yang, X. Hu, Y. Zhao

“…Second, based on the theory of multipoint constraint elements and linear algebra, a set of independent displacement coordinates is established for the connection points between rods and the moving platform, rods and rods, and rods and the fixed platform. …”
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Sensitivity and identifiability analysis of COVID-19 pandemic models by O. I. Krivorotko, S. I. Kabanikhin, M. I. Sosnovskaya, D. V. Andornaya

“…The algorithm is built on the sensitivity matrix analysis using the methods of differential and linear algebra. It allows one to determine the parameters that are the least and most sensitive to data changes to build a regularization for solving an identif ication problem of the most accurate pandemic spread scenarios in the region. …”
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Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations by Qingxue Huang, Fuqiang Zhao, Jiaquan Xie, Lifeng Ma, Jianmei Wang, Yugui Li

“…Then the matrix with the Tau method is utilized to transform this problem into a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. …”
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WSN key recovery attack based on symmetric matrix decomposition by Xiangmin JI, Bo ZHAO, Jinhui LIU, Jianwei JIA, Huanguo ZHANG, Shuang XIANG

“…The key protocol is one of the crucial technologies to ensure the security for wireless sensor network（WSN）.Parakh,et al.proposed a key agreement for WSN based on matrix decomposition.However,the study revealed that the protocol had security risks.A key recovery attack scheme against this protocol was proposed by using the properties of symmetric matrix and permutation matrix.Based on intercepting the row and column vector of the node,elementary transformation was performed to construct a linear algebraic attack algorithm and the equivalent key was obtained.The computational complexity is O(N<sup>6</sup>).Experimental results show that the method can recover the equivalent key of the above protocol within the polynomial computational complexity and the memory consumption is within an acceptable range.In addition,an improved scheme for key agreement was proposed to resist the linear algebraic attack by using a random disturbance matrix,and the correctness and security analysis were also carried out.…”
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Laguerre Collocation Method for Solving Fredholm Integro-Differential Equations with Functional Arguments by Burcu Gürbüz, Mehmet Sezer, Coşkun Güler

“…This method transforms the considered problem to a matrix equation which corresponds to a system of linear algebraic equations. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments. …”
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Some Upper Matrix Bounds for the Solution of the Continuous Algebraic Riccati Matrix Equation by Zübeyde Ulukök, Ramazan Türkmen

“…We propose diverse upper bounds for the solution matrix of the continuous algebraic Riccati matrix equation (CARE) by building the equivalent form of the CARE and using some matrix inequalities and linear algebraic techniques. Finally, numerical example is given to demonstrate the effectiveness of the obtained results in this work as compared with some existing results in the literature. …”
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Numerical Simulation of One-Dimensional Fractional Nonsteady Heat Transfer Model Based on the Second Kind Chebyshev Wavelet by Fuqiang Zhao, Jiaquan Xie, Qingxue Huang

“…The operational matrix of fractional-order integration is utilized to reduce the original problem to a system of linear algebraic equations, and then the numerical solutions obtained by our method are compared with those obtained by CAS wavelet method. …”
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Exponential Collocation Method for Solutions of Singularly Perturbed Delay Differential Equations by Şuayip Yüzbaşı, Mehmet Sezer

“…By aid of the collocation points and the matrix operations, the suggested scheme converts singularly perturbed problem into a matrix equation, and this matrix equation corresponds to a system of linear algebraic equations. Also, an error analysis technique based on the residual function is introduced for the method. …”
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Groupes de Brauer algébriques modulo les constantes d’espaces homogènes et leurs compactifications by Linh, Nguyen Manh

“…We show that this inclusion is not always an isomorphism, even in the case where $X$ is a homogeneous space of a connected linear algebraic group over $K$. A similar result for the smooth compactifications of $X$ is also given.…”
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Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes by G. E. Okecha

“…The problem is reduced to a system of linear algebraic equations. A theoretical convergence result for the approximation is provided. …”
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Numerical Algorithm Based on Haar-Sinc Collocation Method for Solving the Hyperbolic PDEs by A. Pirkhedri, H. H. S. Javadi, H. R. Navidi

“…This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients. …”
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SIMULATION OF THE ELECTROSTATIC DIPOLE FIELD IN THE PRESENCE OF A THIN UNCLOSED OBLATE ELLIPSOIDAL SHELL AND PLANE by G. Ch. Shushkevich

“…Using the addition theorems connecting spherical, ellipsoidal and cylindrical harmonic functions, the solution of the boundary problem is reduced to the solution of dual series equations by the Legendre polynomials that are transformed to an infinite system of linear algebraic equations of the second kind with a completely continuous operator. …”
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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.…”
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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. …”
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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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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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