Bifurcation Analysis of a Singular Bioeconomic Model with Allee Effect and Two Time Delays by Xue Zhang, Qing-ling Zhang, Zhongyi Xiang

“…The singular prey-predator model is transformed into its normal form by using differential-algebraic system theory. We study its dynamics in terms of local analysis and Hopf bifurcation. …”
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Some Properties and Applications of a New General Triple Integral Transform “Gamar Transform’’ by Abdelilah Kamal H. Sedeeg

“…The capacity of general triple integral transforms to change PDEs into simple algebraic equations is demonstrated.…”
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Data distribution strategy based on the X-RDP array codes by Wu-nan WAN, Wang SUO, Yun CHEN, Tuo WANG

“…A theoretical proof that the X-RDP code is an MDS code was given by using algebraic definition. The encoding and decoding procedures were described by geometrical line graphs, which were easily implemented by soft hardware. …”
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A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams by Issam El Hantati, Ahmed Adri, Hatim Fakhreddine, Said Rifai, Rhali Benamar

“…Discrete expressions of the strain energy and kinetic energies are derived, and Hamilton’s principle is applied to reduce the problem to a solution of a nonlinear algebraic system and then solved by an approximate method. …”
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Sphere quantization of Higgs and Coulomb branches and Analytic Symplectic Duality by Davide Gaiotto

“…Localization formulae and dualities applied to these quantizations result in a body of predictions about unitary representations of certain algebras, which may perhaps be understood as an “analytic” form of the symplectic duality program. …”
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Euler Operational Matrix of Integration and Collocation Method for Solving Functional Integral Equations by Sohrab Bazm, Fatemeh Pahlevani

“…This approach transforms the integral equation into a set of nonlinear algebraic equations, which can be efficiently solved by employing standard numerical methods like Newton's method or Picard iteration. …”
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ANALYTICAL STUDY OF THE STATIC THERMOMECHANICAL STRESSES OF THE ASSEMBLIES WITH OPTIONAL RING FLANGES. ROTATION OF THE FLANGE RING AROUND THE CIRCUMFERENCE OF CENTERS FOR BOLT HOLE... by IATAN RADU I., GHEORGHITA TOMESCU, GEORGETA ROMAN (URSE), MELANIA CORLECIUC (MITUCA), IOLANDA CONSTANTA PANAIT

“…Regarding of the above, the compatibility of the deformations of the component elements (radial displacements and rotations) is approached. A linear algebraic system is formed in which both external loads (pressure, temperature) and connecting loads (bending unit moments and unit forces) are present. …”
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Eigenvalue Based Approach for Global Consensus in Multiagent Systems with Nonlinear Dynamics by Wei Qian, Lei Wang

“…The analytical result shows that, for a weakly connected communication graph, the algebraic connectivity of a redefined symmetric matrix associated with the directed graph is used to evaluate the global consensus of the multiagent system with nonlinear dynamics under the common linear consensus protocol. …”
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Analysis of the growth kinetics of Fe2B layers by the integral method by Keddam M., Kulka M.

“…The set of differential algebraic equations (DAE) system was obtained to estimate the value of activation energy for boron diffusion when pack-boriding of Armco iron in the range of 1123 to 1273 K taking into account the boride incubation time. …”
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Stanley Depth of the Edge Ideal of Extended Gear Networks and Application in Circuit Analysis by Guiling Zeng, Muhammad Mobeen Munir, Raheel Farooki, Muhammad Athar, Jia Bao Liu

“…Stanley depth is a geometric invariant of the module which is closely related to an algebraic invariant called depth of the module. At first, we propose a generalization of classical gear graph and extended m−level gear graph and then establish general closed formulas for the sharp bounds of Stanley depth of quotient of edge ideals associated to extended m-level gear graph. …”
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Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response by S. M. Sohel Rana, Umme Kulsum

“…The dynamic behavior of a discrete-time predator-prey system of Leslie type with simplified Holling type IV functional response is examined. We algebraically show that the system undergoes a bifurcation (flip or Neimark-Sacker) in the interior of R+2. …”
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Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations by Abdulnasir Isah, Chang Phang, Piau Phang

“…Collocation method based on these operational matrices is applied to reduce the generalized fractional pantograph equations to a system of algebraic equations. The comparison of the numerical results with some existing methods shows that the present method is an excellent mathematical tool for finding the numerical solutions of generalized fractional pantograph equations.…”
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Stability Analysis of Fractional-Order Bidirectional Associative Memory Neural Networks with Mixed Time-Varying Delays by Zhanying Yang, Jie Zhang

“…In particular, these obtained conditions are expressed as some algebraic inequalities which can be easily calculated in practical applications. …”
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Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems by Hong Shi, Guangming Xie

“…Our criteria are of the geometric type, and they can be transformed into algebraic type conveniently. Finally, a numerical example is given to illustrate the utility of our criteria.…”
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Alternative Legendre Polynomials Method for Nonlinear Fractional Integro-Differential Equations with Weakly Singular Kernel by Guodong Shi, Yanlei Gong, Mingxu Yi

“…The operational matrices of integration and product together with the derived operational matrix are utilized to transform nonlinear fractional integro-differential equations to the nonlinear system of algebraic equations. Furthermore, the proposed method has also been analyzed for convergence, particularly in context of error analysis. …”
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Some Algorithms for Solving Third-Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi Polynomials by W. M. Abd-Elhameed

“…Moreover, the principle idea behind these algorithms is based on converting the boundary value problems governed by their boundary conditions into systems of linear or nonlinear algebraic equations which can be efficiently solved by suitable solvers. …”
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State recovery attack on ACORN v3 in nonce-reuse setting by Guoshuang ZHANG, Xiao CHEN, Dongdai LIN, Fengmei LIU

“…Based on differential-algebraic method and guess-and-determine technique,the state recovery attack of ACORN v3 was presented when one pair of key and Nonce was used to encrypt two messages.The time complexity of the attack was 2^122.5c,where c was the time complexity of solving linear equations.The data complexity and the storage complexity were negligible.Furthermore,according to the analysis on the sense of multiple nonce reuse,it is found that relatively complicated filter function of ACORN v3 makes it infeasible to extract the linear equations about the internal state directly from key streams.Thus,the risk of significantly reducing the attack complexity by increasing the times of nonce reuse can be effectively avoided.…”
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Numerical Solution for the 2D Linear Fredholm Functional Integral Equations by Neda Khaksari, Mahmoud Paripour, Nasrin Karamikabir

“…Using the proposed method, we get a system of linear algebraic equations which are solved by an iteration method. …”
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Numerical Solution of Time-Fractional Diffusion-Wave Equations via Chebyshev Wavelets Collocation Method by Fengying Zhou, Xiaoyong Xu

“…Based on the collocation technique, the second-kind Chebyshev wavelets are used to reduce the problem to the solution of a system of linear algebraic equations. Several examples are provided to confirm the reliability and effectiveness of the proposed method.…”
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Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted Region by Igor Vigdorovich, Holger Foysi

“…The theory provided inside this paper is the building block for a derivation of new algebraic constitutive relations for three-dimensional turbulent flows in the form of expansions of the Reynolds-stress tensor in a tensorial basis formed by the tensors S and Ω, in which the scalar coefficients depend on simultaneous invariants of these tensors.…”
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