Journal articles: 'Operational matrix of differentiation'

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Sharma, Bhuvnesh, Sunil Kumar, M. K. Paswan, and Dindayal Mahato. "Chebyshev Operational Matrix Method for Lane-Emden Problem." Nonlinear Engineering 8, no. 1 (2019): 1–9. http://dx.doi.org/10.1515/nleng-2017-0157.

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AbstractIn the this paper, a new modified method is proposed for solving linear and nonlinear Lane-Emden type equations using first kind Chebyshev operational matrix of differentiation. The properties of first kind Chebyshev polynomial and their shifted polynomial are first presented. These properties together with the operation matrix of differentiation of first kind Chebyshev polynomial are utilized to obtain numerical solutions of a class of linear and nonlinear LaneEmden type singular initial value problems (IVPs). The absolute error of this method is graphically presented. The proposed framework is different from other numerical methods and can be used in differential equations of the same type. Several examples are illuminated to reveal the accuracy and validity of the proposed method.

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SPARIS, PANAGIOTIS D., and SPYRIDON G. MOUROUTSOS. "The operational matrix of differentiation for orthogonal polynomial series." International Journal of Control 44, no. 1 (1986): 1–15. http://dx.doi.org/10.1080/00207178608933579.

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Li, Yuanlu, Chang Pan, Xiao Meng, Yaqing Ding, and Haixiu Chen. "Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement." Measurement Science Review 15, no. 3 (2015): 101–6. http://dx.doi.org/10.1515/msr-2015-0015.

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Abstract Non–integer order differentiation is changing application of traditional differentiation because it can achieve a continuous interpolation of the integer order differentiation. However, implementation of the non–integer order differentiation is much more complex than that of integer order differentiation. For this purpose, a Haar wavelet-based implementation method of non–integer order differentiation is proposed. The basic idea of the proposed method is to use the operational matrix to compute the non–integer order differentiation of a signal through expanding the signal by the Haar wavelets and constructing Haar wavelet operational matrix of the non–integer order differentiation. The effectiveness of the proposed method was verified by comparison of theoretical results and those obtained by another non–integer order differential filtering method. Finally, non–integer order differentiation was applied to enhance signal.

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Jabbar A. Eleiwy. "Indirect Algorithm for Solving Variation Problems." Journal of the College of Basic Education 18, no. 73 (2023): 77–84. http://dx.doi.org/10.35950/cbej.v18i73.9624.

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In this paper, an approximate indirect method to solve some variational problems is proposed in terms of shifted Legendre polynomials. The operational matrix of differentiation for shifted Legendre polynomials is first derived. Using the operational matrix of differentiation, the variational problems are reduced to the solution of system of algebric equations with unknown shifted Legendre coefficients. Numerical example illustrates the efficiency, simplicity and accuracy of the proposed method.

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Guimarães, Osvaldo, José Roberto C. Piqueira, and Marcio Lobo Netto. "Direct Computation of Operational Matrices for Polynomial Bases." Mathematical Problems in Engineering 2010 (2010): 1–12. http://dx.doi.org/10.1155/2010/139198.

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Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

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Bataineh, A. Sami, A. K. Alomari, and I. Hashim. "Approximate Solutions of Singular Two-Point BVPs Using Legendre Operational Matrix of Differentiation." Journal of Applied Mathematics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/547502.

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Exact and approximate analytical solutions of linear and nonlinear singular two-point boundary value problems (BVPs) are obtained for the first time by the Legendre operational matrix of differentiation. Different from other numerical techniques, shifted Legendre polynomials and their properties are employed for deriving a general procedure for forming this matrix. The accuracy of the technique is demonstrated through several linear and nonlinear test examples.

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Pandey, Rajesh K., and Narayan Kumar. "Solution of Lane–Emden type equations using Bernstein operational matrix of differentiation." New Astronomy 17, no. 3 (2012): 303–8. http://dx.doi.org/10.1016/j.newast.2011.09.005.

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Pandey, Rajesh K., Narayan Kumar, Abhinav Bhardwaj, and Goutam Dutta. "Solution of Lane–Emden type equations using Legendre operational matrix of differentiation." Applied Mathematics and Computation 218, no. 14 (2012): 7629–37. http://dx.doi.org/10.1016/j.amc.2012.01.032.

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Tohidi, Emran, and Mohammad Shirazian. "Numerical Solution of Linear HPDEs Via Bernoulli Operational Matrix of Differentiation and Comparison with Taylor Matrix Method." Mathematical Sciences Letters 1, no. 1 (2012): 61–70. http://dx.doi.org/10.12785/msl/010108.

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Ezz–Eldien, Samer S., Ali H. Bhrawy, and Ahmed A. El–Kalaawy. "Direct numerical method for isoperimetric fractional variational problems based on operational matrix." Journal of Vibration and Control 24, no. 14 (2017): 3063–76. http://dx.doi.org/10.1177/1077546317700344.

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In this paper, we applied a direct method for a solution of isoperimetric fractional variational problems. We use shifted Legendre orthonormal polynomials as basis function of operational matrices of fractional differentiation and fractional integration in combination with the Lagrange multipliers technique for converting such isoperimetric fractional variational problems into solving a system of algebraic equations. Also, we show the convergence analysis of the presented technique and introduce some test problems with comparisons between our numerical results with those introduced using different methods.

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Bencheikh, Abdelkrim. "A NUMERICAL STUDY OF 2D-LANE-EMDEN PROBLEM USING 2D-BOUBAKER POLYNOMIALS." Advances in Mathematics: Scientific Journal 12, no. 9 (2023): 805–18. http://dx.doi.org/10.37418/amsj.12.9.1.

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The paper presents a numerical solution for the two-dimensional Lane-Emden problem using two-dimensional Boubaker polynomials. The method involves utilizing the operational matrix of differentiation and collocation method to convert the problem into a system of algebraic equations. The proposed approach, based on two-dimensional Boubaker polynomials operational matrices, is shown to be straightforward and effective. The validity and applicability of the method are demonstrated through illustrative examples.

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Pandey, Prashant, Sachin Kumar, Hossein Jafari, and Subir Das. "An operational matrix for solving time-fractional order Cahn-Hilliard equation." Thermal Science 23, Suppl. 6 (2019): 2045–52. http://dx.doi.org/10.2298/tsci190725369p.

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In the present scientific work, an operational matrix scheme with Laguerre polynomials is applied to solve a space-time fractional order non-linear Cahn-Hilliard equation, which is used to calculate chemical potential and free energy for a non-homogeneous mixture. Constructing operational matrix for fractional differentiation, the collocation method is applied to convert Cahn-Hilliard equation into an algebraic system of equations, which have been solved using Newton method. The prominent features of the manuscript is to providing the stability analysis of the proposed scheme and the pictorial presentations of numerical solution of the concerned equation for different particular cases and showcasing of the effect of advection and reaction terms on the nature of solute concentration of the considered mathematical model for different particular cases.

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Tohidi, E., Kh Erfani, M. Gachpazan, and S. Shateyi. "A New Tau Method for Solving Nonlinear Lane-Emden Type Equations via Bernoulli Operational Matrix of Differentiation." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/850170.

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A new and efficient numerical approach is developed for solving nonlinear Lane-Emden type equations via Bernoulli operational matrix of differentiation. The fundamental structure of the presented method is based on the Tau method together with the Bernoulli polynomial approximations in which a new operational matrix is introduced. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. Also, under several mild conditions the error analysis of the proposed method is provided. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods. All calculations are done in Maple 13.

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Bataineh, Ahmad Sami, Osman Rasit Isik, Moa’ath Oqielat, and Ishak Hashim. "An Enhanced Adaptive Bernstein Collocation Method for Solving Systems of ODEs." Mathematics 9, no. 4 (2021): 425. http://dx.doi.org/10.3390/math9040425.

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In this paper, we introduce two new methods to solve systems of ordinary differential equations. The first method is constituted of the generalized Bernstein functions, which are obtained by Bernstein polynomials, and operational matrix of differentiation with collocation method. The second method depends on tau method, the generalized Bernstein functions and operational matrix of differentiation. These methods produce a series which is obtained by non-polynomial functions set. We give the standard Bernstein polynomials to explain the generalizations for both methods. By applying the residual correction procedure to the methods, one can estimate the absolute errors for both methods and may obtain more accurate results. We apply the methods to some test examples including linear system, non-homogeneous linear system, nonlinear stiff systems, non-homogeneous nonlinear system and chaotic Genesio system. The numerical shows that the methods are efficient and work well. Increasing m yields a decrease on the errors for all methods. One can estimate the errors by using the residual correction procedure.

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M. N. Jasim, Shefaa, and Ghada H. Ibraheem. "Fractional Pantograph Delay Equations Solving by the Meshless Methods." Ibn AL-Haitham Journal For Pure and Applied Sciences 36, no. 3 (2023): 382–97. http://dx.doi.org/10.30526/36.3.3076.

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This work describes two efficient and useful methods for solving fractional pantograph delay equations (FPDEs) with initial and boundary conditions. These two methods depend mainly on orthogonal polynomials, which are the method of the operational matrix of fractional derivative that depends on Bernstein polynomials and the operational matrix of the fractional derivative with Shifted Legendre polynomials. The basic procedure of this method is to convert the pantograph delay equation to a system of linear equations and by using, the operational matrices we get rid of the integration and differentiation operations, which makes solving the problem easier. The concept of Caputo has been used to describe fractional derivatives. Finally, some numerical examples are identified to show the utility and capability of the two proposed approaches. Mathematica®12 program has been relied upon in the calculations.

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Tohidi, Emran, and Adem Kılıçman. "A Collocation Method Based on the Bernoulli Operational Matrix for Solving Nonlinear BVPs Which Arise from the Problems in Calculus of Variation." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/757206.

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A new collocation method is developed for solving BVPs which arise from the problems in calculus of variation. These BVPs result from the Euler-Lagrange equations, which are the necessary conditions of the extremums of problems in calculus of variation. The proposed method is based upon the Bernoulli polynomials approximation together with their operational matrix of differentiation. After imposing the collocation nodes to the main BVPs, we reduce the variational problems to the solution of algebraic equations. It should be noted that the robustness of operational matrices of differentiation with respect to the integration ones is shown through illustrative examples. Complete comparisons with other methods and superior results confirm the validity and applicability of the presented method.

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Loh, Jian Rong, Chang Phang, and Abdulnasir Isah. "New Operational Matrix via Genocchi Polynomials for Solving Fredholm-Volterra Fractional Integro-Differential Equations." Advances in Mathematical Physics 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/3821870.

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It is known that Genocchi polynomials have some advantages over classical orthogonal polynomials in approximating function, such as lesser terms and smaller coefficients of individual terms. In this paper, we apply a new operational matrix via Genocchi polynomials to solve fractional integro-differential equations (FIDEs). We also derive the expressions for computing Genocchi coefficients of the integral kernel and for the integral of product of two Genocchi polynomials. Using the matrix approach, we further derive the operational matrix of fractional differentiation for Genocchi polynomial as well as the kernel matrix. We are able to solve the aforementioned class of FIDE for the unknown function f(x). This is achieved by approximating the FIDE using Genocchi polynomials in matrix representation and using the collocation method at equally spaced points within interval [0,1]. This reduces the FIDE into a system of algebraic equations to be solved for the Genocchi coefficients of the solution f(x). A few numerical examples of FIDE are solved using those expressions derived for Genocchi polynomial approximation. Numerical results show that the Genocchi polynomial approximation adopting the operational matrix of fractional derivative achieves good accuracy comparable to some existing methods. In certain cases, Genocchi polynomial provides better accuracy than the aforementioned methods.

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Anil Kumar, Sachin Kumar. "New Operational Matrix Via Gnocchi Polynomial for Solving Non-Linear Fractional Differential Equations." Communications on Applied Nonlinear Analysis 32, no. 9s (2025): 2969–81. https://doi.org/10.52783/cana.v32.4595.

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Fractional differential equations (FDEs) have emerged as essential tools in modeling complex dynamical systems exhibiting memory and hereditary properties. Traditional operational matrices arising from Legendre, Chebyshev, and Jacobi polynomials are generally known to be numerically unstable, computationally expensive, and inefficient in approximating fractional operators. In this study an operational matrix based on Gnocchi polynomial is introduced for solving non linear fractional differential equations (NFDE) with better sparsity, stability and computational efficiency. The proposed method transforms NFDEs into tractable algebraic systems by constructing a fractional differentiation operational matrix using Gnocchi polynomials. The method is validated by theoretical formulations, spectral convergence analysis, error estimation proofs. It is also compared with existing polynomial based approaches to demonstrate better performance in function approximation and numerical stability. The Gnocchi operational matrix is based on Gnocchi, and it achieves exponential convergence, reduced computational complexity and increased numerical robustness compared to classical techniques. It is effective in fractional modeling because it can accurately approximate non-linear fractional operators. The author develops a mathematically rigorous, computationally efficient framework to solve NFDEs. Further improvements will be done by other researchers in the future for higher dimension applications, for adaptive techniques in the spectral method and for hybrid AI assisted optimization.

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Tohidi, Emran, F. Soleymani, and Adem Kilicman. "Robustness of Operational Matrices of Differentiation for Solving State-Space Analysis and Optimal Control Problems." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/535979.

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The idea of approximation by monomials together with the collocation technique over a uniform mesh for solvingstate-space analysisandoptimal controlproblems (OCPs) has been proposed in this paper. After imposing the Pontryagins maximum principle to the main OCPs, the problems reduce to a linear or nonlinear boundary value problem. In the linear case we propose a monomial collocation matrix approach, while in the nonlinear case, the general collocation method has been applied. We also show the efficiency of the operational matrices of differentiation with respect to the operational matrices of integration in our numerical examples. These matrices of integration are related to the Bessel, Walsh, Triangular, Laguerre, and Hermite functions.

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Tohidi, E., and A. Kılıçman. "An Efficient Spectral Approximation for Solving Several Types of Parabolic PDEs with Nonlocal Boundary Conditions." Mathematical Problems in Engineering 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/369029.

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The problem of solving several types of one-dimensional parabolic partial differential equations (PDEs) subject to the given initial and nonlocal boundary conditions is considered. The main idea is based on direct collocation and transforming the considered PDEs into their associated algebraic equations. After approximating the solution in the Legendre matrix form, we use Legendre operational matrix of differentiation for representing the mentioned algebraic equations clearly. Three numerical illustrations are provided to show the accuracy of the presented scheme. High accurate results with respect to the Bernstein Tau technique and Sinc collocation method confirm this accuracy.

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Khan, Anjum, Basit Ali Reshamwale, Sharan Hegde, and Sowmya Ashwin Shetty. "On RHF and Bernoulli Polynomial for the numerical solution of differential equations." International Journal of Science, Engineering and Management 9, no. 3 (2022): 33–35. http://dx.doi.org/10.36647/ijsem/09.03.a007.

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Approximation of the solution of the differential equations is done by Bernoulli polynomial. Bernoulli polynomial and operational matrix of differentiation were used in reducing differential equations into algebraic equations. The method and its application is demonstrated through illustrative examples and found that the method is computationally attractive. The Bernoulli polynomial method has been applied to compare the numerical solution of differential equations with the existing method of Rationalized Haar Function

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Hegde, Sharan, Anjum Khan, and Vinay Prasad T. "First Redefined Zagreb Index of Generalized Transformation Graph." International Journal of Science, Engineering and Management 9, no. 3 (2022): 28–32. http://dx.doi.org/10.36647/ijsem/09.03.a006.

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Approximation of the solution of the differential equations is done by Bernoulli polynomial. Bernoulli polynomial and operational matrix of differentiation were used in reducing differential equations into algebraic equations. The method and its application is demonstrated through illustrative examples and found that the method is computationally attractive. The Bernoulli polynomial method has been applied to compare the numerical solution of differential equations with the existing method of Rationalized Haar Function.

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Shah, Kamal, Hafsa Naz, Muhammad Sarwar, and Thabet Abdeljawad. "On spectral numerical method for variable-order partial differential equations." AIMS Mathematics 7, no. 6 (2022): 10422–38. http://dx.doi.org/10.3934/math.2022581.

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<abstract>In this research article, we develop a powerful algorithm for numerical solutions to variable-order partial differential equations (PDEs). For the said method, we utilize properties of shifted Legendre polynomials to establish some operational matrices of variable-order differentiation and integration. With the help of the aforementioned operational matrices, we reduce the considered problem to a matrix type equation (equations). The resultant matrix equation is then solved by using computational software like Matlab to get the required numerical solution. Here it should be kept in mind that the proposed algorithm omits discretization and collocation which save much of time and memory. Further the numerical scheme based on operational matrices is one of the important procedure of spectral methods. The mentioned scheme is increasingly used for numerical analysis of various problems of differential as well as integral equations in previous many years. Pertinent examples are given to demonstrate the validity and efficiency of the method. Also some error analysis and comparison with traditional Haar wavelet collocations (HWCs) method is also provided to check the accuracy of the proposed scheme.</abstract>

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Bataineh, Ahmad. "Bernstein polynomials method and it’s error analysis for solving nonlinear problems in the calculus of variations: Convergence analysis via residual function." Filomat 32, no. 4 (2018): 1379–93. http://dx.doi.org/10.2298/fil1804379b.

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In this paper, Bernstein polynomials method (BPM) and their operational matrices are adopted to obtain approximate analytical solutions of variational problems. The operational matrix of differentiation is introduced and utilized to reduce the calculus of variations problems to the solution of system of algebraic equations. The solutions are obtained in the form of rapidly convergent finite series with easily computable terms. Comparison between the present method and the homotopy perturbation method (HPM), the non-polynomial spline method and the B-spline collocation method are made to show the effectiveness and efficiency for obtaining approximate solutions of the calculus of variations problems. Moreover, convergence analysis based on residual function is investigated to verified the numerical results.

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Shah, Kamal, Bahaaeldin Abdalla, Thabet Abdeljawad, and Iyad Suwan. "An efficient matrix method for coupled systems of variable fractional order differential equations." Thermal Science 27, Spec. issue 1 (2023): 195–210. http://dx.doi.org/10.2298/tsci23s1195s.

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We establish a powerful numerical algorithm to compute numerical solutions of coupled system of variable fractional order differential equations. Our numer?ical procedure is based on Bernstein polynomials. The mentioned polynomials are non-orthogonal and have the ability to produce good numerical results as compared to some other numerical method like wavelet. By variable fractional order differentiation and integration, some operational matrices are formed. On using the obtained matrices, the proposed coupled system is reduced to a system of algebraic equations. Using MATLAB, we solve the given equation for required results. Graphical presentations and maximum absolute errors are given to illustrate the results. Some useful features of our sachem are those that we need no discretization or collocation technique prior to develop operational matrices. Due to these features the computational complexity is much more reduced. Further, the efficacy of the procedure is enhanced by increasing the scale level. We also compare our results with that of Haar wavelet method to justify the useful?ness of our adopted method.

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Chohan, Muhammad Ikhlaq, and Kamal Shah. "On a Computational Method for Non-integer Order Partial Differential Equations in Two Dimensions." European Journal of Pure and Applied Mathematics 12, no. 1 (2019): 39–57. http://dx.doi.org/10.29020/nybg.ejpam.v12i1.3377.

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This manuscript is concerning to investigate numerical solutions for different classesincluding parabolic, elliptic and hyperbolic partial differential equations of arbitrary order(PDEs). The proposed technique depends on some operational matrices of fractional order differentiation and integration. To compute the mentioned operational matrices, we apply shifted Jacobi polynomials in two dimension. Thank to these matrices, we convert the (PDE) under consideration to an algebraic equation which is can be easily solved for unknown coefficient matrix required for the numerical solution. The proposed method is very efficient and need no discretization of the data for the proposed (PDE). The approximate solution obtain via this method is highly accurate and the computation is easy. The proposed method is supported by solving various examples from well known articles.

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Dadkhah, Mahmood, and Kamal Mamehrashi. "Numerical solution of time-delay optimal control problems by the operational matrix based on Hartley series." Transactions of the Institute of Measurement and Control 44, no. 6 (2021): 1344–55. http://dx.doi.org/10.1177/01423312211053321.

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In this paper, a numerical technique based on the Hartley series for solving a class of time-delayed optimal control problems (TDOCPs) is introduced. The main idea is converting such TDOCPs into a system of algebraic equations. Thus, we first expand the state and control variables in terms of the Hartley series with undetermined coefficients. The delay terms in the problem under consideration are expanded in terms of the Hartley series. Applying the operational matrices of the Hartley series including integration, differentiation, dual, product, delay, and substituting the estimated functions into the cost function, the given TDOCP is reduced to a system of algebraic equations to be solved. The convergence of the proposed method is extensively investigated. At last, the precision and applicability of the proposed method is studied through different types of numerical examples.

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Youssri, Y. H., and R. M. Hafez. "Exponential Jacobi spectral method for hyperbolic partial differential equations." Mathematical Sciences 13, no. 4 (2019): 347–54. http://dx.doi.org/10.1007/s40096-019-00304-w.

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Abstract Herein, we have proposed a scheme for numerically solving hyperbolic partial differential equations (HPDEs) with given initial conditions. The operational matrix of differentiation for exponential Jacobi functions was derived, and then a collocation method was used to transform the given HPDE into a linear system of equations. The preferences of using the exponential Jacobi spectral collocation method over other techniques were discussed. The convergence and error analyses were discussed in detail. The validity and accuracy of the proposed method are investigated and checked through numerical experiments.

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Liu, Jianping, Xia Li, and Limeng Wu. "An Operational Matrix of Fractional Differentiation of the Second Kind of Chebyshev Polynomial for Solving Multiterm Variable Order Fractional Differential Equation." Mathematical Problems in Engineering 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/7126080.

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The multiterm fractional differential equation has a wide application in engineering problems. Therefore, we propose a method to solve multiterm variable order fractional differential equation based on the second kind of Chebyshev Polynomial. The main idea of this method is that we derive a kind of operational matrix of variable order fractional derivative for the second kind of Chebyshev Polynomial. With the operational matrices, the equation is transformed into the products of several dependent matrices, which can also be viewed as an algebraic system by making use of the collocation points. By solving the algebraic system, the numerical solution of original equation is acquired. Numerical examples show that only a small number of the second kinds of Chebyshev Polynomials are needed to obtain a satisfactory result, which demonstrates the validity of this method.

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Sparis, P. D. "Application of the operational matrix of differentiation for the identification of time-varying linear systems using polynomial series." IEE Proceedings D Control Theory and Applications 134, no. 3 (1987): 180. http://dx.doi.org/10.1049/ip-d.1987.0027.

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Bushnaq, Samia, Kamal Shah, Sana Tahir, Khursheed J. Ansari, Muhammad Sarwar, and Thabet Abdeljawad. "Computation of numerical solutions to variable order fractional differential equations by using non-orthogonal basis." AIMS Mathematics 7, no. 6 (2022): 10917–38. http://dx.doi.org/10.3934/math.2022610.

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<abstract>In this work, we present some numerical results about variable order fractional differential equations (VOFDEs). For the said numerical analysis, we use Bernstein polynomials (BPs) with non-orthogonal basis. The method we use does not need discretization and neither collocation. Hence omitting the said two operations sufficient memory and time can be saved. We establish operational matrices for variable order integration and differentiation which convert the consider problem to some algebraic type matrix equations. The obtained matrix equations are then solved by Matlab 13 to get the required numerical solution for the considered problem. Pertinent examples are provided along with graphical illustration and error analysis to validate the results. Further some theoretical results for time complexity are also discussed.</abstract>

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Wolińska, Agnieszka, Dorota Górniak, Urszula Zielenkiewicz, et al. "Microbial biodiversity in arable soils is affected by agricultural practices." International Agrophysics 31, no. 2 (2017): 259–71. http://dx.doi.org/10.1515/intag-2016-0040.

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Abstract The aim of the study was to examine the differences in microbial community structure as a result of agricultural practices. Sixteen samples of cultivated and the same number of non-cultivated soils were selected. Gel bands were identified using the GelCompar software to create the presence-absence matrix, where each band represented a bacterial operational taxonomic unit. The data were used for principal-component analysis and additionally, the Shannon- Weaver index of general diversity, Simpson index of dominance and Simpson index of diversity were calculated. Denaturing gradient gel electrophoresis profiles clearly indicated differentiation of tested samples into two clusters: cultivated and non-cultivated soils. Greater numbers of dominant operational taxonomic units (65) in non-cultivated soils were noted compared to cultivated soils (47 operational taxonomic units). This implies that there was a reduction of dominant bacterial operational taxonomic units by nearly 30% in cultivated soils. Simpson dominance index expressing the number of species weighted by their abundance amounted to 1.22 in cultivated soils, whereas a 3-fold higher value (3.38) was observed in non-cultivated soils. Land-use practices seemed to be a important factors affected on biodiversity, because more than soil type determined the clustering into groups.

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Kumar, Sachin, and Abdon Atangana. "A numerical study of the nonlinear fractional mathematical model of tumor cells in presence of chemotherapeutic treatment." International Journal of Biomathematics 13, no. 03 (2020): 2050021. http://dx.doi.org/10.1142/s1793524520500217.

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Cancer belongs to the class of diseases which is symbolized by out of control cells growth. These cells affect DNAs and damage them. There exist many treatments available in medical science as radiation therapy, targeted therapy, surgery, palliative care and chemotherapy. Chemotherapy is one of the most popular treatments which depends on the type, location and grade of cancer. In this paper, we are working on modeling and prediction of the effect of chemotherapy on cancer cells using a fractional differential equation by using the differential operator in Caputo’s sense. The presented model depicts the interaction between tumor, normal and immune cells in a tumor by using a system of four coupled fractional partial differential equations (PDEs). For this system, initial conditions of tumor cells and dimensions are taken in such a way that tumor is spread out enough in size and can be detected easily with the clinical machines. An operational matrix method with Genocchi polynomials is applied to study this system of fractional PDEs (FPDEs). An operational matrix for fractional differentiation is derived. Applying the collocation method and using this matrix, the nonlinear system is reduced to a system of algebraic equations, which can be solved using Newton iteration method. The salient features of this paper are the pictorial presentations of the numerical solution of the concerned equation for different particular cases to show the effect of fractional exponent on diffusive nature of immune cells, tumor cells, normal cells and chemotherapeutic drug and depict the interaction among immune cells, normal cells and tumor cells in a tumor site.

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Christiadi, Henry, and Muhammad Alamsyah. "Evaluating Strategic Options Using QSPM: Enhancing Plaza Indonesia Realty's Competitive Edge." International Journal of Indonesian Business Review 3, no. 2 (2024): 125–34. http://dx.doi.org/10.54099/ijibr.v3i2.1109.

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This research explores how Plaza Indonesia Mall aligns its corporate and business strategies in response to challenges like heightened competition, digital advancements, and sustainability requirements. Utilizing a quantitative descriptive methodology, the study relies on secondary data from financial documents, industry reports, and scholarly literature. A SWOT analysis is conducted to assess the mall's internal strengths and weaknesses alongside external opportunities and threats. Subsequently, the Quantitative Strategic Planning Matrix (QSPM) is used to evaluate and prioritize strategic alternatives based on their appeal and feasibility. The QSPM analysis reveals that the digitalization strategy is the most attractive, scoring the highest Total Attractiveness Score (TAS) of 2.83, highlighting the need for enhancing PLIN's digital presence, integrating e-commerce, and leveraging digital marketing to adapt to evolving consumer behaviors. The differentiation strategy, which emphasizes capitalizing on PLIN's prime location and strong brand reputation, also ranks highly with a TAS of 2.81, reinforcing the importance of providing a premium customer experience and differentiating offerings to maintain competitive advantage. Although the Cost Efficiency Strategy scored the lowest TAS of 2.76, it remains vital for operational efficiency and profitability. The findings suggest that a balanced approach prioritizing digitalization, differentiation, and cost efficiency will enable PLIN to effectively navigate market challenges, capitalize on growth opportunities, and sustain long-term success. This study provides strategic insights for PLIN and other property firms seeking to enhance their competitive positioning through targeted strategic initiatives.

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Sriwastav, Nikhil, Amit K. Barnwal, Abdul-Majid Wazwaz, and Mehakpreet Singh. "Bernstein operational matrix of differentiation and collocation approach for a class of three-point singular BVPs: error estimate and convergence analysis." Opuscula Mathematica 43, no. 4 (2023): 575–601. http://dx.doi.org/10.7494/opmath.2023.43.4.575.

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Singular boundary value problems (BVPs) have widespread applications in the field of engineering, chemical science, astrophysics and mathematical biology. Finding an approximate solution to a problem with both singularity and non-linearity is highly challenging. The goal of the current study is to establish a numerical approach for dealing with problems involving three-point boundary conditions. The Bernstein polynomials and collocation nodes of a domain are used for developing the proposed numerical approach. The straightforward mathematical formulation and easy to code, makes the proposed numerical method accessible and adaptable for the researchers working in the field of engineering and sciences. The priori error estimate and convergence analysis are carried out to affirm the viability of the proposed method. Various examples are considered and worked out in order to illustrate its applicability and effectiveness. The results demonstrate excellent accuracy and efficiency compared to the other existing methods.

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Gemeda, Abdurkadir Edeo. "The Solutions of Second Order Nonlinear Two Point Boundary Value Problems." European Journal of Engineering Research and Science 4, no. 8 (2019): 49–54. http://dx.doi.org/10.24018/ejers.2019.4.8.1434.

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In this paper, generalized shifted Legendre polynomial approximation on a given arbitrary interval has been designed to find an approximate solution of a given second order nonlinear two point boundary value problems of ordinary differential equations. Here an approach using Tau method based on Legendre operational matrix of differentiation [2] & [5] has been addressed to generate the nonlinear systems of algebraic equations. The unknown Legendre coefficients of these nonlinear systems are the solutions of the system and they have been solved by continuation method. These unknown Legendre coefficients are then used to write the approximate solutions to the second order nonlinear two point boundary value problems. The validity and efficiency of the method has also been illustrated with numerical examples and graphs assisted by MATLAB.

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Gemeda, Abdurkadir Edeo. "Solutions of Second Order Nonlinear Two Point Boundary Value Problems." European Journal of Engineering and Technology Research 4, no. 8 (2019): 49–54. http://dx.doi.org/10.24018/ejeng.2019.4.8.1434.

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In this paper, generalized shifted Legendre polynomial approximation on a given arbitrary interval has been designed to find an approximate solution of a given second order nonlinear two point boundary value problems of ordinary differential equations. Here an approach using Tau method based on Legendre operational matrix of differentiation [2] & [5] has been addressed to generate the nonlinear systems of algebraic equations. The unknown Legendre coefficients of these nonlinear systems are the solutions of the system and they have been solved by continuation method. These unknown Legendre coefficients are then used to write the approximate solutions to the second order nonlinear two point boundary value problems. The validity and efficiency of the method has also been illustrated with numerical examples and graphs assisted by MATLAB.

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Wang, Hui-Ju. "A brand-based perspective on differentiation of green brand positioning." Management Decision 55, no. 7 (2017): 1460–75. http://dx.doi.org/10.1108/md-04-2016-0251.

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Purpose The purpose of this paper is to offer a perspective of brand-based analysis on green brand positioning differentiation through a network analysis approach. Design/methodology/approach This study employs centrality and distinctiveness as bases to develop a matrix framework of green brand positioning differentiation. The two dimensions are measured from the techniques of network analysis, including analysis of the core-periphery structure and adjacency matrix. Findings The results yield four clusters with different positions in a 2×2 matrix, including 23 core brands with high-positioning distinctiveness, ten core brands with low-positioning distinctiveness, ten peripheral brands with high-positioning distinctiveness, and seven peripheral brands with low-positioning distinctiveness. Research limitations/implications The results contribute to providing brand researchers with different analytical perspectives on the existing knowledge about green brand positioning and offer strategic positioning information for green brand practitioners. Originality/value This research contributes to the literature in three ways. First, this research is a first attempt to offer a brand-based perspective on differentiation of green brand positioning. Second, this research advances the existing knowledge that uses network analysis on green brand positioning by offering different techniques for brand differentiation analysis. Finally, this research complements the strategic positioning information of the current business environment in the context of green branding.

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Tryfonyuk, Liliya, Alexandr Dubolazov, Yuriy Ushenko, Irina Soltys, Natalia Pavlukovich, and Oleksandr Ushenko. "3D Jones-maxtrix scanning of polycrystalline films of blood plasma in the diagnosis of pathological conditions of human organs." Journal of Clinical Oncology 40, no. 16_suppl (2022): e15053-e15053. http://dx.doi.org/10.1200/jco.2022.40.16_suppl.e15053.

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e15053 Background: This work is devoted to the development and experimental verification of a new method of three-dimensional matrix mapping of anisotropic properties of optically thin layers of polycrystalline films of blood plasma of biological tissues for express diagnostics and differentiation of histological sections of a prostate tumor. Methods: Biological samples. Three representative groups of polycrystalline blood plasma films were formed: 1 group consisted of blood plasma samples of polycrystalline adenoma; Group 2 consisted ofpolycrystalline adenocarcinoma, blood plasma samples are moderately differentiated (3+3 on the Gleason scale); Group 3 consisted ofpolycrystalline adenocarcinoma, blood plasma samples are poorly differentiated (4+4 on the Gleason scale). Results: The results obtained can be associated with changes in the ratio between the concentrations of albumin and globulin proteins in the blood plasma from patients with prostate tumors. It is known that malignant processes are accompanied by an increase in the concentration of optically active globulin molecules. Due to this, there is an increase in the magnitude and range of scatter in the magnitude of circular birefringence of samples of polycrystalline blood plasma films from patients with adenocarcinoma (3 + 3) and adenocarcinoma (4 + 4) in comparison with similar maps of blood plasma from patients with benign adenoma. On the contrary, due to a decrease in the concentration of albumin molecules, the values of linear birefringence of blood plasma films from patients with malignant prostate tumors decrease. Conclusions: The method of 3D Jones matrix mapping of blood plasma layers with digital holographic reconstruction of layered maps of linear and circular birefringence is analytically substantiated. The operational characteristics (sensitivity, specificity and balanced accuracy) that demonstrate the diagnostic power of 3D Jones matrix mapping of biological layers. The use of the algorithm for tomographic reproduction of linear birefringence maps provided high accuracy in differentiating benign and malignant conditions of the prostate tissue.[Table: see text]

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Tryfonyuk, Liliya, Alexandr Dubolazov, Yuriy Ushenko, Irina Soltys, Natalia Pavlukovich, and Oleksandr Ushenko. "3D Jones-maxtrix scanning of polycrystalline films of blood plasma in the diagnosis of pathological conditions of human organs." Journal of Clinical Oncology 40, no. 16_suppl (2022): e15053-e15053. http://dx.doi.org/10.1200/jco.2022.40.16_suppl.e15053.

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e15053 Background: This work is devoted to the development and experimental verification of a new method of three-dimensional matrix mapping of anisotropic properties of optically thin layers of polycrystalline films of blood plasma of biological tissues for express diagnostics and differentiation of histological sections of a prostate tumor. Methods: Biological samples. Three representative groups of polycrystalline blood plasma films were formed: 1 group consisted of blood plasma samples of polycrystalline adenoma; Group 2 consisted ofpolycrystalline adenocarcinoma, blood plasma samples are moderately differentiated (3+3 on the Gleason scale); Group 3 consisted ofpolycrystalline adenocarcinoma, blood plasma samples are poorly differentiated (4+4 on the Gleason scale). Results: The results obtained can be associated with changes in the ratio between the concentrations of albumin and globulin proteins in the blood plasma from patients with prostate tumors. It is known that malignant processes are accompanied by an increase in the concentration of optically active globulin molecules. Due to this, there is an increase in the magnitude and range of scatter in the magnitude of circular birefringence of samples of polycrystalline blood plasma films from patients with adenocarcinoma (3 + 3) and adenocarcinoma (4 + 4) in comparison with similar maps of blood plasma from patients with benign adenoma. On the contrary, due to a decrease in the concentration of albumin molecules, the values of linear birefringence of blood plasma films from patients with malignant prostate tumors decrease. Conclusions: The method of 3D Jones matrix mapping of blood plasma layers with digital holographic reconstruction of layered maps of linear and circular birefringence is analytically substantiated. The operational characteristics (sensitivity, specificity and balanced accuracy) that demonstrate the diagnostic power of 3D Jones matrix mapping of biological layers. The use of the algorithm for tomographic reproduction of linear birefringence maps provided high accuracy in differentiating benign and malignant conditions of the prostate tissue.[Table: see text]

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Muliadi, Dedi. "Manajemen Pengelolaan dan Pengembangan Usaha pada UMKM di Kabupaten Bogor (Studi Kasus pada Usaha Makanan Fast Food)." Journal on Education 5, no. 4 (2023): 10976–88. http://dx.doi.org/10.31004/joe.v5i4.2019.

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The purpose of this research is to describe the management and business development of MSMEs in Bogor Regency, to analyze the internal and external environment, and to plan business development in the fast food business. Data collection method used in this research is interview. The data analysis method used is descriptive qualitative analysis. Based on the results of data analysis, the authors found that the management and development of business, especially fast food in the internal environment around the place of business has been going well in terms of human resources, financial aspects, and production and operational aspects. Meanwhile, the analysis of the external environment shows that the fast food business has a weak competitive position because it does not have product differentiation. The strategy used by the company is a market development strategy which is obtained from the results of the SWOT analysis and the grand strategy matrix.

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Fallooh, Noor H., Ahmed T. Sadiq, Eyad I. Abbas, and Ivan A. hashim. "Modifiedment the Performance of Q-learning Algorithm Based on Parameters Setting for Optimal Path Planning." BIO Web of Conferences 97 (2024): 00010. http://dx.doi.org/10.1051/bioconf/20249700010.

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In engineering, the use of mobile robots to teach automatic control is becoming more common because of the interesting experiments that can be conducted with them. In this paper, a mobile robot that applies reinforcement learning in different scenarios is shown, to get rewards, the agent learns by acting in the environment. creating a balance between new information and our current understanding of the environment. In this way, the algorithm can be divided into two stages: the learning stage and the operational stage. In the first phase, the robot learns how to go from where it is to a known destination, it builds a learning matrix that is subsequently utilized during the operational stage using the rewards and environment data. In this paper, the algorithm was studied in terms of rapid learning for the mobile robot and reducing the process of repetition in learning by specifying the values of alpha (α) and gamma (γ) in a way that is appropriate for preserving the variance and differentiation between them. To evaluate the robot’s adaptability to various dynamic situations, several simulated test scenarios were executed. In the testing situations, several target motion kinds and numbers of obstacles with various dynamicity patterns were used. The test scenarios illustrated the robot’s adaptability to various settings.

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Srivastava, Hari Mohan, Waleed Adel, Mohammad Izadi, and Adel A. El-Sayed. "Solving Some Physics Problems Involving Fractional-Order Differential Equations with the Morgan-Voyce Polynomials." Fractal and Fractional 7, no. 4 (2023): 301. http://dx.doi.org/10.3390/fractalfract7040301.

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In this research, we present a new computational technique for solving some physics problems involving fractional-order differential equations including the famous Bagley–Torvik method. The model is considered one of the important models to simulate the coupled oscillator and various other applications in science and engineering. We adapt a collocation technique involving a new operational matrix that utilizes the Liouville–Caputo operator of differentiation and Morgan–Voyce polynomials, in combination with the Tau spectral method. We first present the differentiation matrix of fractional order that is used to convert the problem and its conditions into an algebraic system of equations with unknown coefficients, which are then used to find the solutions to the proposed models. An error analysis for the method is proved to verify the convergence of the acquired solutions. To test the effectiveness of the proposed technique, several examples are simulated using the presented technique and these results are compared with other techniques from the literature. In addition, the computational time is computed and tabulated to ensure the efficacy and robustness of the method. The outcomes of the numerical examples support the theoretical results and show the accuracy and applicability of the presented approach. The method is shown to give better results than the other methods using a lower number of bases and with less spent time, and helped in highlighting some of the important features of the model. The technique proves to be a valuable approach that can be extended in the future for other fractional models having real applications such as the fractional partial differential equations and fractional integro-differential equations.

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Freedman, A. S., K. Rhynhart, Y. Nojima, et al. "Stimulation of protein tyrosine phosphorylation in human B cells after ligation of the beta 1 integrin VLA-4." Journal of Immunology 150, no. 5 (1993): 1645–52. http://dx.doi.org/10.4049/jimmunol.150.5.1645.

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Abstract B lymphocytes express several adhesion molecules that are involved in cell-cell and cell-extracellular matrix interactions. The alpha 4 beta 1 integrin VLA-4, expressed on pre-B and mature/activated B cells, mediates adhesion of these cells to its two ligands, VCAM-1 and fibronectin. Recent evidence suggests that VLA-4 is involved in T lymphocyte activation; however, relatively little is known of the role of VLA-4 in B cell differentiation. To begin to assess the potential involvement of VLA-4 in B cell activation, we have examined the effect of ligation of VLA-4 on protein tyrosine phosphorylation in B cells. We found that cross-linking of VLA-4 by either mAb or natural ligands (i.e., VCAM-1 and the FN-40 cleavage fragment of fibronectin) induced the tyrosine phosphorylation of a 110-kDa protein in a human pre-B cell line (Nalm-6), an EBV-transformed B cell line (SB), and normal tonsillar B cells. These findings suggest that VLA-4 can activate a tyrosine kinase in B cells and B cell lines. These signals may be involved in the subsequent differentiation of pre-B and mature B cells within specific microenvironments where VLA-4 mediated adhesion is operational.

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Nemati, Somayeh, and Delfim F. M. Torres. "Application of Bernoulli Polynomials for Solving Variable-Order Fractional Optimal Control-Affine Problems." Axioms 9, no. 4 (2020): 114. http://dx.doi.org/10.3390/axioms9040114.

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We propose two efficient numerical approaches for solving variable-order fractional optimal control-affine problems. The variable-order fractional derivative is considered in the Caputo sense, which together with the Riemann–Liouville integral operator is used in our new techniques. An accurate operational matrix of variable-order fractional integration for Bernoulli polynomials is introduced. Our methods proceed as follows. First, a specific approximation of the differentiation order of the state function is considered, in terms of Bernoulli polynomials. Such approximation, together with the initial conditions, help us to obtain some approximations for the other existing functions in the dynamical control-affine system. Using these approximations, and the Gauss—Legendre integration formula, the problem is reduced to a system of nonlinear algebraic equations. Some error bounds are then given for the approximate optimal state and control functions, which allow us to obtain an error bound for the approximate value of the performance index. We end by solving some test problems, which demonstrate the high accuracy of our results.

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Ameen, Ismail Gad, Dumitru Baleanu, and Hussien Shafei Hussien. "Efficient method for solving nonlinear weakly singular kernel fractional integro-differential equations." AIMS Mathematics 9, no. 6 (2024): 15819–36. http://dx.doi.org/10.3934/math.2024764.

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<abstract>This paper introduced an efficient method to obtain the solution of linear and nonlinear weakly singular kernel fractional integro-differential equations (WSKFIDEs). It used Riemann-Liouville fractional integration (R-LFI) to remove singularities and approximated the regularized problem with a combined approach using the generalized fractional step-Mittag-Leffler function (GFSMLF) and operational integral fractional Mittag matrix (OIFMM) method. The resulting algebraic equations were turned into an optimization problem. We also proved the method's accuracy in approximating any function, as well as its fractional differentiation and integration within WSKFIDEs. The proposed method was performed on some attractive examples in order to show how their solutions behave at various values of the fractional order $ \digamma $. The paper provided a valuable contribution to the field of fractional calculus (FC) by presenting a novel method for solving WSKFIDEs. Additionally, the accuracy of this method was verified by comparing its results with those obtained using other methods.</abstract>

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Saefullah, Aep, Fuad Gagarin Siregar, M. Arief Noor, Rianti Salima, and Rosliana Rosliana. "Market Analysis and Business Operations of Online Food Delivery Around STIE Ganesha." Jurnal Akuntansi, Keuangan, dan Manajemen 6, no. 3 (2025): 779–95. https://doi.org/10.35912/jakman.v6i3.4278.

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Purpose: This study examines the market dynamics, operational challenges, and competitive strategies of SMEs in the online food delivery sector around STIE Ganesha, with a focus on identifying performance drivers and actionable solutions for business optimization. Methodology/approach: A qualitative descriptive approach was adopted, involving semi-structured interviews with 20 SME owners using GoFood, GrabFood, and ShopeeFood. Data were collected from December 2024 to February 2025 and analyzed thematically to map operational patterns and market behaviors. Results/findings: Key determinants of customer retention included taste quality (highlighted by 85% of respondents), service speed (70%), and promotional effectiveness (65%). SMEs leverage product differentiation (e.g., hyperlocalized menus) and platform partnerships to sustain their market share. However, challenges persist, such as platform instability (reported by 60% of businesses) and insufficient digital literacy for advanced marketing tactics. Conclusions: The study underscores that SMEs’ competitiveness in campus-centric markets hinges on balancing micromarket responsiveness (e.g., adapting to seasonal demand) with operational agility. The strategic integration of digital tools and collaborative logistics, rather than reliance on third-party platforms alone, has emerged as critical for scalability. Limitations: The findings are context-bound to SMEs near STIE Ganesha and major delivery platforms. Future studies should explore rural and non-campus ecosystems to validate the universality of the proposed strategies. Contribution: Theoretical: Expands the Resource Orchestration Framework by contextualizing SME strategies in hyper-localized digital economies. Introduces a micro market analysis model linking campus-specific demand cycles to operational decision-making.Practical: Provides actionable toolkits, including a Dynamic Pricing Matrix for demand fluctuations and a Partnership Optimization Framework for platform collaboration. Methodology/approach: The study was conducted from December 2024 to February 2025, employing a descriptive qualitative approach. Data were collected through semi-structured interviews with 20 business owners using platforms such as GoFood, GrabFood, and ShopeeFood. Results/findings: The taste quality, fast service, and effective promotions are crucial for attracting and retaining customers. Despite high competition, SMEs have maintained their market positions through product differentiation, flavor innovation, and promotional packages. Although online delivery platforms offer substantial support, respondents highlighted the need for improved platform stability and more consistent promotional efforts. They also expressed the importance of training in digital marketing and operational management to enhance competitiveness. Limitations: This study is limited to SMEs operating around STIE Ganesha and on major online platforms. Broader generalizations require similar studies in different regions with varying business models. The research contributes to the fields of entrepreneurship and business management by providing insights for policymakers, platform providers, and business associations. Contribution: These insights focus on supporting SMEs through training, platform partnerships, and strategic collaborations. The research focused on operational processes, customer service, marketing strategies, and platform support. Novelty : The exploration of how platform partnerships, operational innovation, and digital marketing strategies influence the performance of SMEs in the online food delivery market, a topic that has not been extensively explored in prior research.

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Vasilyev, Vladimir A., and Anna S. Resnyanskaya. "Synchronized scanning fluorescence spectra method for grape seed oil authenticity identification." Processes and Food Production Equipment 18, no. 1 (2025): 3–11. https://doi.org/10.17586/2310-1164-2025-18-1-3-11.

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Fluorescence spectroscopy (SF spectroscopy) is one of the most sensitive and inexpensive methods for operational screening of counterfeits. The article analyses the method of simultaneous emission and excitation spectrum scanning for the identification of direct-press grape seed oil. Four samples of Russian-made grape seed oil were analyzed by SF spectroscopy method. The results showed that SF spectroscopy allows not only to identify individual compounds in the structure of the grape seed oil matrix, but also to separate their isomers. The most informative data were obtained at an energy degradation value (∆hem–∆hexcl) of from to 30 and 60 nm. At the same time, in the samples of genuine oils, there was a clear differentiation of maxima for tocopherols and tocotrienols λmax = 287 nm and 305 nm, respectively. At ∆h30 and λmax = 283 nm and 305 nm at ∆h40 nm, no peak separation occurred in the adulterants. Similar band separation was observed for the isomers of chlorophyll  (λmax = 633nm) and chlorophyll β (λmax = 668 nm) at ∆h40 nm. There were no peaks of chlorophyll, carotenoids, and cinnamic acids in the falsified samples. The most informative was the analysis of the full spectrum of synchronous fluorescence scanning (TSFS) with a scan step of ∆h10. Thus, SF spectroscopy allows operational screening of counterfeiting grape-seed oil and analogous food products.

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Putri, Karina Aginta, Kartika Syukla Nasukha, Maria Yosefa Febriyanti, and Sofiani Rasyid. "A Comparative Study of Honda and Toyota Brands in Hybrid Vehicle Sustainability Using the Competitive Profile Matrix (CPM) Framework." EPJ Web of Conferences 328 (2025): 01037. https://doi.org/10.1051/epjconf/202532801037.

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Global climate change and pollution have become critical global issues, necessitating the search for sustainable solutions in various sectors, especially transportation. Sustainable transportation is smart and environmentally friendly vehicles. One example is the HEV or Hybrid Electric Vehicle, a vehicle that uses two types of power sources. This research aims to see and understand the main factors that influence consumers in making decisions to buy HEV cars, especially in the Toyota and Honda brands. This study employs a quantitative approach using surveys as the primary data collection method with targeted number of respondents is 30 per brand (total 60) to ensure data represents the target population and allows relevant statistical analysis. The findings reveal that Toyota holds a slight competitive advantage, particularly in safety perception, internal capabilities related to technology, and responsiveness to government policy and innovation. Meanwhile, Honda competes closely, excelling in cost efficiency, particularly in maintenance and affordability. The use of empirically derived weights highlights a shift in consumer priorities, with operational and maintenance costs outweighing resale value in vehicle choice decisions. While Toyota maintains a slight edge, both brands’ future differentiation will increasingly depend on their ability to respond to cost concerns, regulatory developments, and innovation cycles.

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Lin, Hong-Dar, Victoria Chiu, Hua-Yao Wu, and Yuan-Shyi Peter Chiu. "Multiproduct manufacturer-retailer coordinated supply chain with adjustable rate for common parts, delayed differentiation, and multi-shipment." Uncertain Supply Chain Management 10, no. 1 (2022): 83–94. http://dx.doi.org/10.5267/j.uscm.2021.10.008.

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Operating in today’s turbulent and competitive world marketplaces, manufacturers must find the best production scheme and delivery policy to meet timely client’s multiproduct requirements and minimize the total manufacturing-shipment expenses. This study proposes a two-stage delayed differentiation model for a multiproduct manufacturer-retailer coordinated supply chain featuring the adjustable-rate for making common parts and a multi-shipment policy for transporting finished goods. The aim is to help present-day manufacturers achieve their operational goals mentioned above. The mathematical techniques help us build a specific model to explicitly represent the problem and derive its overall operating expense. Then, the convexity of the total expense is verified by Hessian matrix equations. The differential calculus helps derive the cost-minimized fabrication-shipment decision. This study offers an example to demonstrate the applicability and capabilities of our proposed model numerically. The following crucial information has been made available to the managers to facilitate their operating decision makings: (1) the problem’s best fabrication-shipment policy; (2) the collective influence of various common part’s completion rates and values on the problem’s total expenses and optimal fabrication-shipment policy; (3) the impact of various adjustable-rates in stage one on utilization and stage one’s uptime; (4) the details of cost contributors to the problem; and (5) the collective impacts of critical features on the problem’s performance.

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Journal articles on the topic 'Operational matrix of differentiation'

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