http://scholars.ntou.edu.tw/handle/123456789/11111 Fri, 17 Apr 2026 11:44:48 GMT 2026-04-17T11:44:48Z http://scholars.ntou.edu.tw/handle/123456789/26523 標題: Integral and Numerical Formulations for Seeking the Period of Non-Conservative Nonlinear Oscillator With/Without the First Integral 作者: Liu, Chein-Shan; Tsai, Chia-Cheng; Chang, Chih-Wen 摘要: For a non-conservative nonlinear oscillator (NCNO) having a periodic solution, the existence of the first integral is a certain symmetry of the nonlinear dynamical system, which signifies the balance of kinetic energy and potential energy. A first-order nonlinear ordinary differential equation (ODE) is used to derive the first integral, which, equipped with a right-end boundary condition, can determine an implicit potential function for computing the period by an exact integral formula. However, the integrand is singular, which renders a less accurate value of the period. A generalized integral conservation law endowed with a weight function is constructed, which is proved to be equivalent to the exact integral formula. Minimizing the error to satisfy the periodicity conditions, the optimal initial value of the weight function is determined. Two non-iterative methods are developed by integrating three first-order ODEs or two first-order ODEs to compute the period. Very accurate value of the period can be observed upon testing five examples. For the NCNO without having the first integral, the integral-type period formula is derived. Four examples belong to the Li & eacute;nard equation, involving the van der Pol equation, are evaluated by the proposed iterative method to determine the oscillatory amplitude and period. For the case with one or more limit cycles, the amplitude and period can be estimated very accurately. For the NCNO of a broad type with or without having the first integral, the present paper features a solid theoretical foundation and contributes integral-type formulations for the determination of the oscillatory period. The development of new numerical algorithms and extensive validation across a diverse set of examples is given. Wed, 01 Jan 2025 00:00:00 GMT http://scholars.ntou.edu.tw/handle/123456789/26523 2025-01-01T00:00:00Z http://scholars.ntou.edu.tw/handle/123456789/26465 標題: Optimization of Bai-Parlett-Wang's iteration method for solving saddle-point linear systems with applications to 2D Stokes flow problems 作者: Liu, Chein-Shan; Hong, Hong-Ki; Tsai, Chia-Cheng 摘要: For the two-dimensional Stokes equations we derive a saddle-point linear system to computing the velocities and pressure on nodal points. The equivalent form of the splitting iterative algorithm is expressed in terms of descent vector and residual vector, which are two basic vectors often used in the iterative algorithm. The splitting iterative algorithm is proven to be absolute convergence, if the orthogonality condition is fulfilled. An orthogonalized iterative algorithm (OIA) can be derived by preceding a stabilization factor to the descent vector. For the OIA the Jordan structure correlates the (k + 1)th step residual vector to the kth step residual vector and descent vector is explored. The convergence is happened automatically because the OIA exhibits a pull-back mechanism. By using the orthogonality condition the non-stationary parameter with optimal value per iteration is derived explicitly in Bai-Parlett-Wang's iteration method, which is able to maximally reduce the residual per step. Three splitting iterative algorithms are tested by five examples including the Stokes flow problems. Highly accurate numerical solutions with the accuracy in the order 10-14 for velocities and 10-13 for pressure are obtained by the proposed optimal Bai-Parlett-Wang's iteration method. Wed, 01 Jan 2025 00:00:00 GMT http://scholars.ntou.edu.tw/handle/123456789/26465 2025-01-01T00:00:00Z http://scholars.ntou.edu.tw/handle/123456789/26444 標題: Newly Formulated General Solutions for the Navier Equation in Linear Elasticity 作者: Liu, Chein-Shan; Kuo, Chung-Lun 摘要: The Navier equations are reformulated to be third-order partial differential equations. New anti-Cauchy-Riemann equations can express a general solution in 2D space for incompressible materials. Based on the third-order solutions in 3D space and the Boussinesq-Galerkin method, a third-order method of fundamental solutions (MFS) is developed. For the 3D Navier equation in linear elasticity, we present three new general solutions, which have appeared in the literature for the first time, to signify the theoretical contributions of the present paper. The first one is in terms of a biharmonic function and a harmonic function. The completeness of the proposed general solution is proven by using the solvability conditions of the equations obtained by equating the proposed general solution to the Boussinesq-Galerkin solution. The second general solution is expressed in terms of a harmonic vector, which is simpler than the Slobodianskii general solution, and the traditional MFS. The main achievement is that the general solution is complete, and the number of harmonic functions, three, is minimal. The third general solution is presented by a harmonic vector and a biharmonic vector, which are subjected to a constraint equation. We derive a specific solution by setting the two vectors in the third general solution as the vectorizations of a single harmonic potential. Hence, we have a simple approach to the Slobodianskii general solution. The applications of the new solutions are demonstrated. Owing to the minimality of the harmonic functions, the resulting bases generated from the new general solution are complete and linearly independent. Numerical instability can be avoided by using the new bases. To explore the efficiency and accuracy of the proposed MFS variant methods, some examples are tested. Wed, 01 Jan 2025 00:00:00 GMT http://scholars.ntou.edu.tw/handle/123456789/26444 2025-01-01T00:00:00Z http://scholars.ntou.edu.tw/handle/123456789/26406 標題: Novel centromeric plasmid for stable extrachromosomal gene expression in Aurantiochytrium limacinum 作者: Renta, Person Pesona; Syu, Cian-Huei; Huang, Ta-Yu; Chang, Yi-Ting; Liang, Yu-Feng; Chen, Ssu-Ting; Weng, Po-Wei; Hsu, Ming-Chen; Lin, Keng-Hung; Liu, Tsunglin; Jang, Anna C. -C.; Tsao, Che-Chia; Lin, Han-Jia; Lin, Hung-Yun; Chen, Yi-Min 摘要: Aurantiochytriumlimacinum holds great promise for producing sustainable single-cell oil as an alternative to fish oil. However, research into its complex biological and biochemical characteristics and efforts toward strain improvement have been hampered by insufficient genetic tools. Until now, genetic transformations of A. limacinum have relied solely on chromosome integration, which is inefficient and prone to insertional mutagenesis and other issues related to genetically modified organisms (GMOs). This paper describes the first centromeric plasmid for A. limacinum. Amplification of this shuttle vector by E. coli enables direct delivery into A. limacinum via electroporation, where it undergoes stable replication and segregation into daughter cells. The key to the stable plasmid maintenance lies in a 500 bp segment derived from chromosome 24 of Phaeodactylum tricornutum. While this segment does not significantly enhance the efficiency of vector transformation, it enables the replication and maintenance of the shuttle vector in the host cell as closed circular DNA. The plasmid from three transformants demonstrates a high segregation efficiency of 96.8 +/- 0.3% (n = 3), even in the absence of antibiotic selection. This novel centromeric plasmid considerably enhances the flexibility of genetic manipulations and gene expression in A. limacinum, opening new avenues for its study and industrial application.Key points center dot First centromeric plasmid developed for genetic transformation in A. limacinum.center dot The novel plasmid enhances flexibility in genetic manipulation and gene expression.center dot The plasmid achieves 96.8 +/- 0.3% (n = 3) segregation efficiency without antibiotic selection.Key points center dot First centromeric plasmid developed for genetic transformation in A. limacinum.center dot The novel plasmid enhances flexibility in genetic manipulation and gene expression.center dot The plasmid achieves 96.8 +/- 0.3% (n = 3) segregation efficiency without antibiotic selection.Key points center dot First centromeric plasmid developed for genetic transformation in A. limacinum.center dot The novel plasmid enhances flexibility in genetic manipulation and gene expression.center dot The plasmid achieves 96.8 +/- 0.3% (n = 3) segregation efficiency without antibiotic selection. Wed, 01 Jan 2025 00:00:00 GMT http://scholars.ntou.edu.tw/handle/123456789/26406 2025-01-01T00:00:00Z