1. On the integrability of persistent quadratic three-dimensional systemsBrigita Ferčec, Maja Žulj, Matej Mencinger, 2024, original scientific article Abstract: We consider a nine-parameter familiy of 3D quadratic systems, �˙=�+�2(�,�,�), �˙=−�+�2(�,�,�), �˙=−�+�2(�,�,�), where �2,�2,�2 are quadratic polynomials, in terms of integrability. We find necessary and sufficient conditions for the existence of two independent first integrals of corresponding semi-persistent, weakly persistent, and persistent systems. Unlike some of the earlier works, which primarily focus on planar systems, our research covers three-dimensional spaces, offering new insights into the complex dynamics that are not typically apparent in lower dimensions.
Keywords: ordinary differential equations, three-dimensional systems, integrability problem, persistent systems
Published in DKUM: 23.05.2024; Views: 249; Downloads: 25
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2. Analysis of the influence of parameters when charging and discharging a capacitor using differential equationsMatic Krašovic, Peter Virtič, 2022, original scientific article Abstract: Two different electrical circuits were analysed in this paper. The first was an RC circuit consisting of a resistor R, a capacitor C, and a DC voltage u, while the second was an RLC circuit consisting of a resistor R, a capacitor C, a DC voltage u and an inductor L. Both circuits were described using the state space mathematical model and, on this basis, graphs for charging and discharging a capacitor were plotted. Both circuits were described using differential equations for electrical current through a capacitor and voltage over a capacitor. Finally, different values of the R (resistance), L (inductance) and C (capacitance) parameters were taken, and graphs were plotted for voltage over capacitor. The purpose of the study was to explore how different values of parameters influence capacitor charging and discharging.
Keywords: RC circuit, RLC circuit, state space, transfer function, differential equations, parameters R, L, C, damping
Published in DKUM: 30.10.2023; Views: 278; Downloads: 15
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3. Organization in finance prepared by stohastic differential equations with additive and nonlinear models and continuous optimizationPakize Taylan, Gerhard-Wilhelm Weber, 2008, original scientific article Abstract: A central element in organization of financal means by a person, a company or societal group consists in the constitution, analysis and optimization of portfolios. This requests the time-depending modeling of processes. Likewise many processes in nature, technology and economy, financial processes suffer from stochastic fluctuations. Therefore, we consider stochastic differential equations (Kloeden, Platen and Schurz, 1994) since in reality, especially, in the financial sector, many processes are affected with noise. As a drawback, these equations are hard to represent by a computer and hard to resolve. In our paper, we express them in simplified manner of approximation by both a discretization and additive models based on splines. Our parameter estimation refers to the linearly involved spline coefficients as prepared in (Taylan and Weber, 2007) and the partially nonlinearly involved probabilistic parameters. We construct a penalized residual sum of square for this model and face occuring nonlinearities by Gauss-Newton's and Levenberg-Marquardt's method on determining the iteration step. We also investigate when the related minimization program can be written as a Tikhonov regularization problem (sometimes called ridge regression), and we treat it using continuous optimization techniques. In particular, we prepare access to the elegant framework of conic quadratic programming. These convex optimation problems are very well-structured, herewith resembling linear programs and, hence, permitting the use of interior point methods (Nesterov and Nemirovskii, 1993).
Keywords: stochastic differential equations, regression, statistical learning, parameter estimation, splines, Gauss-Newton method, Levenberg-Marquardt's method, smoothing, stability, penalty methods, Tikhonov regularization, continuous optimization, conic quadratic programming
Published in DKUM: 10.01.2018; Views: 1436; Downloads: 153
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5. Some basic difference equations of Schrodinger boundary value problemsAndreas Ruffing, Maria Meiler, Andrea Bruder, 2009, original scientific article Abstract: We consider special basic difference equations which are related to discretizations of Schrödinger equations on time scales with special symmetry properties, namely, so-called basic discrete grids. These grids are of an adaptive grid type. Solving the boundary value problem of suitable Schrödinger equations on these grids leads to completely new and unexpected analytic properties of the underlying function spaces. Some of them are presented in this work.
Keywords: differential equations, discretization, Schrödinger equations, value problems
Published in DKUM: 26.06.2017; Views: 1353; Downloads: 409
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6. Henríquez, Hernán; Hernández M., Eduardo; dos Santos, José: Asymptotically almost periodic and almost periodic solutions for partial neutral integrodifferential equations. (English). - [J] Z. Anal. Anwend. 26, No. 3, 363-375 (2007). [ISSN 0232-2064; ISSN 1661-4534]Miklavž Mastinšek, 2008, review, book review, critique Keywords: matematika, diferencialne enačbe, mathematics, differential equations, neutral equations
Published in DKUM: 10.07.2015; Views: 1197; Downloads: 27
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7. Liu, Xin-Ge; Wu, Min; Martin, Ralph; Tang, Mei-Lan: Delay-dependent stability analysis for uncertain neutral systems with time-varying delays. (English). - [J] Math. Comput. Simul. 75, No. 1-2, 15-27 (2007). [ISSN 0378-4754]Miklavž Mastinšek, 2008, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, asimptotična stabilnost, mathematics, ordinary differential equations, neutral delay-differential system
Published in DKUM: 10.07.2015; Views: 1498; Downloads: 40
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8. Bertoldi, Marcello; Fornaro, Simona; Lorenzi, Luca: Pointwise gradient estimates in exterior domains. (English). - [J] Arch. Math. 88, No. 1, 77-89 (2007). [ISSN 0003-889X; ISSN 1420-8938]Miklavž Mastinšek, 2007, review, book review, critique Keywords: matematika, parcialne diferencialne enačbe, teorija operatorjev, neomejeni koeficienti, problem Cauchy-Neumanna, polgrupe Markova, mathematics, partial differential equations, operator theory, functional differential equation, unbounded coefficients, Cauchy-Neumann problem, Markov semigroup
Published in DKUM: 10.07.2015; Views: 1509; Downloads: 45
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9. Faria, Teresa: Asymptotic stability for delayed logistic type equations. (English). - [J] Math. Comput. Modelling 43, No. 3-4, 433-445 (2006). [ISSN 0895-7177]Miklavž Mastinšek, 2008, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, populacijska dinamika, mathematics, differential equations, delayed logistic equation, delayed population model, global asymptotic stability
Published in DKUM: 10.07.2015; Views: 1807; Downloads: 25
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10. Balachandran, K.; Ravikumar, R.: Nonlocal Cauchy problem for time varying delay integrodifferential equations of Sobolev type in Banach spaces. (English). - [J] Tamkang J. Math. 37, No. 3, 193-205 (2006). [ISSN 0049-2930]Miklavž Mastinšek, 2008, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, polgrupe nelinearnih operatorjev, mathematics, differential equations, delay integrodifferential equation, nonlocal condition
Published in DKUM: 10.07.2015; Views: 1013; Downloads: 44
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