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1.
Analysis of the influence of parameters when charging and discharging a capacitor using differential equations
Matic 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: 136; Downloads: 8
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2.
Organization in finance prepared by stohastic differential equations with additive and nonlinear models and continuous optimization
Pakize 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: 1237; Downloads: 137
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3.
On the solvability of second-order impulsive differential equations with antiperiodic boundary value conditions
Yepeng Xing, Valery Romanovski, 2008, original scientific article

Abstract: We prove existence results for second-order impulsive differential equations with antiperiodic boundary value conditions in the presence of classical fixed point theorems. We also obtain the expression of Green's function of related linear operator in the space of piecewise continuous functions.
Keywords: second-order impulsive differential equations, antiperiodic boundary value conditions, Green's function
Published in DKUM: 26.06.2017; Views: 1260; Downloads: 399
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4.
Some basic difference equations of Schrodinger boundary value problems
Andreas 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: 1153; Downloads: 394
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