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Projective Geometry and the Law of Mass Action
Gottvald, Aleš
A new law of nature asserts that chemical equilibria and chemical kinetics are governed by fundamental principles of projective geometry. The equilibrium constans of chemical reactions are the invariants of projective geometry in disguise. Chemical reactions may geometrically be represented by incidence structures, which are preserved under projective transformations. Theorems of Ceva, Menelaus, and Carnot for triangles and n-gons represent the chemical equilibria, while Routh's theorem represents non-equilibria. Intrinsically projective Riccati's differential equation, being also generic to many other equations of mathematical physics, governs parametric dependence of the equilibrium constants. The theory offers tangible geometrizations and generalizations to the Law of Mass Action, including a new projective-geometric approach to soft computing of very complex problems.
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Stability analysis of systems of ordinary differential equations
Trejtnar, Miloš ; Opluštil, Zdeněk (referee) ; Tomášek, Petr (advisor)
This thesis deals with a stability analysis of the first order systems of ordinary differential equations. There are introduced some stability approaches in the thesis and they are discussed in the several examples. The attention is focused to the case of linear autonomous systems, where the classification of the singular points is realized. The thesis is closed by the application of the stability theory in mathematical model of electric current conduction in a primary and secondary coil of a transformer.
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In vitro and in vivo antimicrobial effect of lasioglossins on the Candida albicans
Kašperová, A. ; Turánek, J. ; Čeřovský, Václav ; Raška, M.
Lasioglossins represent a new group of amphipathic α-helical peptides with significant antimicrobial effect on the Candida albicans. This study examines the antifungal activity of two peptides LL-III and all D-LL-III as measured by the suppression of Candida proliferation and suppression of induced morphological differentiation both in in vitro and in vivo assays. In the in vitro Candida proliferation assay, the inhibitory effect of lasioglossins LL-III and all D-LL-III was more than 70% within 24 h and more than 84% after 48 h of incubation (final concentration of either peptide was 17.5 .mu.M). Delaying of blastoconidial transition to hyphae in vitro and tendency to suppress vaginal candidiasis in experimental mice were detected.
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Stochastická teorie katastrof
Vošvrda, Miloslav ; Voříšek, Jan
The so called Cusp deterministic catastrophe model extends the classical linear regression adding nonlinearity into a model. A property of a stochatic catastrophe model connected with stochastic differential equation could be described by density, which is known in closed-form only in stationary case. The approximation of the transition density is done here by finite difference metod.
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Incompressible fiscous flow at viscous velocities in interaction with a vibrating profile NACA 0012
Honzátko, R. ; Horáček, Jaromír ; Kozel, Karel
The work presents numerical solution of the interaction of 2D incompressible viscous flow and a freely vibrating profile NACA 0012 with large amplitudes. The upstream flow velocities are consider in the range 5-40 m/s. The profile has two degrees of freedom. It can rotate around an elastic axis and oscillate in the vertical direction. Its motion is described by two nonlinear ordinary differential equations. Fourth-order Runge-Kutta method is used to solve these equations numerically. The incompressible Navier-Stokes equations represent the mathematical model of the laminar viscous flow. Numerical schemes of the FVM are applied on a structured Quadrilateral C-mesh. The method of artificial compressibility and dual-time stepping method is employed for numerical simulations. Deformations of the computational domain are treated using the ALE method. Numerical simulations of the profile motion are performed for the case solved earlier by the FE method, and the results are in good agreement.
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Příspěvek k analýze asynchronního stroje se dvěma třífázovými statorovými vinutími
Schreier, Luděk ; Bendl, Jiří ; Chomát, Miroslav ; Skalka, Miroslav
This paper analyses situation in induction machines with two three-phase windings on the stator fed by two totally independent voltage sources. To analyze the situation in these machines, the method of space vectors has been used. The paper shows a mathematic description of such a machine based on a system of differential equations. The waveforms of currents and torque of the machine for various time shifts of voltages of both the feeding sources are shown. The results of the simulation show the necessity to exactly maintain the optimal time shift of both the voltages.
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Characteristics of the Chen Attractor
Augustová, Petra ; Beran, Zdeněk
Within the paper a mathematical representation of the so-called Chen model is described as a particular parametric three-dimensional chaotic dynamical system, i.e. a system of three nonlinear differential equations evolving in time. The main aim of this paper is to find for the Chen system the properties that are known for the Lorenz system and its famous Lorenz attractor. First, the integrals of motion are derived for some parameters of the Chen system. The integrals of motions play an important role in physics, e.g. for conservation laws. Next, the shape of the global attractor of this system is approximated by volumes that contain the attractor. The shape predicts the future behavior of the system. To obtain these results, the already proved fact that the Chen system is a continued transition of the Lorenz system is used. According to our knowledge, the same approach of shifting the known facts about the Lorenz system to a newdynamical system, the Chen system in this context, has not been presented yet.
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