In 1932 Whitney showed that a graph G with order n ≥ 3 is 2-connected if and only if any two vertices of G are connected by at least two internally-disjoint paths. The above result and its proof have been used in some Graph Theory books, such as in Bondy and Murty’s well-known Graph Theory with Applications. In this note we give a much simple proof of Whitney’s Theorem.
The nonhomogeneous backward Cauchy problem $$u_t +Au(t) = f(t),\quad u(T) = \varphi$$, where $A$ is a positive self-adjoint unbounded operator which has continuous spectrum and $f$ is a given function being given is regularized by the well-posed problem. New error estimates of the regularized solution are obtained. This work extends earlier results by N. Boussetila and by M. Denche and S. Djezzar.
We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.
The paper deals with the rotor vibration in journal bearings to prepare a model for verifying the rotor vibration active control. The rotor is maintained in equilibrium position by forces generated in oil film. Bearing forces can be modelled as a spring and damper system. The main goal of the simulation study is to verify the model principle and to estimate parameters by comparing simulation results with experimental data, namely the instability of motion. Test stand with rotor supported in two journal bearings was designed for these purposes. The stand will be equipped with four piezoactuators enabling excitation of bearings by practically arbitrary dynamic force. Theoretical analysis of the influence of external excitation on rotor behaviour was carried out. Up to now the study shows that simple kinematic excitation is effective for reducing rotor excursion while passing critical speeds. To suppress self-exciting vibration of the rotor it is necessary to look for more sophisticated solution. and Obsahuje seznam literatury
A single-step information-theoretic algorithm that is able to identify possible clusters in dataset is presented. The proposed algorithm consists in representation of data scatter in terms of similarity-based data point entropy and probability descriptions. By using these quantities, an information-theoretic association metric called mutual ambiguity between data points is defined, which then is to be employed in determining particular data points called cluster identifiers. For forming individual clusters corresponding to cluster identifiers determined as such, a cluster relevance rule is defined. Since cluster identifiers and associative cluster member data points can be identified without recursive or iterative search, the algorithm is single-step. The algorithm is tested and justified with experiments by using synthetic and anonymous real datasets. Simulation results demonstrate that the proposed algorithm also exhibits more reliable performance in statistical sense compared to major algorithms.
In the paper is described the construction of the radio telescope for the wavelengths of 56 and 130 cm which has been used on the observatory of the Astronomical Institute of the ČSAV at Ondřejov for radio observations of the sun. Prevailing part of the work is devoted to the receiving equipment for the wavelength of 56 crn, which whole was built in own laboratories and which has been for 3 years in everyday operation. The author explains the determination of the fundamental parameters of the equipment and describes the means necessary to reach them. The design proposal and the realization of the receiver for the wavelength of 56 cm together with a high-stability d. c. amplifier and the design and realization of the calibrating arrangements including diode noisegenerator are described. Further the author considers to the details the influence of different quantities on the measurement accuracy and on the estimation of the resulting power flux density in the antenna apertuře with this instrument. Finally, a servomechanism performing automatic transformation of equatorial to azimuthal coordinates is described. In the next part the 130 cm - equipment is briefly mentioned. This equipment was of substantial part built outside the Institute. The both receiving apparatus use a common mirror of 7‘5m diameter having in its focus two primary feeds with
polarizations perpendicular to each other.
This paper deals with nonlinear diffusion problems involving degenerate parabolic problems, such as the Stefan problem and the porous medium equation, and cross-diffusion systems in population ecology. The degeneracy of the diffusion and the effect of cross-diffusion, that is, nonlinearities of the diffusion, complicate its analysis. In order to avoid the nonlinearities, we propose a reaction-diffusion system with solutions that approximate those of the nonlinear diffusion problems. The reaction-diffusion system includes only a simple reaction and linear diffusion. Resolving semilinear problems is typically easier than dealing with nonlinear diffusion problems. Therefore, our ideas are expected to reveal new and more effective approaches to the study of nonlinear problems.