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.
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.
The south east Asian pest thrips, Thrips parvispinus is recorded breeding in Europe for the first time, damaging Gardenia plants in Greece. Morphological variation in this species from various Asian countries is recorded and compared to the type specimens. As a result Isoneurothrips jenseni Karny, 1925 and Thrips (Isoneurothrips) taiwanus Takahashi, 1936 are placed as synonyms of Thrips parvispinus (Karny, 1922). In contrast, Thrips compressicornis (Sakimura), a species from the Marquesa Islands of the Pacific that has previously been associated with these taxa, represents a very different species. The quarantine significance of T. parvispinus is emphasised.
In this paper we use a duality method to introduce a new space of generalized distributions. This method is exactly the same introduced by Schwartz for the distribution theory. Our space of generalized distributions contains all the Schwartz distributions and all the multipole series of physicists and is, in a certain sense, the smallest space containing all these series.