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602. A simple proof of Whitney's Theorem on connectivity in graphs
- Creator:
- Zhao, Kewen
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- connectivity and graph
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
603. A simple regularization method for the ill-posed evolution equation
- Creator:
- Tuan, Nguyen Huy and Trong, Dang Duc
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- nonlinear parabolic problem, backward problem, semigroup of operators, ill-posed problem, and contraction principle
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
604. A simplified multidimensional integral
- Creator:
- Backhausz, Ágnes M., Komornik, Vilmos, and Szilágyi, Tivadar
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- integral of several variables and characterization of primitives
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
605. A single-step clustering algorithm based on a new information-theoretic sample association metric definition
- Creator:
- Temel, T.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- clustering, clustering algorithms, information theory, mutual information, and unsupervised learning
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
606. A solar radio telescope for the wavelengths of 56 and 130 cm
- Creator:
- Budějický, J.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Ondřejov Observatory, radio telescope, and measurement accuracy
- Language:
- Czech
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
607. A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems
- Creator:
- Murakawa, Hideki
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- reaction-diffusion system approximaton, degenerate parabolic problem, and cross-diffusion system
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
608. A space of generalized distributions
- Creator:
- Loura, L.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- distributions, generalized distributions, and multipole series
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
609. A spatial distribution of the young populations of various age groups in the Sagittarius-Carina arm
- Creator:
- Avedisová, V. S.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- space research, spiral pattern parameters, and Sagittarius-Carina arm
- Language:
- Czech
- Description:
- The spatial distribution of the young objects of varioue age groups - HII regions and open clusters - in the Saglttarius-Carina arm (SC arm) at 1 « 280°- 25° ie Inyestlgated. Both transverse and longitudinal age gradients have been found in the arm, Two giant star formation complexes with the size of about 1 kpc at 1 = 285°-300° at 1 = 340°-20° are existed, Each of them contains several giant HII regions, a number of glant moleoular clouds (GMCa) and some extremely young clusters, Between these complexes we have found an elder one of the same aime.This complex contains 24 (3-6)»10^7 years old clusters and a small number of faint HII regions. Assuming that it is a remnant of a giant star formation complex the upper limit of lifetimes for such complexes and GMCs is (3-6)•10^7 years, The estimations of spiral pattem parameters are made.The value of the pitch-angle is 21°+3°. The value of spiral pattem velocity, -26.8+2.2 km/s«kpc, leads us to conclusion that the Sun is near the oorrotation radius of the Galaxy. The star formation efficiency in these complexes is discussed.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
610. A spectral bound for graph irregularity
- Creator:
- Goldberg, Felix
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, irregularity, Laplacian matrix, degree, Laplacian index, 13, and 51
- Language:
- English
- Description:
- The imbalance of an edge e = {u, v} in a graph is defined as i(e) = |d(u)−d(v)|, where d(·) is the vertex degree. The irregularity I(G) of G is then defined as the sum of imbalances over all edges of G. This concept was introduced by Albertson who proved that I(G)\leqslant 4n^{3}/27 (where n = |V(G)|) and obtained stronger bounds for bipartite and triangle-free graphs. Since then a number of additional bounds were given by various authors. In this paper we prove a new upper bound, which improves a bound found by Zhou and Luo in 2008. Our bound involves the Laplacian spectral radius λ., Felix Goldberg., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public