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Abstract  

The aim of this article is to give some property of continued fraction with matrices arguments, about their convergence and others applications. At the end of this work, we present a resolution of the Algebraic Riccati Equation by giving an explicit continued fraction development of its solution.

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This paper establishes the general moduli of continuity for l -valued Gaussian random fields {X(t):= (X 1(t),X 2(t), h.), t ∈ [0, ∞)N} indexed by the N-dimensional parameter t:= (t 1,…,t N), under the explicit condition yielding that the covariance function of distinct increments of X k(t) for fixed k ≧ 1 is positive or nonpositive.

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Abstract  

The stochastic processes of activation, disintegration and counting have been studied, taking into account reactor noise. Deviation of the variance of the number of counts from Poisson limit is shown to result. Explicit expressions for the variance in the case of Markovian autocorrelation function of the neutron flux density are presented and their relevance to neutron activation analysis is discussed.

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Abstract  

Criteria for independence, both algebraic and linear, are derived for continued fraction expansions of elements in the field of Laurent series. These criteria are then applied to examples involving elements recently discovered to have explicit series and continued fraction expansions.

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We analyse the oscillation and non-oscillation of second-order half-linear differential equations with periodic and asymptotically almost periodic coefficients, where the equations have the so-called Riemann-Weber form. For these equations, we find an explicit oscillation constant. Corollaries and examples are mentioned as well.

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We classify the extreme 2-homogeneous polynomials on 2 with the hexagonal norm of weight ½. As applications, using its extreme points with the Krein-Milman Theorem, we explicitly compute the polarization and unconditional constants of P(2h(12)2).

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The oscillatory properties of half-linear second order Euler type differential equations are studied, where the coefficients of the considered equations can be unbounded. For these equations, we prove an oscillation criterion and a non-oscillation one. We also mention a corollary which shows how our criteria improve the known results. In the corollary, the criteria give an explicit oscillation constant.

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The main result of the paper provides an explicit description of an embedded resolution of the hypersurface germ (f f(x; y) +z 2 = 0 g; 0)(C 3; 0) for an arbitrary f : (C 2;0)(C; 0), The topological data of the exceptional divisors, their intersections and embeddings is codified in a (two-dimensional) \resolution graph".

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Across Languages and Cultures
Authors: Pál Heltai, Mátyás Bánhegyi, Mónika Kusztor, and Votisky Anna

Heltai, P. 2005. Explicitation, Redundancy, Ellipsis and Translation. In: Károly, K. & Fóris, Á. (eds.) New Trends in Translation Studies . Budapest: Akadémiai Kiadó. 45

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Detection of cracks in mechanical components as early as possible enables monitoring structural health and scheduling efficiently the maintenance tasks such as replacing the critical parts just in time. Vibration analysis based techniques for crack detection have been largely considered in the framework of beam-like structures. This methodology relies essentially on the observed changes of beam frequencies and mode shapes induced by the presence of damage. In the present work, using an explicit analytical model assessing the effect of a crack on beam strain energy, the beam first resonance frequencies as they depend on a single crack defect characteristics were evaluated. The crack equations were obtained by means of fracture mechanics approach. Variations of the first beam frequencies and modes shapes were then related explicitly to the location and depth of the crack. Measuring the beam frequency changes and monitoring their variations can be used to perform identification of the crack defect parameters by solution of an inverse problem.

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