Analysis of two degrees of freedom systems through weighted mean square linearization approach

In this paper a study of the free, forced and self-excited vibrations of non-linear, two degrees of freedom systems is reported. The responses are obtained by linearizing the nonlinear equations using the weighted mean square linearization approach. The scope of this approach, in terms of the type of non-linearities the method can tackle, is also discussed.

A note on non-separable solutions of linear partial differential equation

A method has been presented for constructing non-separable solutions of homogeneous linear partial differential equations of the type F(D, D′)W = 0, where D = ∂/∂x, D′ = ∂/∂y, Image where crs are constants and n stands for the order of the equation. The method has also been extended for equations of the form Φ(D, D′, D″)W = 0, where D = ∂/∂x, D′ = ∂/∂y, D″ = ∂/∂z and Image As illustration, the method has been applied to obtain nonseparable solutions of the two and three dimensional Helmholtz equations.

Digestion of forages in the rumen is increased by the amount but not the type of protein supplement

Three polyester bag experiments were conducted with fistulated Bos indicus steers to determine the effect of the amount and type of nitrogen (N) supplement on the digestion rate of forages different in quality. In Experiment 1, test substrates were incubated in polyester bags in the rumen of steers fed ryegrass, pangola grass, speargrass and Mitchell grass hays in a 4 by 4 Latin-square design. In Experiment 2, test substrates were incubated in polyester bags in the rumen of steers fed speargrass hay supplemented with urea and ammonium sulfate (US), branched-chain amino acids with US (USAA), casein, cottonseed meal, yeast and Chlorella algae in a 7 by 3 incomplete Latin-square design. In Experiment 3, test substrates were incubated in polyester bags in the rumen of steers fed Mitchell grass hay supplemented with increasing amounts of US or Spirulina algae (Spirulina platensis). The test substrates used in all experiments were speargrass, Mitchell grass, pangola grass or ryegrass hays. Digestion rate of the ryegrass substrate was higher than that of the speargrass substrate (P < 0.05) in Experiment 1. Supplementation with various N sources increased the degradation rate and effective degradability of all incubated substrates above that apparent in Control steers (P < 0.05; Experiment 2). Supplementation of US and Spirulina increased degradation rate and effective degradability of ryegrass, pangola grass and Mitchell grass substrates above that apparent in Control steers (P < 0.05; Experiment 3). However, there was no further response on digestion rate of the substrates in increasing supplementation levels either for US or Spirulina. In conclusion, rate of digestion was affected by forage physical and anatomical properties. Supplementation with various N sources increased rate of digestion when the Control forage ration was very low in N but once a minimum level of N supplementation was reached, irrespective of form of N or other potential growth factors, there was no further increase in rate of digestion.

Boundedness and convergence of singular integrals on fractal type sets

The topic of this dissertation lies in the intersection of harmonic analysis and fractal geometry. We particulary consider singular integrals in Euclidean spaces with respect to general measures, and we study how the geometric structure of the measures affects certain analytic properties of the operators. The thesis consists of three research articles and an overview. In the first article we construct singular integral operators on lower dimensional Sierpinski gaskets associated with homogeneous Calderón-Zygmund kernels. While these operators are bounded their principal values fail to exist almost everywhere. Conformal iterated function systems generate a broad range of fractal sets. In the second article we prove that many of these limit sets are porous in a very strong sense, by showing that they contain holes spread in every direction. In the following we connect these results with singular integrals. We exploit the fractal structure of these limit sets, in order to establish that singular integrals associated with very general kernels converge weakly. Boundedness questions consist a central topic of investigation in the theory of singular integrals. In the third article we study singular integrals of different measures. We prove a very general boundedness result in the case where the two underlying measures are separated by a Lipshitz graph. As a consequence we show that a certain weak convergence holds for a large class of singular integrals.

Boundedness of weakly singular integral operators on domains

The monograph dissertation deals with kernel integral operators and their mapping properties on Euclidean domains. The associated kernels are weakly singular and examples of such are given by Green functions of certain elliptic partial differential equations. It is well known that mapping properties of the corresponding Green operators can be used to deduce a priori estimates for the solutions of these equations. In the dissertation, natural size- and cancellation conditions are quantified for kernels defined in domains. These kernels induce integral operators which are then composed with any partial differential operator of prescribed order, depending on the size of the kernel. The main object of study in this dissertation being the boundedness properties of such compositions, the main result is the characterization of their Lp-boundedness on suitably regular domains. In case the aforementioned kernels are defined in the whole Euclidean space, their partial derivatives of prescribed order turn out to be so called standard kernels that arise in connection with singular integral operators. The Lp-boundedness of singular integrals is characterized by the T1 theorem, which is originally due to David and Journé and was published in 1984 (Ann. of Math. 120). The main result in the dissertation can be interpreted as a T1 theorem for weakly singular integral operators. The dissertation deals also with special convolution type weakly singular integral operators that are defined on Euclidean spaces.

On Orlicz-Sobolev capacities

This thesis consists of three articles on Orlicz-Sobolev capacities. Capacity is a set function which gives information of the size of sets. Capacity is useful concept in the study of partial differential equations, and generalizations of exponential-type inequalities and Lebesgue point theory, and other topics related to weakly differentiable functions such as functions belonging to some Sobolev space or Orlicz-Sobolev space. In this thesis it is assumed that the defining function of the Orlicz-Sobolev space, the Young function, satisfies certain growth conditions. In the first article, the null sets of two different versions of Orlicz-Sobolev capacity are studied. Sufficient conditions are given so that these two versions of capacity have the same null sets. The importance of having information about null sets lies in the fact that the sets of capacity zero play similar role in the Orlicz-Sobolev space setting as the sets of measure zero do in the Lebesgue space and Orlicz space setting. The second article continues the work of the first article. In this article, it is shown that if a Young function satisfies certain conditions, then two versions of Orlicz-Sobolev capacity have the same null sets for its complementary Young function. In the third article the metric properties of Orlicz-Sobolev capacities are studied. It is usually difficult or impossible to calculate a capacity of a set. In applications it is often useful to have estimates for the Orlicz-Sobolev capacities of balls. Such estimates are obtained in this paper, when the Young function satisfies some growth conditions.

Development of type I genetic markers from expressed sequence tags in highly polymorphic species

Expressed sequence tag (EST) databases provide a primary source of nuclear DNA sequences for genetic marker development in non-model organisms. To date, the process has been relatively inefficient for several reasons: - 1) priming site polymorphism in the template leads to inferior or erratic amplification; - 2) introns in the target amplicon are too large and/or numerous to allow effective amplification under standard screening conditions, and; - 3) at least occasionally, a PCR primer straddles an exon–intron junction and is unable to bind to genomic DNA template. The first is only a minor issue for species or strains with low heterozygosity but becomes a significant problem for species with high genomic variation, such as marine organisms with extremely large effective population sizes. Problems arising from unanticipated introns are unavoidable but are most pronounced in intron-rich species, such as vertebrates and lophotrochozoans. We present an approach to marker development in the Pacific oyster Crassostrea gigas, a highly polymorphic and intron-rich species, which minimizes these problems, and should be applicable to other non-model species for which EST databases are available. Placement of PCR primers in the 3′ end of coding sequence and 3′ UTR improved PCR success rate from 51% to 97%. Almost all (37 of 39) markers developed for the Pacific oyster were polymorphic in a small test panel of wild and domesticated oysters.

Numerical studies on quasilinear and linear elliptic equations

We explore here the acceleration of convergence of iterative methods for the solution of a class of quasilinear and linear algebraic equations. The specific systems are the finite difference form of the Navier-Stokes equations and the energy equation for recirculating flows. The acceleration procedures considered are: the successive over relaxation scheme; several implicit methods; and a second-order procedure. A new implicit method—the alternating direction line iterative method—is proposed in this paper. The method combines the advantages of the line successive over relaxation and alternating direction implicit methods. The various methods are tested for their computational economy and accuracy on a typical recirculating flow situation. The numerical experiments show that the alternating direction line iterative method is the most economical method of solving the Navier-Stokes equations for all Reynolds numbers in the laminar regime. The usual ADI method is shown to be not so attractive for large Reynolds numbers because of the loss of diagonal dominance. This loss can however be restored by a suitable choice of the relaxation parameter, but at the cost of accuracy. The accuracy of the new procedure is comparable to that of the well-tested successive overrelaxation method and to the available results in the literature. The second-order procedure turns out to be the most efficient method for the solution of the linear energy equation.

A note on the evaluation of dielectric dispersion parameters of non-debije type liquids

A simple method for evaluating dielectric relaxation parameters ie given whioh can be used for analyeing the arelaxation times of a liquid into two absorptions.

The averaging principle and the diagram technique

Rae and Davidson have found a striking connection between the averaging method generalised by Kruskal and the diagram technique used by the Brussels school in statistical mechanics. They have considered conservative systems whose evolution is governed by the Liouville equation. In this paper we have considered a class of dissipative systems whose evolution is governed not by the Liouville equation but by the last-multiplier equation of Jacobi whose Fourier transform has been shown to be the Hopf equation. The application of the diagram technique to the interaction representation of the Jacobi equation reveals the presence of two kinds of interactions, namely the transition from one mode to another and the persistence of a mode. The first kind occurs in the treatment of conservative systems while the latter type is unique to dissipative fields and is precisely the one that determines the asymptotic Jacobi equation. The dynamical equations of motion equivalent to this limiting Jacobi equation have been shown to be the same as averaged equations.

Iterative solution of a class of linear equations with application to reconstruction of three-dimensional object arrays

An iterative algorithm baaed on probabilistic estimation is described for obtaining the minimum-norm solution of a very large, consistent, linear system of equations AX = g where A is an (m times n) matrix with non-negative elements, x and g are respectively (n times 1) and (m times 1) vectors with positive components.