Uniform Approximations by the Poisson Threeharmonic Integrals on the Sobolev Classes

The author considers classes of periodic functions given by variation diminishing convolutions. These classes include, for example, the Sobolev class and the class , where is any polynomial with real coefficients and real roots. The Poisson kernel, the de la Vallee-Poussin kernel and many others have the variation diminishing property.For classes given by variation diminishing convolutions the author proves optimality of the rectangle formula among all quadrature formulas of the form with . In addition, a solution of Favard's problem is given and an optimal method of reconstructing functions of these classes is found.Bibliography: 22 titles.

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The purpose of the study is to substantiate the design scheme and parameters of the working bodies of a combined machine for tillage and sowing grain on sloping lands. The authors have developed a machine that performs technological operations for tillage, grain sowing, and ridge formation to prevent water erosion. The design diagram is given. The basic principles and methods of classical mechanics, mathematical analysis, and statistics were used in this study. Theoretical and experimental studies have established that using a chisel-shaped ripper with loosening knives as a loosening working body provides high-quality loosening of the soil. When the longitudinal and transverse distances between the rippers are 62.5 and 15 cm, respectively, the longitudinal distance between the rear ripper and the housing is 60 cm, and the transverse distance between the buildings is 90 cm, high-quality soil loosening, and grain sowing are achieved with minimal energy consumption.

The purpose of the study is the theoretical justification of the parameters of the slitter for embedding manure in the soil. A slitter has been developed for lifting the formation, forming a gap along the manure strip lying on the field's surface, pushing it into the gap, and leveling the gap with soil. The basic principles and methods of classical mechanics, mathematical analysis, and statistics were used in this study. The slitter includes a rack, large and small cheeks connected to a soil-supporting plate with an increasing slope from the bottom to the top towards the small cheek and adjacent to the soil-supporting plate. A window is made in the big cheek for the passage of manure. The large cheek is somewhat pushed forward relative to the soil-bearing plate, and its front face is pointed. It is established that when planting fertilizers, the following operations must be carried out: lifting the formation, forming a gap along the manure strip lying on the field's surface, pushing the latter into the gap, and leveling the gap with soil. The working bodies of the dump type are the most acceptable for lifting the formation and the formation of a gap. The following optimal values of the parameters of the slitter are established: the removal of the large cheek is 710 mm, the width is 200 mm, the length and height of the window are 550 and 250 mm, respectively, and the angle between the forming and field edge in the horizontal plane is 42°, the height of the small and large cheeks of the slitter is 300 and 250 mm, respectively.

The physical basis of the mixture formation is analyzed. The study aims to increase the intensity of the process of continuous mixing of feed in the mixer. The basic principles and methods of classical mechanics, mathematical analysis, and statistics were used in this study. The design of the mixer cover in the form of a three-sided box is justified, which eliminates additional resistance to the rotation of the screw due to the impact of the feed masses reflected from the cover. When using a lid in the form of a three-sided box, the mixing quality improves by 4-5% and reaches 93% or more at a capacity of 15 t/h. It is established that the optimal angle of inclination of the reflecting plane of the mixing chamber cover is 31-35° with a screw diameter of 400 mm, the height of the reflecting plane from the screw axis of 350 mm, and a rotation speed of 36.61 s-1. The following indicators of the mixer were determined: the productivity that ensures the mixing quality of more than 90% when mixing green mass and silage with mixed feed - 19 t/h, crushed feed root crops with mixed feed-23 t / h, the speed of the screw - 36.61 s-1.

Substantiation of differences between payback and break-even points in the production activities of enterprises is concerned. The method of modeling and research of economic phenomena and processes is offered. The methodological basis of this approach are two elements: the creation of a formalized economic categorical apparatus and the construction of mathematical models of economic processes. The essence of the formation of the categorical apparatus is as follows: three primary categories are proposed, on the basis of which all secondary ones are defined axiomatically. The application of this categorical apparatus makes it possible to solve the following main issues: to formulate the content of qualitative economic concepts (categories) of "stock" and "flow"; to introduce into economic practice such an important indicator as "economic acceleration", as a result of which there is an opportunity to reasonably model and study nonlinear economic processes; change the understanding of many economic concepts - "value", "price", etc., because they become categories that have separate units of measurement, and therefore formed indicators that are significantly different from traditional ("cost", "profit price", etc.). But most importantly, it ultimately provides an opportunity to model and explore important economic processes and indicators. The application of the proposed category apparatus is shown on the example of modeling and research of economic processes occurring at the enterprise in the implementation of operational activities - production and sale of manufactured products. The most important element of this activity is the substantiation of payback and break-even points that correspond to a given technological process. The disadvantage of existing approaches to substantiate these indicators is that when describing these processes using traditional concepts, researchers often confuse which point they consider - payback or break-even, as the main indicators in the obtained models are almost the same - on the X-axis "production volumes ” are put, and on the Y axis -“ costs ”and“ sales ”. Therefore, the main difference between these points is not in the name of the elements of the study (their name is the same in both cases), but in their essence. In the first case, when the payback point is determined, these indicators are considered as a "stock", and in the second - when determining the break-even point - in the form of flows. This means that in order to avoid mistakes, it is necessary to understand clearly in which space (stocks or flows) research should be carried out. Keywords: economic categories, stock, flow, economic acceleration, payback point, break-even point, fixed and variable costs, one-time and current costs.

Convergence analysis for hierarchical longitudinal data

A Partial Characterization of Poised Hermite–Birkhoff Interpolation Problems

The accuracy and effectiveness of the pseudoinverse technique as a means of determining the operating vibratory loads on a structural system, from acceleration mobilities obtained by modal superposition, can be severely undermined by lack of proper consideration of the participation of the structural modes at the frequency of interest. Methods of linear algebra and modal analysis are used to establish the limitations of this technique with regard to the number of independent forces determinable at a given frequency in relation to the number and significance of structural modes participating in the response at that frequency. Results of numerical calculations based on two uniform beams, one cantilevered and the other free-free, show that for an assumed level of random error in the acceleration mobility matrix, the accuracy of the determined forces correlates well with a parameter that is related to the number of modes contributing to the response of the structure at a given frequency.

Uniform convergence of regularization methods for linear ill-posed problems

Graded mesh modified backward finite difference method for two parameters singularly perturbed second-order boundary value problems

Wiener's tauberian theorems for the Fourier–Bessel transformation and uniform approximation by RBF networks of Delsarte translates

The approximation characteristics of trigonometric sums Un,pψ of special type on the class Cβ,∞ψ of (ψ,β)-differentiable (in the sense of A. I. Stepanets) periodical functions are studied. Because of agreement between parameters of approximative sums and approximated classes, the solution of Kolmogorov-Nikol’skii problem is obtained in a sufficiently general case. It is shown that in a number of important cases these sums provide higher order of approximation in comparison with Fourier sums, de la Vallée Poussin sums, and others on the class Cβ,∞ψ in the uniform metric. The range of parameters in which the sums Un,pψ give the order of the best uniform approximation on the classes Cβ,∞ψ is indicated.

Factor analysis is a statistical method used to describe a set of variables based on common dimensions. Factor analysis that is often used is the classical factor analysis with principal components method. Classical factor analysis can not work properly if the data contained many outliers. In order factor analysis remains optimal in explaining a set of variables even in conditions of data containing many outliers, we need a robust estimator. Through factor analysis is expected to obtain robust high accuracy analysis results for data containing many outliers. Estimator fast-MCD is one of the robust estimator that aims to get the smallest determinant of the covariance matrix. Robust factor analysis with fast-MCD method in this thesis is applied to explain the many subgroups of food at food inflation rate in Central Java into a more modest dimensions. The total proportion of the data variance can be explained by factors that are formed through a robust method of factor analysis in foodstuffs inflation data in Central Java that is equal to 72.9 percent larger than the classical factor analysis method which generates at 53.5 percent. This suggests that a more robust factor analysis method is able to cope with food inflation data in Central Java group containing outliers of the classical factor analysis method.

Previous article Next article Uniform Generalized Weight Function Polynomial Approximation with InterpolationH. L. Loeb, D. G. Moursund, L. L. Schumaker, and G. D. TaylorH. L. Loeb, D. G. Moursund, L. L. Schumaker, and G. D. Taylorhttps://doi.org/10.1137/0706026PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. Paszkowski, On approximation with nodes, Rozprawy Mat., 14 (1957), 63– MR0092888 0083.29002 Google Scholar[2] Frank Deutsch, On uniform approximation with interpolatory constraints, J. Math. Anal. Appl., 24 (1968), 62–79 10.1016/0022-247X(68)90049-8 MR0230017 0174.35501 CrossrefISIGoogle Scholar[3] E. W. Cheney and , H. L. Loeb, Generalized rational approximation, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., 1 (1964), 11–25 MR0178288 0138.04403 LinkGoogle Scholar[4] Samuel Karlin and , William J. Studden, Tchebycheff systems: With applications in analysis and statistics, Pure and Applied Mathematics, Vol. XV, Interscience Publishers John Wiley & Sons, New York-London-Sydney, 1966xviii+586 MR0204922 0153.38902 Google Scholar[5] David G. Moursund, Chebyshev approximation using a generalized weight function, SIAM J. Numer. Anal., 3 (1966), 435–450 10.1137/0703038 MR0204936 0163.07302 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails A general framework for the optimal approximation of circular arcs by parametric polynomial curvesJournal of Computational and Applied Mathematics, Vol. 345 | 1 Jan 2019 Cross Ref Strong unicity of order 2 in C(T)Journal of Approximation Theory, Vol. 56, No. 3 | 1 Mar 1989 Cross Ref The Best Interpolating Approximation is a Limit of Best Weighted ApproximationsCanadian Mathematical Bulletin, Vol. 25, No. 4 | 20 November 2018 Cross Ref The best interpolating approximation and weighted approximationJournal of Approximation Theory, Vol. 35, No. 1 | 1 Oct 1982 Cross Ref Remez algorithm for Chebyshev approximation with interpolationComputing, Vol. 28, No. 1 | 1 Mar 1982 Cross Ref Discrete chebyshev approximation with interpolationInternational Journal of Computer Mathematics, Vol. 11, No. 3-4 | 19 March 2007 Cross Ref Approximation with interpolatory constraintsJournal of Mathematical Analysis and Applications, Vol. 64, No. 2 | 1 Jun 1978 Cross Ref Approximation with constraints in normed linear spacesJournal of Approximation Theory, Vol. 21, No. 3 | 1 Nov 1977 Cross Ref An alternation theory for copositive approximationJournal of Approximation Theory, Vol. 19, No. 2 | 1 Feb 1977 Cross Ref The Remez exchange algorithm for approximation with linear restrictionsTransactions of the American Mathematical Society, Vol. 223, No. 0 | 1 January 1976 Cross Ref Best uniform approximation with Hermite-Birkhoff interpolatory side conditionsJournal of Approximation Theory, Vol. 15, No. 2 | 1 Oct 1975 Cross Ref Optimal rational starting approximationsJournal of Approximation Theory, Vol. 12, No. 2 | 1 Oct 1974 Cross Ref Optimal starting approximations for iterative schemesJournal of Approximation Theory, Vol. 9, No. 1 | 1 Sep 1973 Cross Ref Approximation with Convex ConstraintsJames T. LewisSIAM Review, Vol. 15, No. 1 | 18 July 2006AbstractPDF (2399 KB)A generalization of the varisolvency and unisolvency propertiesJournal of Approximation Theory, Vol. 7, No. 1 | 1 Jan 1973 Cross Ref Nonlinear Tchebycheff approximation with constraintsJournal of Approximation Theory, Vol. 6, No. 3 | 1 Oct 1972 Cross Ref A unified approach to uniform real approximation by polynomials with linear restrictionsTransactions of the American Mathematical Society, Vol. 166, No. 0 | 1 January 1972 Cross Ref Kolmogoroff's criterion for constrained rational approximationJournal of Approximation Theory, Vol. 4, No. 2 | 1 Jun 1971 Cross Ref Uniform rational approximation with osculatory interpolationJournal of Computer and System Sciences, Vol. 4, No. 6 | 1 Dec 1970 Cross Ref Approximation by functions having restricted ranges: Equality caseNumerische Mathematik, Vol. 14, No. 1 | 1 Dec 1969 Cross Ref Volume 6, Issue 2| 1969SIAM Journal on Numerical Analysis161-315 History Submitted:30 September 1968Published online:14 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0706026Article page range:pp. 284-293ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics