A pair correlation hypothesis and the exceptional set in Goldbach's problem

Mathematika ◽  
1996 ◽  
Vol 43 (2) ◽  
pp. 349-361 ◽  
Author(s):  
A. Languasco ◽  
A. Perelli
Keyword(s):  
Pair Correlation ◽  
Exceptional Set

THE MODEL FOR MANAGING INVESTMENTS IN THE MOSCOW ENVIRONMENT BASED ON A POWER REGRESSION EQUATION

2020 ◽  
Vol 2 (7) ◽  
pp. 91-99
Author(s):  
E. V. KOSTYRIN ◽  
◽  
M. S. SINODSKAYA ◽  
Keyword(s):  
Solid Waste ◽  
Influencing Factors ◽  
Pair Correlation ◽  
Approximation Error ◽  
Regression Equation ◽  
Regression Equations ◽  
The Impact ◽  
The Relationship ◽  
Average Approximation ◽  
Average Approximation Error

The article analyzes the impact of certain factors on the volume of investments in the environment. Regression equations describing the relationship between the volume of investment in the environment and each of the influencing factors are constructed, the coefficients of the Pearson pair correlation between the dependent variable and the influencing factors, as well as pairwise between the influencing factors, are calculated. The average approximation error for each regression equation is determined. A correlation matrix is constructed and a conclusion is made. The developed econometric model is implemented in the program of separate collection of municipal solid waste (MSW) in Moscow. The efficiency of the model of investment management in the environment is evaluated on the example of the growth of planned investments in the activities of companies specializing in the export and processing of solid waste.

PROGRAM OF PREDICTION AND MANAGEMENT OF COINTEGED DYNAMIC ECONOMIC PROCESSES BASED ON THE CYBERNETIC APPROACH

2019 ◽  
Author(s):  
Olena Bundak ◽  
Nataliia Zubovetska
Keyword(s):  
Computer Program ◽  
Pair Correlation ◽  
Time History ◽  
Critical Area ◽  
Concrete Object ◽  
Graphic Arts ◽  
Ex Post ◽  
History Of ◽  
Successive Change ◽  
Rms Errors

A method and computer program ConRow, which prognostication of development of the dynamically CPLD economic transients is executed by, is described in the article. Such prognostication of economic processes is very important in the cases when their development can result in undesirable consequences, that to go out in the so-called critical area. Extrapolation in a critical area with the use of information about the conduct of the system at an area, near to it, allows to estimate to the lead through of experiment in the critical area of his consequence. For the imitation of conduct of object the function of review is set on entrance influence. For a concrete object this function can express, for example, dependence of change of level sale from time-history of charges on advertising and set as a numeral row. Statistics as a result of analysis of row are represented in a table, where the level of meaningfulness is set statistician, and also parameters of the handed over criteria. The graphic reflection of information is intended for visualization of analysis. Here represented on the points of graphic arts, the crooked smoothing which are calculated as полиномиальные regressions is added. The best approaching is controlled by sight on the proper graph, and also by minimization of their rms errors. Models of prognostication by sight and as formulas represented on graphic arts, the middle is here determined tailings and their chance is checked up on statistics of signs. After the got models determined also and prognosis values of influences and reviews. Establishing an order models of Сr(p) of co integrate regression is carried out separate custom controls. The coefficient of clay correlation of ruФ shows by itself pair correlation between lines with a successive change in relation to each other on a size to лагу of l = 1, 2, 3 . The program was tested on the example of ex-post prognosis at establishing an integration connection and possibility of prognostication of growth of nominal average monthly settlings on the basis of these statistical indexes of consumer inflation in Ukraine.

scholarly journals Dimension of the Exceptional Set in the Aronszajn–Donoghue Theorem for Finite Rank Perturbations

2020 ◽  
Author(s):  
Constanze Liaw ◽  
Sergei Treil ◽  
Alexander Volberg
Keyword(s):  
Finite Rank ◽  
Measure Zero ◽  
Adjoint Operator ◽  
Cyclic Vector ◽  
Spectral Measures ◽  
Hermitian Matrices ◽  
Exceptional Set ◽  
Direct Sum ◽  
Rank One Perturbation ◽  
Rank One

Abstract The classical Aronszajn–Donoghue theorem states that for a rank-one perturbation of a self-adjoint operator (by a cyclic vector) the singular parts of the spectral measures of the original and perturbed operators are mutually singular. As simple direct sum type examples show, this result does not hold for finite rank perturbations. However, the set of exceptional perturbations is pretty small. Namely, for a family of rank $d$ perturbations $A_{\boldsymbol{\alpha }}:= A + {\textbf{B}} {\boldsymbol{\alpha }} {\textbf{B}}^*$, ${\textbf{B}}:{\mathbb C}^d\to{{\mathcal{H}}}$, with ${\operatorname{Ran}}{\textbf{B}}$ being cyclic for $A$, parametrized by $d\times d$ Hermitian matrices ${\boldsymbol{\alpha }}$, the singular parts of the spectral measures of $A$ and $A_{\boldsymbol{\alpha }}$ are mutually singular for all ${\boldsymbol{\alpha }}$ except for a small exceptional set $E$. It was shown earlier by the 1st two authors, see [4], that $E$ is a subset of measure zero of the space $\textbf{H}(d)$ of $d\times d$ Hermitian matrices. In this paper, we show that the set $E$ has small Hausdorff dimension, $\dim E \le \dim \textbf{H}(d)-1 = d^2-1$.

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