scholarly journals Research of Asymptotic Properties related to Model of Hydrodynamic Stage of Classification Process Evolution in Cyclonic Type Devices

10.12737/719 ◽  
2013 ◽  
Vol 2 (4) ◽  
pp. 36-42 ◽  
Author(s):  
Крохина ◽  
A. Krokhina ◽  
Львов ◽  
V. Lvov ◽  
Павлихин ◽  
...  
Keyword(s):  
Distribution Function ◽  
Kinetic Equation ◽  
Statistical Model ◽  
Disperse Phase ◽  
Asymptotic Properties ◽  
Stationary Solutions ◽  
Centrifugal Forces ◽  
Practical Application ◽  
Cyclonic Type ◽  
Over Time

The practical application features of probabilistic and statistical model related to hydrodynamic stage of classification process evolution in the cylinder-conic hydroclones with additional injector are considered in this paper. Expression for the distribution function of firm disperse phase particles in the qualifier is given over time of their stay in the device, as well as depending on its constructive and technical characteristics. The stationary solutions of Fokker-Plank-Kolmogorov kinetic equation have been got for considered process of classification within reasonable assumptions. At the description related to the change of characteristics of division of suspensions in qualifiers the application of three-parametrical curves family which parameters depend not only on hydrodynamic features of streams in the device, but also are defined by relative values of classification influence intensity and centrifugal forces in comparison with intensity of casual influences is offered.

scholarly journals Sterile Neutrinos as Dark Matter: Alternative Production Mechanisms in the Early Universe

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 264
Author(s):  
Daniel Boyanovsky
Keyword(s):  
Dark Matter ◽  
Distribution Function ◽  
Kinetic Equation ◽  
Standard Model ◽  
Early Universe ◽  
Quantum Kinetic Equation ◽  
Sterile Neutrinos ◽  
The Standard Model ◽  
Production Mechanisms ◽  
Freeze Out

We study various production mechanisms of sterile neutrinos in the early universe beyond and within the standard model. We obtain the quantum kinetic equations for production and the distribution function of sterile-like neutrinos at freeze-out, from which we obtain free streaming lengths, equations of state and coarse grained phase space densities. In a simple extension beyond the standard model, in which neutrinos are Yukawa coupled to a Higgs-like scalar, we derive and solve the quantum kinetic equation for sterile production and analyze the freeze-out conditions and clustering properties of this dark matter constituent. We argue that in the mass basis, standard model processes that produce active neutrinos also yield sterile-like neutrinos, leading to various possible production channels. Hence, the final distribution function of sterile-like neutrinos is a result of the various kinematically allowed production processes in the early universe. As an explicit example, we consider production of light sterile neutrinos from pion decay after the QCD phase transition, obtaining the quantum kinetic equation and the distribution function at freeze-out. A sterile-like neutrino with a mass in the keV range produced by this process is a suitable warm dark matter candidate with a free-streaming length of the order of few kpc consistent with cores in dwarf galaxies.

scholarly journals A construction of the general relativistic Boltzmann equation

1984 ◽  
Vol 7 (3) ◽  
pp. 591-597 ◽  
Author(s):  
P. Dolan ◽  
A. C. Zenios
Keyword(s):  
Distribution Function ◽  
Boltzmann Equation ◽  
Kinetic Equation ◽  
Simple Model ◽  
State Space ◽  
Differential Forms ◽  
Relativistic Boltzmann Equation ◽  
Dimensional State Space ◽  
General Relativistic ◽  
Invariant Differential

Our work depends essentially on the notion of a one-particle seven-dimensional state-space. In constructing a general relativistic theory we assume that all measurable quantities arise from invariant differential forms. In this paper, we study only the case when instantaneous, binary, elastic collisions occur between the particles of the gas. With a simple model for colliding particles and their collisions, we derive the kinetic equation, which gives the change of the distribution function along flows in state-space.

scholarly journals Three Evidence Based Methods to Compensate for a Lack of Subject Background when Ordering Chemistry Monographs

2008 ◽  
Vol 3 (3) ◽  
pp. 3
Author(s):  
Robert A. Wright
Keyword(s):  
Statistical Analysis ◽  
Statistical Significance ◽  
Evidence Base ◽  
Circulation Rate ◽  
Evidence Based ◽  
Practical Application ◽  
Present Evidence ◽  
Library System ◽  
Over Time ◽  
Selection Of

Objective – The aim of this article is to present evidence based methods for the selection of chemistry monographs, particularly for librarians lacking a background in chemistry. These methods will be described in detail, their practical application illustrated, and their efficacy tested by analyzing circulation data. Methods – Two hundred and ninety-five chemistry monographs were selected between 2005 and 2007 using rigorously-applied evidence based methods involving the Library's integrated library system (ILS), Google, and SciFinder Scholar. The average circulation rate of this group of monographs was compared to the average circulation rate of 254 chemistry monographs selected between 2002 and 2004 when the methods were not used or were in an incomplete state of development. Results – Circulations/month were on average 9% greater in the cohort of monographs selected with the rigorously-applied evidence based methods. Further statistical analysis, however, finds that this result can not be attributed to the different application of these methods. Conclusion – The methods discussed in this article appear to provide an evidence base for the selection of chemistry monographs, but their application does not change circulation rates in a statistically significant way. Further research is needed to determine if this lack of statistical significance is real or a product of the organic development and application of these methods over time, making definitive comparisons difficult.

scholarly journals Estimating a Distribution Function at the Boundary

2020 ◽  
Vol 49 (1) ◽  
pp. 1-23
Author(s):  
Shunpu Zhang ◽  
Zhong Li ◽  
Zhiying Zhang
Keyword(s):  
Distribution Function ◽  
Kernel Estimation ◽  
Kernel Estimator ◽  
Distribution Functions ◽  
Practical Application ◽  
Real World Applications ◽  
Distribution Kernel ◽  
Estimation Of Distribution ◽  
Simulation Results ◽  
Boundary Correction

Estimation of distribution functions has many real-world applications. We study kernel estimation of a distribution function when the density function has compact support. We show that, for densities taking value zero at the endpoints of the support, the kernel distribution estimator does not need boundary correction. Otherwise, boundary correction is necessary. In this paper, we propose a boundary distribution kernel estimator which is free of boundary problem and provides non-negative and non-decreasing distribution estimates between zero and one. Extensive simulation results show that boundary distribution kernel estimator provides better distribution estimates than the existing boundary correction methods. For practical application of the proposed methods, a data-dependent method for choosing the bandwidth is also proposed.

scholarly journals On hydrodynamics in the presense of strong external potential field

2021 ◽  
Vol 29 (1) ◽  
pp. 21-28
Author(s):  
A. I. Sokolovsky ◽  
S. A. Sokolovsky
Keyword(s):  
Distribution Function ◽  
Kinetic Equation ◽  
Potential Field ◽  
Chemical Potential ◽  
Local Equilibrium ◽  
Practical Importance ◽  
External Potential ◽  
Equilibrium Distribution Function ◽  
Kinetic Coefficients ◽  
Functional Hypothesis

On the base of the Boltzmann kinetic equation, hydrodynamics of a dilute gas in the presence of the strong external potential field is investigated. First of all, a gravitational field is meant, because the consistent development of hydrodynamics in this environment is of great practical importance. In the present paper it is assumed that it is possible to neglect the influence of the field on the particle collisions. The study is based on the Chapman–Enskog method in a Bogolyubov’s formulation, which uses the idea of the functional hypothesis. Consideration is limited to steady gas states, which are subjected to a simpler experimental study. Chemical potential μ0 of the gas at the point where the external field has zero value and its temperature T are selected as the reduced description parameters of the system. In equilibrium, in the presence of the field, these values do not depend on the coordinates. It is assumed that in thehydrodynamic states T and μ0 are weakly dependent on the coordinates and therefore their gradients, considered on the scale of the free path length of the gas, are small. The kinetic equation, accounting for the functional hypothesis, gives an integro-differential equation for a gas distribution function at the hydrodynamic stage of evolution. This equation is solved in perturbation theory in gradients of T and μ0. The main approximation is analyzed for possibility of the system to be in a local equilibrium by means of comparing it with an equilibrium distribution function. Next, the distribution function is calculated in the first approximation in gradients and it is expressed in terms of solutions Ap , Bp of some first kind integral Fredholm equations. An approach to the approximate solution of these equations is discussed. The found distribution function is used to calculate the fluxes of the number of gas particles and their energy in the first order in gradients T and μ0 . Kinetic coefficients, which describe the structure of these fluxes, are introduced. Matrix elements of the operator of the linearized collision integral (integral brackets) are used for their research. It is a question of validity of the principle of symmetry of kinetic coefficients and definition of their signs.

A clustering law for some discrete order statistics

2003 ◽  
Vol 40 (01) ◽  
pp. 226-241 ◽  
Author(s):  
Sunder Sethuraman
Keyword(s):  
Distribution Function ◽  
Positive Integer ◽  
Order Statistics ◽  
Law Of Large Numbers ◽  
Asymptotic Properties ◽  
Random Variables ◽  
Large Numbers ◽  
The Law ◽  
Sample Maximum ◽  
Independent Identically Distributed

Let X 1, X 2, …, X n be a sequence of independent, identically distributed positive integer random variables with distribution function F. Anderson (1970) proved a variant of the law of large numbers by showing that the sample maximum moves asymptotically on two values if and only if F satisfies a ‘clustering’ condition, In this article, we generalize Anderson's result and show that it is robust by proving that, for any r ≥ 0, the sample maximum and other extremes asymptotically cluster on r + 2 values if and only if Together with previous work which considered other asymptotic properties of these sample extremes, a more detailed asymptotic clustering structure for discrete order statistics is presented.

Part II Vertical Agreements Under Regulation 330/2010, 5 Article 3: Market Share Threshold

2018 ◽  
Author(s):  
Wijckmans Frank ◽  
Tuytschaever Filip
Keyword(s):  
Market Share ◽  
Practical Application ◽  
Relevant Market ◽  
Market Shares ◽  
Definition Of ◽  
Over Time

This chapter discusses the market share limits that determine the applicability of Regulation 330/2010. Each of the supplier and the buyer must in principle remain below an individual limit of 30 per cent. In order to assess the market share limits, the chapter addresses the following steps of the analysis: (i) ninth step: definition of the relevant market; and (ii) tenth step: calculation of the market shares. It concludes by addressing the concrete and practical application of the market share limits in accordance with Regulation 330/2010 and offers easy-to-read overview tables illustrating the effect of changes in the market share levels over time.

scholarly journals Note Concerning the Distribution Function of the Total Loss Excluding the Largest Individual Claims

1964 ◽  
Vol 3 (2) ◽  
pp. 132-143 ◽  
Author(s):  
Hans Ammeter
Keyword(s):  
Distribution Function ◽  
Extreme Values ◽  
Excess Risk ◽  
Total Loss ◽  
Mathematical Statistics ◽  
Practical Application ◽  
Remarkable Result ◽  
Accounting Period ◽  
Insurance Business

The theory of extreme values is a special branch of mathematical statistics and was mainly treated by E. J. Gumbel [4]). This theory has only been applied in a few cases to problems in the insurance business. The first practical application to insurance known to the author of the present paper is due to A. Thépaut who has invented a new reinsurance system called ECOMOR [5]. According to this system the reinsurer covers the excess risk for the m largest claims and the ceding company retains an amount equal to the (m + I) largest claim. The credit for having pointed out the importance of the theory of extreme values belongs to R. E. Beard [1]. Recently E. Franckx [3] has found a most remarkable result by disclosing the general form of the distribution for the largest claim occurring in a certain accounting period.The present paper starts from the consideration that not only is the distribution of major claims, which might be eliminated by means of reinsurance, of interest to an insurer but also the distribution of the remaining total loss after excluding the largest claims. The nature of this distribution is important not only in connection with stability and security, but also for statistical investigations of the observed claim ratio. The credibility of such an investigation might be greatly improved if a suitable number of major claims were excluded. To simplify matters, the present paper considers the case where only the largest claim is excluded.

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