Determination of the mean multiplicity of particles produced in a nuclear interaction using the method of the inverse problem

1968 ◽  
Vol 46 (10) ◽  
pp. S718-S721
Author(s):  
V. A. Astafiev
Keyword(s):  
Inverse Problem ◽  
Simple Model ◽  
Energy Range ◽  
Good Accuracy ◽  
Nuclear Interaction ◽  
Energy Spectra ◽  
Low Energies ◽  
The Mean ◽  
The Given

The possibility of the determination of the mean multiplicity of secondaries, n(E), with the aid of the cascade characteristics has been studied using the nuclear cascade with one-type particles as an example. For the simple model of interaction with the inelasticity coefficient k = 1 the energy spectra of particles in the showers produced by the particles of various energies have been calculated. The function n(E) has been restored in the higher-energy range on the assumption that the calculated spectra are known from the "experiment," and the function n(E) at low energies has been measured within good accuracy. Estimates of the accuracy of the cascade data necessary for determining n(E) within the given accuracy are presented.

scholarly journals Some Problems Connected with the Calculation of Stop Loss Premiums for Large Portfolios

1967 ◽  
Vol 4 (2) ◽  
pp. 170-174 ◽  
Author(s):  
Fredrik Esscher
Keyword(s):  
Distribution Function ◽  
Expected Number ◽  
Limit Values ◽  
Empirical Determination ◽  
The Mean ◽  
Premium Rates ◽  
Image Position ◽  
Stop Loss ◽  
The Given

When experience is insufficient to permit a direct empirical determination of the premium rates of a Stop Loss Cover, we have to fall back upon mathematical models from the theory of probability—especially the collective theory of risk—and upon such assumptions as may be considered reasonable.The paper deals with some problems connected with such calculations of Stop Loss premiums for a portfolio consisting of non-life insurances. The portfolio was so large that the values of the premium rates and other quantities required could be approximated by their limit values, obtained according to theory when the expected number of claims tends to infinity.The calculations were based on the following assumptions.Let F(x, t) denote the probability that the total amount of claims paid during a given period of time is ≤ x when the expected number of claims during the same period increases from o to t. The net premium II (x, t) for a Stop Loss reinsurance covering the amount by which the total amount of claims paid during this period may exceed x, is defined by the formula and the variance of the amount (z—x) to be paid on account of the Stop Loss Cover, by the formula As to the distribution function F(x, t) it is assumed that wherePn(t) is the probability that n claims have occurred during the given period, when the expected number of claims increases from o to t,V(x) is the distribution function of the claims, giving the conditioned probability that the amount of a claim is ≤ x when it is known that a claim has occurred, andVn*(x) is the nth convolution of the function V(x) with itself.V(x) is supposed to be normalized so that the mean = I.

scholarly journals On an Identification Problem on the Determination of the Parameters of the Dynamic System

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Dossan Baigereyev ◽  
Nevazi Ismailov ◽  
Yusif Gasimov ◽  
Atif Namazov
Keyword(s):  
Inverse Problem ◽  
Dynamic System ◽  
Calculation Method ◽  
Identification Problem ◽  
Quadratic Functional ◽  
Nonlinear Ordinary Differential Equations ◽  
Quasilinearization Method ◽  
The Right ◽  
The Given

An inverse problem is considered for the determination of the parameters, involved in the right-hand side of the system of nonlinear ordinary differential equations by given initial and final conditions. The solution of the problem is reduced to the minimization of the quadratic functional, which indeed is a deviation of the value of the solution from the given values at the end points. Using the quasilinearization method a calculation method is proposed to the solution of the considered problem. The application of this method is demonstrated on the example of the determination of the hydraulic resistance in the tubes.

Deconvolution of the Lorentzian Linewidth and Determination of Fraction Lorentzian Character from the Observed Profile of a Raman Line by a Comparison Technique

1982 ◽  
Vol 36 (3) ◽  
pp. 250-257 ◽  
Author(s):  
B. P. Asthana ◽  
W. Kiefer
Keyword(s):  
Experimental Determination ◽  
Raman Line ◽  
Good Accuracy ◽  
Half Maximum ◽  
Difference Spectroscopy ◽  
Simple Method ◽  
Spectrometer Slit ◽  
The Given ◽  
Comparison Technique

We report on a simple method to derive the Lorentzian linewidth of a Raman line as well as its fraction Lorentzian character. The method is based on the experimental determination of the bandwidths at half maximum obtained from recorded Raman and plasma lines with same spectrometer slit settings. From the ratio of the two half bandwidths, the Lorentzian Raman linewidth can be easily derived from the given table. This table was compiled by explicit calculations of Voigt profiles. The fraction Lorentzian character, needed for instance for Raman difference spectroscopy, can be obtained directly from this table to a good accuracy.

scholarly journals On determination of the permittivity through the module of the vector of the electric strength of the high-frequency electromagnetic field

2019 ◽  
Vol 484 (3) ◽  
pp. 269-272
Author(s):  
V. G. Romanov
Keyword(s):  
Inverse Problem ◽  
Electric Fields ◽  
High Frequency ◽  
Inverse Kinematic ◽  
Point Sources ◽  
Electric Strength ◽  
Inverse Kinematic Problem ◽  
High Frequency Electromagnetic Field ◽  
The Given

For nonmagnetic and nonconductive medium the system of electrodynamic equations that corresponds to periodic in time oscillations is considered. An inverse problem of determining permittivity in this system by the given module of the electric strength is studied. It is supposed that the electric fields is a result of the interference of two fields created by point sources. The permittivity e(x) is assumed to be differ from a given positive constant e0 inside of a compact domain W0 Ì R3 only. An information on module of the electric strength is given on the boundary of the domain W contained W0 inside itself and for all frequencies beginning with some fixed frequency w0. The asymptotic behavior of solution of a direct problem related to the electrodynamic equations is studied and the original inverse problem is reduced to the well known inverse kinematic problem. This reduction open a way for constructive solution of the inverse phaseless problem.

scholarly journals Experience Rating and Credibility

1967 ◽  
Vol 4 (3) ◽  
pp. 199-207 ◽  
Author(s):  
Hans Bühlmann
Keyword(s):  
Distribution Function ◽  
Random Variables ◽  
Experience Rating ◽  
Standard Problem ◽  
Identical Distribution ◽  
Classical Statistics ◽  
The Mean ◽  
The Given ◽  
Independent Identically Distributed

Classical statistics deals with the following standard problem of estimation:Given: random variables X1, X2 … Xn independent, identically distributed, andobservations x1, X2 … xn,Estimate: parameter (or function thereof) of the distribution function common to all Xi.It is not surprising that the “classical actuary” has mostly been involved in solving the actuarial equivalent of this problem in insurance, namelyGiven: risks R1R2 … Rn no contagion, homogeneous group,Find: the proper (common) rate for all risks in the given class.There have, of course, always been actuaries who have questioned the assumptions of independence (no contagion) and/or identical distribution (homogeneity). As long as ratemaking is considered equivalent to the determination of the mean, there seem to be no additional difficulties if the hypothesis of independence is dropped. But is there a way to drop the condition of homogeneity (identical distribution)?

Influence of Humidy on Radon Volume Activity on Lands

2020 ◽  
Vol 838 ◽  
pp. 111-117
Author(s):  
Jana Bouchalova ◽  
Helena Raclavská ◽  
Vendula Klimantová
Keyword(s):  
Middle Class ◽  
Soil Profile ◽  
Gas Permeability ◽  
Soil Samples ◽  
Soil Gas ◽  
Volume Activity ◽  
The Third ◽  
The Mean ◽  
The Given

The research is primarily focused on the determination of humidity on radon volume activity in different soil gas permeabilities in a given land. The research also included the detrermination of the radon index in the given land. The mean concentrations of radon in soil gas during the drought ranged from 15.9 - 24.1 kBq/m3 and in the precipitation period 16.3 - 26.7 kBq/m3. The first area was characterized by low gas permeability of soils, where a low radon index was determined during the dry season and a medium radon index was determined in the precipitation period. The second area, the medium gas permeability of the soils was determined from the analysis of the collected soil samples. The values of the third quartile in both cases measurements of radon volume activity in soil gas fall into the middle class of radon index. The third location would be determined by high gas permeability of soils. The radon index of the given land during the drought was determined as the medium, as in the case of measurement of radon volume activity in soil gas in the period with added moisture in the soil profile. The analysis confirmed the effect of moisture on the volume activity of radon.

scholarly journals Determination of zenith hydrostatic delay and its impact on GNSS-derived integrated water vapor

2017 ◽  
Vol 10 (8) ◽  
pp. 2807-2820 ◽  
Author(s):  
Xiaoming Wang ◽  
Kefei Zhang ◽  
Suqin Wu ◽  
Changyong He ◽  
Yingyan Cheng ◽  
...  
Keyword(s):  
Water Vapor ◽  
Relative Error ◽  
Surface Pressure ◽  
High Latitude ◽  
Good Accuracy ◽  
Mean Value ◽  
The Mean ◽  
Zenith Hydrostatic Delay ◽  
Mean Square Errors

Abstract. Surface pressure is a necessary meteorological variable for the accurate determination of integrated water vapor (IWV) using Global Navigation Satellite System (GNSS). The lack of pressure observations is a big issue for the conversion of historical GNSS observations, which is a relatively new area of GNSS applications in climatology. Hence the use of the surface pressure derived from either a blind model (e.g., Global Pressure and Temperature 2 wet, GPT2w) or a global atmospheric reanalysis (e.g., ERA-Interim) becomes an important alternative solution. In this study, pressure derived from these two methods is compared against the pressure observed at 108 global GNSS stations at four epochs (00:00, 06:00, 12:00 and 18:00 UTC) each day for the period 2000–2013. Results show that a good accuracy is achieved from the GPT2w-derived pressure in the latitude band between −30 and 30° and the average value of 6 h root-mean-square errors (RMSEs) across all the stations in this region is 2.5 hPa. Correspondingly, an error of 5.8 mm and 0.9 kg m−2 in its resultant zenith hydrostatic delay (ZHD) and IWV is expected. However, for the stations located in the mid-latitude bands between −30 and −60° and between 30 and 60°, the mean value of the RMSEs is 7.3 hPa, and for the stations located in the high-latitude bands from −60 to −90° and from 60 to 90°, the mean value of the RMSEs is 9.9 hPa. The mean of the RMSEs of the ERA-Interim-derived pressure across at the selected 100 stations is 0.9 hPa, which will lead to an equivalent error of 2.1 mm and 0.3 kg m−2 in the ZHD and IWV, respectively, determined from this ERA-Interim-derived pressure. Results also show that the monthly IWV determined using pressure from ERA-Interim has a good accuracy − with a relative error of better than 3 % on a global scale; thus, the monthly IWV resulting from ERA-Interim-derived pressure has the potential to be used for climate studies, whilst the monthly IWV resulting from GPT2w-derived pressure has a relative error of 6.7 % in the mid-latitude regions and even reaches 20.8 % in the high-latitude regions. The comparison between GPT2w and seasonal models of pressure–ZHD derived from ERA-Interim and pressure observations indicates that GPT2w captures the seasonal variations in pressure–ZHD very well.

scholarly journals Determination of source term for the fractional Rayleigh–Stokes equation with random data

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Tran Thanh Binh ◽  
Dumitru Baleanu ◽  
Nguyen Hoang Luc ◽  
Nguyen-H Can
Keyword(s):  
Stokes Equation ◽  
Source Term ◽  
Convergence Rates ◽  
Mean Square ◽  
New Techniques ◽  
The Mean ◽  
The Given ◽  
Well Posed ◽  
Regularized Solution

AbstractIn this article, we consider the problem of finding a source term of a Rayleigh–Stokes equation. Our problem is not well-posed in the sense of Hadamard. The sought solution does not depend continuously on the given data. Using the truncation method and some new techniques on trigonometric estimators, we give the regularized solution. Moreover, the mean square error and convergence rates are established.

scholarly journals Modeling the plane radiation structures consisting of discrete elements

2020 ◽  
Vol 1 (1) ◽  
pp. 1-10
Author(s):  
M. Andriychuk
Keyword(s):  
Iterative Procedure ◽  
Discrete Elements ◽  
System Of Integral Equations ◽  
Operator Form ◽  
Near Zone ◽  
Optimal Excitation ◽  
The Mean ◽  
The Given ◽  
Minimization Of Functional

Modeling the radiation pattern (RP) of plane arrays has been carried out using the strict electrodynamical solution of the respective direct problem that allows obtaining the representation of RP in the explicit operator form. The system of integral equations of the Hallen type is used for the determination of the current distribution in the apertures of radiators. The optimal excitation coefficients in apertures are determined while minimization of functional presenting the mean-square deviation of the given and synthesized amplitude RPs. The additional terms in the functions are applied for the minimization of radiation in a near zone of array and limitation on the values of excitation coefficients. The computational results demonstrate the quick convergence of the proposed iterative procedure and the ability to synthesize the prescribed amplitude RPs of the various types.

scholarly journals Nonpotentiality of a diffusion system and the construction of a semi-bounded functional

2021 ◽  
Vol 104 (4) ◽  
pp. 118-129
Author(s):  
V.M. Savchin ◽  
◽  
L.T. Huyen
Keyword(s):  
Inverse Problem ◽  
Boundary Value Problem ◽  
Variational Methods ◽  
Variational Principles ◽  
Boundary Value ◽  
Diffusion System ◽  
System Of Equations ◽  
The Given ◽  
Variational Formulations

The wide prevalence and the systematic variational principles are used in mathematics and applications due to a series of remarkable consequences among which the possibility to establish the existence of the solutions of the initial equations, and the determination of stable approximations of the solutions of the considered equations by the so-called variational methods. In this connection, it is natural for a given system of equations to investigate the problem of the existence of its variational formulations. It can be considered as the inverse problem of the calculus of variations. The main goal of this work is to study this problem for a diffusion system of partial differential equations. A key object is the criterion of potentiality. On its ground, the nonpotentiality of the operator of the given boundary value problem with respect to the classical bilinear form is proved. This system does not admit a matrix variational multiplier of the given form. Thus, the diffusion system cannot be deduced from the classical Hamilton’s principle. We posed the question that whether there exists a functional semi-bounded on solutions to the boundary value problem. We have done the algorithm of the constructive determination of such a functional. The main value of constructed functional action will be in applications of direct variational methods.

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