Limit distribution of the sum of dependent random functions in the series scheme

1989 ◽  
Vol 41 (2) ◽  
pp. 143-147
Author(s):  
O. M. Dzhneid
Keyword(s):  
Limit Distribution ◽  
Random Functions ◽  
Series Scheme

PHYTOMONITORING AS A METOD OF THE ASSESSMENT OF ATMOSPHERIC AIR POLLUTION BY URBAN ENVIRONMENT BY FINE DUST

2019 ◽  
pp. 42-53
Author(s):  
Irina Glinyanova ◽  
Valery Azarov ◽  
Valery Fomichev
Keyword(s):  
Urban Environment ◽  
Urban Areas ◽  
Fine Particles ◽  
Prunus Armeniaca ◽  
Dust Particles ◽  
Fine Dust ◽  
Control Zone ◽  
Atmospheric Air ◽  
Random Functions ◽  
The City

Fine dust: (PM2.5, PM10) is a priority pollutant that contributes to the development of numerous dis-eases in urban areas. The purpose of this scientific work is to study the dispersed composition of dust parti-cles on the leaves of apricot trees (Prúnus armeníaca) in the residential zone of Volgograd. The novelty of the work lies in the study of the dispersed composition of dust particles on the leaves of apricot trees (Prúnus armeníaca) in the residential zone in the city of Volgograd near the construction industry enterprise, me-chanical engineering, leather production and railway transport line in comparison with the conditionally clean (control) zone of the SNT “Orocenets” ”(Sovetsky District, Volgograd) from the standpoint of random functions expressed by integral distribution curves of the mass of particles over their equivalent diameters. As a result of the research, the dispersed composition of dust on the leaves of apricot trees (Prúnus ar-meníaca) in the residential area of Volgograd was revealed. Fine particles were found: PM2.5, PM10 in each of the studied points, which by their values, both in their number and mass fraction, significantly exceed the data on fine dust in a conditionally clean area (control) in the SNT “Oroshanets” (Sovetsky district Volgo-grad), which creates certain environmental risks for local residents. The dispersed analysis of particles from the standpoint of random functions in the future will allow with a sufficiently high degree of accuracy to pre-dict the dust content of urban atmospheric air in the range of monthly and / or seasonal average values compared to the traditional measurement of fine dust concentration in atmospheric air of the urban environ-ment as the maximum single or daily average. At the same time, further studies of dust on the leaves of plants in an urban environment, namely, the study of the density of its sedimentation, will also reveal a group of ur-ban plants that are best suited to retain PM2.5 and PM10 on leaf plates in this region, which can significantly increase the quality of the atmospheric air of the urban environment and be of a recommendatory nature for the state-owned landscaping services of the city of Volgograd when improving the green areas of a megacity.

scholarly journals Local strength properties of steel bars as random functions

2021 ◽  
Vol 300 ◽  
pp. 124021
Author(s):  
Andrzej Machowski ◽  
Mariusz Maslak ◽  
Michal Pazdanowski
Keyword(s):  
Strength Properties ◽  
Random Functions ◽  
Local Strength ◽  
Steel Bars

On the first zero of an empirical characteristic function

1991 ◽  
Vol 28 (3) ◽  
pp. 593-601 ◽  
Author(s):  
H. U. Bräker ◽  
J. Hüsler
Keyword(s):  
Characteristic Function ◽  
Limit Distribution ◽  
Random Variable ◽  
Empirical Characteristic Function ◽  
The Real ◽  
Exponential Decrease ◽  
Characteristic Process

We deal with the distribution of the first zero Rn of the real part of the empirical characteristic process related to a random variable X. Depending on the behaviour of the theoretical real part of the underlying characteristic function, cases with a slow exponential decrease to zero are considered. We derive the limit distribution of Rn in this case, which clarifies some recent results on Rn in relation to the behaviour of the characteristic function.

scholarly journals Non-local Solvable Birth–Death Processes

2021 ◽  
Author(s):  
Giacomo Ascione ◽  
Nikolai Leonenko ◽  
Enrica Pirozzi
Keyword(s):  
Differential Equations ◽  
Orthogonal Polynomials ◽  
Limit Distribution ◽  
Spectral Decomposition ◽  
Strong Solutions ◽  
Stochastic Representation ◽  
Discrete Approximations ◽  
Local Difference ◽  
Non Local ◽  
Birth Death

AbstractIn this paper, we study strong solutions of some non-local difference–differential equations linked to a class of birth–death processes arising as discrete approximations of Pearson diffusions by means of a spectral decomposition in terms of orthogonal polynomials and eigenfunctions of some non-local derivatives. Moreover, we give a stochastic representation of such solutions in terms of time-changed birth–death processes and study their invariant and their limit distribution. Finally, we describe the correlation structure of the aforementioned time-changed birth–death processes.

scholarly journals A Novel Construction of Constrained Verifiable Random Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Muhua Liu ◽  
Ping Zhang ◽  
Qingtao Wu
Keyword(s):  
Random Function ◽  
Secret Key ◽  
Bilinear Maps ◽  
Random Functions ◽  
Compute Function ◽  
Multilinear Maps ◽  
Verifiable Random Functions ◽  
Selective Security

Constrained verifiable random functions (VRFs) were introduced by Fuchsbauer. In a constrained VRF, one can drive a constrained key skS from the master secret key sk, where S is a subset of the domain. Using the constrained key skS, one can compute function values at points which are not in the set S. The security of constrained VRFs requires that the VRFs’ output should be indistinguishable from a random value in the range. They showed how to construct constrained VRFs for the bit-fixing class and the circuit constrained class based on multilinear maps. Their construction can only achieve selective security where an attacker must declare which point he will attack at the beginning of experiment. In this work, we propose a novel construction for constrained verifiable random function from bilinear maps and prove that it satisfies a new security definition which is stronger than the selective security. We call it semiadaptive security where the attacker is allowed to make the evaluation queries before it outputs the challenge point. It can immediately get that if a scheme satisfied semiadaptive security, and it must satisfy selective security.

Queues in transportation systems, II: An independently-dispatched system

1974 ◽  
Vol 11 (01) ◽  
pp. 145-158 ◽  
Author(s):  
Michael A. Crane
Keyword(s):  
Limit Theorems ◽  
Transportation Systems ◽  
Linear Network ◽  
Random Functions ◽  
Arrival Processes ◽  
Vehicle Fleet ◽  
Vehicle Capacity ◽  
Service Groups ◽  
Functional Central Limit Theorems ◽  
Functional Central Limit

We consider a transportation system consisting of a linear network of N + 1 terminals served by S vehicles of fixed capacity. Customers arrive stochastically at terminal i, 1 ≦ i ≦ N, seeking transportation to some terminal j, 0 ≦ j ≦ i − 1, and are served as empty units of vehicle capacity become available at i. The vehicle fleet is partitioned into N service groups, with vehicles in the ith group stopping at terminals i, i − 1,···,0. Travel times between terminals and idle times at terminals are stochastic and are independent of the customer arrival processes. Functional central limit theorems are proved for random functions induced by processes of interest, including customer queue size processes. The results are of most interest in cases where the system is unstable. This occurs whenever, at some terminal, the rate of customer arrivals is at least as great as the rate at which vehicle capacity is made available.

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