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EN
The paper is devoted to building a probabilistic method of analyzing the operation of a certain production supply system. The analysis is carried out for non-extreme states of the level in store, into which two separate streams of production (the product) are directed. A system of partial differential equations describing this case was derived which is satisfied by the joint density function defining the probabilities of states of the three-dimensional process characterizing the system’s functioning.
EN
The paper is devoted to building a probabilistic method of analyzing the operation of a certain production supply system. The analysis is carried out for non-extreme states of the level in store, into which two separate streams of production (the product) are directed. A system of partial differential equations describing this case was derived which is satisfied by the joint density function defining the probabilities of states of the three-dimensional process characterizing the system’s functioning.
EN
The paper is dedicated to constructing a method for the probabilistic analysis of the functioning a certain production-supply system. Previously a set of partial differential equations has been derived satisfied by the joint density function of the state of a three-dimensional process characterizing the functioning of the system. The operation of the system at the boundaries of the stock levels is analyzed. Two sets of differential equations have been derived, one describing the operation of the system when the stock level is zero and one describing the operation of the system when the stocks are full.
EN
The paper is dedicated to constructing a method for the probabilistic analysis of the functioning a certain production-supply system. Previously a set of partial differential equations has been derived satisfied by the joint density function of the state of a three-dimensional process characterizing the functioning of the system. The operation of the system at the boundaries of the stock levels is analyzed. Two sets of differential equations have been derived, one describing the operation of the system when the stock level is zero and one describing the operation of the system when the stocks are full.
Open Physics
|
2014
|
tom 12
|
nr 9
637-653
EN
In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach
EN
The paper investigates a barrier in the functioning of certain inventory system. Assuming that the storage input is a non-aggregated dynamic-parameter process, the paper derives a system of differential equations satisfied by the probabilities of a lower-limit barrier in subsysyem L. The system of equations expresses relations between the distributions of the probability of the lower-limit barrier on the one hand and the parameters of the product supply process and the parameters of the functioning of the transport subsystem on the other hand.
PL
Obiektem badania jest bariera działania pewnego systemu gospodarki zapasami. Przyjmując, że wejście magazynu–zbiornika jest procesem niezagregowanym o dynamicznych parametrach, wyprowadzono układ równań różniczkowych, który spełniają prawdopodobieństwa bariery dolnej podsystemu L. Układ ten wyraża powiązania między rozkładami prawdopodobieństwa bariery dolnej a parametrami procesu podaży produktu oraz parametrami funkcjonowania podsystemu transportowego.
EN
The subject matter of the investigation of a certain inventory system in the case where the storage input is a non-aggregated dynamic-parameter process. The authors derive a system of differential equations satisfied by probability distribution density functions for the intermediate states of subsystem L. The system of equations expresses relations between the densities and the parameters of the functioning of the transport subsystem and the parameters of the products supply process.
PL
Przedmiotem badania jest bariera działania pewnego systemu gospodarki zapasami w przypadku, gdy wejście magazynu-zbiornika jest procesem niezagregowanym o dynamicznych parametrach. Wprowadzono układ równań różniczkowych, który spełniają funkcje gęstości rozkładów prawdopodobieństwa stanów pośrednich podsystemu L. Układ ten wyraża związki między gęstościami i parametrami funkcjonowania podsystemu transportowego i parametrami procesu podaży produktu.
EN
This paper presents the homotopy perturbation method for solving linear and non–linear two–point boundary value problems in the form of a fourth–order differential equation and five boundary conditions. Three initial and two final conditions were taken into account. The solution of this problem is possible only when the considered equation includes an unknown parameter. The presented method has been illustrated with a numerical example.
PL
W artykule przedstawiono homotopijną metodę perturbacyjną zastosowaną do rozwiązywania zarówno liniowego, jak i nieliniowego dwupunktowego zagadnienia brzegowego składającego się z równania różniczkowego czwartego rzędu oraz pięciu warunków brzegowych. Pod uwagę wzięto trzy początkowe i dwa końcowe warunki brzegowe. Rozwiązanie tak postawionego problemu jest możliwe tylko wtedy, gdy rozpatrywane równanie zawiera nieznany parametr. Prezentowaną metodę zilustrowano przykładem obliczeniowym.
10
63%
EN
The paper presents the theoretical basis and results of numerical modeling of corona discharge phenomenon carried out to determine the value of body force that induces the flow of surrounding fluid. The system of two partial differential equations is solved with the values of electric potential ϕ and space charge density ρq as unknowns. The first equation is of Poisson-type with Laplacian acting on the value of potential and source term dependent on space charge density as well as electric permittivity of the medium. The second equation is current continuity equation, where the current density is composed of charge carrier diffusion term and the term describing their drift in electric field. Particular attention was given to the boundary condition of space charge density due to its indirect nature. Geometry of the problem assumes that positive corona discharge takes place on the sharp edge of the blade-shaped anode while flat grounded plate acts as a cathode. Such configuration enables simplified analysis in 2D Cartesian coordinates assuming that the section plane is sufficiently far from the lateral edges of the blade. The system of equations is solved with MOOSE (Multiphysics Object-Oriented Simulation Environment) Framework released in public domain on GNU LGPL license by Idaho National Laboratory. Presented results include 2D distributions of electric potential, electric field strength, space charge density and body force in air surrounding electrodes.
PL