Some arithmetic properties of a recurrent function with variable coefficients

1967 ◽  
Vol 1 (1) ◽  
pp. 29-33
Author(s):  
A. M. Polosuev
Keyword(s):  
Variable Coefficients ◽  
Arithmetic Properties ◽  
Recurrent Function

Convergence of Finite Fifference Method for Parabolic Problem

2003 ◽  
Vol 3 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Dejan Bojović
Keyword(s):  
Convergence Rate ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Parabolic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variable Coefficients ◽  
Rate Estimate ◽  
Convergence Rate Estimate ◽  
Initial Boundary Value

Abstract In this paper we consider the first initial boundary-value problem for the heat equation with variable coefficients in a domain (0; 1)x(0; 1)x(0; T]. We assume that the solution of the problem and the coefficients of the equation belong to the corresponding anisotropic Sobolev spaces. Convergence rate estimate which is consistent with the smoothness of the data is obtained.

MODELING OF NONLINEAR VIBRATION PROBLEMS WITH FLUID FLOWS THROUGH PIPELINES

2018 ◽  
pp. 44-47
Author(s):  
F.J. Тurayev
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Viscoelastic Properties ◽  
Construction Material ◽  
Fluid Flows ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Flowing Liquid ◽  
Vibration Problems

In this paper, mathematical model of nonlinear vibration problems with fluid flows through pipelines have been developed. Using the Bubnov–Galerkin method for the boundary conditions, the resulting nonlinear integro-differential equations with partial derivatives are reduced to solving systems of nonlinear ordinary integro-differential equations with both constant and variable coefficients as functions of time.A system of algebraic equations is obtained according to numerical method for the unknowns. The influence of the singularity of heredity kernels on the vibrations of structures possessing viscoelastic properties is numerically investigated.It was found that the determination of the effect of viscoelastic properties of the construction material on vibrations of the pipeline with a flowing liquid requires applying weakly singular hereditary kernels with an Abel type singularity.

Designing Experiments for Model Identification of the Nitrification Process

1991 ◽  
Vol 24 (6) ◽  
pp. 9-16 ◽  
Author(s):  
P. J. Ossenbruggen ◽  
H. Spanjers ◽  
H. Aspegren ◽  
A. Klapwijk
Keyword(s):  
Mechanistic Model ◽  
Nonlinear Differential Equations ◽  
Model Identification ◽  
Reaction Rates ◽  
Variable Coefficients ◽  
Model Specification ◽  
First Order ◽  
Interactive Behavior ◽  
Batch Tests ◽  
Nitrification Process

A series of batch tests were performed to study the competition for oxygen by Nitrosomonas and Nitrobacter in the nitrification of ammonia in activated sludge. Oxygen uptake rate (OUR) and dynamic (compartment) models describing the process are proposed and tested. The OUR model is described by a Monod relationship and the biogradation process by a set of first order nonlinear differential equations with variable coefficients. The results show a mechanistic model and ten reaction rates are sufficient to capture the interactive behavior of the nitrification process. Methods for model specification, calibrating, and testing the model and the design of additional experiments are described.

The (α, β)-ramification invariants of a number field

2021 ◽  
Vol 71 (1) ◽  
pp. 251-263
Author(s):  
Guillermo Mantilla-Soler
Keyword(s):  
Zeta Function ◽  
Number Field ◽  
Residue Class ◽  
Interesting Application ◽  
Dedekind Zeta Function ◽  
Arithmetic Properties

Abstract Let L be a number field. For a given prime p, we define integers α p L $ \alpha_{p}^{L} $ and β p L $ \beta_{p}^{L} $ with some interesting arithmetic properties. For instance, β p L $ \beta_{p}^{L} $ is equal to 1 whenever p does not ramify in L and α p L $ \alpha_{p}^{L} $ is divisible by p whenever p is wildly ramified in L. The aforementioned properties, although interesting, follow easily from definitions; however a more interesting application of these invariants is the fact that they completely characterize the Dedekind zeta function of L. Moreover, if the residue class mod p of α p L $ \alpha_{p}^{L} $ is not zero for all p then such residues determine the genus of the integral trace.

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