Browsing by Subject "integral equation"

Now showing 1 - 6 of 6

Access status: Open Access ,
Convolutions, integral transforms and integral equations by means of the theory of reproducing kernels
(2012) Castro, Luís P.; Saitoh, Saburou; Nguyen, Minh Tuan
This paper introduces a general concept of convolutions by means of the theory of reproducing kernels which turns out to be useful for several concrete examples and applications. Consequent properties are exposed (including, in particular, associated norm inequalities).
Access status: Open Access ,
Developing a new approach in diagnostic methods of technical state of propeller of gas pumping unit
(2013) Zamìhovs'kij, Leonìd Mihajlovič; Ìvanûk, Natalìâ Ìvanìvna
To estimate the influence of changes in aerodynamic and shape characteristics of propellers of the gas pumping unit on process variables of gas pumping unit using the mathematical modeling methods. The method theoretically based Fredholm equation of the second kind for the tangential velocity component, its computational solution, and estimation of aerodynamical characteristics of airfoil of blades in special chosen frame of reference depending on the airfoil and attack angle. For the estimation of influence of shape configuration changes, which are determined by the configuration of blades of propeller on vibration characteristics of blades, cross-sectional area of blades and its second moment the numerical methods are used. Different methods of reproducing of shape configuration of airfoil of blades using experimental data of coordinates of relevant set points of airfoil are considered. Theoretical results could be used in the research and estimation of influences of configuration blade change and quantity of strained blades on the productivity of pumping units. The conducted research and its results can be the basis of creating of new non-destructive testing methods for gas pumping units and creating a new system of control. Shown results allow increasing operational reliability of facilities that were under research and systems, which can be helpful for Ukrainian gas and oil industry facilities.
Access status: Open Access ,
Fixed points and stability in neutral nonlinear differential equations with variable delays
(2012) Ardjouni, Abdelouaheb; Djoudi, Ahcene
By means of Krasnoselskii’s fixed point theorem we obtain boundedness and stability results of a neutral nonlinear differential equation with variable delays. A stability theorem with a necessary and sufficient condition is given. The results obtained here extend and improve the work of C.H. Jin and J.W. Luo [Nonlinear Anal. 68 (2008), 3307–3315], and also those of T.A. Burton [Fixed Point Theory 4 (2003), 15-32; Dynam. Systems Appl. 11 (2002), 499–519] and B. Zhang [Nonlinear Anal. 63 (2005), e233–e242]. In the end we provide an example to illustrate our claim.
Access status: Restricted ,
Metody rozwiązywania równania Fredholma drugiego rodzaju
(Data obrony: 2016-10-25) Widło, Katarzyna
Wydział Matematyki Stosowanej
Access status: Open Access ,
On some application of biorthogonal spline systems to integral equations
(2005) Wronicz, Zygmunt
We consider an operator $P_N: L_p(I) \to S_n(\Delta_N)$, such that $P_Nf=f$ for $f\in S_n(\Delta_N)$, where $S_n(\Delta_N)$ is the space of splines of degree $n$ with respect to a given partition $\Delta_N$ of the interval $I$. This operator is defined by means of a system of step functions biorthogonal to $B$-splines. Then we use this operator to approximation to the solution of the Fredholm integral equation of the second kind. Convergence rates for the approximation of the solution of this equation are given.
Access status: Open Access ,
On the summability of divergent power series solutions for certain first-order linear PDES
(2015) Hibino, Masaki
This article is concerned with the study of the Borel summability of divergent power series solutions for certain singular first-order linear partial differential equations of nilpotent type. Our main purpose is to obtain conditions which coefficients of equations should satisfy in order to ensure the Borel summability of divergent solutions. We will see that there is a close affinity between the Borel summability of divergent solutions and global analytic continuation properties for coefficients of equations.