scholarly journals METRICAL ESTIMATIONS OF DETERMINANT OF THE INTEGRAL PROBLEM FOR EQUATION OF VIBRATING OF STRING

2018 ◽  
pp. 38-46
Author(s):  
О. M. Medvid ◽  
M. M. Symotyuk ◽  
I. R. Tymkiv
Keyword(s):  
Spatial Variable ◽  
Integral Conditions ◽  
Small Denominators ◽  
Fractal Measure ◽  
Integral Problem

Metrical theorems are inprocess set about estimations from below small denominators that arose up at investigational existence of periodic at times decision of task with integral conditions as moments after a spatial variable for equalization of small vibrating of string. For leading to of metrical estimations the concept of fractal measure and dimension of Hausdorff is from below applied.

scholarly journals Problem for hyperbolic system of equations having constant coefficients with integral conditions with respect to the time variable

2014 ◽  
Vol 6 (2) ◽  
pp. 282-299 ◽  
Author(s):  
A.M. Kuz ◽  
B.Yo. Ptashnyk
Keyword(s):  
Hyperbolic System ◽  
Cartesian Product ◽  
Sufficient Conditions ◽  
Time Variable ◽  
System Of Equations ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Integral Conditions ◽  
Small Denominators ◽  
Constant Coefficients

In a domain specified in the form of a Cartesian product of a segment $\left[0,T\right]$ and the space ${\mathbb R}^{p}$, we study a problem with integral conditions with respect to the time variable for  hyperbolic system with constant coefficients in a class of almost periodic functions in the space variables. A criterion for the unique solvability of this problem and sufficient conditions for the existence of its solution are established. To solve the problem of small denominators arising in the construction of solutions of the posed problem, we use the metric approach.

Appllication Analysis of the Improved HASM-AD in the Spatial Variable Simulation

2013 ◽  
Vol 15 (5) ◽  
pp. 655
Author(s):  
Mingwei ZHAO ◽  
Tianxiang YUE ◽  
Na ZHAO
Keyword(s):  
Spatial Variable
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