The field of a finite defect in a plate

AbstractIn this paper we first study the structure of the scalar and vector-valued nearly invariant subspaces with a finite defect. We then subsequently produce some fruitful applications of our new results. We produce a decomposition theorem for the vector-valued nearly invariant subspaces with a finite defect. More specifically, we show every vector-valued nearly invariant subspace with a finite defect can be written as the isometric image of a backwards shift invariant subspace. We also show that there is a link between the vector-valued nearly invariant subspaces and the scalar-valued nearly invariant subspaces with a finite defect. This is a powerful result which allows us to gain insight in to the structure of scalar subspaces of the Hardy space using vector-valued Hardy space techniques. These results have far reaching applications, in particular they allow us to develop an all encompassing approach to the study of the kernels of: the Toeplitz operator, the truncated Toeplitz operator, the truncated Toeplitz operator on the multiband space and the dual truncated Toeplitz operator.

Download Full-text

К расчету поля конечного магнитного цилиндра с внутренним соосным цилиндрическим дефектом

Дефектоскопия ◽

10.31857/s0130308221070022 ◽

2021 ◽

Vol 7 ◽

pp. 11-18

Author(s):

В.В. Дякин ◽

О.В. Кудряшова ◽

В.Я. Раевский

Keyword(s):

Magnetic Permeability ◽

Solution Method ◽

Grid Method ◽

Coaxial Cylinder ◽

Finite Cylinder ◽

Control Problems ◽

Magnetic Control ◽

Internal Defect ◽

Source Data ◽

Finite Defect

Using the grid method, a numerical solution of the direct problem of magnetostatics for calculating the field of a finite cylinder with a constant magnetic permeability containing an internal inclusion in the form of a coaxial cylinder with a different magnetic permeability is carried out. The algorithm is created for an arbitrary external field. In order to assess the reliability and accuracy of the solution method, the results were tested using precisely solved problems. A comparison is also made with the results of the previously solved problem of a finite defect-free cylinder. The coordinate dependences of the components of the resulting field are constructed for different source data. The program adds to the library of magnetic control problems and can be used for high-quality verification with the results of model experiments, as well as for evaluating the geometric characteristics of an internal defect.

Download Full-text