Normal and compact solvability of the exterior differentiation operator under homogeneous boundary conditions

V. M. Gol'dshtein; V. I. Kuz'minov; I. A. Shvedov

doi:10.1007/bf00973846

Normal and compact solvability of the exterior differentiation operator under homogeneous boundary conditions

Siberian Mathematical Journal ◽

10.1007/bf00973846 ◽

1988 ◽

Vol 28 (4) ◽

pp. 582-593

Author(s):

V. M. Gol'dshtein ◽

V. I. Kuz'minov ◽

I. A. Shvedov

Keyword(s):

Boundary Conditions ◽

Differentiation Operator ◽

Exterior Differentiation ◽

Compact Solvability

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On Stability of Basis Property of Root Vectors System of the Sturm-Liouville Operator with an Integral Perturbation of Conditions in Nonstrongly Regular Samarskii-Ionkin Type Problems

International Journal of Differential Equations ◽

10.1155/2015/641481 ◽

2015 ◽

Vol 2015 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

N. S. Imanbaev

Keyword(s):

Boundary Conditions ◽

Liouville Operator ◽

Basis Property ◽

Differentiation Operator ◽

Stability And Instability ◽

Associated Functions ◽

Sturm Liouville ◽

Type Boundary ◽

Eigenfunctions And Associated Functions ◽

Integral Perturbation

We study a question on stability and instability of basis property of system of eigenfunctions and associated functions of the double differentiation operator with an integral perturbation of Samarskii-Ionkin type boundary conditions.

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On compact solvability of the exterior derivative forG-invariant boundary conditions

Siberian Mathematical Journal ◽

10.1007/bf02679766 ◽

1999 ◽

Vol 40 (3) ◽

pp. 585-589

Author(s):

K. V. Storozhuk

Keyword(s):

Boundary Conditions ◽

Exterior Derivative ◽

Compact Solvability

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Tests for completeness of root subspaces of a differentiation operator with abstract boundary conditions

Mathematical Notes ◽

10.1007/bf01137805 ◽

1981 ◽

Vol 30 (4) ◽

pp. 765-770

Author(s):

G. M. Gubreev ◽

A. I. Kovalenko

Keyword(s):

Boundary Conditions ◽

Differentiation Operator ◽

Abstract Boundary

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Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100068795 ◽

1970 ◽

Vol 28 ◽

pp. 360-361

Author(s):

John W. Coleman

Keyword(s):

Boundary Conditions ◽

High Performance ◽

Force Fields ◽

Optical Design ◽

Direct Conversion ◽

Design Engineering ◽

Design Data ◽

Scalar Potentials ◽

Geometric Elements ◽

At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

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