Coercivity

It is known that diagram " Stress - Deformation " ( SD) is more vividly specifying the current metalwork condition. However, such diagram can be obtained only by destructive testing. The suggested non-destructive magnetic method in the report for the evaluation of SD condition and for the prediction of residual resource of metalwork, where the measurement of coercive force (CF) is assumed as a basis. 

For the practical implementation of the above mentioned facts, the portable electronic digital coercive force meter with self-contained power supply, attached converter and closed type magnetic core. Instrument error is 5 %. ... 

Energetic analysis shows the dependence of using magnetie materials from relation of coercive force on magnetization to remanent induction. The permanent magnets... 

Theorem 1.11. Let V be a reflexive Banach space, and K c V be a closed convex set. Assume that J V R is a coercive and weakly lower semicontinuous functional. Then the problem... 

Theorem 1.16. Let V be a reflexive separable Banach space, and K be a closed convex subset in V. Assume that an operator A V V is pseudomonotonous, and A is coercive or K is bounded. Then the inequality (1.86) has a solution. 

This property obviously implies coercivity and strict monotonicity of A. The right-hand side of (1.105) belongs to V since H c V. Then, by Theorem 1.14, there exists a unique solution V,n = 0,1,2,..., to... 

The angular brackets ( , ) denote the integration over flc- In virtue of the linearity, boundedness, and coercivity of the form a(-, ), there exists a unique solution to (2.165). 

Let us prove a complementary statement concerning the coercivity of the functional Hg (compare Vorovich, Lebedev, 1972). We should remark at this point that the coercivity of H, has been used to prove the solvability of the problem (2.223). 

We first note that the coercivity and weak lower semicontinuity of the functional n imply that the problem (2.248) has a (unique) solution The coercivity is provided by the following two inequalities,... 

In accordance with (3.53) the functional II/(x) + Ilg( ) is coercive and weakly lower semicontinuous on the space H, consequently, the problem (3.48) (or the problem (3.54)) has a solution. The solution is unique. Note that the equilibrium equations... 

The rationale of this definition of a solution will become clear in the sequel. Observe that the operator L is pseudomonotone (see a definition in Section 1.2) but is not coercive on U. Therefore, solvability of problem (3.98) does not follow from known results. 

Because g is nonnegative, one can see that ff is a coercive, strongly convex and lower semicontinuous functional. Therefore, there exists a unique solution w G H Qc) of the problem (3.204) or (3.205) (see Section 1.2). 

At the beginning we study the (5-dependence of the solution and next we consider the problem of finding extreme crack shapes. First, let us note that the problem (4.168) has a solution owing to the coercivity and the weak lower semicontinuity of II5 on the space The solution is unique for... 

Remark. The specific choice of bijki as the inverse of the Uijki for the elliptic regularization appears to be natural, since in the case of pure elastic (with K = [I/ (R)] , respectively p a) = 0), the boundary condition (5.16) reduces to (5.9). However, the proof of Theorem 5.1 works with any other choice of bijki as long as requirements of symmetry, boundedness and coercivity are met. 

More information on noncommercially available ferrites can be found in the Hterature (4,24). Extended reviews on soft (4,24—29) and hard (4,29—32) ferrites are also available. Explanations of magnetic concepts used in this article, such as permeabiHty and coercivity, may be found in magnetism textbooks. 

The maximum coercivity corresponds to but refers to the external field. It expHcidy takes into account the self-demagnetising field of the... 

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