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We show that for any simple piecewise Ljapunov contour there exists a power weight such that the essential norm |S
| in the spaceL
2(, ) does not depend on the angles of the contour and it is given by formula (2). All such weights are described. For the union =12 of two simple piecewise Lyapunov curves we prove that the essential norm |S
| inL
2() is minimal if both 1 and 2 are smooth in some neighborhoods of the common points. It is the case when the norm |S
| in the spaceL
2() as well as inL
2(, ) does not depend on the values of the angles and it can be calculated by formula (5). 相似文献
2.
The Iosipescu shear test, utilizing a notched specimen in bending and a modification—the asymmetrical four-point bend (AFPB)
test—were evaluated as shear tests for composites. This paper summarizes the results of an extensive numerical and experimental
investigation of the Iosipescu and AFPB test methods. Finite-element analyses were conducted to assess the influence of notch
parameters and load locations on the stress state in the specimen. The shear moduli and the shear strengths were experimentally
measured for a quasiisotropic graphite/epoxy laminate using both the Iosipescu and the AFPB test methods. The tests were conducted
for various combinations of notch parameters and load locations. The test results indicate that changes in the notch geometry
and load locations aimed at improving the stress distribution in the test section resulted in unexpected changes in the failure
mode.
Paper was presented at the 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 9–14. 相似文献
3.
A Banach algebra generated by two idempotentsp, r, identitye and a shiftv which satisfy the conditionspv=vp andrv=v(e–r) is investigated. It is proved that all irreducible representations of algebraA are two- and four-dimensional. The explicit form of these representations is obtained. An Invertibility Symbol is constructed. Some examples are considered. 相似文献
4.
5.
Two classes of Banach algebras which admit a matrix symbol of order 2 are described, and an explicit form of the symbol is obtained. Also we describe all polynomialsF(X, Y) andF(X, Y, Z) such that the norms of polynomialsF(B, B
*) (whenB
2=0) andF(S, W, W
*
) (whenS
2
=I, W
2
=0, S
*=S) depend only on the polynomialF and on the norms B, W. Applications to Banach algebras generated by singular integral operators and some their perturbations are considered. 相似文献
6.
7.
Y. Spigel 《Integral Equations and Operator Theory》1997,27(1):103-110
The problem of factorization of the matrices of form (5) is investigated. The problem is solved by method from [GGK]. A new criterion for canonical factorization is represented. The explicit form for factors and two examples are given. 相似文献
8.
Consider a functionL() defined on an interval of the real axis whose values are linear bounded selfadjoint operators in a Hilbert spaceH. A point 0 and a vector
0 H(
0 0) are called eigenvalue and eigenvector ofL() ifL() ifL(0)
0 = 0. Supposing that the functionL() can be represented as an absolutely convergent Fourier integral, the interval is sufficiently small and the derivative will be positive at some point, it has been proved that all the eigenvectors of the operator-functionL() corresponding to the eigenvalues from the interval form an unconditional basis in the subspace spanned by them. 相似文献
9.
LetP be a projection (non-selfadjoint in general), andV a selfadjoint involution acting in a Hilbert spaceH. In this paper the polynomialsF(X, Y, Z) of three non-commuting variables are described such that the norms F(P, P
*,V) depend only on P. A method of calculation of the norms F(P, P
*,V) for such polynomials is given. For polynomialsF(P, P
*) this problem was investigated in [KMF], [FKM]. 相似文献
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