The family of general Jacobi polynomials P (α,β) n where α, β ∈ C can be characterised by complex (nonhermitian) orthogonality relations (cf. [15]). The special subclass of Jacobi polynomials P (α,β) n where α, β ∈ R are classical and the real orthogonality, quasi-orthogonality as well as related properties, such as the behaviour of the n real zeros, have been well studied. There is another spe...

In a semiorthogonal Lanczos algorithm, the orthogonality of the Lanczos vectors is allowed to deteriorate to roughly the square root of the rounding unit, after which the current vectors are reorthogonalized. A theorem of Simon 4] shows that the Rayleigh quotient | i.e., the tridiagonal matrix produced by the Lanczos recursion | contains fully accurate approximations to the Ritz values in spite...

In a semiorthogonal Lanczos algorithm, the orthogonality of the Lanczos vectors is allowed to deteriorate to roughly the square root of the rounding unit, after which the current vectors are reorthogonalized. A theorem of Simon 4] shows that the Rayleigh quotient | i.e., the tridiagonal matrix produced by the Lanczos recursion | contains fully accurate approximations to the Ritz values in spite...

Zernike polynomials are an orthogonal set over a unit circle and are often used to represent surface distortions from FEA analyses. There are several reasons why these coefficients may lose their orthogonality in an FEA analysis. The effects, their importance, and techniques for identifying and improving orthogonality are discussed. Alternative representations are presented.

A $\ast$-ring
 $R$ is called a $\pi$-Baer $\ast$-ring, if for any projection invariant left ideal $Y$ of $R$, the right annihilator $Y $
 generated, as ideal, by projection.
 In this note, we
 study some properties such $\ast$-rings.
 We indicate interrelationships between $\ast$-rings and related classes rings as
 rings, Baer $\ast$-rings, quasi-Baer $\ast$-rings....

Acute suppurative thyroiditis (AST) is a rare condition, as the thyroid gland is relatively resistant to infection. Thyroid function tests are usually normal in AST. A few cases of AST associated with thyrotoxicosis have been reported in adults. We report a case of AST that was associated with thyrotoxicosis in a 70-year-old woman. We diagnosed AST with thyroid ultrasonography and fine needle a...

BACKGROUND Acid suppression therapy (AST) is routinely used in critically ill patients to prevent stress-related mucosal bleeding (SRMB). OBJECTIVE Our objective was to determine the impact of a structured educational intervention on AST used for prevention of SRMB on appropriateness of AST. METHODS A single-center, retrospective, cohort study of appropriate use of AST in critically ill pat...

We generalize the array orthogonality property for perfect autocorrelation sequences to n-dimensional arrays. The generalized array orthogonality property is used to derive a number of ndimensional perfect array constructions.