Determination of diamine oxidase by a kinetic method with 2,2''-azino-di(3-ethylbenzthiazoline-6-sulfonate)

Hydrogen peroxide, the product of diamine oxidase-catalyzed putrescine or cadaverine oxidation, formed in proportion to the enzyme activity, is measured spectrophotometrically by using the above sulfonate (ABTS) and peroxidase. Only one reagent solution containing 3 mmol of putrescine or 10 mmol of cadaverine, 4 mmol of ABTS and 3000 U of peroxidase per litre of 0.2 mol l^-1 Tris—0.1 mol l^-1 HCl buffer pH 7.5 is needed. Absorbance changes are measured at 410 nm over the first 3 min of the reaction. This initial oxidation rate of the chromogen enables diamine oxidase activity up to 230 U l^-1 to be determined.     

-Weyl's theorem for operator matrices

If is a upper triangular matrix on the Hilbert space , then -Weyl's theorem for and need not imply -Weyl's theorem for , even when . In this note we explore how -Weyl's theorem and -Browder's theorem survive for operator matrices on the Hilbert space.

     

On the a-Browder and a-Weyl spectra of tensor products

Given Banach space operators A ∈ B( ) and B ∈ B( ), let A?B ∈ B( ? ) denote the tensor product of A and B. Let σ _a , σ _aw and σ _ab denote the approximate point spectrum, the Weyl approximate point spectrum and the Browder approximate point spectrum, respectively. Then σ _aw (A?B) ? σ _a (A)σ _aw (B) ? σ _aw (A)σ _a (B) ? σ _a (A)σ _ab (B) ? σ _ab (A)σ _a (B) = σ _ab (A?B), and a sufficient condition for the (a-Weyl spectrum) identity σ _aw (A?B) = σ _a (A)σ _aw (B) ? σ _aw (A)σ _a (B) to hold is that σ _aw (A?B) = σ _ab (A?B). Equivalent conditions are proved in Theorem 1, and the problem of the transference of a-Weyl’s theorem for a-isoloid operators A and B to their tensor product A?B is considered in Theorem 2. Necessary and sufficient conditions for the (plain) Weyl spectrum identity are revisited in Theorem 3.     

Operator Matrices: SVEP and Weyl’s Theorem

It is known that if and are Banach space operators with the single-valued extension property, SVEP, then the matrix operator has SVEP for every operator and hence obeys Browder’s theorem. This paper considers conditions on operators A, B, and M₀ ensuring Weyls theorem for operators M_C.     

Embedding optimization in computational science workflows

Workflows support the automation of scientific processes, providing mechanisms that underpin modern computational science. They facilitate access to remote instruments, databases and parallel and distributed computers. Importantly, they allow software pipelines that perform multiple complex simulations (leveraging distributed platforms), with one simulation driving another. Such an environment is ideal for computational science experiments that require the evaluation of a range of different scenarios “in silico” in an attempt to find ones that optimize a particular outcome. However, in general, existing workflow tools do not incorporate optimization algorithms, and thus whilst users can specify simulation pipelines, they need to invoke the workflow as a stand-alone computation within an external optimization tool. Moreover, many existing workflow engines do not leverage parallel and distributed computers, making them unsuitable for executing computational science simulations. To solve this problem, we have developed a methodology for integrating optimization algorithms directly into workflows. We implement a range of generic actors for an existing workflow system called Kepler, and discuss how they can be combined in flexible ways to support various different design strategies. We illustrate the system by applying it to an existing bio-engineering design problem running on a Grid of distributed clusters.     

A note on Weyl's theorem for operator matrices

When and are given we denote by an operator acting on the Banach space of the form

In this note we examine the relation of Weyl's theorem for and through local spectral theory.