Stable isotope ratios are biogeochemical tracers that can be used to determine the source of nutrients and contaminants in avian eggs. However, the interpretation of stable carbon ratios in lipid-rich eggs is complicated because (13)C is depleted in lipids. Variation in (13)C abundance can therefore be obscured by variation in percent lipids. Past attempts to establish an algebraic equation to ...

the extracts of piper sarmentosum, a medicinal plant, are being used to prepare phytopharmaceuticals while the information about chemical kinetics of constituents of the extract is unavailable to assign precise shelf life (t90) and find optimum storage conditions of the product for patient safety, and to avoid economic repercussions of launching an unstable product. the extract was exposed to t...

The Hurwitz stable polynomials are important in the study of differential equations systems and control theory (see [7] and [19]). A property of these polynomials is related to Hadamard product. Consider two polynomials p, q ∈ R[x]: p(x) = anx n + an−1x n−1 + · · ·+ a1x + a0 q(x) = bmx m + bm−1x m−1 + · · ·+ b1x + b0 the Hadamard product (p ∗ q) is defined as (p ∗ q)(x) = akbkx + ak−1bk−1x + · ...

We prove, using the subspace embedding guarantee in a black box way, that one can achieve the spectral norm guarantee for approximate matrix multiplication with a dimensionality-reducing map having m = O(r̃/ 2) rows. Here r̃ is the maximum stable rank, i.e., the squared ratio of Frobenius and operator norms, of the two matrices being multiplied. This is a quantitative improvement over previous wo...

We consider a variational problem for three-dimensional (3D) classical lattice models. We construct the trial state as a two-dimensional product of local variational weights that contain auxiliary variables. We propose a stable numerical algorithm for the maximization of the variational partition function per layer. The numerical stability and efficiency of the new method are examined through i...

We describe how to prepare, store, and use a hemolyzed blood product for simultaneous pH, pCO2, and pO2 quality control. Tonometry of the blood product with two oxygen and two carbon dioxide concentrations resulted in consistent and reproducible values during 38 weeks. The resulting pH values were consistent and reproducible, demonstrating the metabolic acid-base stability of the blood product....

The method of product integration is used to obtain solutions to the time dependent Banach space differential equation u'(t) = A(t)(u(t)), iäO, where A is a function from [0, oo) to the set of nonlinear operators from the Banach space X to itself and « is a function from [0, oo) to X. The main requirements placed on A are that A is m-dissipative and product stable on its domain. Applications ar...

It is proved that the reduced group C∗-algebra C∗ red(G) has stable rank one (i.e. its group of invertible elements is a dense subset) if G is a discrete group arising as a free product G1 ∗G2 where |G1| ≥ 2 and |G2| ≥ 3. This follows from a more general result where it is proved that if (A, τ) is the reduced free product of a family (Ai, τi), i ∈ I, of unital C∗-algebras Ai with normalized fai...