Herein are solutions to the exercises given in [1]. Let K be a field, and f(X) ∈ K[X] an irreducible polynomial. The root quantum number rK(f) is the number of roots of f in the stem field K(α), where α is an arbitrary choice of root of f . It was shown that rK(f) is well-defined and divides the degree of f . We start by establishing the connection with Galois theory. Let f be irreducible and s...

IV Vainio PJ, Viluksela M, Tuominen RK. Nicotine-like effects of cotinine on protein kinase C activity and noradrenaline release in bovine adrenal chromaffin cells. VI Vainio PJ, Tuominen RK. Cotinine binding to nicotinic acetylcholine receptors in bovine chromaffin cell and rat brain membranes. A submitted manuscript.

We present the equations of condition up to sixth order for Runge-Kutta (RK) methods, when integrating scalar autonomous problems. Two RK pairs of orders 5(4) are derived. The first at a cost of only five stages per step, while the other having an extremely small principal truncation error. Numerical tests show the superiority of the new pairs over traditional ones.

In this paper we study general nonlinear stochastic differential equations, where the usual Brownian motion is replaced by a Lévy process. We also suppose that the coefficient multiplying the increments of this process is merely Lipschitz continuous and not necessarily linear in the time-marginals of the solution as is the case in the classical McKean-Vlasov model. We first study existence, uni...

Using actinophage Bl and Streptomyces griseus as a convenient prescreening1* for antiviral substances, a new antibiotic, enopeptin A was isolated from a culture broth of Streptomyces sp. RK-1051. Strain RK-1051 was isolated from a soil sample collected in Tsuruoka city, Yamagata Prefecture, Japan, and deposited at the Fermentation Research Institute, Agency of Industrial Science and Technology,...

A personal view of the historical development of software based on explicit Runge-Kutta formulas is presented, and some future developments are suggested.

A high-passage rabbit kidney RK-13 cell line (HP-RK-13[KY], originally derived from the ATCC CCL-37 cell line) used in certain laboratories worldwide is contaminated with noncytopathic bovine viral diarrhea virus (ncpBVDV). On complete genome sequence analysis, the virus strain was found to belong to BVDV group 1b.