Two early and potential rate-limiting steps in the biosynthesis of isoquinoline alkaloids, such as morphine and codeine, in opium poppy (Papaver somniferum) involve decarboxylation of L-tyrosine and L-dihydroxyphenylalanine (L-dopa) to yield tyramine and dopamine, respectively. A DNA fragment was amplified by polymerase chain reaction (PCR) using degenerate primers designed to two highly conser...

For simplicity, we adopt the following rules: x denotes a set, r, s denote real numbers, n denotes a natural number, V denotes a real linear space, v, u, w, p denote vectors of V , A, B denote subsets of V , A1 denotes a finite subset of V , I denotes an affinely-independent subset of V , I1 denotes a finite affinelyindependent subset of V , F denotes a family of subsets of V , and L1, L2 denot...

(1) For all subsets A, B of E2 T such that A meets B holds proj1 ◦A meets proj1◦B. (2) Let A, B be subsets of E2 T and s be a real number. If A misses B and A⊆HorizontalLine(s) and B⊆ HorizontalLine(s), then proj1◦A misses proj1◦B. (3) For every closed subset S of E2 T such that S is Bounded holds proj1 ◦ S is closed. (4) For every compact subset S of E2 T holds proj1 ◦ S is compact. (5) Let p,...

Let L be a recursive algebraic extension of Q. Assume that, given α ∈ L, we can compute the roots in L of its minimal polynomial over Q and we can determine which roots are Aut(L)-conjugate to α. We prove there exists a pair of polynomials that characterizes the Aut(L)-conjugates of α, and that these polynomials can be effectively computed. Assume furthermore that L can be embedded in R, or in ...

in this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring r. these fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

A λ − Triple System(v), or a λ–TS(V,B), is a pair (V, B) where V is a set and B is a subset of the 3-subsets of V so that every pair is in exactly λ elements of B. A regular configuration on p points with regularity ρ on l blocks is a pair (P,L) where L is a collection of 3-subsets of a (usually small) set P so that every p in P is in exactly ρ elements of L, and |L| = l. The Pasch configuratio...

The growth function for a class of subsets C of a set X is defined by m’(N) = max {AC(F): F G X, IFI = N} , N = 1,2,. . . , where AC(F) = ({F n C: C E C}l, the number of possible sets obtained by intersecting an element of C with the set F. Sauer (1972) showed that if C forms a Vapnik-Chervonenkis class with dimension V(C), then V(C)-1 mC(N) < c 7 0 for N > V(C) 1. j=o The collection C of Eucli...

In this paper we prove the convergence of a nite volume scheme to the solution of a Stefan problem, namely the nonlinear diiusion equation ut ?'(u) = v, together with a homogeneous Neumann boundary condition and an initial condition. This is done by means of a priori estimates in L 1 and use of Kolmogorov's theorem on relative compactness of subsets of L 2 .

The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...