Let $(K,v)$ be a valued field and let $(K^h,v^h)$ the henselization determined by choice of an extension $v$ to algebraic closure $K$. Consider embedding $v(K^*)\hookrightarrow\Lambda$ value group into divisible ordered abelian group. $T(K,\Lambda)$, $T(K^h,\Lambda)$ trees formed all $\Lambda$-valued extensions $v$, $v^h$ polynomial rings $K[x]$, $K^h[x]$, respectively. We show that natural res...

Tiller angle, an important agronomic trait, contributes to crop production and plays a vital role in breeding for plant architecture. A barley line V-V-HD, which has prostrate tillers during vegetative growth and erect tillers after booting, is considered the ideal type for repressing weed growth and increasing leaf area during early growth. Genetic analysis identified that the prostrate trait ...

Let V and V ′ be 2n-dimensional vector spaces over fields F and F ′. Let also : V × V → F and ′: V ′ × V ′ → F ′ be non-degenerate symplectic forms. Denote by and ′ the associated (2n − 1)-dimensional projective spaces. The sets of kdimensional totally isotropic subspaces of and ′ will be denoted by Gk and G ′ k , respectively. Apartments of the associated buildings intersect Gk and G ′ k by so...

| In order to calculate the transmit power in shell{mapping{based transmission schemes, the frequencies of the shells are required. In this paper, a simple but general method for the calculation of these frequencies is derived. The method has approximately the same complexity as the shell{mapping encoder. As an example, the method is shown in detail for the shell{mapping scheme speci ed for the...

The approximation-solvability of a generalized system of nonlinear variational inequalities (SNVI) involving relaxed pseudococoercive mappings, based on the convergence of a system of projection methods, is presented. The class of relaxed pseudococoercive mappings is more general than classes of strongly monotone and relaxed cocoercive mappings. Let K1 and K2 be nonempty closed convex subsets o...

Let C be a nonempty closed and convex subset of a real Hilbert space H. Let Am, Bm : C → H be relaxed cocoercive mappings for each 1 ≤ m ≤ r, where r ≥ 1 is integer. Let f : C → C be a contraction with coefficient k ∈ (0, 1). Let G : C → C be ξ-strongly monotone and L-Lipschitz continuous mappings. Under the assumption ∩m=1GV I(C,Bm, Am) 6= ∅, where GV I(C,Bm, Am) is the solution set of a gener...

This paper applies Whitney's embedding theorem to the data reduction problem and introduces a new approach motivated in part by the (constructive) proof of the theorem. The notion of a good projection is introduced which involves picking projections of the high-dimensional system that are optimized such that they are easy to invert. The basic theory of the approach is outlined and algorithms fo...

A signed graph is a simple with two types of edges. Switching vertex v corresponds to changing the type each edge incident v. homomorphism from G another H mapping φ:V(G)→V(H) such that, after switching any number vertices G, φ maps every an same in H. The chromatic χs(G) order smallest that there We show triangular grids at most 10 and hexagonal 4.

We consider a perturbation of a periodic Schrr odinger operator H 0 by a nonnegative potential V with asymptotics V (x) f x j j jxj 2 q(x); > 0; jxj ! 1 where q is also periodic. The total number of eigenvalues of the operator H() = H 0 +V , > 0, in a gap of H 0 is studied. We discuss a diierence of its asymptotics as ! 1 compared to the case q(x) = 1 Abstract. Let (M;) (M; 0 0) be two measure ...