For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector‎, ‎and so $T$ has a nontrivial hyperinvariant subspace‎.

For a Banach algebra $A$, $A''$ is $(-1)$-Weakly amenable if $A'$ is a Banach $A''$-bimodule and $H^1(A'',A')={0}$. In this paper, among other things,  we study the relationships between the $(-1)$-Weakly amenability of $A''$ and the weak amenability of $A''$ or $A$. Moreover, we show that the second dual of every $C^ast$-algebra is $(-1)$-Weakly amenable.

It is shown that, if IJ is a subvariety of the join of a nilpotent variety and a metabelian variety and if V̂ is a variety with a finite basis for its laws, then UV also has a finite basis for its laws. The special cases IJ nilpotent and IJ metabelian have been established by Higman (1959) and Ivanjuta (1969) respectively. The proof here, which is independent of Ivanjuta's, depends on a rather g...

We prove that the Bohmian arrival time of the 1D Schrödinger evolution violates the quadratic form structure on which Kijowski's axiomatic treatment of arrival times is based. Within Kijowski's framework, for a free right moving wave packet Ψ, the various notions of arrival time (at a fixed point x on the real line) all yield the same average arrival time tK ij (Ψ). We derive the inequality tB ...

i x i s = 1, x i s ≥ 0, x ij s ≥ 0 . • x i s ∈ [0, 1]: indicates whether label i is chosen at voxel s • y ij s = x ij s − x s ∈ [−1, 1]: presence of a surface and its direction • ρs: unary term, cost for label i at location s •φij s : convex smoothness term at voxel s for labels i and j • ek ∈ R: k-th canonical basis vector • T : alignment between prior and input data •α: normalization factor f...

We describe here the characteristics of two types of high-quality PbTe p-njunctions, prepared in this work: (1) by thermal diffusion of In4Te3 gas (TDJ), and (2) by ion implantation (implanted junction, IJ) of In (In-IJ) and Zn (Zn-IJ). The results, as presented here, demonstrate the high quality of these PbTe diodes. Capacitance-voltage (C-V) and current-voltage (I-V) characteristics have been...

24 bounded regions of spacetime. Gravitational physics and its mathematical expression have been smoothly melded. 23 ^ @ 0 g ij = ?2NK ij ; (82) that has no slicing term analogous to S ij. It has characteristics along the light cone and @ 0. It is not quasi-diagonal because of third order derivatives of g ij arising in (81) from r 2 N. This system is hyperbolic non-strict 21]. On the other hand...

In many area of medical research, a relation analysis between one response variable and some explanatory variables is desirable. Regression is the most common tool in this situation. If we have some assumptions for such normality for response variable, we could use it. In this paper we propose a nonparametric regression that does not have normality assumption for response variable and we focus ...

Electrons confined in silicon quantum dots exhibit orbital, spin, and valley degrees of freedom. The degree freedom originates from the bulk bandstructure silicon, which has six degenerate electronic minima. degeneracy can be lifted wells due to strain confinement, but "valley splitting" two lowest lying valleys is known sensitive atomic-scale disorder. Large splittings are desirable have a wel...

In this paper, block distance matrices are introduced. Suppose F is a square block matrix in which each block is a symmetric matrix of some given order. If F is positive semidefinite, the block distance matrix D is defined as a matrix whose (i, j)-block is given by D ij = F ii +F jj −2F ij. When each block in F is 1 × 1 (i.e., a real number), D is a usual Euclidean distance matrix. Many interes...