THE BI-SELF-CONJUGATE AND NONNEGATIVE DEFINITE SOLUTIONS TO THE INVERSE EIGENVALUE PROBLEM OF QUATERNION MATRICES

The main aim of this paper is to discuss the following two problems:λm)∈Hm×m, find A ∈ BSH≥n×n such that AX= X∧, where BSH≥n×n denotes the set of all n × n quaternion matrices which are bi-self-conjugate and nonnegative definite.Problem Ⅱ:Given B ∈ Hn×m, find -B∈SE such that ||B- B||Q = minA∈sE ||B - A||Q,necessary and sufficient conditions for SE being nonempty are obtained. The general form of elements in SE and the expression of the unique solution B of problem Ⅱ are given.     

Complete noncompact manifolds with harmonic curvature

Let (M ⁿ , g) be an n-dimensional complete noncompact Riemannian manifold with harmonic curvature and positive Sobolev constant. In this paper, by employing an elliptic estimation method, we show that (M ⁿ , g) is a space form if it has sufficiently small L ^n/2-norms of trace-free curvature tensor and nonnegative scalar curvature. Moreover, we get a gap theorem for (M ⁿ , g) with positive scalar curvature.     

Bounds for the perimeter of an ellipse

In this paper, we present several bounds for the perimeter of an ellipse, which improve some well-known results.     

Polymer Optical Fiber Photosensitivities and Highly Tunable Fiber Gratings

In this paper, recent progress in the investigation of photosensitivities of polymer optical fibers and the development of polymer optical fiber grating is reported. Photosensitivities in various polymer fibers, including doped and undoped, multimode and single-mode polymer fibers, have been experimentally characterized and evaluated for fiber grating application. In particular, the wavelength dependence of material absorption and photosensitivity has been found essential to the fabrication of polymer optical fiber grating. Based on the results of photosensitivity research, polymer optical fiber gratings have been successfully fabricated. More importantly, polymer optical fiber grating has been demonstrated highly tunable, with a tuning range more than 70 nm. The unique feature of high tunability in polymer optical fiber grating has great potential in various applications including optical fiber WDM systems and fiber sensor systems. Several important issues that remain to be investigated will also be discussed.     

Failure of Kak quantum key distribution protocol

Kak’s quantum key distribution (QKD) protocol provides not only the distribution but also the integrity of secret key simultaneously in quantum channel. Consequently the additional exchange of information, used to check whether an eavesdropper exists, is unnecessary. In this comment, we will point out the failure of Kak’s protocol and show that Kak’s protocol does not have the joint distribution and integration that the author declares in [1].     

An old conjecture of Erdos-Turán on additive bases

There is a 1941 conjecture of Erdos and Turán on what is now called additive basis that we restate:

Conjecture 0.1(Erdos and Turán). Suppose that is an increasing sequence of integers and

Suppose that

If 0$"> for all , then is unbounded.

Our main purpose is to show that the sequence cannot be bounded by . There is a surprisingly simple, though computationally very intensive, algorithm that establishes this.

     

Enhanced Fermi-surface nesting in superconducting BaFe2(As(1-x)P(x))2 revealed by the de Haas-van Alphen effect

The three-dimensional Fermi-surface morphology of superconducting BaFe2(As0.37P0.63)2 with T(c)=9 K is determined using the de Haas-van Alphen effect. The inner electron pocket has a similar area and k(z) interplane warping to the observed hole pocket, revealing that the Fermi surfaces are geometrically well nested in the (π,π) direction. These results are in stark contrast to the fermiology of the nonsuperconducting phosphides (x=1), and therefore suggest an important role for nesting in pnictide superconductivity.     

Surface-enhanced Raman scattering from silver nanostructures with different morphologies

Scanning electron microscopy and X-ray diffraction reveal that four different types of crystalline silver nanostructures including nanoparticles, nanowires, nanocubes, and bipyramids are synthesized by a solvothermal method by reducing silver nitrate with ethylene glycol using poly(vinylpyrrolidone) as an adsorption agent and adding different quantities of sodium chloride to the solution. These nanostructures which exhibit different surface plasma resonance properties in the ultraviolet–visible region are shown to be good surface-enhanced Raman scattering (SERS) substrates using rhodamine 6G molecules. Our results demonstrate that the silver nanocubes, bipyramids with sharp corners and edges, and aggregated silver nanoparticles possess better SERS properties than the silver nanowires, indicating that they can serve as high-sensitivity substrates in SERS-based measurements.