On a theorem of Burnside on fixed-point-free automorphisms

We prove that a finite group having a fixed-point-free automorphism in the Fitting subgroup of its automorphism group must be abelian of rather restricted structure. As a consequence, no finite nonabelian group could have a fixed-point-free automorphism in the Frattini subgroup of its automorphism group. Received: 21 April 2007, Revised: 18 May 2007     

On spherical expansions of zonal functions on Euclidean spheres

This paper describes a new approach to the problem of computing spherical expansions of zonal functions on Euclidean spheres. We derive an explicit formula for the coefficients of the expansion expressing them in terms of the Taylor coefficients of the profile function rather than (as done usually) in terms of its integrals against Gegenbauer polynomials. Our proof of this result is based on a polynomial identity equivalent to the canonical decomposition of homogeneous polynomials and uses only basic properties of this decomposition together with simple facts concerning zonal harmonic polynomials. As corollaries, we obtain direct and apparently new derivations of the so-called plane wave expansion and of the expansion of the Poisson kernel for the unit ball. Received: 26 January 2007     

Thermodynamics approach of the formation of Ni catalyst particles for carbon nanotubes growth

Size-dependent thermodynamic parameters, such as Gibbs free energy, enthalpy and entropy, for the transition of a Ni nanofilm to catalyst particles for subsequent carbon nanotube growth have been explored. In this investigation, we consider the derived equations of the size-dependent melting temperature of nanosolids based on our previous works. Using this thermodynamic approach, it is found that the diameter of Ni particles is 3 times greater than the thickness of the original film. From the critical and stable sizes of transformed Ni nanoparticles, a minimum film thickness for transformation of film to nanoparticles was obtained. Our predictions are in good agreement with experimental results.     

茴香醛丙氨酸席夫碱的合成及还原

希夫碱在配位化学中占有重要的地位,是配位化学研究的重点内容之一[1].氨基酸希夫碱在化学研究、医药、军事、工业、农业、海洋等各个领域中已经得到了广泛的应用[2].     

New carbasugars from Streptomyces lincolnensis

Two new carbasugars (9 and 10) were isolated from Streptomyces lincolnensis DSM 40355 along with streptol (valienol, 8), gabosine I (valienone, 14), and glucosylglycerate. The reported ¹H and ¹³C assignments are based on 1D (¹H, ¹³C, 1D‐TOCSY, homodecoupling) and 2D (gCOSY, J‐resolved, TOCSY, ROESY, gHSQC, gHMBC) NMR techniques and electrospray ionization FT mass spectrometry (ESI FTMS). Copyright © 2009 John Wiley & Sons, Ltd.     

T2 relaxation measurement with solvent suppression and implications to solvent suppression in general

A number of suppression pulse sequences including Excitation Sculpting and WATERGATE were incorporated into the standard Carr‐Purcell‐Meiboom‐Gill (CPMG) program for T₂ measurement and experimentally evaluated. The chosen suppression schemes were of varying complexity encompassing pulse program elements, such as presaturation, gradients, and selective pulses, which are typically utilized for solvent suppression. The quality of the spectral data and the accuracy of T₂ measurements of the investigated suppression schemes were evaluated using three aqueous samples with increasing proton content in the water solvent, i.e. by volume 100% D₂O, 80/20% D₂O/H₂O, and 20/80% D₂O/H₂O. For signals removed from the water signal, the T₂ values were generally very consistent between all pulse sequences tested. T₂ measurements can be unreliable for signals too close to the water signal such that they are significantly suppressed as well. Their intensity may actually grow initially through cross relaxation that transfers magnetization back to the solute signal. In turn, this relaxation phenomenon can be exploited to improve the spectral quality of conventional solvent suppression schemes. In favorable cases, even signals that are completely masked by the water signal can be recovered by adding a carefully chosen number of spin echoes with optimized evolution time to conventional water suppression pulse programs, such as Excitation Sculpting or WATERGATE. Copyright © 2009 John Wiley & Sons, Ltd.     

The Erd?s-Ginzburg-Ziv theorem for dihedral groups

Let n≥23 be an integer and let D_2n be the dihedral group of order 2n. It is proved that, if g₁,g₂,…,g_3n is a sequence of 3n elements in D_2n, then there exist 2n distinct indices i₁,i₂,…,i_2n such that g_i1g_i2?g_i2n=1. This result is a sharpening of the famous Erd?s-Ginzburg-Ziv theorem for G=D_2n.     

On the α-amenability of hypergroups

Let UC(K) denote the Banach space of all bounded uniformly continuous functions on a hypergroup K. The main results of this article concern the α-amenability of UC(K) and quotient and product of hypergroups. It is also shown that a Sturm-Liouville hypergroup with a positive index is α-amenable if and only if α = 1. Author’s address: Dietlinden Stra?e 16, 80802 München, Germany     

Optimal Control for the Degenerate Elliptic Logistic Equation

We consider the optimal control of harvesting the diffusive degenerate elliptic logistic equation. Under certain assumptions, we prove the existence and uniqueness of an optimal control. Moreover, the optimality system and a characterization of the optimal control are also derived. The sub-supersolution method, the singular eigenvalue problem and differentiability with respect to the positive cone are the techniques used to obtain our results.