Numerical analysis of an inverse problem for the eikonal equation

We are concerned with the inverse problem for an eikonal equation of determining the speed function using observations of the arrival time on a fixed surface. This is formulated as an optimisation problem for a quadratic functional with the state equation being the eikonal equation coupled to the so-called Soner boundary condition. The state equation is discretised by a suitable finite difference scheme for which we obtain existence, uniqueness and an error bound. We set up an approximate optimisation problem and show that a subsequence of the discrete mimina converges to a solution of the continuous optimisation problem as the mesh size goes to zero. The derivative of the discrete functional is calculated with the help of an adjoint equation which can be solved efficiently by using fast marching techniques. Finally we describe some numerical results.     

Homogeneous manifolds with nonpositive curvature operator

Homgeneous manifolds of nonpositive sectional curvature can be identified with a certain class of solvable Lie groups. We determine, which of these groups also admit metrics with nonpositive curvature operator; this class is smaller, but still contains many examples.     

Fourier transforms related to a root system of rank 1

We introduce an algebra consisting of difference-reflection operators and multiplication operators that can be considered as a q = 1 analogue of Sahi's double affine Hecke algebra related to the affine root system of type . We study eigenfunctions of a Dunkl-Cherednik-type operator in the algebra , and the corresponding Fourier transforms. These eigenfunctions are nonsymmetric versions of the Wilson polynomials and the Wilson functions.     

Colour diversification in octocorals based on conjugated polyenes: A Raman spectroscopic view

Polyenic pigments in octocorals have been investigated by Raman spectroscopy using laser excitation at 532, 785 and 1064 nm. The spectral features suggest the structural nature of carotenoids from Phyllogorgia dilatata, Leptogorgia punicea, Muricea atlantica, Carijoa riisei and conjugated polyenals from L. punicea, L. setacea, Muricea flamma and Renilla muelleri. The observed vibrational bands at ca. 1540–1520 ν₁(C=C), 1159 ν₂(C–C) and 1005 cm⁻¹ ρ₃(C–CH₃) were assigned to carotenoids, whereas the identification of non‐methylated conjugated polyenals have been proposed due to two major Raman bands at ca. 1500 and 1120 cm^‐1, assigned to ν(C=C) and ν(C–C), respectively. Copyright © 2012 John Wiley & Sons, Ltd.     

The conserved protein kinase-A target motif in synapsin of Drosophila is effectively modified by pre-mRNA editing

Background  

Synapsins are abundant synaptic vesicle associated phosphoproteins that are involved in the fine regulation of neurotransmitter release. The Drosophila member of this protein family contains three conserved domains (A, C, and E) and is expressed in most or all synaptic terminals. Similar to mouse mutants, synapsin knock-out flies show no obvious structural defects but are disturbed in complex behaviour, notably learning and memory.     

The Peierls transition of Perylene radical cation salts with 2:1 stoichiometry containing tetrahydrofuran

Crystal structure, microwave conductivity and static magnetic susceptibility were analyzed for the conducting perylene (PE) radical cation salts of nominal composition (PE)₂(PF₆)_1–x (AsF₆) _x ·2/3 THF for 0x1. Crystallographic phase transitions in the high-temperature metal phase were also characterized by differential scanning calorimetry and electron spin resonance. The Peierls transition occuring at 100–120 K (depending onx) and the opening of the energy gap in the semiconductor phase were determined from the magnetic data. The dependence of these properties on the size of the complex anions and the packing of the PE molecules is discussed.     

纳米粘土增强环氧树脂复合材料抗原子氧性能的研究

本文采用激光爆破法高能原子氧束源研究了纳米粘土增强环氧树脂复合材料的抗原子氧性能. 研究了四种样品：纯环氧树脂,纳米粘土含量为1 wt%,2 wt%和4 wt%的纳米粘土增强环氧树脂复合材料,结果表明腐蚀深度随着纳米粘土含量的增加而降低,当掺杂纳米粘土含量为4 wt%时,腐蚀深度为纯环氧树脂腐蚀深度的28%∽37%;X射线光电子能谱(XPS)分析表明原子氧轰击后,材料表面C-C/C-H键比例减少,C-O键、酮类比例增加,表面氧化程度增加,掺杂纳米粘土的材料表面生成了新的碳酸盐,掺杂4 wt%纳米粘土的复合材料表面氧化程度增加最小;扫描电子显微镜(SEM)结果显示含有纳米粘土的复合材料表面被原子氧轰击后在纳米粘土团簇处形成了“块状”物质,掺杂4 wt%纳米粘土的复合材料,“块状”物质尺寸和分布密度最大;综合腐蚀深度,XPS,以及SEM结果表明,虽然所有表面都一定程度地被原子氧腐蚀和氧化,但掺杂纳米粘土的复合材料表面由于生成了“块状”物质,阻挡了原子氧进一步腐蚀其下的材料,提高了抗原子氧性能.     

Novel and facile solution-phase synthesis of 2,5-diketopiperazines and O-glycosylated analogs

This work describes the synthesis in solution of a series of related diketopiperazines with potential biological activities: cyclo(l-Pro-l-Ser), cyclo(l-Phe-l-Ser), cyclo(d-Phe-l-Ser) and the corresponding glycosylated analogs of the latter, cyclo[d-Phe-l-Ser(αGlcNAc)] and cyclo[d-Phe-l-Ser(βGlcNAc)]. The synthetic approach involved coupling reactions of -OH or O-glycosylated serine benzyl esters with NFmoc-protected amino acids (Pro or Phe), followed by one-pot deprotection-cyclization reaction in the presence of 20% piperidine in DMF.     

Asymmetry of velocity distributions in peripheral reactions with heavy ions at Fermi energies

The asymmetry of velocity distributions of projectile-like fragments produced in heavy ion collisions is considered. The calculations performed in the transport model approach (Vlasov kinetic equation with the collision term) are compared with the experimental data for the ²²Ne (40MeV/nucleon) + ⁹Be and ¹⁸O (35 MeV/nucleon) + ⁹Be(¹⁸¹Ta) reactions. It is found that the velocity distributions contain two components: a direct component centered at the beam velocity and a dissipative component at lower energies, leading to asymmetry of velocity distributions. The direct component is interpreted empirically within the Goldhaber model, and the centroids and widths σ₀ of the distributions for each fragment are extracted. It is found that value of σ₀ derived from experimental data is smaller by a factor of 2 than the theoretical one. The dissipative (also called deep inelastic) component is described well by the transport calculations. It is shown that the ratio of yields of direct and dissipative components, which determines the asymmetry of velocity distributions, depends on shape of the deflection function. Original Russian Text ? T.I. Mikhailova, B. Erdemchimeg, G. Kaminski, A.G. Artyukh, M. Colonna, M. Di Toro, I.N. Mikhailov, Yu.M. Sereda, H.H. Wolter, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 6, pp. 898–903.