Common fixed point theorems for weakly compatible quasi contraction mappings

Summary Recently, Pathak [13] has made an extension of the notion of compatibility to weak compatibility, and extended the coincidence theorem for compatible mappings in Kaneko and Sessa [11] to weakly compatible mappings [13]. In the present paper, we define a new class of weakly compatible mappings (Definition 4) and prove some common fixed point theorems for these mappings, which satisfy Condition (2) below. Although our main theorem is formulated for weakly compatible mappings, its corresponding formulation for commutative mappings is also a new result, thus presenting a generalization of some theorems of Fisher, Das and Naik, Khan and Kubiaczyk, Reich, Ćirić and Rhoades and Watson.     

The electric quadrupole interaction of 111Cd in ZrZn2 and Zn in the samples prepared at 8 GPa

The perturbed angular correlation (PAC) measurements with the ¹¹¹In-¹¹¹Cd nuclear probe embedded into the lattice of the cubic (C15) Laves compound ZrZn₂ showed that ¹¹¹Cd nuclei experienced an axially symmetric electric quadrupole interaction with a frequency ν _Q  = 132.4 MHz at room temperature. The samples were synthesized and doped with the probe at a pressure 8 GPa. The temperature dependence of ν _Q was shown to be linear: ν _Q (T) = 147(1 − 0.033 T) MHz. Since the value of ν _Q is very close to that known for ¹¹¹Cd in the lattice of Zn, we have checked if it could be assigned to residual Zn metal in the sample. For the Zn sample melted and doped with ¹¹¹In at 8 GPa we have obtained ν _Q  = 117.3 MHz at 300 K and 127 MHz at 80 K – both values considerably lower than that for ¹¹¹In doped Zn samples prepared at an ambient pressure. These data, and the fact that ν _Q (T) in Zn is known to follow the T ^3/2 law, allow to attribute the ν _Q value quoted above to ¹¹¹Cd nuclei at the substitutional sites with tetrahedral symmetry in the Zn sublattice of ZrZn₂.     

区间周期系统的平稳振荡

本文给出了区间周期系统平稳振荡的概念，建立了区间矩阵稳定性与区间周期系统平稳振荡之间的关系，推广和改进了文[1]的结果．     

∫e~(it(|z_(n-1)~m|~2+∑_(j-1)~(n-2)|z_j~m-z_nz_(j+1)|~2g(z)dz∧d之渐近估计

建立了振荡积分渐近性态之奇性指数与(?)-Neumman问题中交换子型边界不变量之间的关系,证明了定理: 与t无关,使得     

一类新的复合核的二次时频分布

提出了一类新的复合核的二次时频分布，并和几种主要的二次时频分布作了比较研究，实验结果说明的分布具有高的时频分辨力和强的抑制交叉干扰能力。     

A weighted Lq‐approach to Oseen flow around a rotating body

We study time-periodic Oseen flows past a rotating body in ℝ³ proving weighted a priori estimates in L^q-spaces using Muckenhoupt weights. After a time-dependent change of coordinates the problem is reduced to a stationary Oseen equation with the additional terms (ω ∧ x) ⋅ ∇ u and −ω ∧ u in the equation of momentum where ω denotes the angular velocity. Due to the asymmetry of Oseen flow and to describe its wake we use anisotropic Muckenhoupt weights, a weighted theory of Littlewood–Paley decomposition and of maximal operators as well as one-sided univariate weights, one-sided maximal operators and a new version of Jones' factorization theorem. Copyright © 2007 John Wiley & Sons, Ltd.     

Comparison of Separation Efficiency of Macrocyclic Glycopeptide-Based Chiral Stationary Phases for the LC Enantioseparation of β-Amino Acids

Direct reversed-phase high-performance liquid chromatographic methods were developed for the separation of enantiomers of eighteen unnatural β-amino acids, including several β-3-homo-amino acids. The direct separations of the underivatized analytes were performed on chiral stationary phases containing macrocyclic glycopeptide antibiotics such as teicoplanin (Chirobiotic T and T2), teicoplanin aglycone (Chirobiotic TAG), vancomycin (Chirobiotic V and V2), and ristocetin A (Chirobiotic R) as chiral selectors. The effects of the organic modifier, mobile phase composition and pH on the separations were investigated. A comparison of the separation performances of the macrocyclic glycopeptide stationary phases revealed that the Chirobiotic T2 column exhibited better selectivity than the Chirobiotic T column for the separation of β-3-homo-amino acid enantiomers; vancomycin or ristocetin A exhibited lower selectivity. The elution sequence was determined in some cases: the S enantiomers eluted before the R enantiomers, with the exception of the Chirobiotic R column, where the elution sequence R < S was observed.     

SIMS direct surface imaging of Cu1−xCrx formation

Cu-Cr alloys, irradiated with a low-energy, high-current electron beam, are analyzed by high-resolution secondary ion mass spectrometry. Mass spectra and images of Cu⁺ and Cr⁺ surface distributions finely reveal the regions enriched in Cu and Cr. For electron beam energies above a threshold value, the formation of a non-equilibrium Cu_1−xCr_x solid solution, extending over sub-micrometer areas is highlighted for the first time. A discussion of the process leading to Cu_1−xCr_x formation is given.     

一维可压缩粘性流体稳态流的渐近稳定性

本文研究一维可压缩粘性流体解的大时间渐近性态，在任意大的外力ｆ（ｘ）的作用下，证明了在初始小扰动下流动将渐近趋向于稳态流。