Phase transition in the one-dimensional pair-hopping model with unusual one-electron hopping

By modifying the conventional one-electron hopping behavior, we study effects of an occupation-dependent hopping on the ground state of the half-filled one-dimensional pair-hopping model. At weak coupling, the use of bosonization and renormalization-group analysis techniques helps to derive the phase diagram. Such unusual hopping is shown to drive a spin-gap transition and to introduce a new region where the triplet superconducting instability dominates for positively small pair-hopping interaction.     

Formation of low-temperature deformation-induced segregations of nickel in Fe–Ni-based austenitic alloys

ABSTRACT

The authors present the results of an investigation in Fe–Ni-Cr austenitic alloys of the low-temperature deformation-induced segregations of nickel that form in the micro regions being (i) located close to grain- and subgrain boundaries and (ii) characteristic of the concentration and magnetic inhomogeneities indicated by the appearance of a dark diffraction contrast at the electron diffraction patterns taken from these regions typical (at the same time) of an enhanced value of Curie temperature. The observed effects were connected with the micro distortions caused by the local change of lattice parameter because of an increase in nickel concentration, as well as in the result of a magnetostriction dilatation. Using methods of the X-ray energy dispersive spectroscopy (XEDS) and atomic-probe body-section radiography (tomography – APT) has made it possible to determine the borders of those regions of austenite that were characteristic of an enhanced concentration of nickel in the fields of the localisation of a deformation-induced segregation of nickel in the vicinity of grain (subgrain) boundaries of austenitic alloys of the types Fe–13Cr–30Ni and Fe–37Ni–3Ti.     

Corners of self-conjugate (s,s + 1)-cores and (s‾,s+1‾)-cores

In this paper, we describe a result on self-conjugate $(s,s+1)$-core partitions with the fixed number of corners. We also define shifted corners of a distinct partition and find formulas for the number of $(\stackrel{￣}{s},\stackrel{￣}{s+1})$-core partitions and the number of $(s,s+1)$-core shifted Young diagrams with the fixed number of shifted corners.     

Boundedness of semilinear Duffing equations at resonance in a critical situation

In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation $\ddot{x}+n^{2}x+g(x)=p(t)$ with the critical situation that $|{\int }_0^{2\pi }p(t)e^{?int}dt|=2|g(+\infty )?g(?\infty )|$ on g and p, where $n\in {\mathbb{N}}^{+}$, $p(t)$ is periodic and $g(x)$ is bounded.     

Measured and Predicted Solubility Phase Diagrams of Quaternary Systems LiBr-NaBr-MgBr2-H2O and LiBr-KBr-MgBr2-H2O at 298.15 K

The stable phase equilibria of quaternary systems LiBr-NaBr-MgBr₂-H₂O and LiBr-KBr-MgBr₂-H₂O at 298.15 K were studied by both experimental measurement(isothermal solution saturation method) and theoretical prediction(Pitzer model). The solubilities of the saturated solution have been determined experimentally and two stable phase diagrams and relevant water diagrams of the two quaternary systems were obtained. Results show that quaternary system LiBr-NaBr-MgBr₂-H₂O is hydrate II type as NaBr and NaBr·2H₂O coexistence. Its phase diagram consists of only one invariant point, four univariant curves, and five crystallization fields. The quaternary system LiBr-KBr-MgBr₂-H₂O is a complex type as the double salt KBr·MgBr₂·6H₂O formed. In addition to this double salt, the three single salts LiBr·2H₂O, KBr and MgBr₂·6H₂O also crystallize. In this paper, the solubilities of phase equilibria in above quaternary systems were also calculated by the Pitzer's electrolyte solution model. All the needed parameters can be obtained from the literature or be fitted by experimental data. On the Basis of the experimental and calculated results, the phase diagram of the quaternary system was plotted for comparison. It shows that the calculation results are consistent with the experimental ones.     

电路过渡过程的计算机辅助分析

电路过渡过程所列方程是微分方程，本文中采用的是方框图模型分析法，即将微分方程的复杂示解分解成最基本的加（减）、乘（除）、积分（微分）、增益等运算，采用VB设计用户界面产进行计算，并给出了一算例。     

Spectra and Transport in Almost Periodic Dimers

We study spectral properties of discrete Schrödinger operators with potentials obtained via dimerization of a class of aperiodic sequences. It is shown that both the nature of the autocorrelation measure of a regular sequence and the presence of generic (full probability) singular continuous spectrum in the hull of primitive and palindromic (four block substitution) potentials are robust under dimerization. Generic results also hold for circle potentials. We illustrate these results with numerical studies of the quantum mean square displacement as a function of time. The numerical techniques provide a very fast algorithm for the time evolution of wave packets.