(2+1)维Konopelchenko-Dubrovsky方程新的多孤子解

利用齐次平衡方法,将(2+1)维Konopelchenko-Dubrovsky方程转化为两个变量分离的线性偏微分方程,然后采用三种不同的函数假设,得到相应的常系数微分方程,通过求解特征方程,方便地构造出Konopelchenko-Dubrovsky方程新的多孤子解.     

Lower bound for the ratios of eigenvalues of Schrödinger with nonpositive single‐barrier potentials

Horváth and Kiss (Proc. Amer. Math. Soc., 2005) proved the upper bound estimate for Dirichlet eigenvalue ratios of the Schrödinger problem ?y^′′ + q(x)y = λy with nonnegative and single‐well potential q. In this paper, we prove that if q(x) is a nonpositive, continuous, and single‐barrier potential, then for λ_n > λ_m≥ ? 2q^?, where . In particular, if q(x) satisfies the additional condition , then λ₁ > 0 and for n > m ≥ 1. For this result, we develop a new approach to study the monotonicity of the modified Prüfer angle function.     

Concentration on curves for a nonlinear Schrödinger problem with electromagnetic potential

We prove the existence of solutions to the nonlinear Schrödinger equation ${\epsilon }^2{(i\mathrm{?}+\mathit{A})}^{2}u+V(y)u?|u{|}^{p?1}u=0$ in ${\mathbb{R}}^2$ with a magnetic potential $\mathit{A}=(A_1,A_2)$. Here V represents the electric potential, the index p is greater than 1. Along some sequence $\{{\epsilon }_n\}$ tending to zero we exhibit complex-value solutions that concentrate along some closed curves.     

一类特定的AF-代数

讨论了一类特定的AF-代数,其上的恒等同态可以用一列有限维值域的自同态逐点逼近.给出了这类AF-代数的K-理论刻画,并给出了一个不在这一类中的RFD AF-代数的例子.     

Spin–orbit stiffness of the spin‐polarized electron gas

In a spin‐polarized electron gas, Coulomb interaction couples the spin and motion degrees of freedom to build propagating spin waves. The spin wave stiffness S_sw quantifies the energy cost to trigger such excitation by perturbing the kinetic energy of the electron gas (i.e. putting it in motion). Here we introduce the concept of spin–orbit stiffness, S_so, as the energy necessary to excite a spin wave with a spin polarization induced by spin–orbit coupling. This quantity governs the Coulombic enhancement of the spin–orbit field acting of the spin wave. First‐principles calculations and electronic Raman scattering experiments carried out on a model spin‐polarized electron gas, embedded in a CdMnTe quantum well, demonstrate that S_so = S_sw. Through optical gating of the structure, we demonstrate the reproducible tuning of S_so by a factor of 3, highlighting the great potential of spin–orbit control of spin waves in view of spintronics applications. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

A novel nanoscale fin field effect transistor by amended channel: Investigation and fundamental physics

The present paper proposes a new Fin Field Effect Transistor (FinFET) with an amended Channel (AC). The fin region consists of two sections; the lower part which has a rounded shape and the upper part of fin as conventional FinFETs, is cubic. The AC-FinFET devices are proven to have a lower threshold voltage roll-off, reduced DIBL, better subthreshold slope characteristics, and a better gate capacitance in comparison with the C-FinFET. Moreover, the simulation result with three-dimensional and two-carrier device simulator demonstrates an improved output characteristic of the proposed structure due to reduction of self-heating effect. Due to the rounded shape of the lower fin region and decreasing corner effects there, the heat can flow easily, and the device temperature will decrease. Also the gate control over the channel increases due to the narrow upper part of the fin. The paper, thus, attempts to show the advantages of higher performance AC-FinFET device over the conventional one, and its effect on the operation of nanoscale devices.     

Higher‐Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions

We first review the Coset Space Dimensional Reduction (CSDR) programme and present the best model constructed so far based on the , 10‐dimensional E₈ gauge theory reduced over the nearly‐Kähler manifold with the additional use of the Wilson flux mechanism. Then we present the corresponding programme in the case that the extra dimensions are considered to be fuzzy coset spaces and the best model that has been constructed in this framework too. In both cases the best model appears to be the trinification GUT .     

Investigation of Metastable Low Dimensional Halometallates

The solvothermal synthesis, structure determination and optical characterization of five new metastable halometallate compounds, [1,10-phenH][Pb_3.5I₈] (1), [1,10-phenH₂][Pb₅I₁₂]·(H₂O) (2), [1,10-phen][Pb₂I₄] (3), [1,10-phen]₂[Pb₅Br₁₀] (4) and [1,10-phenH][SbI₄]·(H₂O) (5), are reported. The materials exhibit rich structural diversity and exhibit structural dimensionalities that include 1D chains, 2D sheets and 3D frameworks. The optical spectra of these materials are consistent with bandgaps ranging from 2.70 to 3.44 eV. We show that the optical behavior depends on the structural dimensionality of the reported materials, which are potential candidates for semiconductor applications.     

Bone Dimensional Change Following Immediate Implant Placement in Posterior Teeth with CBCT: A 6-Month Prospective Clinical Study

This prospective clinical study aimed to evaluate the peri-implant hard tissue dimensional change at 6 months of immediate implant placement with bone graft materials in the posterior area using cone-beam computed tomography (CBCT). Twelve dental implants were placed concurrently following tooth extraction in the posterior area and filled with xenograft particles. The CBCT images were taken immediately after surgical procedures and then at 6 months follow-up. To evaluate the hard tissue changes, the vertical and horizontal bone thickness were analyzed and measured using ImageJ software. Paired t-test or Wilcoxon match-pair signed-rank test was done to analyze the changes of hard tissue values at the same level between immediately and 6 months following immediate implant placement. Independent t-test or Mann–Whitney U test was used to analyze the dimensional change in the vertical and horizontal direction in buccal and lingual aspects. The level of significance was set at p value = 0.05. All implants were successfully osseointegrated. At 6 months follow-up, the vertical bone change at the buccal aspect was −0.69 mm and at the lingual aspect −0.39 mm. For horizontal bone thickness, the bone dimensional changes at 0, 1, 5, and 9 mm levels from the implant platform were −0.62 mm, −0.70 mm, −0.24 mm, and −0.22 mm, respectively. A significant bone reduction was observed in all measurement levels during the 6 months after implant placement (p value < 0.05). It was noted that even with bone grafting, a decrease in bone thickness was seen following the immediate implant placement. Therefore, this technique can be an alternative method to place the implant in the posterior area.