Bäcklund transformations and abundant exact explicit solutions of the Sharma-Tasso-Olver equation

By using an extension of the homogeneous balance method and Maple, the Bäcklund transformations for the Sharma-Tasso-Olver equation are derived. The connections between the Sharma-Tasso-Olver equation and some linear partial differential equations are found. With the aid of the transformations given here and the computer program Maple 12, abundant exact explicit special solutions to the Sharma-Tasso-Olver equation are constructed. In addition to all known solutions re-deriving in a systematic way, several entirely new and more general exact explicit solitary wave solutions can also be obtained. These solutions include (a) the algebraic solitary wave solution of rational function, (b) single-soliton solutions, (c) double-soliton solutions, (d) N-soliton solutions, (e) singular traveling solutions, (f) the periodic wave solutions of trigonometric function type, and (g) many non-traveling solutions. By using the Airy’s function and the Bäcklund transformations obtained here, the exact explicit solution of the initial value problem for the STO equation is presented. The variety of the structure of the solutions for the Sharma-Tasso-Olver equation is illustrated.     

Non-Abelian gauge potentials driven localization transition in quasiperiodic optical lattices

Derived from quantum waves immersed in an Abelian gauge potential, the quasiperiodic Aubry-André-Harper (AAH) model is a simple yet powerful Hamiltonian to study the Anderson localization of ultracold atoms. Here, we investigate the localization properties of ultracold atoms in quasiperiodic optical lattices subject to a non-Abelian gauge potential, which are depicted by non-Abelian AAH models. We identify that the non-Abelian AAH models can bear the self-duality. We analyze the localization of such non-Abelian self-dual optical lattices, revealing a rich phase diagram driven by the non-Abelian gauge potential involved: a transition from a pure delocalization phase, then to coexistence phases, and finally to a pure localization phase. This is in stark contrast to the Abelian counterpart that does not support the coexistence phases. Our results establish the connection between localization and gauge symmetry, and thus comprise a new insight on the fundamental aspects of localization in quasiperiodic systems, from the perspective of non-Abelian gauge potential.     

The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification

We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper R and lower length λ scales (infrared/ultraviolet cutoff). The invariance symmetry leads naturally to the real Clifford algebra Cl (2, 6, R) and complexified Clifford Cl_C (4) algebra related to Twistors. A unified theory of all Noncommutative branes in Clifford-spaces is developed based on the Moyal-Yang star product deformation quantization whose deformation parameter involves the lower/upper scale . Previous work led us to show from first principles why the observed value of the vacuum energy density (cosmological constant) is given by a geometric mean relationship , and can be obtained when the infrared scale R is set to be of the order of the present value of the Hubble radius. We proceed with an extensive review of Smith’s 8D model based on the Clifford algebra Cl (1, 7) that reproduces at low energies the physics of the Standard Model and Gravity, including the derivation of all the coupling constants, particle masses, mixing angles, ....with high precision. Geometric actions are presented like the Clifford-Space extension of Maxwell’s Electrodynamics, and Brandt’s action related to the 8D spacetime tangent-bundle involving coordinates and velocities (Finsler geometries). Finally we outline the reasons why a Clifford-Space Geometric Unification of all forces is a very reasonable avenue to consider and propose an Einstein-Hilbert type action in Clifford-Phase spaces (associated with the 8D Phase space) as a Unified Field theory action candidate that should reproduce the physics of the Standard Model plus Gravity in the low energy limit.     

扩展的Sinh—Gordon方程展开法与Kaup—Kupershmidt方程的Jacobi椭圆函数解

利用扩展的Sinh—Gordon方程展开法研究了Kaup—Kupershmidt方程的Jacobi椭圆函数解,此方法也适用于求解其他非线性演化方程,从而丰富了方程解的范围．     

Nonmonotone Inexact Newton Method for the Extended Linear Complementarity Problem

This paper presents a nonmonotone inexact Newton-type method for the extended linear complementarity problem (ELCP). We first reformulate the optimization system of the ELCP problem into a system of smoothed equations. Then we solve this system by a nonmonotone inexact Newton-type algorithm. The global convergence is obtained and numerical tests for some classes of ELCP include linear complementarity, horizontal linear complementarity, and generalized linear complementarity problems are also given to show the e?ciency of the proposed algorithm.     

钢桥面板顶板与纵肋连接疲劳开裂局部加固分析

正交异性钢桥面板纵肋与顶板连接细节处极易产生疲劳裂纹.本文通过精细化有限元模型,分析了栓接角钢加固法和粘贴纤维增强复合材料(Fiber Reinforced Polymer, FRP)型材加固法对钢桥面板疲劳性能的影响.结果表明:采用角钢、FRP型材对顶板与纵肋连接细节的疲劳裂纹进行加固,焊缝裂纹附近热点应力峰值降幅可达56.2%和46.5%;焊缝裂纹尖端附近应力强度因子随着板件整体尺寸的增大而减小;改变板件厚度对应力强度因子结果值影响最大,最高可使其下降约80%,改变板件纵向长度和单肢长度对其有一定影响;随着裂纹的持续扩展,栓接角钢法的加固效果开始下降.建议在监测到构造细节处疲劳裂纹后应尽早加固.     

Complexation and Fluorescence of Tricyclic Basic Dyes Encapsulated in Cucurbiturils

Tricyclic basic dyes (proflavine, acridine orange, pyronine, pyronine Y, oxonine, thionine and methylene blue) often form one‐to‐one or two‐to‐one complexes with CB[7] and CB[8], respectively. In the case of pyronine Y, the complexes with CB[7] and CB[8] have a one‐to‐one and three‐to‐one stoichiometry, respectively. The binding constants for CB[7] complexes range from 3.07×10⁶ to 1.70×10⁷ m ^?1. In the case of CB[8], the association constant varies between 3.24×10¹³ and 2.50×10¹⁶ m ^?2. Overall, these binding constants are four orders of magnitude higher than those reported for the same dyes in β and γ‐cyclodextrins. Formation of the host–guest complexes leads to an increase in the fluorescence quantum yields in the case of CB[7], while the dimeric or trimeric dye encapsulated in CB[8] are remarkably less fluorescent than the same dye in diluted solutions.     

Fabrication,characterization, and drug release study of vitamin C–loaded alginate/polyethylene oxide nanofibers for the treatment of a skin disorder

Pigmented purpuric dermatosis (PPD) is a skin disorder mainly seen in the lower limbs. The nanofibrous web has been shown to be an appropriate alternative for the treatment of skin diseases as a drug delivery vehicle. In this study, sodium alginate (SA)/polyethylene oxide (PEO) nanofibers containing vitamin C (VC) were fabricated using both blended electrospinning and core/shell electrospinning. The resultant nanofibers were characterized using Fourier transform infrared spectroscopy and scanning electron microscopy. Enhancing the VC content resulted in increasing the nanofibers diameter. Also, the degradation rate and drug release were investigated. Drug release was evaluated using the in vitro dissolution and permeation method. The degradation rate and the drug release of the core/shell nanofibers were found to be lower than those of the blended nanofibers. The drug release of the extended nanofibers followed a different pattern, indicating that the extension of the nanofibers could be a promising way to control the drug release.