Integrable Couplings of the Boiti-Pempinelli-Tu Hierarchy and Their Hamiltonian Structures

Integrable couplings of the Boiti-Pempinelli-Tu hierarchy are constructed by a class of non-semisimple block matrix loop algebras. Further, through using the variational identity theory, the Hamiltonian structures of those integrable couplings are obtained. The method can be applied to obtain other integrable hierarchies.     

New differential properties of sup-type functions

In this paper, we study the directional derivative, subderivative, and subdifferential of sup-type functions without any compactness assumption on the index set. As applications, we provide an estimate of the Lipschitz modulus for sup-type functions.     

Geometry on Probability Spaces

Partial differential equations and the Laplacian operator on domains in Euclidean spaces have played a central role in understanding natural phenomena. However, this avenue has been limited in many areas where calculus is obstructed, as in singular spaces, and in function spaces of functions on a space X where X itself is a function space. Examples of the latter occur in vision and quantum field theory. In vision it would be useful to do analysis on the space of images and an image is a function on a patch. Moreover, in analysis and geometry, the Lebesgue measure and its counterpart on manifolds are central. These measures are unavailable in the vision example and even in learning theory in general. There is one situation where, in the last several decades, the problem has been studied with some success. That is when the underlying space is finite (or even discrete). The introduction of the graph Laplacian has been a major development in algorithm research and is certainly useful for unsupervised learning theory. The approach taken here is to take advantage of both the classical research and the newer graph theoretic ideas to develop geometry on probability spaces. This starts with a space X equipped with a kernel (like a Mercer kernel) which gives a topology and geometry; X is to be equipped as well with a probability measure. The main focus is on a construction of a (normalized) Laplacian, an associated heat equation, diffusion distance, etc. In this setting, the point estimates of calculus are replaced by integral quantities. One thinks of secants rather than tangents. Our main result bounds the error of an empirical approximation to this Laplacian on X.     

Global convergence of the nonmonotone MBFGS method for nonconvex unconstrained minimization

In this paper, we propose a new nonmonotone Armijo type line search and prove that the MBFGS method proposed by Li and Fukushima with this new line search converges globally for nonconvex minimization. Some numerical experiments show that this nonmonotone MBFGS method is efficient for the given test problems.     

The negative electromagnetic attractive forces arising from kinetic energy of conduction electrons in double-layer metallic nanowire arrays

The coupled-nanowire plasmatic resonances and very strong negative electromagnetic force between the double-layer metallic nanowire arrays is investigated theoretically. The negative electromagnetic force indicates attractive interaction between the metallic nanowires with the air-gap cavity local resonance effect. Plasmon resonances lead to extremely large localized ?eld, thereby resulting in large mutual coupling forces between the double-layer metallic nanowire arrays. The light coupling into metallic microcavity can stimulate collective electron oscillations of plasmatic resonance, and cause the contraction of the negative pressure in metallic cavity wall. The electromagnetic field of the plasmatic resonance mode is mainly localized inside the air-gap region between the two wires.     

A minimum single-band model for low-energy excitations in superconducting A x Fe2−y Se2

We investigate the coherent electronic transport properties of square-shaped zigzag graphene nanoconstrictions (ZGNC) under transverse strain using recursive Green’s function method. We find that the low-bias conductance of ZGNCs is monotonically dependent on the strain in contrast to that of zigzag graphene nanoribbons (ZGNRs), which is unaffected by strain. This result suggests that ZGNCs can be used as elementary building blocks in graphene nanomechanical system devices. In addition, a simplified analytical model is employed to qualitatively explain the strain tuning of the low-bias conductance of ZGNCs.     

Large-scale synthesis and growth habit of 3-D flower-like crystal of PbTe

In this paper, 3-D flower-like crystal of PbTe was successfully synthesized using Pb(CH₃COO)₂·3H₂O and Na₂TeO₃ as precursors under hydrothermal conditions, and characterized by means of scanning electron microscopy (SEM), transmission electron microscopy (TEM) and X-ray diffraction pattern (XRD). The reaction parameters that influenced the evolution of PbTe synthesis and morphology were investigated. It was shown that the flower-like crystal of PbTe was composed of a nucleus with eight pods. A possible growth mechanism was proposed based on the calculation of the surface energies of PbTe and the SEM observation. Furthermore, the temperature-dependent transport properties of 3-D flower-like crystal of PbTe specimen have been evaluated with an average thermoelectric power of 120 S cm^?1 and electrical conductivity of 220 μV K^?1 at 740 K.     

Comparison of the solutions from a novel variational method with numerical results for the study of beam propagation in a Kerr medium with nonlinear absorption

We present results from a novel variational method for the study of beam propagation in a Kerr medium with nonlinear absorption. This new method combines the variational method and a nonlinear absorption equation and gives a concise expression for the combination. The results obtained with this method show good quantitative agreement with numerical solutions obtained with the finite-difference method. It is shown that the variational method takes much less time than a numerical simulation with the finite-difference method for analysis of beam propagation in a thick medium with nonlinear absorption and nonlinear refraction. The new method makes detailed analysis of beam propagation in a Kerr medium with nonlinear absorption very simple and fast.     

Demixing of amphiphile–polymer mixtures investigated using density functional theory

We construct a functional for amphiphile–polymer mixtures and investigate the demixing transition by using a proposed version of density functional theory. It is found that increase of the amphiphilic size ratio and polymer length can effectively promote phase separation of the systems. Phase diagrams are plotted to clarify these influences. The results provide an effective way of controlling the stability of the fluid–fluid phase equilibrium of the mixtures.     

Superhydrophobic surfaces fabricated by microstructuring of stainless steel using a femtosecond laser

Fabrication of superhydrophobic surfaces induced by femtosecond laser is a research hotspot of superhydrophobic surface studies nowadays. We present a simple and easily-controlled method for fabricating stainless steel-based superhydrophobic surfaces. The method consists of microstructuring stainless steel surfaces by irradiating samples with femtosecond laser pulses and silanizing the surfaces. By low laser fluence, we fabricated typical laser-induced periodic surface structures (LIPSS) on the submicron level. The apparent contact angle (CA) on the surface is 150.3°. With laser fluence increasing, we fabricated periodic ripples and periodic cone-shaped spikes on the micron scale, both covered with LIPSS. The stainless steel-based surfaces with micro- and submicron double-scale structure have higher apparent CAs. On the surface of double-scale structure, the maximal apparent CA is 166.3° and at the same time, the sliding angle (SA) is 4.2°.