An integrable semi-discrete equation and combinatorial numbers with their combinatorial interpretations

A Hankel type determinant solution for an integrable semi-discrete equation is presented. As an application, the relations between the solution and combinatorial numbers are discussed, which lead to new combinatorial numbers. The so-called Motzkin-like numbers are obtained, and the corresponding combinatorial interpretation is given. Additionally, it is also shown that some lattice paths have connections with the special solution.     

Volt-ampere characteristics of a nitrogen DC plasma arc with anode melting

The characteristics of a nitrogen arc using a graphite cathode and a melting anode in a pilot-scale plasma furnace are investigated. The voltage is examined as a function of current and apparent plasma length. The voltage increases non-linearly with the increase of apparent plasma length, with the current fixed. The experimental data so obtained are compared with the predictions of the Bowman model for the electric arc, and with numerical simulations as well. The level of agreement between the experimental data at the melting anode and the numerical predictions confirms the suitability of the proposed the Bowman model. These characteristics are relevant to the engineering design and evaluation of a DC plasma furnace and reactor for the treatment of hazardous fly ash waste.     

Novel Wronskian Condition and New Exact Solutions to a （3＋1）-Dimensional Generalized KP Equation

Utilizing the Wronskian technique, a combined Wronskian condition is established for a （3＋1）-dimensional generalized KP equation. The generating functions for matrix entries satisfy a linear system of new partial differential equations. Moreover, as applications, examples of Wronskian determinant solutions, including N-soliton solutions, periodic solutions and rational solutions, are computed.     

Dependence of the Intensity of the Spectral Lines and the Composition of the Sample and the Plasma Parameters of the Unipolar Arc

The investigation was made of the dependence of the intensity of Tl, Ga, Mo, Mg, Mn, Sn, Bi, Ni, Zn, Pt and Au spectral lines and the plasma parameters (temperature T, electron concentration n_e, degree of 6 ionnization α) from concentration of lithium additive.     

Exclusion sets in eigenvalue localization sets for tensors

ABSTRACT

By excluding some proper subsets, which do not include any eigenvalues of tensors, from an existing eigenvalue localization set provided by Zhao and Sang, a new eigenvalue localization set for tensors is given. As an application, a sufficient condition such that the determinant of a tensor is not zero is provided.     

A note on determinants,minors and a boundary map

We give an explicit formula for the first non-trivial boundary map of the Akin–Buchsbaum–Weyman resolution (Schur functors and Schur complexes, Adv. Math 1982;44:207-278). The role of the Laplace expansion formula is emphasized.     

Wronskian and Grammian Determinant Solutions for a Variable-Coefficient Kadomtsev-Petviashvili Equation

In this paper, we derive the bilinear form for a variable-coefficient Kadomtsev Petviashvili-typed equation. Based on the bilinear form, we obtain the Wronskian determinant solution, which is proved to be indeed an exact solution of this equation through the Wronskian technique. In addition, we testify that this equation can be reduced to a Jacobi identity by considering its solution as a Grammian determinant by means of Pfaffian derivative formulae.     

Photocatalysts of Cr Doped TiO2 Film Prepared by Micro Arc Oxidation

通过微弧氧化法在Na3PO4+K2Cr2O7电解液中制备了系列铬掺杂二氧化钛薄膜. X射线和扫描电镜显示薄膜的主要晶相为锐钛矿型二氧化钛,且表面为多孔结构. 在可见光照射下,薄膜对降解亚甲基蓝和分解水有着较好的光催化性能,这主要是由铬的掺杂引起的.由于铬的掺杂,一方面在二氧化钛中形成了Cr3+/Cr4+离子对,另一方面在带隙中形成了氧的空位能级. 前者降低了电子-空穴的复合几率,而后者在二氧化钛的禁带中形成了新的能级. 新能级的形成使得由二氧化钛价带跃迁至氧空位能级所需的光子能量减少. 另外探讨了微弧氧化形成掺杂二氧化钛薄膜的机制.     

Mercury arc lamp based super-resolution imaging with conventional fluorescence microscopes

We present an implementation of localization based three-dimensional super-resolution imaging on a regular microscope. We retain the original arc lamp as the photoactivation light source, and incorporate an inexpensive diode laser for imaging. As alterations to the standard microscope is minimal, this optical setup can be easily adapted in a typical research laboratory and even undergraduate teaching experiments, providing an inexpensive system for students and research scientists who require such super resolution capabilities. With this simple design, a spatial resolution of better than 40 nm at a reasonable frame rate has been achieved, adequate for most routine applications.