Factorization method and new potentials from the inverted oscillator

In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some special properties; in particular, only very specific second-order transformations produce non-singular real potentials. It will be shown that these transformations turn out to be the so-called complex ones. Moreover, we will study the factorization method applied to the inverted oscillator and the algebraic structure of the new Hamiltonians.     

The extended Hulburt–Hirschfelder‐long‐range oscillator model for direct‐potential‐fit analysis

In the present work, an extended Hulburt–Hirschfelder oscillator model is proposed as a means of simplifying potential energy functions for direct‐potential‐fit analyses. The new potential energy function is joined smoothly to the long‐range inverse‐power dispersion energy expression. The new model is employed in direct‐potential‐fits using spectroscopic line positions that involve the ground electronic states of the principal isotopologues of hydrogen iodide and carbon monoxide, and the ground and first singlet‐sigma excited states of hydrogen fluoride and hydrogen chloride. The present methodology is found to lead to compact, flexible, and robust representations for the potential energy that compare favorably with the results of past work where more complicated models were employed.     

Performance of ring oscillators composed of gate-all-around FETs with varying numbers of nanowire channels using TCAD simulation

In this paper, we investigate the performance of ring oscillators composed of gate-all-around (GAA) silicon nanowire (NW) field-effect transistors (FETs) with four different numbers of NW channels, for sub-10-nm logic applications. Our simulations reveal that ring oscillators with double, triple, and quadruple NW channels exhibit improvements of up to 50%, 85%, and 97%, respectively, in the oscillation frequencies (f_osc), compared to a ring oscillator with a single NW channel, due to the large drive current, in spite of the increased intrinsic capacitance of a given device. Moreover, our work shows that the f_osc improvement ratio of the ring oscillators becomes saturated with triple NW channels with additional load capacitances of 0.1 fF and 0.01 fF, which are similar to, or less than the intrinsic device capacitance (∼0.1 fF). Thus, our study provides an insight for determining the capacitive load and optimal number of NW channels, for device development and circuit design of GAA NW FETs.     

Interbasis expansions for isotropic harmonic oscillator

The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n.     

变形谐振子势的能谱方程

讨论了3种变形谐振子势:左右两边不同参数的谐振子势、左边方形势加右边谐振子势和谐振子势中间加δ势中的能量本征态函数.这些函数都可以由厄米函数表示.由波函数及其一次导数在原点的衔接条件,得到了能谱方程.     

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

Complete Moment Convergence for the Dependent Linear Processes with Random Coefficients

In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form     

差异化需求下考虑患者预约行为的医疗服务供需匹配方法

如何根据患者的差异化需求,撮合医生与患者双方形成合理有效的医疗服务供需匹配,是医疗服务运作管理中重要的研究问题。本文针对医疗服务中医生与患者的实际需求,提出了一种考虑患者预约行为的匹配决策方法。在该方法中,首先依据患者的预约行为及特征分类;然后,通过计算不同情形下医患双方的差异度,获得了医患双方的满意度矩阵;在此基础上,提出了匹配预约患者与医生的E-HR算法,并进一步构建了匹配剩余患者和医生的多目标优化模型,通过模型求解得到最优匹配结果;最后,通过算例说明了本文提出方法的可行性和实用性。     

Adsorption of Eu(III) on titanate nanotubes studied by a combination of batch and EXAFS technique

The effects of pH,contact time and natural organic ligands on radionuclide Eu(Ⅲ) adsorption and mechanism on titanate nanotubes(TNTs) are studied by a combination of batch and extended X-ray absorption fine structure(EXAFS) techniques.Macroscopic measurements show that the adsorption is ionic strength dependent at pH < 6.0,but ionic strength independent at pH > 6.0.The presence of humic acid(HA) /fulvic acid(FA) increases Eu(Ⅲ) adsorption on TNTs at low pH,but reduces Eu(Ⅲ) adsorption at high pH.The results of EXAFS analysis indicate that Eu(Ⅲ) adsorption on TNTs is dominated by outer-sphere surface complexation at pH < 6.0,whereas by inner-sphere surface complexation at pH > 6.0.At pH < 6.0,Eu(Ⅲ) consists of ～ 9 O atoms at REu?O ≈ 2.40  in the first coordination sphere,and a decrease in NEu-O with increasing pH indicates the introduction of more asymmetry in the first sphere of adsorbed Eu(Ⅲ).At long contact time or high pH values,the Eu(Ⅲ) consists of ～2 Eu at REu-Eu ≈ 3.60  and ～ 1 Ti at REu-Ti ≈ 4.40 ,indicating the formation of inner-sphere surface complexation,surface precipitation or surface polymers.Surface adsorbed HA/FA on TNTs modifies the species of adsorbed Eu(Ⅲ) as well as the local atomic structures of adsorbed Eu(Ⅲ) on HA/FA-TNT hybrids.Adsorbed Eu(Ⅲ) on HA/FA-TNT hybrids forms both ligand-bridging ternary surface complexes(Eu-HA/FA-TNTs) as well as surface complexes in which Eu(Ⅲ) remains directly bound to TNT surface hydroxyl groups(i.e.,binary Eu-TNTs or Eu-bridging ternary surface complexes(HA/FA-Eu-TNTs)).The findings in this work are important to describe Eu(Ⅲ) interaction with nanomaterials at molecular level and will help to improve the understanding of Eu(Ⅲ) physicochemical behavior in the natural environment.     

Interaction of modulated pulses in nonlinear oscillator chains

We formally derive and rigorously justify the modulation equations of lowest order for the interaction of two modulated pulses on a one-dimensional nonlinear oscillator chain. We show that solutions with the initial form of the assumed ansatz preserve this form over time intervals with positive macroscopic length, and we show a bound on the possible shift of the envelope caused by the interaction. Thus, we rigorously justify and quantify the statement that under the given conditions there is almost no interaction of the modulated pulses.