Effect of quantization and positron concentration on shielding potentials in electron-positron-ion plasma

The kinetic theory of plasma has been employed to compute the test-charge potential distributions accounting for quantization effects in magnetized electron-positron-ion (EPI) plasmas. In this regard, the degenerate positrons and electrons are assumed to follow the Fermi-Dirac distribution, while inertial ions are modelled by Maxwellian velocity distribution. By solving the Fourier-transformed Vlasov–Poisson equations, a modified dielectric function and electrostatic potential is obtained. By imposing various constraints on the test-charge speed, the potential profile has been analysed in terms of Debye–Hückel (DH), far-field (FF), and wake-field (WF) potentials. It has been found that the amplitude of DH and FF potentials increases by the inclusion of quantization effects, and it becomes the opposite for the WF potential profile. Furthermore, the variation of positron concentration significantly affects the DH, FF, and WF potentials. The present findings are important to understand the shielding phenomenon in degenerate multi-species plasmas.     

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.     

A Hybrid Method Based on Extreme Learning Machine and Wavelet Transform Denoising for Stock Prediction

The trend prediction of the stock is a main challenge. Accidental factors often lead to short-term sharp fluctuations in stock markets, deviating from the original normal trend. The short-term fluctuation of stock price has high noise, which is not conducive to the prediction of stock trends. Therefore, we used discrete wavelet transform (DWT)-based denoising to denoise stock data. Denoising the stock data assisted us to eliminate the influences of short-term random events on the continuous trend of the stock. The denoised data showed more stable trend characteristics and smoothness. Extreme learning machine (ELM) is one of the effective training algorithms for fully connected single-hidden-layer feedforward neural networks (SLFNs), which possesses the advantages of fast convergence, unique results, and it does not converge to a local minimum. Therefore, this paper proposed a combination of ELM- and DWT-based denoising to predict the trend of stocks. The proposed method was used to predict the trend of 400 stocks in China. The prediction results of the proposed method are a good proof of the efficacy of DWT-based denoising for stock trends, and showed an excellent performance compared to 12 machine learning algorithms (e.g., recurrent neural network (RNN) and long short-term memory (LSTM)).     

An Analytical Technique,Based on Natural Transform to Solve Fractional-Order Parabolic Equations

This research article is dedicated to solving fractional-order parabolic equations using an innovative analytical technique. The Adomian decomposition method is well supported by natural transform to establish closed form solutions for targeted problems. The procedure is simple, attractive and is preferred over other methods because it provides a closed form solution for the given problems. The solution graphs are plotted for both integer and fractional-order, which shows that the obtained results are in good contact with the exact solution of the problems. It is also observed that the solution of fractional-order problems are convergent to the solution of integer-order problem. In conclusion, the current technique is an accurate and straightforward approximate method that can be applied to solve other fractional-order partial differential equations.     

基于分数阶傅里叶变换的模式测控一体化方法

提出了一种基于分数阶傅里叶变换的模式测控一体化方法。利用分数阶傅里叶变换光路对光纤模式耦合态进行空间调制和相位调制,以实现模式的有效分解。与双重傅里叶变换（F²）法以及空间和频谱成像（S²）法相比,采用的分数阶傅里叶变换法,通过改变分数阶参数,控制模式的空间分布以及模式间的叠加状态,更易于分解出高阶模式。基于分数阶傅里叶变换的模式测量方法可在更广泛空间,研究模式的空间和相位叠加以及模式分解,也可退化为F²法和S²法。     

The equation-transform model for Dirac–Morse problem including Coulomb tensor interaction

The approximate solutions of Dirac equation with Morse potential in the presence of Coulomb-like tensor potential are obtained by using Laplace transform (LT) approach. The energy eigenvalue equation of the Dirac particles is found and some numerical results are obtained. By using convolution integral, the corresponding radial wave functions are presented in terms of confluent hypergeometric functions.     

Simple model for blistering mechanism

A simple model for blistering mechanism is proposed for energies higher than 20 keV. The model assumes that through the nucleation of smaller bubbles, a critical bubble radius is reached. The planar stress results of Jeffery for a semi-infinite plate with a circular hole subject to a uniform inner normal pressure are roughly taken as valid for the three-dimensional case. Under this assumption, the thickness of the blister's cover and critical ion dose for blister formation are calculated from the knowledge of the mean projected range of ions and blister diameter taken from experimental results. The resulting values are in agreement with the experimental values reported. The model can qualitatively explain breakage at the top of the dome-shaped blisters observed in molybdenum at 1100 K.     

Effect of Temperature and Comonomer Content on Thermal Behavior and Crystallization Property of the Propylene–Ethylene Random Copolymers

The effects of ethylene units content and crystallization temperature on the conformations, and the thermal and crystallization behavior were investigated by a combination of Fourier transform infrared (FTIR) spectroscopy, wide angle X-ray diffraction (WAXD), and differential scanning calorimetry (DSC). The characterization of FTIR spectroscopy proves that the longer helical conformation sequences of the propylene–ethylene random (PER) samples decrease, whereas the shorter helical conformation sequences increase with the increase in ethylene units content. The increase of the shorter helical conformation sequences is favorable for the formation of the γ-phase in the crystals. A group of broad endothermic peaks can be seen clearly in the DSC curves of PER copolymers, which may be associated with the melting of mixtures of the α- and γ-forms in the crystals. The melting point, crystallization temperature, and crystallinity degree of the PER copolymers decrease with the increase in ethylene units contents. Three typical melting peaks of the PER copolymers crystallized isothermally between 80°C and 130°C were observed. The two higher melting peaks result from melting of the α- and γ-phase in the crystals, whereas the materials crystallized on quenching give the lowest peak. The WAXD results confirm that the PER copolymers crystallize from the melt, as mixtures of α and γ forms, in a wide temperature range. The critical number ζ_lim of the crystallizable units for the α-form increases with the increase in crystallization temperature for PER copolymers, which is favorable for the formation of the γ phases. The amount of γ-form increases with the increase in crystallization temperature at the expense of its α component, then reaches a maximum value at the crystallization temperature of 115°C, and finally decreases with further increase in the crystallization temperature.     

Ftir Studies on LB Film of Amphiphile with Schiff Base as Headgroup and Its Copper Complex

Two different ways to form monolayers and LB films (surface film and subphase film) of the complex have been used, where a novel amphiphile containing Schiff base as a headgroup was used as a ligand. the monolayer behavior at the air/water interface was characterized by π-A isotherms and two-dimensional molecular orientation of alkyl chains in LB films and thermal stability were measured by polarized and variable temperature FTIR transmission spectra, indicating that the LB film of the novel amphiphile and its copper(II) complex are very stable as well as stearic acid. Because incorporating the metal ion into the monolayer makes it more condensed, thermal stability of the LB film was enhanced. as can be compared from their structure and properties, subphase films are superior to surface films.     

Image denoising using trivariate prior model in nonsubsampled dual-tree complex contourlet transform domain and non-local means filter in spatial domain

Image denoising is always the basic problem of image processing, and the main challenge is how to effectively remove the noise and preserve the detailed information. This paper presents a new image denoising algorithm based on the combination of trivariate prior model in nonsubsampled dual-tree complex contourlet transformlet transform (NSDTCT) domain and non-local means filter (NLMF) in spatial domain. Firstly, NSDTCT is constructed by combining the dual-tree complex wavelet transform (DTCWT) and nonsubsampled directional filter banks (NSDFB). The noisy image is decomposed by using NSDTCT. Secondly, based on the correlation between the interscale and intrascale dependencies of NSDTCT coefficients, the distribution of the high frequency coefficients is modeled with the trivariate non-Gaussian distribution model. A nonlinear trivariate shrinkage function is derived in the framework of Bayesian theory, and then the denoised coefficients are obtained and inverse NSDTCT is performed to get the initial denoised image. Finally, NLMF is used to smooth the initial denoised image. Simulation experiment shows that our algorithm can obtain better performances than those outstanding denoising algorithms in terms of peak signal-to-noise ratio (PSNR), mean structural similarity (MSSIM) as well as visual quality.