Mixed Solutions in the Wronskian Form for a Nonisospectral Equation

N-soliton solutions in the Wronskian form for the KdV equation with loss and nonuniformity terms were obtained. New rational-like solutions and mixed solutions were further derived. All these solutions were verified by direct substitutions into bilinear equation.

The Interaction and Degeneracy of Mixed Solutions for Derivative Nonlinear Schrodinger Equation

The mixed solutions of the derivative nonlinear Schrödinger equation from the trivial seed (zero solution) are derived by using the determinant representation. By adjusting the interaction and degeneracy of mixed solutions, it is possible to obtain different types of solutions: phase solutions, breather solutions, phase-breather solutions and rogue waves.

Dynamic behaviors of the lump solutions and mixed solutions to a(2+1)-dimensional nonlinear model

In this paper,we propose a combined form of the bilinear Kadomtsev-Petviashvili equation and the bilinear extended(2+1)-dimensional shallow water wave equation,which is linked with a novel(2+1)-dimensional nonlinear model.This model might be applied to describe the evolution of nonlinear waves in the ocean.Under the effect of a novel combination of nonlinearity and dispersion terms,two cases of lump solutions to the(2+1)-dimensional nonlinear model are derived by searching for the quadratic function solutions to the bilinear form.Moreover,the one-lump-multi-stripe solutions are constructed by the test function combining quadratic functions and multiple exponential functions.The one-lump-multi-soliton solutions are derived by the test function combining quadratic functions and multiple hyperbolic cosine functions.Dynamic behaviors of the lump solutions and mixed solutions are analyzed via numerical simulation.The result is of importance to provide efficient expressions to model nonlinear waves and explain some interaction mechanism of nonlinear waves in physics.

Superposition formulas of multi-solution to a reduced(3+1)-dimensional nonlinear evolution equation

We gave the localized solutions,the interaction solutions and the mixed solutions to a reduced(3+1)-dimensional nonlinear evolution equation.These solutions were characterized by superposition formulas of positive quadratic functions,the exponential and hyperbolic functions.According to the known lump solution in the outset,we obtained the superposition formulas of positive quadratic functions by plausible reasoning.Next,we constructed the interaction solutions between the localized solutions and the exponential function solutions with the similar theory.These two kinds of solutions contained superposition formulas of positive quadratic functions,which were turned into general ternary quadratic functions,the coefficients of which were all rational operation of vector inner product.Then we obtained linear superposition formulas of exponential and hyperbolic function solutions.Finally,for aforementioned various solutions,their dynamic properties were showed by choosing specific values for parameters.From concrete plots,we observed wave characteristics of three kinds of solutions.Especially,we could observe distinct generation and separation situations when the localized wave and the stripe wave interacted at different time points.

Modification of FGD gypsum in hydrothermal mixed salt solution

A novel utilization way of the sludge from wet calcium-based flue gas desulfurization （FGD） processes has been developed in this paper. This study focused on the conversion of the FGD gypsum into α-hemihydrate calcium sulfate by a hydrothermal salt solution method at atmospheric pressure. Experimental study has been carried out in a batch reactor. Qualitative and quantitative analyses were made by DSC/TG thermal analysis, SEM, XRD, metalloscope and chemical analysis. The experimental results showed that the modification of FGD gypsum was controlled by the dissolution and recrystallization mechanisms. With the introduction of FGD gypsum the salt solution was supersaturated, then crystal nucleus of α-hemihydrate calcium sulfate were produced in the solution. With the submicroscopic structure of FGD gypsum crystal changed, the crystal nucleus grew up into α-hemihydrate calcium sulfate crystals. Thus ,the modification of FGD gypsum was fulfilled.

Bright-Dark Mixed N-Soliton Solution of the Two-Dimensional Maccari System

The general bright-dark mixed N-soliton solution of the two-dimensional Maccari system is obtained with the KP hierarchy reduction method. The dynamics of single and two solitons are discussed in detail. Asymptotic analysis shows that two solitons undergo elastic collision accompanied by a position shift. Furthermore, our analysis on mixed soliton bound states shows that arbitrary higher-order soliton bound states can take place.

Fabrication of homogeneously dispersed graphene/Al composites by solution mixing and powder metallurgy

Graphene-reinforced aluminum （AI） matrix composites were successfully prepared via solution mixing and powder metallurgy in this study. The mechanical properties of the composites were studied using microhardness and tensile tests. Compared to the pure Al alloy, the graphene/Al composites showed increased strength and hardness. A tensile strength of 255 MPa was achieved for the graphene/Al com- posite with only 0.3wt% graphene, which has a 25% increase over the tensile strength of the pure Al matrix. Raman spectroscopy, Fourier transform infrared spectroscopy, scanning electron microscopy, and transmission electron microscopy were used to investigate the morphol- ogies, chemical compositions, and microstructures of the graphene and the graphene/A1 composites. On the basis of fractographic evidence, a relevant fracture mechanism is proposed.

ON THE EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE NAVIER－STOKES EQUATIONS

In this paper we discuss the mixed boundary problem (1)-(3) of the NavierStokes equations for the flow of an incompressible viscous fluid in a bounded domain. we prove that when g,and,there exists a weak solution of (1)-(3),and when u,the weak solution is unique,if it exists.

Solution for Energies and Mixing of Two 0^+ States in ^(10)He

Using results from various reactions that populate 10He, I conclude that the ground state has E2n = 1.07（7） MeV and the excited 0＋ state is in the region of 2.1-3.1 MeV. The amount of the （sd）2 component in the ground state is less than about 0.075.

Simple Preparation, Structure and Conductivity of Nickel(Ⅱ) Benzenetricarboxylate Ni_3(BTC)_2·12H_2O

Proton-conductive crystalline metal-organic framework nickel（Ⅱ） benzenetricar- boxylate Ni3（BTC）2A12H2O（MOF-Ni） was prepared by the reaction of nickel（Ⅱ） nitrate and 1,3,5- benzenetricarboxylic（BTC） acid in a mixed solvent of N,N-dimethylformamide（DMF）/C2H5OH/ H2O （1：1：1, ν/ν） at low temperature and short reaction time. It was characterized by thermo- gravimetric analyses （TG）, FT-IR and N2 adsorption-desorption. Single-crystal X-ray diffraction analysis indicated that the complex belongs to monoclinic system, space group C2 with α = 17.407（6）, b = 12.878（5）, c = 6.542（2） A, β = 112.07°, V = 1359.0（8） A^3, Dc = 1.971 g/cm3, μ = 2.166 mm^-1 and Z = 2. Linear polarization resistance （LPR） analysis showed that the complex possesses semiconducting properties.

Dynamical rational solutions and their interaction phenomena for an extended nonlinear equation

In this paper,we analyze the extended Bogoyavlenskii-Kadomtsev-Petviashvili(eBKP)equation utilizing the condensed Hirota's approach.In accordance with a logarithmic derivative transform,we produce solutions for single,double,and triple M-lump waves.Additionally,we investigate the interaction solutions of a single M-lump with a single soliton,a single M-lump with a double soliton,and a double M-lump with a single soliton.Furthermore,we create sophisticated single,double,and triple complex soliton wave solutions.The extended Bogoyavlenskii-Kadomtsev-Petviashvili equation describes nonlinear wave phenomena in fluid mechanics,plasma,and shallow water theory.By selecting appropriate values for the related free parameters we also create three-dimensional surfaces and associated counter plots to simulate the dynamical characteristics of the solutions offered.

Determining osmotic suction through electrical conductivity for unsaturated low-plasticity soils

Determining osmotic suction from the electrical conductivity(EC)of soil pore water was widely reported in the literature.However,while dealing with unsaturated soils,they do not have enough soil pore water to be extracted for a reliable measurement of EC.In this paper,the chilled-mirror dew-point hygrometer and contact filter paper method were used to determine the total and matric suctions for low-plasticity soils with different salinities(0.05‰,2.1‰,and 6.76‰).A new piecewise function was proposed to calculate the osmotic suction,with the piecewise point corresponding to the first occurrence of precipitated salt in mixed salt solutions(synthetic seawater).EC,ion and salt concentrations used for osmotic suction calculation were transformed from the established relationships of mixed salt solution instead of experimental measurement.The calculated osmotic suction by the proposed equation and the equations in the literature was compared with the indirectly measured one(the difference between the measured total and matric suctions).Results showed that the calculated osmotic suction,especially the one calculated using the proposed function,was in fair agreement with the indirectly measured data(especially for specimens with higher salinity of 6.76‰),suggesting that the transformation of EC and concentrations from the established relationship is a good alternative to direct measurement for lowplasticity soil.In particular,the proposed method could be applied to unsaturated low-plasticity soils which do not have enough soil pore water for a proper EC measurement.

Mixing of two different electrolyte solutions in electromagnetic rectangular mixers

This study proposes a new electromagnetic rectangular mixer, and numerically examines the mixing characteristics of two different electrolyte solutions in the device under a uniform magnetic field. The mixer consists of a conduit with electrodes equipped on its top and bottom walls. The difference in the electric potentials applied to the sets of electrodes induces the current. The combination of the induced current and magnetic field yields Lorentz force, resulting in the fluid motion for pumping and mixing of the two different fluids. The numerical simulation is carried out with the use of commercial software CFX. The present numerical model is validated by an existing numerical work. The effect of different variables on mixing efficiency is investigated in many different cases with two different heights of the duct and various input voltages of the electrodes. The current simulation results indicate that the mixing performance can be enhanced by using multiple sets of electrodes and applying higher input voltages（absolute values） to the electrodes.

Exact solutions of the nonlocal Gerdjikov-Ivanov equation

The nonlocal nonlinear Gerdjikov-Ivanov(GI)equation is one of the most important integrable equations,which can be reduced from the third generic deformation of the derivative nonlinear Schr?dinger equation.The Darboux transformation is a successful method in solving many nonlocal equations with the help of symbolic computation.As applications,we obtain the bright-dark soliton,breather,rogue wave,kink,W-shaped soliton and periodic solutions of the nonlocal GI equation by constructing its 2 n-fold Darboux transformation.These solutions show rich wave structures for selections of different parameters.In all these instances we practically show that these solutions have different properties than the ones for local case.