The Regularity of Solutions to Mixed Boundary Value Problems of Second-Order Elliptic Equations with Small Angles

This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.

Iterative Solution for Systems of Binary Non-mixed Monotone Operator Equations

With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.

Uncertainty Evaluation of Preparation of Organophosphorus Pesticide Mixed Standard Solution

The uncertainty of standard solution plays an important role in detection of pesticide residues. It may affect the accuracy of detection results. In this study, the 14 organophosphorus pesticides mixed standard solution was used as the material to analyze all the influencing factors for the preparation of mixed standard solution with uncertainty as the only judging index. The preparation uncertainty of mixed standard solution was calculated with the top-down calculation method. In the end, the expanded uncertainty was presented. The results showed that the preparation of mixed standard solution from stock solution with precise pipettes had a relatively low uncertainty.

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.

Mixed rare earth concentrate leaching with HCl-AlCl_3 solution

Abstract A method of Baotou mixed rare earth concen- trate leaching was investigated. According to the principle of complex leaching, the quadratic orthogonal regression experiment was used to investigate effect of six factors. An optimal condition of low energy and environment friendly was determined as follows： HCl acidity is 4 mol.L-1, AlCl3 concentration is 2 mol.L-l, reaction temperature is 85 ℃, reaction time is 90 rain, liquid to solid ratio is 35 ml.g-1, and stirring speed is 100 r.min-1. According to this condition, the leaching ratio of mixed rare earth con- centrate is 76.5 %. The analyses of X-ray diffraction shows that bastnasite disappears, and the main peaks of filter residue is monazite and cheralite after leaching of HCl- AlCl3 solution. The result indicates that REFCO3 of the mixed rare earth concentrate can be dissolved, but REPO4 remains in the leaching residue. This method provides a way to separate and extract rare earth.

TBM tunneling in mixed-face ground: Problems and solutions

Mixed-face ground encountered in Tunnel Boring Machine(TBM) tunneling presents great challenges and may trigger potential hazards without warning. A detailed understanding of such unfavorable conditions is therefore critical to a successful bored tunnel. In this paper, we firstly present a brief review of the definition, classification and the factors related to mixed-face conditions. Secondly, for a better understanding of this topic, we investigate the main difficulties and problems involved in TBM tunnelling under mixed-face ground with detailed cases. Thirdly, from the viewpoint of rock-machine interaction, we give some suggestions on the corresponding mitigation measurements from three categories:(i) selection of TBM type and modification of TBM,(ii) condition of ground and(iii) optimization of TBM operation.

Periodic Solutions of Mixed Type p-Laplacian Equations with Deviating Arguments

Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,which are complement of previously known results.

GLOBAL EXISTENCE OF WEAKLY DISCONTINUOUS SOLUTIONS TO A KIND OF MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS

In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {（t, x） ｜ t ≥ 0, x ≥0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.

WEIGHTED PSEUDO ALMOST-PERIODIC SOLUTIONS OF SHUNTING INHIBITORY CELLULAR NEURAL NETWORKS WITH MIXED DELAYS

In this paper, we prove the existence and the global exponential stability of the unique weighted pseudo almost-periodic solution of shunting inhibitory cellular neural networks with mixed time-varying delays comprising different discrete and distributed time delays. Some sufficient conditions are given for the existence and the global exponential stability of the weighted pseudo almost-periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper complement the previously known ones. Finally, an illustrative example is given to demonstrate the effectiveness of our results.

Prediction of Water Activity for Mixed Aqueous Solutions from the Data of Their Binary Constituent Solutions

The equation of Patwardhan and Kumar for water activities of mixed electrolyte solutions is extended to aqueous solutions containing non-electrolytes. This equation and the linear isopiestic relation are used to predict water activities of 56 ternary aqueous solutions in terms of the data of their binary subsystems. Both equation of Patwardhan and Kumar and the linear isopiestic relation can provide good predictions for water activities of the present 40 electrolyte solutions, and the linear isopiestic relation generally yields better predictions. The predictions of the extended equation of Patwardhan and Kumar and the linear isopiestic relation are in general quite reasonable for the present 8 ternary solutions of electrolytes and non-electrolytes, and the results of the linear isopiestic relation are usually better. The predictions of these two methods generally agree well with the experimental data for the 8 non-electrolyte mixtures being studied, and the linear isopiestic relation is better.

Self-Similar Solution of Heat and Mass Transfer of Unsteady Mixed Convection Flow on a Rotating Cone Embedded in a Porous Medium Saturated with a Rotating Fluid

A self-similar solution of unsteady mixed convection flow on a rotating cone embedded in a porous medium saturated with a rotating fluid in the presence of the first and second orders resistances has been obtained. It has been shown that a self-similar solution is possible when the free stream angular velocity and the angular velocity of the cone vary inversely as a linear function of time. The system of ordinary differential equations governing the flow has been solved numerically using an implicit finite difference scheme in combination with the quasi-linearization technique. Both prescribe wall temperature and prescribed heat flux conditions are considered. Numerical results are reported for the skin friction coefficients, Nusselt number and Sherwood number. The effect of various parameters on the velocity, temperature and concentration profiles are also presented here.

Sparse Solutions of Mixed Complementarity Problems

In this paper, we consider an extragradient thresholding algorithm for finding the sparse solution of mixed complementarity problems (MCPs). We establish a relaxation l1 regularized projection minimization model for the original problem and design an extragradient thresholding algorithm (ETA) to solve the regularized model. Furthermore, we prove that any cluster point of the sequence generated by ETA is a solution of MCP. Finally, numerical experiments show that the ETA algorithm can effectively solve the l1 regularized projection minimization model and obtain the sparse solution of the mixed complementarity problem.

EXISTENCE OF MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS WITH MIXED BOUNDARY CONDITIONS

The paper is concerned with the multiplicity of solutions for some nonlinear elliptic equations involving critical Sobolev exponents and mixed boundary conditions.

THE EXISTENCE OF PERIODIC SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS OF MIXED TYPE

The existence of periodic solutions for a class of impulsive differential equations of mixed type is studied by constructing periodic sequence solutions of difference equations.

Construction of solitonary and periodic solutions to some nonlinear equations using EXP-function method

This paper applies the EXP-function method to find exact solutions of various nonlinear equations. Tzitzeica- Dodd-Bullough (TDB) equation was selected to illustrate the effectiveness and convenience of the suggested method. More generalized solitonary solutions with free parameters were obtained by suitable choice of the free parameters, and also the obtained solitonary solutions can be converted into periodic solutions.

Dual solutions in mixed convection with variable physical properties

Assisting and opposing flows in a mixed convection boundary layer flow over an isothermal vertical plate are studied for the case of variable physical properties and uniform free stream.Fluid viscosity and thermal conductivity are assumed to be linear functions of temperature.Using local similarity the flow and heat transfer quantities are found to be functions of four parameters,i.e. Richardson number,Prandtl number,a viscosity variation parameter and a thermal conductivity variation parameter.Numerical solutions are obtained by two methods,a shooting technique and Nachtsheim-Swigert technique,for selected values of parameters appropriate for the fluids considered and specific temperatures of the plate and ambient fluid.For assisting flows,there exist solutions for all values of Richardson number while for opposing flows solutions exist only for a finite set of its values and,in addition,there also exist dual solutions.Important flow and heat transfer quantities of practical interest are determined and the influence of different parameters is discussed.

Positive Periodic Solutions for Three Species Lotka-Volterra Mixed Ecosystems with Periodic Stocking

By using a new method, a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for three\|species Lotka\|Volterra mixed systems with periodic stocking:x 1′(t)=x 1(t)(b 1(t)-a 11 (t)x 1(t)-a 12 (t)x 2(t)-a 13 (t)x 3(t))+S 1(t) x 2′(t)=x 2(t)(-b 2(t)+a 21 (t)x 1(t)-a 22 (t)x 2(t)-a 23 (t)x 3(t))+S 2(t) x 3′(t)=x 3(t)(-b 3(t)+a 31 (t)x 1(t)-a 32 (t)x 2(t)-a 33 (t)x 3(t))+S 3(t)where b i(t),a ij (t)(i,j=1,2,3) are positive continuous T \|periodic functions, S i(t)(i=1,2,3) are nonnegative continuous T \|periodic functions.

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.

Existence and Exponential Stability of the Anti-Periodic Solutions for a Class of Impulsive CohenGrossberg Neural Networks with Mixed Delays

In this paper,we study the anti-periodic solutions for a class of impulsive Cohen-Grossberg neural networks with mixed delays.By using analysis techniques,some sufficient conditions are obtained which guarantee the existence and global exponential stability of the anti-periodic solutions.The criteria extend and improve some earlier results.Moreover,we give an examples to illustrate our main results.

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.