Nonsingle-valley Continuous Solutions of p-order Feigenbaum's Functional Equation

The author considers the Feigenbaum's functional equation fp(λx) = λf(x) for each p > 2. The existence of nonsingle-valley continuous solutions to this equation is discussed and a feasible method to construct such solutions is given.

Continuous Dependence of Bounded Φ-Variation Solutions on Parameters for Kurzweil Equations

The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results are essential generalizations of continuous dependence of bounded variation solutions on parameters for Kurzweil equations.

Continuous Dependence of Bounded Φ-variation Solutions on Parameter for a Class of Discontinuous Systems

The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded D-variation solutions on parameter for a class of discontinuous systems on the base of D-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems.

L^P SOLUTION OF GENERAL MEAN-FIELD BSDES WITH CONTINUOUS COEFFICIENTS

In this paper we consider one dimensional mean-field backward stochastic differential equations(BSDEs)under weak assumptions on the coefficient.Unlike[3],the generator of our mean-field BSDEs depends not only on the solution(Y,Z)but also on the law PY of Y.The first part of the paper is devoted to the existence and uniqueness of solutions in Lp,1<p≤2,where the monotonicity conditions are satisfied.Next,we show that if the generator/is uniformly continuous in(μ,y,z),uniformly with respect to(t,ω) and if the terminal valueξbelongs to Lp(Ω,F,P)with 1<p≤2,the mean-field BSDE has a unique Lp solution.

CONTINUOUS THERMODYNAMICS FOR POLYMER SOLUTIONS II . LATTICE FLUID MODEL

Using lattice-fluid model, a continuous thermodynamic framework is presented for phase-equilibrium calculations for binary solutions with a polydisperse polymer solute. A two-step process is designed to form a real polymer solution containing a solvent and a polydisperse polymer solute occupying a volume at fixed temperature and pressure. In the first step, close-packed pure components including solvent and polymers with different molar masses or different chain lengths are mixed to form a closed-packed polymer solution. In the second step, the close-packed mixture, considered to be a pseudo-pure substance is mixed with holes to form a real polymer solution with a volume dependent on temperature and pressure. Revised Freed's model developed previously is adopted for both steps. Besides pure-component parameters, a binary size parameter cr and a binary energy parameter e12 are used. They are all temperature dependent. The discrete-multicomponent approach is adopted to derive expressions for chemical potentials, spinodals and critical points. The continuous distribution function is then used in calculations of moments occurring in those expressions. Computation procedures are established for cloud-point-curve, shadow-curve, spinodal and critical-point calculations using standard distribution or arbitrary distribution on molar mass or on chain length. Illustrative examples are also presented.

CONTINUOUS THERMODYNAMICS FOR POLYMER SOLUTIONS I.CLOSE-PACKED LATTICE MODEL

using close-packed lattice models,a continuous thermodynamic framework is presented forphase-equilibrium calculations for binary solutions with a polydisperse polymer solute.An expressionfor the Helmholtz function of mixing is based on the revised Freed model developed previously.Asize parameter c_r and an energy parameter ε are used;the former can be temperature dependent,while the latter can depend on both temperature and chain-length of the polymer.The discretemulticomponent approach is adopted to derive expressions for chemical potentials,spinodals and criti-cal points.The continuous distribution function is then used in calculations of moments occurring inthose expressions.Computation programs are established for cloud-point-curve,shadow-curve,spinodal and critical-point calculations for polymer solutions with standard distribution or arbitrarydistribution of polymer.In the latter case,the derivative method developed previously is applied.lllustrations for phase-equilibrium calculations are

EXACT SOLUTION FOR LAMINATED CONTINUOUSOPEN CYLINDRICAL SHELLS

Discarding any assumption about displacement models and stress distribution andintroducing δ-function into the present study, we established the state equation for thecontinuous orthotropic open cylindrical shells. An thentical exocl solution is presentedfor the statics of thin. moderately thick and thick laminated continuous openrylindrical shells. Numerical results are obtained and compared with those calculatedusing SAP5.

PIECEWISE CONTINUOUS SOLUTIONS OF INITIAL VALUE PROBLEMS OF SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS

Results on the existence of piecewise continuous solutions for two classes of initial value problems of impulsive singular fractional differential equations are obtained.

HLDER CONTINUOUS SOLUTIONS OF BOUSSINESQ EQUATIONS

We show the existence of dissipative Hhlder continuous solutions of the Boussi- nesq equations. More precise, for anyβ∈ （0, 1/5）, a time interval [0, T] and any given smooth energy profile e ： [0, T] → （0, ∞）, there exist a weak solution （v, θ） of the 3d Boussinesq equations such that （v, 8） ∈ Cβ（T3 × [0, T]） with e（t） = ∫T3 ｜v（x, t）｜2dx for all t ∈ [0, T]. This extend the result of [2] about Onsager＇s conjecture into Boussinesq equation and improve our previous result in [30].

A New One-Twelfth Step Continuous Block Method for the Solution of Modeled Problems of Ordinary Differential Equations

In this paper, we developed a new continuous block method by the method of interpolation and collocation to derive new scheme. We adopted the use of power series as a basis function for approximate solution. We evaluated at off grid points to get a continuous hybrid multistep method. The continuous hybrid multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected points to yield a discrete block method. The basic properties of the block method were investigated and found to be consistent, zero stable and convergent. The results were found to compete favorably with the existing methods in terms of accuracy and error bound. In particular, the scheme was found to have a large region of absolute stability. The new method was tested on real life problem namely: Dynamic model.

EXISTENCE AND NONEXISTENCE OF GLOBAL CONTINUOUS SOLUTIONS TO RIEMANN PROBLEM FOR DAMPED P-SYSTEM

In this paper, we extend the result in [16] to general p(v). We prove that, under condition (M), when P greater-than-or-equal-to 3/2, where P=pp triple overdot/p2, there exists a unique global continuous solution to the Riemann problem (E), (R), whose structure is similar to the local solution. When 1 < P* less-than-or-equal-to P* < 5/4, or P* = P* = 5/4, or 5 < P* less-than-or-equal-to P* < 3/2 where P*-inf/v P and P* = sup/v P for all v under consideration, if at least one of the initial centered rarefaction waves is sufficiently strong, then the solution must be breakdown in a finite time.

Lipschitz continuity of the optimal value function and KKT solution set in indefinite quadratic programs

When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Lipschtiz continuity of the KKT solution set. Finally, the similar conclusion for the corresponding optimal value function is obtained.

THE CONTINUAL DIFFERENTIABLE PEAK-UNIMODAL SOLUTIONS OF FEIGENBAUM’S FUNCTIONAL EQUATIONS

For the famous Feigenbaum's equations, in this paper, we established its constructive theorem of the peak-unimodal, then we found out other paths to explore the peak-unimodal solutions. For example, we proceed on the direction to try the non-symmetrical continuous peak-unimodal solutions and C1 solutions.

Solute redistribution and macrosegregation in continuous casting slab of carbon steel during solidification process

Based on the modified Scheil model of solute redistribution,the effects of solidification rate,molten steel flow,and alloy composition on solute macrosegregation during the solidification of carbon steel continuous casting billet are calculated and analyzed. The formation mechanism of "white band "segregation under the condition of electromagnetic stirring is also involved,and some practical countermeasures to restrain the central segregation are suggested. The results show that the modified Scheil model can be applied to predict and analyze the macrosegregation of casting slab effectively. The ratio vx/R of the flow velocity of molten steel to solidification rate has decisive formations of segregation such as linear,V,and "white band"types. It is an effective way to select sufficient terminal cooling and reasonable electromagnetic stirring in order to decrease macrosegregation in the slab. The concept of the characteristic distance of solute enrichment layer can drastically simplify the calculation of solute redistribution at the solid/liquid interface of various elements in carbon steel.

Hlder continuity for solutions of elltptic equations involving measures

The Hoider continuity is proved to bounded solutions of degenerate elliptic e-quations involving measures. The structural conditions of the equation are more general and therestrictions on the structural coofficients are weaker.

THE HOLDER CONTINUITY OF GENERALIZED SOLUTIONS OF A CLASS QUASILINEAR PARABOLIC EQUATIONS

Let A and B satisfy the structural conditions (2), the local Holder continuity interior to Q = G X (0, T) is proved for the generalized solutions of quasilinear parabolic equations as follows: u(t) - divA(x, t, u, del u) + B(x, t, U, del u) = 0.

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS

By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].

EXISTENCE OF POSITIVE SOLUTION FOR A TWO-PATCHES COMPETITION SYSTEM WITH DIFFUSION AND TIME DELAY AND FUNCTIONAL RESPONSE

By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]′ 1 (t)=x 1(t)a 1(t)-b 1(t)x 1(t)-c 1(t)y(t)1+m(t)x 1(t)+D 1(t)[x 2(t)-x 1(t)], x [FK(W1*3/4。*2/3]′ 2 (t)=x 2(t)a 2(t)-b 2(t)x 2(t)-c 2(t)∫ 0 -τ k(s)x 2(t+s) d s+D 2(t)[x 1(t)-x 2(t)], y′(t)=y(t)a 3(t)-b 3(t)y(t)-c 3(t)x 1(t)1+m(t)x 1(t)is established, where a i(t),b i(t),c i(t)(i=1,2,3),m(t) and D i(t)(i=1,2) are all positive periodic continuous functions with period w >0, τ is a nonnegative constant and k(s) is a continuous nonnegative function on [- τ ,0].

Direct extraction of Mo(VI) from acidic leach solution of molybdenite ore by ion exchange resin:Batch and column adsorption studies

The adsorption behavior of ion exchange resin D301 in the extraction of hexavalent molybdenum from high acidic leach solution was investigated. SEM, EDS and Raman spectra analyses were applied to studying the adsorption capacity, reaction kinetics and possible adsorption mechanism in detail. Results showed that the adsorption capacity of D301 resin for molybdenum from high acidic leach solution was up to 463.63 mg/g. Results of the kinetic analysis indicated that the adsorption process was controlled by the particle diffusion with the activation energy 25.47 k J/mol（0.9-1.2 mm） and 20.38 k J/mol（0.6-0.9 mm）. Furthermore, the molybdenum loaded on the resin could be eluted by using 2 mol/L ammonia hydroxide solution. Besides, dynamic continuous column experiments verified direct extraction of molybdenum from acidic leach solutions by ion exchange resin D301 and the upstream flow improved dynamic continuous absorption.

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.