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.

ON THE EXISTENCE AND UNIQUENESS THEOREMS OF SOLUTIONS FOR THE SYSTEMS OF MIXED MONOTONE OPERATOR EQUATIONS WITH APPLICATIONS

The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2].

Fixed Point Theorems of Mixed Monotone Operators with Applications

In this paper,we get fixed point theorems of mixed monotone operators in much weaker condition and give some applications for nonmonotone operators and differential equations.

Existence and Uniqueness of Fixed Points for Mixed Monotone Operators with Application

In this paper, a class of mixed monotone operators is studied. Some new fixed point theorems are presented by means of partial order theory, and the uniqueness and existence of fixed points are obtained without assuming the operator to be compact or continuous. Our conclusions extend the relevant results. Moreover,as an application of our result, the existence and uniqueness of positive solution for a class of fractional differential equation boundary value problem are proved.

Double coupled fixed point for multi-valued mixed increasing operators in ordered Banach spaces

In this paper, a new concept of double coupled fixed point for multi-valued mixed increasing operators is given and some new double coupled fixed point theorems for multi-valued mixed increasing operators in ordered Banach spaces are also given. These results extend and generalize some results of Huang and Fang.

A novel 3-layer mixed cultural evolutionary optimization framework for optimal operation of syngas production in a Texaco coal-water slurry gasifier

Optimizing operational parameters for syngas production of Texaco coal-water slurry gasifier studied in this paper is a complicated nonlinear constrained problem concerning 3 BP(Error Back Propagation) neural networks. To solve this model, a new 3-layer cultural evolving algorithm framework which has a population space, a medium space and a belief space is firstly conceived. Standard differential evolution algorithm(DE), genetic algorithm(GA), and particle swarm optimization algorithm(PSO) are embedded in this framework to build 3-layer mixed cultural DE/GA/PSO(3LM-CDE, 3LM-CGA, and 3LM-CPSO) algorithms. The accuracy and efficiency of the proposed hybrid algorithms are firstly tested in 20 benchmark nonlinear constrained functions. Then, the operational optimization model for syngas production in a Texaco coal-water slurry gasifier of a real-world chemical plant is solved effectively. The simulation results are encouraging that the 3-layer cultural algorithm evolving framework suggests ways in which the performance of DE, GA, PSO and other population-based evolutionary algorithms(EAs) can be improved,and the optimal operational parameters based on 3LM-CDE algorithm of the syngas production in the Texaco coalwater slurry gasifier shows outstanding computing results than actual industry use and other algorithms.

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR NONLINEAR SINGULAR 2mth-ORDER CONTINUOUS AND DISCRETE LIDSTONE BOUNDARY VALUE PROBLEMS

By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existence and uniqueness of positive solution to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.

The Fixed Point Theorems of α-concave Covex Operators with Application

The coceptions of two element α-concave convex and mixed α-concave convex operators are introduced. The fixed point theorems of the two type operators are obtained. By these theorems,the existence and uniquence of solution of three type nonlinear integral equations is studied.

Verification of an operational ocean circulation-surface wave coupled forecasting system for the China＇s seas

An operational ocean circulation-surface wave coupled forecasting system for the seas off China and adjacent areas（OCFS-C） is developed based on parallelized circulation and wave models. It has been in operation since November 1, 2007. In this paper we comprehensively present the simulation and verification of the system, whose distinguishing feature is that the wave-induced mixing is coupled in the circulation model. In particular, with nested technique the resolution in the China＇s seas has been updated to（1/24）° from the global model with（1/2）°resolution. Besides, daily remote sensing sea surface temperature（SST） data have been assimilated into the model to generate a hot restart field for OCFS-C. Moreover, inter-comparisons between forecasting and independent observational data are performed to evaluate the effectiveness of OCFS-C in upper-ocean quantities predictions, including SST, mixed layer depth（MLD） and subsurface temperature. Except in conventional statistical metrics, non-dimensional skill scores（SS） is also used to evaluate forecast skill. Observations from buoys and Argo profiles are used for lead time and real time validations, which give a large SS value（more than 0.90）. Besides, prediction skill for the seasonal variation of SST is confirmed. Comparisons of subsurface temperatures with Argo profiles data indicate that OCFS-C has low skill in predicting subsurface temperatures between 100 m and 150 m. Nevertheless, inter-comparisons of MLD reveal that the MLD from model is shallower than that from Argo profiles by about 12 m, i.e., OCFS-C is successful and steady in MLD predictions. Validation of 1-d, 2-d and 3-d forecasting SST shows that our operational ocean circulation-surface wave coupled forecasting model has reasonable accuracy in the upper ocean.

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR INITIAL VALUE PROBLEMS OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES

In this paper, the initial value problems of second order ordinary differential equations in Banach spaces are discussed. By using the monotone iterative technique, some existence and uniqueness theorems for solutions are obtained.

The Existence of Coupled Solutions for a Kind of Nonlinear Operator Equations in Partial Ordered Linear Topology Space

The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing the semi-order method. Some new existence results are obtained.

Existence and Uniqueness of Solutions to Singular Higher Order Two-point BVPs on Time Scales

This paper investigates the existence and uniqueness of solutions for singular higher order boundary value problems on time scales by using mixed monotone method.The theorems obtained are very general. For the different time scale, the problem may be the corresponding continuous or discrete boundary value problem.

The Existence of Positive Almost Periodic Type Solutions for Some Nonlinear Delay Integral Equations

This paper presents the conditions of existence of positive almost periodic type solutions for some nonlinear delay integral equations, by using a fixed point theorem in the mixed monotone operators （Ma, Y.： On a class of mixed monotone operators and a kind of two-point bounded value problem. Indian J. Math., 41（2）, 211-220 （1999]]. Some known results are operators.

Symmetry properties of nonlocal quark bilinear operators on a Lattice(LP~3 Collaboration)

Using symmetry properties, we determine the mixing pattern of a class of nonlocal quark bilinear operators containing a straight Wilson line along a spatial direction.We confirm the previous study that mixing among the lowest dimensional operators, which have a mass dimension equal to three, can occur if chiral symmetry is broken in the lattice action.For higher dimensional operators, we find that the dimension-three operators will always mix with dimension-four operators, even if chiral symmetry is preserved.Also, the number of dimension-four operators involved in the mixing is large, and hence it is impractical to remove the mixing by the improvement procedure.Our result is important for determining the Bjorken-xdependence of the parton distribution functions using the quasi-distribution method on a Euclidean lattice.The requirement of using large hadron momentum in this approach makes the control of errors from dimension-four operators even more important.

EXISTENCE OF POSITIVE SOLUTION TO TWO-POINT BOUNDARY VALUE PROBLEM FOR A SYSTEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we consider a two-point boundary value problem for a system of second order ordinary differential equations. Under some conditions, we show the existence of positive solution to the system of second order ordinary differential equa-tions.