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Monotone finite difference schemes are proposed for nonlinear systems with mixed quasi-monotonicity. Two monotone iteration processes for the corresponding discrete problems are presented, which converge monotonically to the quasi-solutions of the discrete problems. The limits are the exact solutions under some conditions. A monotone finite difference scheme on uniform mesh with the accuracy of fourth order is constructed. The numerical results coincide with theoretical analysis.

This paper is concerned with the asymptotic behavior of the finite difference solutions of a coupled system of nonlinear integrodifferential reaction–diffusion equations. The existence of the finite difference solution and the monotone iteration process for solving the finite difference system are given. This includes an existence-uniqueness-comparison theorem. From the monotone iteration process, an attractor of the numerical time-dependent solution is obtained. This attractor is a sector between the pair of coupled quasisolutions of the corresponding numerical steady-state problem, which are obtained from a monotone iteration process. A sufficient condition, ensuring that the two coupled quasisolutions coincide, is given. Also given is the application to a reaction–diffusion problem with three different types of reaction functions, including some numerical results which validate the theory analysis.

This paper is a survey of some recent developments of Numerov's method for solving nonlinear two-point boundary value problems. The survey consists of three different parts: the existence-uniqueness of a solution, computational algorithm for computing a solution, and some extensions of Numerov's method. The sufficient conditions for the existence and uniqueness of a solution are presented. Some of them are best possible. Various iterative methods are reviewed, including Picard's iterative method, modified Newton's iterative method, monotone iterative method, and accelerated monotone iterative method. In particular, two more direct monotone iterative methods are presented to save computational work. Each of these iterative methods not only gives a computational algorithm for computing a solution, but also leads to an existence (and uniqueness) theorem. The estimate on the rate of convergence of the iterative sequence is given. The extensions of Numerov's method to a coupled problem and a general problem are addressed. The numerical results are presented to validate the theoretical analysis.

Petrov–Galerkin method is investigated for solving nonlinear systems without monotonicity. A new concept of ordered pair of supersolution and subsolution is proposed. The existence of numerical solutions is studied. A new monotone iteration is provided for solving the resulting problem. Two conditions are given, ensuring the geometric convergence rate. The numerical results show the advantages of this method.

An accelerated monotone iterative method for a boundary value problem of second-order discrete equations is presented. This method leads to an existence-comparison theorem as well as a computational algorithm for the solutions. The monotone property of the iterations gives improved upper and lower bounds of the solution in each iteration, and the rate of convergence of the iterations is either quadratic or nearly quadratic depending on the property of the nonlinear function. Some numerical results are presented to illustrate the monotone convergence of the iterative sequences and the rate of convergence of the iterations.

A new monotone iterative method for the periodic boundary value problems of first order discrete systems is developed. The numerical results are given.

A new concept of a pair of upper and lower solutions is introduced for a boundary value problem of second order discrete system. A comparison result is given. An existence theorem for a solution is established in terms of upper and lower solutions. A monotone iterative scheme is proposed, and the monotone convergence rate of the iteration is compared and analyzed. The numerical results are given.

A new concept of a pair of upper and lower solutions is introduced for a class of discrete boundary value problems without monotone nonlinearities. Some comparison results are established. An existence and enclosing theorem for the solutions is given in terms of upper and lower solutions. A new monotone iterative scheme is proposed. The numerical example is given.

Almost monotone approximation is proposed for nonlinear two‐points problem. A general framework is given for studying the existence and uniqueness of numerical solutions. A discrete approximation with high accuracy is constructed. Nonlinear Jacobi iteration and Gauss–Seidel iteration are introduced to save work. The continuous approximation is also considered. The numerical results show the advantages of such an approach.

Eight structure-based pharmacophore models of Interleukin-1β converting enzyme (ICE) inhibitors were generated by LigandScout based on ICE inhibitor complexes from the Protein Data Bank (PDB). A combinatorial screening method based on multiple pharmacophore models were proposed in present study, since the binding pockets of different complexes were different, the structure-based pharmacophore models have a high specificity and cannot cover all the active molecules. Based on the screening results of MDDR and the metrics of E and A%, a new metric CAI (comprehensive appraisal index) was defined and used to determine the threshold of hit frequency of molecules which screened by the combinatorial screening method. According to the threshold, the potential ICE inhibitors were then identified from traditional Chinese medicine with the method of combinatorial screening with eight models. The molecules hit by not less than five pharmacophore models were taken as the screening objects of ICE inhibitor, and 781 molecules were obtained.

Ten structure-based pharmacophore models of Cyclooxygenase 2 (COX-2) inhibitors were generated by LigandScout based on COX-2 inhibitor complexes from the Protein Data Bank (PDB). The potential COX-2 inhibitors were identified from traditional Chinese medicine with the method of combinatorial screening with ten models. Based on the screening results of MDDR and the metrics of E, A% and comprehensive appraisal index (CAI), the threshold of hit frequency of molecules was defined and used to identify the active molecules from Chinese herbs. The molecules hit by not less than six pharmacophore models were taken as the screening objects of COX-2 inhibitor, and 1103 molecules were obtained.

According to a given control law, an automatic cruise controller (ACC) is a driver-assisting device used to control the headway with respect to the vehicle in front. However, various kinds of ACC systems with different complexity exist and a modeling and simulation platform is thus required. In order to assist design engineers in obtaining the suitable control parameters for desired performance, this paper has proposed a systematical approach to the modeling and development of an ACC simulator. In the proposed approach, the standard unified modeling language (UML) is adopted to model the system, while the Java is used to implement it. An example of an ACC system based on Proportional-Integral-Derivative (PID) design has been provided to show the practicability of the proposed method. It is believed that the approach presented in this paper would benefit application engineers in designing the automatic cruise controller.

ZigBee is an emerging standard specifically designed for low-rate wireless personal area networks (LR-WPAN) with a focus on enabling the wireless sensor networks. It attempts to provide a low data rate, low power, and low cost wireless networking on the device-level communication. In this paper, we have established a realistic environment for the performance evaluation of the ZigBee wireless networks. Several sets of practical experiments are conducted to study its various features, including the 1) packet loss rate, and 2) transmission throughput. The results show that our developed ZigBee platforms could work well under multi-hop transmission over a long period of time.

For complicated pharmaceutical manufacturing processes, using real devices for system integration and testing not only increases the cost but also takes a longer time. In this paper, a systematic approach to the model construction for system integration in pharmaceutical manufacturing processes is proposed. In the present approach, the integration definition language zero (IDEF0) for function modeling and Petri net (PN) are applied to perform the functional and behavior analyses of the processes, and a verified PN model can be then obtained for the implementation of system integration. An application of a monomer synthesis process in pharmaceutical manufacturing systems is provided to illustrate the design procedure of the developed approach.

From the physical point of view, the cohesive energy of a reactant is preferable to its formation energy for characterizing its influence on the reaction processes from the reactants to the products. In fact it has been found that there is a certain correlation between the experimental hydrogen desorption temperature and the cohesive energy calculated by a first principles method for a series of A(m)(MH(4))(n) (A = Li, Na, Mg; M = Be, B, Al) light complex hydrides (including Na(2)BeH(4), Li(2)BeH(4), NaAlH(4), LiAlH(4), Mg(AlH(4))(2), LiBH(4) and NaBH(4)), which suggests that cohesive energy may be a useful physical quantity for evaluating the hydrogen desorption ability of complex hydrides, especially in cases when dehydrogenation products have unknown crystal structures, or may even be unknown. To understand this correlation more deeply, the ionic interaction between A and the MH(4) complex and the covalent interaction between M and H were calculated and their contributions to the cohesive energy evaluated quantitatively. The calculated results show that the covalent M-H interaction in the MH(4) complex is the dominant part of the cohesive energy E(coh) (up to more than 75%) and hardly changes during high-pressure structural transitions of A(m)(MH(4))(n). It was also found that low electronegativity of M or high electronegativity of A is responsible for the weak covalent M-H interaction and finally leads to the low thermodynamic stability of A(m)(MH(4))(n), suggesting that complex hydrides A(m)(MH(4))(n) can be destabilized by partial substitution of M (A) with an element with electronegativity lower (higher) than Ms (As). This conclusion has been confirmed by lots of experimental results and may be a useful guideline for the future design of new complex hydrides of the type A(m)(MH(4))(n).

In remotely operated weapon systems (ROWS), since the human soldier is involved in the control loop, particular improper operations may cause accidents and result in catastrophes. For such systems, this paper has used a command-filter-based framework to accept or reject the human-issued commands so that undesirable executions would never be performed. In the present approach, Petri nets (PN) are used to model the operated behaviors and to synthesize the command filter for supervision. An application to missile loading and launching processes is provided to show the feasibility of the developed approach. It is believed that the technique presented in this paper could be further applied to large-scale military weapon systems.

AIM:To assess the diagnostic values of tumor markers for pancreatic cancer.METHODS:Pancreatic cancer-associated antigen from colonic mucosa (PCAAc), pancreas-specific antigen (PaA), pancreatic oncofetal antigen (POA) and minimolecular pancreatic antigen (mPOA) were detected by double antibodies Sandwich ELISA; CA19-9,elastase 1 (E1), human pancreatic elastase 1 (HPE1) and carcinoembryonic antigen (CEA) by radioimmunoassay (RIA); general activities of ribo-nuclease (RNase) and its isoenzymes (RNase I and RNase I) by biochemistry and PAEG;glycylproline dipeptidyl aminopeptidase (GPDA) by biochemistry andalpha 1-antitrypsin (alpha1AT) by rocket immunoelectrophoresis (rocket-IE).RESULTS:The detection of serum POA,mPOA,PaA,PCAAc,CA19-9,RNase and RNase I was able to differentiate pancreatic cancer from the benign disorders and non-pancreatic malignancies with a sensitivity from 66.75% to 80.0% and a specificity from 88.5% to 96.69%. POA, mPOA, PCAAc, HPE1, E1 and GPDA were related to the pancreatic cancer at the head which demonstrated higher sensitivity from 63.64% to 85.71%. The detection of serum HPE1 was especially helpful for the diagnosis of pancreatic cancer with smaller diameters. The determination of 3 or 4 kinds of tumor markers simultaneously would increase the detection rate of pancreatic cancer, which will be an important procedure for the diagnosis of this malignancy.CONCLUSION:A single test of tumor markers is helpful to detect pancreatic cancer clinically,but the determination of 3 or 4 kinds of tumor markers simultaneously would significantly increase the detection rate of pancreatic cancer, which will be an important procedure for the diagnosis of this malignancy.

This work is concerned with the convergence of a monotone method for fourth-order semilinear elliptic boundary value problems. A comparison result for the rate of convergence is given. The global error is analyzed, and some sufficient conditions are formulated for guaranteeing a geometric rate of convergence.

This paper is concerned with a compact finite difference method for solving systems of two-dimensional reaction–diffusion equations. This method has the accuracy of fourth-order in both space and time. The existence and uniqueness of the finite difference solution are investigated by the method of upper and lower solutions, without any monotone requirement on the nonlinear term. Three monotone iterative algorithms are provided for solving the resulting discrete system efficiently, and the sequences of iterations converge monotonically to a unique solution of the system. A theoretical comparison result for the various monotone sequences is given. The convergence of the finite difference solution to the continuous solution is proved, and Richardson extrapolation is used to achieve fourth-order accuracy in time. An application is given to an enzyme–substrate reaction–diffusion problem, and some numerical results are presented to demonstrate the high efficiency and advantages of this new approach.

A compact finite difference method with non-isotropic mesh is proposed for a two-dimensional fourth-order nonlinear elliptic boundary value problem. The existence and uniqueness of its solutions are investigated by the method of upper and lower solutions, without any requirement of the monotonicity of the nonlinear term. Three monotone and convergent iterations are provided for resolving the resulting discrete systems efficiently. The convergence and the fourth-order accuracy of the proposed method are proved. Numerical results demonstrate the high efficiency and advantages of this new approach.

This paper is concerned with the error and stability analysis of the monotone method for numerical solutions of fourth-order semilinear elliptic boundary value problems. A comparison result among the various monotone sequences is given. The global error is analyzed, and some sufficient conditions are formulated to guarantee a geometric rate of convergence. The stability of the monotone method is proved. Some numerical results are presented.

A parallel monotone iterative relaxation method for a class of two-dimensional discrete boundary value problems is established, and the sequence of iterations is shown to converge monotonically either from above or below to a solution of the problem. This monotone convergence results yields a parallel computational algorithm as well as an existence-comparison result for the solutions. To compute the sequence of iterations, the Thomas algorithm can be used in the same fashion as for one-dimensional problem. The existence and comparison results of the upper and lower solutions are given. The local as well as global existence-uniqueness of the solution are obtained. The global convergence of the iterations is investigated, and the influence of the parameters on the rate of convergence of the iterations is analyzed. Numerical results are given to corroborate the analytical results.

This paper is concerned with the solutions of a class of 2nth-order Lidstone boundary value problems. Sufficient conditions for the existence and uniqueness of a solution are given. A monotone iteration is developed so that the iteration sequence converges monotonically to a maximal or a minimal solution. The approach to the problem is by the method of upper and lower solutions with a new maximum principle.

This paper is concerned with monotone algorithms for the finite difference solutions of a class of nonlinear reaction–diffusion–convection equations with nonlinear boundary conditions. A modified accelerated monotone iterative method is presented to solve the finite difference systems for both the time-dependent problem and its corresponding steady-state problem. This method leads to a simple and yet efficient linear iterative algorithm. It yields two sequences of iterations that converge monotonically from above and below, respectively, to a unique solution of the system. The monotone property of the iterations gives concurrently improving upper and lower bounds for the solution. It is shown that the rate of convergence for the sum of the two sequences is quadratic. Under an additional requirement, quadratic convergence is attained for one of these two sequences. In contrast with the existing accelerated monotone iterative methods, our new method avoids computing local maxima in the construction of these sequences. An application using a model problem gives numerical results that illustrate the effectiveness of the proposed method.

The aim of this paper is to show the existence and uniqueness of a solution for a class of 2nth-order elliptic Lidstone boundary value problems where the nonlinear functions depend on the higher-order derivatives. Sufficient conditions are given for the existence and uniqueness of a solution. It is also shown that there exist two sequences which converge monotonically from above and below, respectively, to the unique solution. The approach to the problem is by the method of upper and lower solutions together with monotone iterative technique for nonquasimonotone functions. All the results are directly applicable to 2nth-order two-point Lidstone boundary value problems.

This paper is concerned with a Lotka-Volterra cooperation-diffusion model with a saturating interaction term for one species. The goal of the paper is to investigate the asymptotic behavior of the time- dependent solution in relation to the corresponding steady-state solutions under homogeneous Neumann boundary condition. Some simple and easily verifiable conditions are given to the rate constants so that for every nontrivial nonnegative initial function the corresponding time-dependent solution converges to one of the nonnegative constant steady-state solutions as time tends to infinity. This convergence result leads to the existence and uniqueness of a positive (or nonnegative) steady-state solution and the global asymptotic stability of a given nonnegative constant steady-state solution. In terms of ecological dynamics, it also gives some coexistence, permanence and extinction results for the model.