High‐performance liquid chromatographic column packings with different particle sizes: Chromatographic behavior for the quality analysis of HuanglianShangqing pill

The chromatographic separation of traditional Chinese medicines is still a highly challenging task in analytical science with respect to its hundreds and thousands of chemical compounds, while increase of separation efficiency can greatly improve the separation power of chromatographic column for traditional Chinese medicine. In this study, 13 bioactive components in HuanglianShangqing pill were selected as an index to optimize the separation conditions and evaluate the system suitability of three commercially available columns packed with 1.8, 3.5, and 5.0 μm particles. The chromatographic separations were obtained by the most appropriate Eclipse Plus C₁₈ column (100 × 2.1 mm, 3.5 μm) within 45 min using gradient elution with aqueous‐ammonium acetate (10 mmol/L, pH 5.0) and acetonitrile, at a flow rate of 0.3 mL/min and an operating temperature of 30°C. The quality of HuanglianShangqing pill was assessed through combining simultaneous quantification of 13 compounds with fingerprint analysis. For the qualitative analysis, mass spectrometry was used to confirm the 13 compounds. All the validation data conformed to the acceptable requirements. For the fingerprint analysis, 32 peaks were selected as the common peaks at 254 nm to evaluate the similarities among HuanglianShangqing pills obtained from ten manufacturers.     

Overloading control of gas chromatographic systems

Increasing the interlaboratory reproducibility of gas chromatographic retention indices requires avoiding measurements distorted by overloading effects. Several criteria of evaluating the limits of the mass overloading of gas chromatographic systems are compared and reconsidered. The criteria mostly appropriate for practical purposes are based on (i) the dependences of factors of peak broadening (ratio of peak height and its width) vs. amount of analyte injected into the chromatographic column and (ii) the dependence of parameters characterizing the peak distortion (asymmetry factor) vs. the amount of analyte. Both these criteria provide mutually comparable evaluations of the overloading limits for analytes of different polarity. At the same time, the dependence of retention indices vs. amounts of analyte injected in the chromatographic column cannot be recommended for overloading control, because the parameters of the corresponding linear regressions indicate temperature dependence. The interpretation of certain gas chromatographic anomalies requires the correct evaluation of overloading limits. For example, the unusual temperature dependence of retention indices of polar analytes on non‐polar stationary phases and the dependence of retention indices on ratio of amounts of target analytes and reference compounds.     

Development of a method using high‐performance liquid chromatographic fingerprint and multi‐ingredients quantitative analysis for the quality control of Yangxinshi Pian

A simple and reliable method of high‐performance liquid chromatography with diode array detection method was developed for fingerprint analysis and simultaneous determination of six compounds including puerarin, salvianolic acid B, berberine hydrochloride, palmatine chloride, dehydrocorydaline, and icariin in the Chinese medicine preparation Yangxinshi Pian. The separation was performed on an Agilent Eclipse XDB‐C₁₈ reserved‐phase column (250 mm × 4.6mm I.D., 5 μm) using gradient elution with 50 mmol/L monopotassium phosphate aqueous solution and methanol as mobile phase at a flow rate of 1.0 mL/min. The column operating temperature was set at 30°C, and the detection wavelength was 280 nm. The method was validated by linearity, precision, accuracy, stability, and recovery. For fingerprint analysis, 25 peaks were selected as the common peaks, and four kinds of similarities including cosine similarity (S), ratio of similarity (S′), projection content similarity (C), and content similarity (P) were applied to evaluate the quality consistency of different batches of Yangxinshi Pian. The results showed that the developed method was an efficient tool for quality evaluation of Yangxinshi Pian.     

Error Estimates for a Class of Elliptic Optimal Control Problems

In this article, functional type a posteriori error estimates are presented for a certain class of optimal control problems with elliptic partial differential equation constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state equation. The functional a posteriori error estimates developed by Repin in the late 1990s are applied to estimate the cost function value from both sides without requiring the exact solution of the state equation. Moreover, a lower bound for the minimal cost functional value is derived. A meaningful error quantity coinciding with the gap between the cost functional values of an arbitrary admissible control and the optimal control is introduced. This error quantity can be estimated from both sides using the estimates for the cost functional value. The theoretical results are confirmed by numerical tests.     

Optimal investment strategies for participating contracts

Participating contracts are popular insurance policies, in which the payoff to a policyholder is linked to the performance of a portfolio managed by the insurer. We consider the portfolio selection problem of an insurer that offers participating contracts and has an S-shaped utility function. Applying the martingale approach, closed-form solutions are obtained. The resulting optimal strategies are compared with portfolio insurance hedging strategies (CPPI and OBPI). We also study numerical solutions of the portfolio selection problem with constraints on the portfolio weights.     

Finite Difference Method for an Optimal Control Problem for a Nonlinear Time-dependent Schrödinger Equation

The finite difference method is applied to an optimal control problem for a system governed by a nonlinear Schrödinger equation with a complex coe?cient. The optimal control problem is discretized by the finite difference method, the error estimate for the finite difference scheme is established and the convergence of difference approximations of the optimal control according to the functional is proved.     

A schistosomiasis compartment model with incubation and its optimal control

A new mathematical model included an exposed compartment is established in consideration of incubation period of schistosoma in human body. The basic reproduction number is calculated to illustrate the threshold of disease outbreak. The existence of the disease free equilibrium and the endemic equilibrium are proved. Studies about stability behaviors of the model are exploited. Moreover, control measure assessments are investigated in order to seek out effective control interventions for anti‐schistosomiasis. Then, the corresponding optimal control problem according to the model is presented and solved. Theoretical analyses and numerical simulations induce several prevention and control strategies for anti‐schistosomiasis. At last, a discussion is provided about our results and further work. Copyright © 2017 John Wiley & Sons, Ltd.     

Lot‐sizing policies for deterioration items under two‐level trade credit with partial trade credit to credit‐risk retailer and limited storage capacity

The main purpose of this article is to investigate the optimal wholesaler's replenishment decisions for deterioration items under two levels of the trade credit policy and two storage facilities in order to reflect the supply chain management situation within the economic order quantity framework. In this study, each of the following assumptions have been made: (1) The own warehouse with limited capacity always is not sufficient to store the order quantity, so that a rented warehouse is needed to store the excess units over the capacity of the own warehouse; (2) The wholesaler always obtains the partial trade credit, which is independent of the order quantity offered by the supplier, but the wholesaler offers the full trade credit to the retailer; (3) The wholesaler must take a loan to pay his or her supplier the partial payment immediately when the order is received and then pay off the loan with the entire revenue. Under these three conditions, the wholesaler can obtain the least costs. Furthermore, this study models the wholesaler's optimal replenishment decisions under the aforementioned conditions in the supply chain management. Two theorems are developed to efficiently determine the optimal replenishment decisions for the wholesaler. Finally, numerical examples are given to illustrate the theorems that are proven in this study, and the sensitivity analysis with respect to the major parameters in this study is performed. Copyright © 2016 John Wiley & Sons, Ltd.     

A modified pseudospectral method for solving trajectory optimization problems with singular arc

This paper presents a direct method based on Legendre–Radau pseudospectral method for efficient and accurate solution of a class of singular optimal control problems. In this scheme, based on a priori knowledge of control, the problem is transformed to a multidomain formulation, in which the switching points appear as unknown parameters. Then, by utilizing Legendre‐Radau pseudospectral method, a nonlinear programming problem is derived which can be solved by the well‐developed parameter optimization algorithms. The main advantages of the present method are its superior accuracy and ability to capture the switching times. Accuracy and performance of the proposed method are examined by means of some numerical experiments. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal control problem in a domain with branched structure and homogenization

We consider a linear parabolic problem in a thick junction domain which is the union of a fixed domain and a collection of periodic branched trees of height of order 1 and small width connected on a part of the boundary. We consider a three‐branched structure, but the analysis can be extended to n‐branched structures. We use unfolding operator to study the asymptotic behavior of the solution of the problem. In the limit problem, we get a multi‐sheeted function in which each sheet is the limit of restriction of the solution to various branches of the domain. Homogenization of an optimal control problem posed on the above setting is also investigated. One of the novelty of the paper is the characterization of the optimal control via the appropriately defined unfolding operators. Finally, we obtain the limit of the optimal control problem. Copyright © 2016 John Wiley & Sons, Ltd.