Stability in terms of two measures of solutions to stochastic partial differential delay equations with switching

In this paper, the problem of stability in terms of two measures is considered for a class of stochastic partial differential delay equations with switching. Sufficient conditions for stability in terms of two measures are obtained based on the technique of constructing a proper approximating strong solution system and conducting a limiting type of argument to pass on stability of strong solutions to mild ones. In particular, the stochastic stability under the fixed‐index sequence monotonicity condition and under the average dwell‐time switching are considered.     

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.     

On input-to-state stability for stochastic multi-group models with multi-dispersal

This paper focuses on the input-to-state stability for a general class of stochastic multi-group models with multi-dispersal. By incorporating graph theory with Lyapunov method as well as stochastic analysis techniques, novel sufficient criteria are derived, which are in the form of Lyapunov-type theorem and coefficient-type criterion, respectively. Moreover, to show the applicability of our findings, we employ coefficient-type criterion to analyze the input-to-state stability for stochastic coupled oscillators. Finally, a numerical example and its simulations are offered to demonstrate the validity and feasibility of the theoretic results.     

Qualitative and quantitative analysis of chemical constituents in Ardisiae Japonicae Herba

Ardisiae Japonicae Herba is a well‐known traditional Chinese medicine for the treatment of bronchitis conjunctivitis, pneumonia, and trauma. In this work, a high‐performance liquid chromatography coupled with quadrupole time‐of‐flight mass spectrometry method was first established for the separation and structural identification of the chemical constituents in Ardisiae Japonicae Herba. A total of 15 compounds including coumarins, flavonoid glycosides, and catechins were identified or tentatively characterized based on their chromatographic behaviors and mass spectral fragmentation and by comparisons with the reference standards. Furthermore, a simple high‐performance liquid chromatography with diode array detection method was developed for the simultaneous determination of five major constituents. Results obtained from method validation, including linearity, precision, repeatability, stability, and recovery, showed that the established method was reliable and accurate. Bergenin and quercitrin were found to be the most abundant constituents and could be served as chemical markers for quality control of Ardisiae Japonicae Herba.     

Kinetically Controlled Layer-by-Layer Stacking of Metal Oxide 2D Nanosheets

An efficient chemical way to finely control the layer-by-layer stacking of inorganic nanosheets (NS) is developed by tuning the type and composition of intercalant ion, and the reaction temperature for restacking process. The finely controlled stacking of NS relies on a kinetic control of the self-assembly of NS in the presence of coordinating organic cations. A critical role of organic cations in this assembly highlights the importance of the appropriate activation energy. Of prime importance is that a fine-control of the interstratification of 2D NS is highly effective not only in tailoring its pore structure but also in enhancing its electrode activity. The present study clearly demonstrates that the kinetically controlled restacking of NS provides a facile and powerful method to tailor their stacking number and functionality.     

Dynamic Modulation of Enzyme Activity by Near-Infrared Light

Engineering near-infrared (NIR) light-sensitive enzymes remains a huge challenge. A photothermal effect-associated method is developed for tailoring the enzymatic activity of enzymes by exposure to NIR light. An ultrasmall platinum nanoparticle was anchored in an enzyme to generate local heating upon NIR irradiation, which enhanced the enzyme activity without increasing bulk temperature. Following NIR irradiation, the enzyme activity was tailored rapidly and reversibly, and was modulated by varying laser power density and irradiation time. Four enzymes were engineered, including glucoamylase, glucose oxidase, catalase, and proteinase K with NIR-light sensitivity, and demonstrated their utility in practical applications such as photolithography and NIR light-responsive antibacterial or anticancer actions. Our investigation suggests that this approach could be broadly used to engineer enzymes with NIR-light sensitivity for many biological applications.