Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations

A discrete stochastic Razumikhin-type theorem is established to investigate whether the Euler--Maruyama (EM) scheme can reproduce the moment exponential stability of exact solutions of stochastic functional differential equations (SFDEs). In addition, the Chebyshev inequality and the Borel-Cantelli lemma are applied to show the almost sure stability of the EM approximate solutions of SFDEs. To show our idea clearly, these results are used to discuss stability of numerical solutions of two classes of special SFDEs, including stochastic delay differential equations (SDDEs) with variable delay and stochastically perturbed equations

Distributed state estimation in sensor networks with randomly occurring nonlinearities subject to time delays

This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2012 ACM.This article is concerned with a new distributed state estimation problem for a class of dynamical systems in sensor networks. The target plant is described by a set of differential equations disturbed by a Brownian motion and randomly occurring nonlinearities (RONs) subject to time delays. The RONs are investigated here to reflect network-induced randomly occurring regulation of the delayed states on the current ones. Through available measurement output transmitted from the sensors, a distributed state estimator is designed to estimate the states of the target system, where each sensor can communicate with the neighboring sensors according to the given topology by means of a directed graph. The state estimation is carried out in a distributed way and is therefore applicable to online application. By resorting to the Lyapunov functional combined with stochastic analysis techniques, several delay-dependent criteria are established that not only ensure the estimation error to be globally asymptotically stable in the mean square, but also guarantee the existence of the desired estimator gains that can then be explicitly expressed when certain matrix inequalities are solved. A numerical example is given to verify the designed distributed state estimators.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008, 60804028 and 61174136, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Antioxidant enzyme activities and lipid peroxidation in corn (Zea mays L.) following soil application of superabsorbent polymer at different fertilizer regimes

In arid and semiarid regions of northern China, there is an increasing interest in using reduced rate of inorganic fertilizer together with water-saving superabsorbent polymer (SAP) for field crop production. Thus, an efficient management of fertilizer and study of metabolic changes in response to SAP application is important for improved production of corn. 24 undisturbed soil lysimeters (35 cm in diameter and 150 cm in depth) were installed in a field lysimeter facility during 2010, to study yield and physiological mechanisms in corn (Zea mays L.) subjected to application (30 kg ha-1) or without application of SAP at different fertilization levels (standard, medium or 75% and low or 50% of conventional fertilization rate). The results show that the corn yield fell by 19.7% under medium and 37.7% under low fertilization; the application of SAP increased it significantly by 80.3%. Although SAP had marginal effect under standard fertilization, plants treated with SAP under reduced fertilization showed a significant decrease in superoxide dismutase (SOD), catalase (CAT), peroxidase (POD), ascorbate peroxidase (APX) and glutathione reductase (GR) activities in leaves when compared with control plants. Our results suggest that drought stress as well as fertilizer reduction leads to production of oxygen radicals, which results to oxidative stress in the plant and the application of superabsorbent polymer could conserve soil water and nutrients, making same available for plants to reduce oxidative stress and increase biomass accumulation, especially under reduced fertilization level.Key words: Antioxidant enzymes, lysimeter, corn, drought stress, superabsorbent polymer

Crystal structure of LaTiO_3.41 under pressure

The crystal structure of the layered, perovskite-related LaTiO_3.41 (La_5Ti_5O_{17+\delta}) has been studied by synchrotron powder x-ray diffraction under hydrostatic pressure up to 27 GPa (T = 295 K). The ambient-pressure phase was found to remain stable up to 18 GPa. A sluggish, but reversible phase transition occurs in the range 18--24 GPa. The structural changes of the low-pressure phase are characterized by a pronounced anisotropy in the axis compressibilities, which are at a ratio of approximately 1:2:3 for the a, b, and c axes. Possible effects of pressure on the electronic properties of LaTiO_3.41 are discussed.Comment: 5 pages, 6 figure

OsCAND1 is required for crown root emergence in rice

Crown roots are main components of the fibrous root system and important for crops to anchor and absorb water and nutrition. To understand the molecular mechanisms of crown root formation, we isolated a rice mutant defective in crown root emergence designated as Oscand1 (named after the Arabidopsis homologous gene AtCAND1). The defect of visible crown root in the Oscand1 mutant is the result of cessation of the G2/M cell cycle transition in the crown root meristem. Map-based cloning revealed that OsCAND1 is a homolog of Arabidopsis CAND1. During crown root primordium development, the expression of OsCAND1 is confined to the root cap after the establishment of fundamental organization. The transgenic plants harboring DR5::GUS showed that auxin signaling in crown root tip is abnormal in the mutant. Exogenous auxin application can partially rescue the defect of crown root development in Oscand1. Taken together, these data show that OsCAND1 is involved in auxin signaling to maintain the G2/M cell cycle transition in crown root meristem and, consequently, the emergence of crown root. Our findings provide new information about the molecular regulation of the emergence of crown root in rice