A stochastic model for microbial fermentation process under Gaussian white noise environment

In this paper, we propose a stochastic model for the microbial fermentation process under the framework of white noise analysis, where Gaussian white noises are used to model the environmental noises and the specific growth rate is driven by Gaussian white noises. In order to keep the regularity of the terminal time, the adjustment factors are added in the volatility coefficients of the stochastic model. Then we prove some fundamental properties of the stochastic model: the regularity of the terminal time, the existence and uniqueness of a solution and the continuous dependence of the solution on the initial values

Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer

We study an optimal investment and dividend problem of an insurer, where the aggregate insurance claims process is modeled by a pure jump Lévy process. We allow the management of the dividend payment policy and the investment of surplus in a continuous-time financial market, which is composed of a risk free asset and a risky asset. The information available to the insurer is partial information. We generalize this problem as a partial information regular-singular stochastic control problem, where the control variable consists of regular control and singular control. Then maximum principles are established to give sufficient and necessary optimality conditions for the solutions of the regular-singular control problem. Finally we apply the maximum principles to solve the investment and dividend problem of an insurer

Generalized local and nonlocal master equations for some stochastic processes

In this paper, we present a study on generalized local and nonlocal equations for some stochastic processes. By considering the net flux change in a region determined by the transition probability, we derive the master equation to describe the evolution of the probability density function. Some examples, such as classical Fokker-Planck equations, models for Lévy process, and stochastic coagulation equations, are provided as illustrations. A particular application is a consistent derivation of coupled dynamical systems for spatially inhomogeneous stochastic coagulation processes

Analgesic Tolerance of Opioid Agonists in Mutant Mu-Opioid Receptors Expressed in Sensory Neurons Following Intrathecal Plasmid Gene Delivery

Background: Phosphorylation sites in the C-terminus of mu-opioid receptors (MORs) are known to play critical roles in the receptor functions. Our understanding of their participation in opioid analgesia is mostly based on studies of opioid effects on mutant receptors expressed in in vitro preparations, including cell lines, isolated neurons and brain slices. The behavioral consequences of the mutation have not been fully explored due to the complexity in studies of mutant receptors in vivo. To facilitate the determination of the contribution of phosphorylation sites in MOR to opioid-induced analgesic behaviors, we expressed mutant and wild-type human MORs (hMORs) in sensory dorsal root ganglion (DRG) neurons, a major site for nociceptive (pain) signaling and determined morphine- and the full MOR agonist, DAMGO,-induced effects on heat-induced hyperalgesic behaviors and potassium current (IK) desensitization in these rats. Findings: A mutant hMOR DNA with the putative phosphorylation threonine site at position 394 replaced by an alanine (T394A), i.e., hMOR-T, or a plasmid containing wild type hMOR (as a positive control) was intrathecally delivered. The plasmid containing GFP or saline was used as the negative control. To limit the expression of exogenous DNA to neurons of DRGs, a neuron-specific promoter was included in the plasmid. Following a plasmid injection, hMOR-T or hMOR receptors were expressed in small and medium DRG neurons. Compared with saline or GFP rats, the analgesic potency of morphine was increased to a similar extent in hMOR-T and hMOR rats. Morphine induced minimum IK desensitization in both rat groups. In contrast, DAMGO increased analgesic potency and elicited IK desensitization to a significantly less extent in hMOR-T than in hMOR rats. The development and extent of acute and chronic tolerance induced by repeated morphine or DAMGO applications were not altered by the T394A mutation. Conclusions: These results indicate that phosphorylation of T394 plays a critical role in determining the potency of DAMGO-induced analgesia and IK desensitization, but has limited effect on morphine-induced responses. On the other hand, the mutation contributes minimally to both DAMGO- and morphine-induced behavioral tolerance. Furthermore, the study shows that plasmid gene delivery of mutant receptors to DRG neurons is a useful strategy to explore nociceptive behavioral consequences of the mutation

A Study of the Impact of Micro-Blog Marketing on Consumers’ Brand Loyalty

Micro-blog marketing has developed rapidly in our country, its commercial value is getting more and more attention by the enterprises. This paper regards the enterprise micro-blog marketing as the research context, placing the authenticity, the professional, the humanity, the brand trust and brand loyalty into a frame, setting up a theory model, putting forward the research hypothesis. In the end, this paper makes some conclusions and puts forward some suggestions on enterprise micro-blog marketing through the empirical analysis. Key words: Micro-blog marketing; Brand trust; Brand loyalt