General Response Surface Reliability Analysis for Fuzzy-Random Uncertainty both in Basic Variables and in State Variables

A general response surface（RS） method is presented for reliability analysis of complex structure/mechanism with fuzzy-random uncertainty both in basic variables and in failure state variables. On the basis of equivalent transformation from fuzzy basic variable to random basic variable, the fuzziness and randomness in the basic variables are considered simultaneously in the presented general RS method. Once the fuzzy basic variables are transformed into the random basic variables, the conventional RS method is employed to establish the general RS for the complex structure/mechanism with implicit limit state equation by finite element numerical simulation. Furthermore, the general failure probability is defined according to the probability formula for fuzzy-random event by taking the fuzziness and randomness in the failure-safety state into consideration, and an appropriate fuzzy operator is adopted to calculate the general failure probability for the complex structure/mechanism with multiple implicit failure modes. Finally, a general reliability analysis of an elastic linkage mechanism is introduced to illustrate the present method.

Multiplicity results for the unstirred chemostat model with general response functions

We investigate the multiplicity of positive steady state solutions to the unstirred chemostat model with general response functions. It turns out that all positive steady state solutions to this model lie on a single smooth solution curve, whose properties determine the multiplicity of positive steady state solutions. The key point of our analysis is to study the ＂turning points＂ on this positive steady state solution curve, and to prove that any nontrivial solution to the associated linearized problem is one of sign by constructing a suitable test function. The main tools used here include bifurcation theory, monotone method, mountain passing lemma and Sturm comnarison theorem.

Determinants of timing and amplitude in the plant general stress response

Plants have evolved intricate signaling cascades to rapidly and effectively respond to biotic and abiotic challenges. The precise timing of these responses enables optimal resource reallocation to maintain the balance between stress adaptation and growth. Thus, an in-depth understanding of the immediate and long-term mechanisms regulating resource allocation is critical in deciphering how plants withstand environmental challenges. To date however, understanding of this tradeoff has focused on the amplitude of long-term responses, rather than the timing of rapid stress responses. This review presents current knowledge on kinetics of secondary messengers involved in regulation of rapid and general stress responses, followed by rapid stress responsive transduction machinery, and finally the transcriptional response of a functional general stress responsive cis-element. Within this context we discuss the role of timing of initial peak activation and later oscillating peak responses, and explore hormonal and stress signaling crosstalk confounding greater understanding of these cascades.

ROLE OF DISEASE PROPAGATION IN MIGRATORY BIRD POPULATION

Chatterjee considered a predator prey model with avian migration in the migration prey population IS. Chatterjee, Alternative prey source coupled with prey recovery enhance stability between migratory prey and their predator in the presence of disease, Nonlinear Anal. Real World Appl. 11 （2010） 4415-4430]. In this paper, we modify and analyze the model by taking time dependent parameters and the general flmctional response into consideration. The conditions for the persistence of the system and the extinction of the disease are obtained. The global attractivity of the system is also studied. By numerical simulations, we find that the qualitative behavior of the system independent on the choice of the functional response. Moreover, it is observed that the infection rate, recruitment rate and the predation rate play a vital role in predicting the behavior of the dynamics.