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In this paper, we have attempted optimization of production of enzyme carboxymethylcellulase or endoglucanase from the bacterium Bacillus amyloliquefaciens SS35. Optimization has been carried out in two stages using statistical experimental design, viz. medium optimization and optimization of fermentation parameters. For medium optimization, Plackett–Burman design followed by central composite design (CCD) was used, while for optimization of fermentation parameters one-variable-at-a-time method followed by CCD was used. Carbon and nitrogen sources in the medium have been revealed to be the significant factors for enzyme production (carboxymethylcellulose 18.05 g/L; yeast extract 8 g/L and peptone 2 g/L). The inorganic salts have been found to be insignificant components of medium. Optimum fermentation parameters for optimized medium were: initial medium pH 5.65, incubation temperature = 40 °C, shaking speed = 120 rpm, and inoculum size = 6.96 %, v/v. Interestingly, the influence of all four parameters was almost independent with no interlinks. Secondly, the overall effect of all parameters was also low, as indicated by linear, square and interaction regression coefficients that were at least one order of magnitude lower than the intercept in the model equation. These results essentially meant that medium components dominate overall enzyme production process in comparison to fermentation parameters. Electronic supplementary material The online version of this article (doi:10.1007/s13205-013-0169-6) contains supplementary material, which is available to authorized users.

We propose and study the numerical approximation of an advection-diffusion-reaction model equation by a modified Brezzi–Douglas–Marini mixed finite element method.Nonlinear advection is admitted, arising in complex and coupled flow and transport systems.In contrast to the classical variant of this approach, optimal second-order convergence of the scalar and the vector variable is ensured.No loss of rate of convergence due to the presence of the advection term is observed.

Higher speed of train and the change of environment temperature could have a great impact on normal operation of equipments in the equipment compartment. By using continuity equation, Reynolds-Averaged Navier-Stokes equation, and RNG k-eturbulence model equation, the temperature field in the equipment compartment is simulated numerically when EMU is running at speed of 350km/h on open line. For the heating dissipation of the traction convertor and the transformer in the equipment compartment is higher, this paper creates a 3-D model of interior and exterior flow field of high speed EMU consisting of 5 carriages running at the speed of 350km/h on open line. The temperature distribution of the inner equipment compartments of the model is researched numerically and the detailed information of temperature distribution in each equipment compartment is obtained when the environment temperature is 40℃, 35℃, 30℃, 20℃, 10℃, 0℃, -25℃, -40℃ respectively. The numerical calculation result shows that when the temperature is 40℃, the surface temperature distribution of the traction convertor in the first carriage is about 41.2~45.5℃, the maximum temperature is 52.5℃. The surface temperature distribution of the transformer in the second carriage is about 43~48.1℃, the maximum temperature is 65.4℃. The surface temperature distribution of the traction convertor in the third carriage is about 43.0~46.7℃, the maximum temperature is 68.7℃. Besides, the surface temperature distribution of these three equipments is same in different environment temperatures. The calculation results can give a strong technical support especially for designing the grilles of numbers and location on side skirts, and the layout of the equipments in the equipment compartments of the high-speed EMU.

Starting from analyzing dynamic characteristics of the general energy system, this article discusses the mathematical mechanism of the GM (1, 1) model for producing AGO/IAGO data and the mathematical mechanism for constructing “the model equation” and the mathematical mechanism for parameter estimation. It also discusses other aspects of the application of the GM (1, 1) model. It points out: A. the classic GM (1, 1) model follows the principle of RMI model, but there exist background defects of the "planning predictions" and internal discords of the model caused by the prior assumptions in which both development coefficient and gray effective amount are constant, which restricts the application of the model. B. The classic GM (1, 1) model, in principle, only applies to fitting modeling of time sequences which tend to be slow and with wider intervals and positive stable values. C. Gray differential equation as a tool for estimating the parameters is not indispensible, so this article suggests optimizing parameter calculation method: gray differential equation providing initial iteration, using the end of AGO generating sequence as the boundary condition, etc. to improve the precision and explicability of the GM (1, 1) model.

Let us consider the activator–inhibitor system. The general model equation is given by the reaction–diffusion system $$\begin{cases}\frac{\partial u}{\partial t}=a\varDelta u+\gamma f(u,v)&\text{in}\ \varOmega\times(0,\infty), \\\noalign{\vspace{3pt}}\frac{\partial v}{\partial t}=b\varDelta v+\gamma g(u,v)&\text{in}\ \varOmega\times(0,\infty),\end{cases}$$ (9.1) in a domain Ω⊂ℝ d . Here, u denotes the concentration of the activator, and v the concentration of the inhibitor in Ω, respectively. The functions f(u,v) and g(u,v) denote the kinetics and are real smooth functions defined for u≥0 and v≥0. The activator and the inhibitor diffuse in Ω with diffusion rates a>0 and b>0, respectively. The constant γ>0 denotes the reaction rate. Species of the activator or inhibitor must be specified in each activator–inhibitor system under consideration. The form of kinetic functions f(u,v) and g(u,v) must also be fixed in an adequate manner.

The two gradients agree well. The present method reduces CPU time by a factor of about 10 compared with the finite difference mrethod.

Relaxation dynamics, scaling limits, and relaxation schemes are three main topics on hyperbolic relaxation problems that, remarkably, can be well understood with one model equation. The criterion that leads to desired results for the three problems is the so called “sub-characteristic condition”. The criterion of this nature is also pivotal in the study of general hyperbolic relaxation problems.

In Section 2.1 of this chapter, the model equations of rigid-body mechanisms which were derived in Volume I and represented in DAE form (see [1]), will be briefly summarized. Two approaches to map the DAEs into DEs will be discussed in Section 2.2, together with the algorithms which may perform this task.

This article discusses the use of constraints to build quantitative physiological models and the application of these models to assist anaesthetists in decision making. The constraint formalism is a declarative form of knowledge representation. Each constraint embodies a model equation. A set of constraints constitutes a model. Constraint models can be extended and modified easily and the representation of model knowledge is separated from its use. The model knowledge is used by means of a constraint satisfaction mechanism. This allows the application of the same knowledge for different purposes.

The theory of two species competing for the same resources plays an extremely important role in present day ecology, both applied and theoretical. The role played by age structure in competitive interactions has not, however, been investigated to the extent that it has been for predator-prey interactions. The purpose of this work is to provide some insight into the dynamics of competitive interactions with age structure. To make the model simple and tractable we consider a two-species competition model where only one species has age-structure. This is not purely a mathematical simplification but has some biological justification as well. For example, for some populations of birds and lizards competing for insects only the lizards have a significant age-structure (we thank R.M. May who suggested this biological application in a personal conversation). The existence and stability of the equilibria of the general model equation (2.3) is studied as it depends on the inherent net reproductive rate n of the age-structured population.

The evolution of density and velocity inhomogeneities in gravitationally unstable medium is discussed. The model equation of nonlinear diffusion is used for describing the nonlinear stage of the gravitational instability. Together with the equation of continuity it provides an approximate description of the formation of the nonlinear structures (“pancakes”, filaments and clumps of mass) as well as the merging of the clumps.