Analysis of Suzuki, Shanker, and Kumar formulations under strong compressions

A critical analysis of the Suzuki, Shanker, and Kumar formulations is presented by studying different classes of materials under high pressure. A similar trend for all the materials studied in the present work, demonstrates that Suzuki formulation is not capable to yield compression behaviour of solids. The Shanker formulation improves the results obtained by the Suzuki formulation in small compression range (0.9<V/V₀<1). For further compressions Shanker formulation also fails. On the other hand, the Kumar formulation is found to work well for the entire range of pressure. The reasons for the failure of Suzuki and Shanker formulations are discussed.     

Parametric study of cylindrical and spherical dust ion acoustic shock waves with two temperature electrons in dusty plasma relevant to Saturn's E ring

We have performed numerical analysis of the one-dimensional dynamics of the cylindrical/spherical dust ion acoustic shock waves in unmagnetized dusty plasma consisting of positive ions, immobile dust particles, and nonextensive distributed cold and hot electrons. A multiple-scale expansion method is used to derive Burgers Equation (BE) and modified Burgers equation (MBE) by including higher order nonlinearity. The basic characteristics of the shock waves have been analysed numerically and graphically for different physical parameters relevant to Saturn' E ring through 2D figures. The parametric dependence of dust ion acoustic shock waves on some plasma parameters nonextensive index, density, and temperature of cold and hot electrons, concentration of dust particles, thermal effects and kinematic viscosity of ions is explored. Furthermore, it is found that the nonplanar geometry effects have an important impact on the establishment of shock waves. The amplitude of the wave decreases faster as one departs away from the axis of the cylinder or centre of the sphere. Such decaying behaviour continues as time progresses. It is also found that an increasing dust concentration decreases the amplitude of the dust ion acoustic shock waves.     

Response Surface Optimization of Medium Components for Naringinase Production from <Emphasis Type="Italic">Staphylococcus xylosus MAK2</Emphasis>

Response surface methodology was used to optimize the fermentation medium for enhancing naringinase production by Staphylococcus xylosus. The first step of this process involved the individual adjustment and optimization of various medium components at shake flask level. Sources of carbon (sucrose) and nitrogen (sodium nitrate), as well as an inducer (naringin) and pH levels were all found to be the important factors significantly affecting naringinase production. In the second step, a 22 full factorial central composite design was applied to determine the optimal levels of each of the significant variables. A second-order polynomial was derived by multiple regression analysis on the experimental data. Using this methodology, the optimum values for the critical components were obtained as follows: sucrose, 10.0%; sodium nitrate, 10.0%; pH 5.6; biomass concentration, 1.58%; and naringin, 0.50% (w/v), respectively. Under optimal conditions, the experimental naringinase production was 8.45 U/mL. The determination coefficients (R ²) were 0.9908 and 0.9950 for naringinase activity and biomass production, respectively, indicating an adequate degree of reliability in the model.     

Cell Disruption Optimization and Covalent Immobilization of β-D-Galactosidase from <Emphasis Type="Italic">Kluyveromyces marxianus</Emphasis> YW-1 for Lactose Hydrolysis in Milk

β-D-galactosidase (EC 3.2.1.23) from Kluyveromyces marxianus YW-1, an isolate from whey, has been studied in terms of cell disruption to liberate the useful enzyme. The enzyme produced in a bioreactor on a wheat bran medium has been successfully immobilized with a view to developing a commercially usable technology for lactose hydrolysis in the food industry. Three chemical and three physical methods of cell disruption were tested and a method of grinding with river sand was found to give highest enzyme activity (720 U). The enzyme was covalently immobilized on gelatin. Immobilized enzyme had optimum pH and temperature of 7.0 and 40 °C, respectively and was found to give 49% hydrolysis of lactose in milk after 4 h of incubation. The immobilized enzyme was used for eight hydrolysis batches without appreciable loss in activity. The retention of high catalytic activity compared with the losses experienced with several previously reported immobilized versions of the enzyme is significant. The method of immobilization is simple, effective, and can be used for the immobilization of other enzymes.     

Prolongations of valuations to finite extensions

Let ${K=\mathbb{Q}(\theta)}$ be an algebraic number field with θ in the ring A _K of algebraic integers of K and f(x) be the minimal polynomial of θ over the field ${\mathbb{Q}}$ of rational numbers. For a rational prime p, let ${\bar{f}(x)\,=\,\bar{g}_{1}(x)^{e_{1}}....\bar{g}_{r}(x)^{e_{r}}}$ be the factorization of the polynomial ${\bar{f}(x)}$ obtained by reducing coefficients of f(x) modulo p into a product of powers of distinct irreducible polynomials over ${\mathbb{Z}/p\mathbb{Z}}$ with g _i (x) monic. Dedekind proved that if p does not divide [ ${A_{K}:\mathbb{Z}}$ [θ]], then ${pA_{K}=\wp_{1}^{e_{1}}\ldots\wp_{r}^{e_{r}}}$ , where ${\wp_{1},\ldots,\wp_{r}}$ are distinct prime ideals of A _K , ${\wp_{i}=pA_{K}+g_{i}(\theta)A_{K}}$ having residual degree equal to the degree of ${\bar{g}_{i}(x)}$ . He also proved that p does not divide [ ${A_{K}:\mathbb{Z}}$ [θ]] if and only if for each i, either e _i  = 1 or ${\bar{g}_{i}(x)}$ does not divide ${\bar{M}(x)}$ where ${M(x)=\frac{1}{p}(f(x)-g_{1}(x)^{e_{1}}....g_{r}(x)^{e_{r}})}$ . Our aim is to give a weaker condition than the one given by Dedekind which ensures that if the polynomial ${\bar{f}(x)}$ factors as above over ${\mathbb{Z}/p\mathbb{Z}}$ , then there are exactly r prime ideals of A _K lying over p, with respective residual degrees ${\deg \bar {g}_{1}(x),...,\deg \bar {g}_{r}(x)}$ and ramification indices e ₁, ..., e _r . In this paper, the above problem has been dealt with in a more general situation when the base field is a valued field (K, v) of arbitrary rank and K(θ) is any finite extension of K.     

Efficient derivative-free variants of Hansen-Patrick’s family with memory for solving nonlinear equations

In this paper, we present a new tri-parametric derivative-free family of Hansen-Patrick type methods for solving nonlinear equations numerically. The proposed family requires only three functional evaluations to achieve optimal fourth order of convergence. In addition, acceleration of convergence speed is attained by suitable variation of free parameters in each iterative step. The self-accelerating parameters are estimated from the current and previous iteration. These self-accelerating parameters are calculated using Newton’s interpolation polynomials of third and fourth degrees. Consequently, the R-order of convergence is increased from 4 to 7, without any additional functional evaluation. Furthermore, the most striking feature of this contribution is that the proposed schemes can also determine the complex zeros without having to start from a complex initial guess as would be necessary with other methods. Numerical experiments and the comparison of the existing robust methods are included to confirm the theoretical results and high computational efficiency.