The cubic semilocal convergence on two variants of Newton's method

In this paper, we discuss two variants of Newton's method without using any second derivative for solving nonlinear equations. By using the majorant function and confirming the majorant sequences, we obtain the cubic semilocal convergence and the error estimation in the Kantorovich-type theorems. The numerical examples are presented to support the usefulness and significance.     

Dsc Evaluations in F.c.c. Solid Solutions of Short-range-order Kinetics As Influenced by Bound Vacancies

A modified first order kinetic law, which describes the roles of bound and unbound vacancies, is proposed in order to predict defect decay and short-range-order kinetics of quenched binary alloys during linear heating experiments. The model has been applied to differential scanning calorimetry (DSC) curves of Cu–5 at%Zn quenched from different temperatures. Activation energy for migration of solute-vacancy complexes was also assessed from the kinetics of short-range-order using DSC traces. A value of 89.5±0.32 kJ mol^–1 was obtained. The relative contribution of bound and unbound vacancies to the ordering process as influenced by quenching temperature was determined. In conjunction, a parametric study of the initial total defect concentration and effective energy for defect migration was performed in order to envisage their influence on the calculated DSC profiles. This revised version was published online in August 2006 with corrections to the Cover Date.     

Recovering risk-neutral probability density functions from options prices using cubic splines and ensuring nonnegativity

We present a new approach to estimate the risk-neutral probability density function (pdf) of the future prices of an underlying asset from the prices of options written on the asset. The estimation is carried out in the space of cubic spline functions, yielding appropriate smoothness. The resulting optimization problem, used to invert the data and determine the corresponding density function, is a convex quadratic or semidefinite programming problem, depending on the formulation. Both of these problems can be efficiently solved by numerical optimization software.     

On the Number of Facets of Three-Dimensional Dirichlet Stereohedra III: Full Cubic Groups

We are interested in the maximum possible number of facets that Dirichlet stereohedra for three-dimensional crystallographic groups can have. In two previous papers, D. Bochiş and the second author studied the problem for noncubic groups. This paper deals with “full” cubic groups, while “quarter” cubic groups are left for a subsequent paper. Here, “full” and “quarter” refers to the recent classification of three-dimensional crystallographic groups by Conway, Delgado-Friedrichs, Huson and Thurston. This paper’s main result is that Dirichlet stereohedra for any of the 27 full groups cannot have more than 25 facets. We also find stereohedra with 17 facets for one of these groups. Research partially supported by the Spanish Ministry of Education and Science, grant number MTM2005-08618-C02-02.     

SRK equation of state: Predicting binary interaction parameters of hydrocarbons and related compounds

The parameter mixing rules of the Soave–Redlich–Kwong (SRK) equation of state are rewritten as Huron–Vidal mixing rules, where infinite-pressure activity coefficients are predicted by group contributions. Alkanes are treated as composed by one group type and aromatics by two types, aliphatic and aromatic. Hydrocarbon mixtures can be treated using one universal interaction parameter. Light compounds like methane, N₂, CO₂, H₂S, etc. are treated as separate groups; each one requires a pair of parameters for its interactions with aliphatic and aromatic groups. Group interaction parameters were determined from experimental VLE data. From them, binary interaction constants of the classical quadratic mixing rules can directly be derived.     

Efficient and reliable mixture critical points calculation by global optimization

Multicomponent systems may exhibit several critical points or no critical point at all. Local methods can find only one critical point for a given initial guess. Recently, several global methods have been proposed for finding all the solutions of the problem. In the present work, we propose a gradient-based calculation method using global optimization, with temperature and molar volume as primary variables, and with analytical partial derivatives calculated from a two-parameter cubic equation of state. The Tunneling global optimization method is used for finding all the global minima. The implementation is based on a unique feature of the Tunneling method, which is able to find efficiently and reliably multiple minima at the same level. Several mixtures from binaries to petroleum reservoir fluids are used to test the proposed method. Numerical experiments proved the efficiency and reliability of the Tunneling method for finding all mixture critical points.     

Mixed convection boundary layer flow of non-Newtonian fluids along vertical wavy plates

Mixed convection boundary layer flows of non-Newtonian fluids over the wavy surfaces are studied by the coordinate transformation and the cubic spline collocation numerical method. The effects of the wavy geometry, the buoyancy parameter and the generalized Prandtl number for pseudoplastic fluids, Newtonian fluids and dilatant fluids on the skin-friction coefficient, local and mean Nusselt numbers have been graphically studied. Results show that both higher generalized Prandtl numbers and buoyancy parameters are seen to enhance the influence of wavy surfaces on the local Nusselt number, irrespective of whether the fluids are Newtonian fluids or non-Newtonian fluids. Moreover, the irregular surfaces have higher total heat flux than that of corresponding flats plate for any fluid.     

NS方程在隧道通风工程中的应用

在隧道通风工程中,为了研究通风过程中风压风速度的变化情况,将隧道中空气的流动看成流体力学中所研究的粘性不可压缩流体的非定常流动。用NS方程作为隧道通风的数学模型,采用三次插值伪质点法求解NS方程。以浙江台州104国道黄土岭隧道风改建工程为研究对象,对不同长度和高度的引洞通风状况给出计算机数值模拟,并进一步分析通风过程中风压风速的变化情况。从达到通风要求、提高通风效率的角度出发,可根据本文的计算结果与数据分析,选择最优化的通风方案。     

Progress in liquid crystalline dispersions: Cubosomes

Dispersed particles of bicontinuous cubic liquid crystalline phase, cubosomes, are self-assembled nanostructured particles that can be formed in aqueous lipid and surfactant systems. Contributions to cubosome research have come from the fields of biology, material science, medicine, and mathematics and much is known about their formation and properties. At the center of much of the discovery and innovation is the technique of cryo-transmission electron microscopy. Most of the research into cubosomes is motivated by potential applications in drug delivery and material synthesis although no commercialized product based on cubosomes is known. Recent advances in understanding and use of cubosomes are discussed in the context of some of the more promising application areas and the opportunities for microscopy techniques to make unique contributions to these areas.     

Kalman filter deconvolution after cubic splines background removal in the HPLC determination of Cr(III) and Al(III) as 8-hydroxyquinolines

Summary A procedure for the simultaneous quantitation of Al(III) and Cr(III) ions by reversed-phase HPLC, after pre-column complexation with 8-hydroxyquinoline, is described. The deconvolution of the partially overlapped peaks was by the Kalman filter method which yielded accurate and precise results. Background removal from the chromatograms was by a new approach employing cubic splines as interpolators between the peak valleys. Finally, it is shown that the Kalman filter deconvolution, after subtraction of the background by cubic spline interpolation, allowed quantitation of Al(III) and Cr(III) down to 25 ppb for each metal. These concentrations were not detectable by conventional integration methods due to a very low signal-to-noise ratio.