Univalent Functions, <Emphasis Type="Italic">VMOA</Emphasis> and Related Spaces

This paper is concerned mainly with the logarithmic Bloch space ℬ_log which consists of those functions f which are analytic in the unit disc \mathbbD{\mathbb{D}} and satisfy sup_{|z| < 1}(1-|z|)log\frac11-|z||f^￠(z)| < ￥\sup_{\vert z\vert <1}(1-\vert z\vert )\log\frac{1}{1-\vert z\vert}\vert f^{\prime}(z)\vert <\infty , and the analytic Besov spaces B ^p , 1≤p<∞. They are all subspaces of the space VMOA. We study the relation between these spaces, paying special attention to the membership of univalent functions in them. We give explicit examples of:

A second-order unsplit Godunov scheme for cell-centered MHD: The CTU-GLM scheme

We assess the validity of a single step Godunov scheme for the solution of the magnetohydrodynamics equations in more than one dimension. The scheme is second-order accurate and the temporal discretization is based on the dimensionally unsplit Corner Transport Upwind (CTU) method of Colella. The proposed scheme employs a cell-centered representation of the primary fluid variables (including magnetic field) and conserves mass, momentum, magnetic induction and energy. A variant of the scheme, which breaks momentum and energy conservation, is also considered. Divergence errors are transported out of the domain and damped using the mixed hyperbolic/parabolic divergence cleaning technique by Dedner et al. (2002) [11]. The strength and accuracy of the scheme are verified by a direct comparison with the eight-wave formulation (also employing a cell-centered representation) and with the popular constrained transport method, where magnetic field components retain a staggered collocation inside the computational cell. Results obtained from two- and three-dimensional test problems indicate that the newly proposed scheme is robust, accurate and competitive with recent implementations of the constrained transport method while being considerably easier to implement in existing hydro codes.     

Spectroscopic determination of the degree of esterification of pectic substances from kenaf

Pectins were isolated from bark, wood and pith of four kenaf (Hibiscus cannabinus L.) varieties. The degree of esterification of isolated pectins was studied using Fourier transform infrared spectroscopy. It was determined as being between 57 and 90% and there were no notable differences between kenaf varieties. The higher value of the degree of esterification was presented in wood pectins (86-90%), the interim in pith (75-83%) and the lower in bark (57-64%).     

Spectroscopic and computational investigation of the ground and low excited states of some symmetrical heterocyclic disulfides

The electronic absorption and emission spectra of some symmetrical heterocyclic disulfides are investigated. The reversible disulfide — thione transformation in water is discussed in view of the complex equilibrium processes present. UV irradiation and pH influence on the above transformation is also studied. The emission properties at room and low temperature are related to the computed molecular geometries of the ground and low excited states of the compounds.     

Bifurcations and transition states

Bifurcations of reaction channels are related to valley-ridge inflection points and it is examined what happens when these do not coincide with transition states. Under such conditions there result bifurcating regions. There exist a number of different prototypes for such regions which are discussed explicitly on the basis of the pertinent Taylor expansions. When bifurcations occur close enough to transition states then there result bifurcating transition regions. An example for a bifurcating transition region is exhibited which is obtained from a quantum mechanical ab initio calculation for the ring opening of cyclopropylidene to aliene. In general there exist no orthogonal trajectory patterns which could serve as simplified models for channel bifurcations.Operated for the U.S. Department of Energy by Iowa State University under Contract No. W-7405-ENG-82. This work was supported by the Office of Basic Energy Sciences     

HPLC study of the inhibiting effect of phosphate and bicarbonate buffers on the leaching pattern of dental resin composites

A high-performance liquid chromatographic method was applied to evaluate the effect of bicarbonate (NaHCO₃) and phosphate (NaH₂PO₄, Na₂HPO₄) buffers on monomer leachability of dental resin composites. Evetric was the restorative resin composite that was investigated in current study. Forty disk-shaped resin composite specimens (n?=?40) were immersed by means of a silk string in the following solutions: Distilled water (A), phosphate buffer (B), bicarbonate buffer (C), artificial saliva (D). After seven (7) and fourteen (14) days, the eluates were analyzed by means of High Performance Liquid Chromatography (HPLC). Subsequently, new specimens were fabricated and immersed in fresh solutions in which methanol 12% (v/v) was added. After seven and fourteen days of storage, the leaching of monomers was examined by means of HPLC, which was proved to be an effective tool to buffers demonstrate the inhibiting effect of phosphate and bicarbonate ions on the leaching pattern of dental resin composites.     

Model Studies on the Interaction of Amino Acids with Biominerals: The Effect of L-Serine at the Hydroxyapatite-Water Interface

The effect of L-serine in supersaturated solutions of calcium phosphate was investigated under plethostatic conditions. The rates of crystal growth measured in the presence of L-serine at relatively high concentrations and in the range between 2x10(-3) and 1x10(-2) mol dm(-3) were appreciably reduced. The inhibitory effect of L-serine was found to be due to blocking of a portion of the active growth sites by adsorption. Kinetics measurements in the presence of L-serine as well as adsorption isotherm analysis suggested Langmuir-type adsorption of L-serine on the surface of hydroxyapatite (HAP) with a relatively low affinity for the substrate. Adsorption experiments showed that at pH 7.4 considerable adsorption of L-serine onto HAP takes place, whereas at pH 10.0 the adsorption was negligible, suggesting that electrostatic interactions are dominant. Attraction between the positively charged protonated amino group of the L-serine molecule and the negatively charged HAP surface contributed largely to the adsorption. This was corroborated by the fact that, in the presence of L-serine in the solution, a significant shift of zeta-potential of the HAP particles to less negative values was found at pH values close to 7.4. At pH values higher than 10.0 essentially no shift of zeta-potential takes place. On the basis of the experimental results, a model was proposed according to which L-serine absorbs on the surface of HAP through electrostatic attractions exerted between one negative site of the HAP surface, i.e., phosphate or hydroxyl ion, and the positively charged protonated amino group of one L-serine molecule, forming a surface ion pair. Copyright 2001 Academic Press.     

Faster least squares approximation

Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets n be the number of constraints and d be the number of variables, with n >> d{n \gg d}. Then, existing exact methods find a solution vector in O(nd ²) time. We present two randomized algorithms that provide accurate relative-error approximations to the optimal value and the solution vector of a least squares approximation problem more rapidly than existing exact algorithms. Both of our algorithms preprocess the data with the Randomized Hadamard transform. One then uniformly randomly samples constraints and solves the smaller problem on those constraints, and the other performs a sparse random projection and solves the smaller problem on those projected coordinates. In both cases, solving the smaller problem provides relative-error approximations, and, if n is sufficiently larger than d, the approximate solution can be computed in O(nd ln d) time.     

Optimization and data mining in medicine

Mathematical theory of optimization has found many applications in the area of medicine over the last few decades. Several data analysis and decision making problems in medicine can be formulated using optimization and data mining techniques. The significance of the mathematical models is greatly realized in the recent years owing to the growing technological capabilities and the large amounts of data available. In this paper, we attempt to give a brief overview of some of the most interesting applications of mathematical programming and data mining in medicine. In the overview, we include applications like radiation therapy treatment, microarray data analysis, and computational neuroscience.     

Variability of dissolution rates at constant undersaturation

Dissolution processes play an important role in marble weathering. Investigation of the dissolution kinetics of powdered Pentelic marble, a calcitic natural stone, showed that the rates measured at constant undersaturation decreased with time. It was found that the rate of dissolution decreased sharply to about 50% of the initial value before 5% of the initially suspended powder was dissolved. Past a dissolution extent corresponding to 25% with respect to the suspended solid, the rates of dissolution at the same constant undersaturation reached a stable value corresponding to 20-25% of the initial rate measured. The reduction in the rates of dissolution up to 25% of mass loss was in agreement with the reduction in the total surface area exposed to the solution, suggesting a dependence of the rate on the number of active sites on the surface of the dissolving material. The decrease in the dissolution rates did not depend on the undersaturation of the solution or on the physical characteristics of the particles such as specific surface area, porosity, and particle size distribution. Equal mass losses, with respect to the initially suspended solid, of different samples exhibited the same relative decrease in rate regardless of the conditions of the aqueous solutions.