On General Mixed Quasivariational Inequalities

In this paper, we suggest and analyze several iterative methods for solving general mixed quasivariational inequalities by using the technique of updating the solution and the auxiliary principle. It is shown that the convergence of these methods requires either the pseudomonotonicity or the partially relaxed strong monotonicity of the operator. Proofs of convergence is very simple. Our new methods differ from the existing methods for solving various classes of variational inequalities and related optimization problems. Various special cases are also discussed.     

Parametric Quintic-Spline Approach to the Solution of a System of Fourth-Order Boundary-Value Problems

In this paper, we use parametric quintic splines to derive some consistency relations which are then used to develop a numerical method for computing the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is known that a class of variational inequalities related to contact problems in elastostatics can be characterized by a sequence of variational inequations, which are solved using some numerical method. Numerical evidence is presented to show the applicability and superiority of the new method over other collocation, finite difference, and spline methods.     

Some algorithms for hemiequilibrium problems

In this paper, we suggest and analyze a class of iterative methods for solving hemiequilibrium problems using the auxiliary principle technique. We prove that the convergence of these new methods either requires partially relaxed strongly monotonicity or pseudomonotonicity, which is a weaker condition than monotonicity. Results obtained in this paper include several new and known results as special cases.     

Modified Householder iterative method free from second derivatives for nonlinear equations

In this paper, we suggest and analyze a new two-step predictor–corrector type iterative method free from second derivatives for solving nonlinear equations of the type f(x)=0. This new method includes the two-step Newton method as a special case. We prove that the new iterative method is of fourth-order. Several examples are given to illustrate the efficiency of this new method and its comparison with other iterative methods. This method can be considered as a significant improvement of the Newton method and its variant forms.     

Iterative Schemes for Nonconvex Variational Inequalities

In this paper, we suggest and analyze some iterative methods for solving nonconvex variational inequalities using the auxiliary principle technique, the convergence of which requires either only pseudomonotonicity or partially relaxed strong monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier results for solving general variational inequalities involving convex sets.     

Selected valence electron split-shell molecular orbital calculations on the diatomic interhalogen molecules

Selected valence electron split-shell molecular orbital calculations have been performed on the diatomic interhalogen molecules in order to obtain their binding energies, equilibrium internuclear distances, vibrational force constants, dipole moments and nuclear quadrupole coupling constants. The results are compared with the corresponding closedshell values and with those of some previous semiempirical and nonempirical all valence electron calculations. It is observed that the selected valence electron split-shell molecular orbital method which involves the least amount of computations yields results in better agreement with experiment than other methods.     

Analysis of effective molecular diffusion rates for verteporfin in subcutaneous versus orthotopic Dunning prostate tumors

Photosensitizer biodistribution change inside tissue is one of the dominant factors in photodynamic therapy efficacy. In this study, the pharmacokinetics of a benzoporphyrin derivative (BPD), delivered in verteporfin for injection formulation, have been quantified in the rat Dunning prostate tumor MAT-LyLu model, using both subcutaneous and orthotopic sites. Blood plasma sampling indicated that BPD had a bi-exponential metabolic lifetime in vivo, with the two lifetimes being 9.6 min and 8.3 h. The spatial distributions in the tumor were quantified as a function of distance from the perfused blood vessels, using fluorescence histologic images of the tumor. A fluorescent vascular marker was used to obtain locations and shapes of perfused capillaries at a wavelength of emission different from that of BPD and to allow colocalized images to be acquired of vessel and BPD locations. Using the BPD fluorescence images obtained 15 min after intravenous administration, a forward finite-element solution to the diffusion equation was used to predict the drug distribution by matching the fluorescence intensity images observed microscopically. An inverse solver was used to minimize the root mean square error between the image of simulated diffusion and the experimental image, resulting in estimation of the diffusion coefficient of BPD in the tumor models. Effective diffusion coefficients were 0.88 and 1.59 microm2/s for the subcutaneous and orthotopically grown tumors, respectively, indicating that orthotopic tumors have significantly higher vascular extravasation rates as compared with subcutaneous tumors. This analysis supports the hypothesis that leakage rates of the photosensitizer vary considerably. Thus, although varying the time between injection and optical irradiation may be used to vary the targeting between vascular and less vascular areas, the precise time of treatment will depend on the nature of the permeability of the vasculature in the tissue being treated.     

Light Dosimetry for Intraperitoneal Photodynamic Therapy in a Murine Xenograft Model of Human Epithelial Ovarian Carcinoma

Few studies have been published to date measuring spatially resolved fluence rates in complex tissue geometries. Here the light distributions of three different intraperitoneal light delivery geometries in a murine ovarian cancer model were investigated to assess their influence on the tumorcidal efficacy of photodynamic therapy (PDT). In vivo fluence rate measurements in the peritoneal cavities of mice, with the light intensity being mapped in three transverse planes, were performed using fiber-optic detectors. Three different source fiber designs and placements were tested for their ability to provide uniform irradiation of the peritoneal cavity. The biological response to a PDT protocol comprising three separate treatments administered at 72 h intervals, each consisting of a 0.25 mg kg intraperitoneal injection of benzopor-phyrin derivative-mono acid ring A followed 90 min later by delivery of 15 J of 690 nm light, was measured. The tissue response was evaluated by measuring the number of remaining visible lesions and the total residual tumor mass. Fluence rate measurements showed large variations in the fluence rate distribution for similar intended treatments. The most uniform and reproducible illumination was achieved using two 18 mm long cylindrical emitting optical fibers. The biological response was comparable to that produced when a flat-cleaved end optical fiber is used to illuminate the four quadrants of the abdomen sequentially. While a good reproducibility in tumor induction in this animal model exists, no correlation was found between the fluence rate distribution measured in one group of animals and the biological response in a separate group of similarly treated animals. Due to the large intra-animal variability in fluence rate distribution, representative fluence rate mapping in complex tissue geometries is of limited value when applied to an individual PDT treatment. Thus, surveillance of the fluence rate during individual treatments will be required for acceptable PDT dosimetry. To improve the versatility of this particular animal model for PDT research, a large number of extended sources are required to increase uniformity of the illumination in order to reduce unwanted cytotoxic side effects resulting from foci of high fluence rates. In this way, subsequent increase of the total energy delivered to the tumor may be possible.     

Removal of oxygen from silicon by electron beam melting

Small amounts of multicrystalline silicon were melted in an electron beam furnace in different experimental conditions in order to investigate the oxygen evaporation behavior during the electron beam melting (EBM) process. The oxygen content level before and after EBM was determined by secondary ion mass spectroscopy. The oxygen content was reduced from 6.177 to 1.629 ppmw when silicon was melted completely at 15 kW with removal efficiency up to 73.6 %. After that, it decreased continually to <0.0517 ppmw when the refining time exceeded 600 s with a removal efficiency of more than 99.08 %. During the melting process, the evaporation rate of silicon is 1.10 × 10^?5 kg/s. The loss of silicon could be reduced up to 1.7 % during oxygen removal process to a desirable figure, indicating EBM is an effective method to remove oxygen from silicon and decrease the loss of silicon.     

Split-shell molecular orbital calculations on the diatomic alkali metal molecules

Absolute g-tensor calculations for planar hydrocarbon and for non-planar phenyl substituted hydrocarbon radicals are reported. The relevant interactions determining g are discussed. Calculations are performed on the basis of a second-order perturbation expansion. The electronic wavefunctions are obtained from a simplified version of Hoffmann's extended Hückel model (SEH), where all valence electrons are taken into account explicitly. For planar systems the observed linear dependence of g on the energy of the half filled π orbital is well reproduced. A qualitative analysis of this dependence, making restrictive assumptions about the σ electrons, was given earlier by Stone. The calculations for non-planar model systems reproduce the g-factor anomalies which are observed for highly twisted phenyl substituted hydrocarbon radicals. The results show the necessity of direct π-σ mixing and are consistent with recent investigations of the proton hyperfine couplings in such systems.