Solutions to fuzzy integral equations with arbitrary kernels

Using a parametric Riemann integral representation, a numerical algorithm for solving fuzzy Fredholm and Voltera integral equations of the second kind with arbitrary kernel is proposed and illustrated with examples.     

On the retrieval of ice cloud particle shapes from POLDER measurements

Shapes of ice crystals can significantly affect the radiative transfer in ice clouds. The angular distribution of the polarized reflectance over ice clouds strongly depends on ice crystal shapes. Although the angular-distribution features of the total or polarized reflectance over ice clouds imply a possibility of retrieving ice cloud particle shapes by use of remote sensing data, the accuracy of the retrieval must be evaluated. In this study, a technique that applies single ice crystal habit and multidirectional polarized radiance to retrieve ice cloud particle shapes is assessed. Our sensitivity studies show that the retrieved particle shapes from this algorithm can be considered good approximations to those in actual clouds in calculation of the phase matrix elements. However, this algorithm can only work well under the following conditions: (1) the retrievable must be overcast and thick ice cloud pixels, (2) the particles in the cloud must be randomly oriented, (3) the particle shapes and size distributions used in the lookup tables must be representative, and (4) the multi-angle polarized measurements must be accurate and sufficient to identify ice cloud pixels of randomly oriented particles. In practice, these conditions will exclude most of the measured cloud pixels. Additionally, because the polarized measurements are only sensitive to the upper cloud part not deeper than an optical thickness of 4, the retrieved particle shapes with the polarized radiance may only approximate those in the upper parts of the clouds. In other words, for thicker clouds with vertical inhomogeneity in particle shapes, these retrieved particle shapes cannot represent those of whole clouds. More robust algorithm is needed in accurate retrieval of ice cloud particle shapes.     

Total reflection X-ray fluorescence analysis of oral fluids of women affected by osteoporosis and osteopenia

Osteoporosis is a disease characterized by low bone mass and microarchitectural deterioration of bone tissue, leading to bone fragility and an increased susceptibility to fractures; the early stage of decreased bone density is called osteopenia. More than 200 million people are affected and about 50% of post-menopausic women are expected to develop the disease. Osteoporosis, osteopenia and periodontal disease have in common several risk factors, being hyperthyroidism and smoking habits the most important ones. There is scarce information in the literature about the association between periodontal disease and osteoporosis and/or osteopenia. Some works suggest that osteoporotic women are susceptible to a higher loss of periodontal insertion, alveolar bones, and teeth.     

Curriculum developers and problem solving: the case of Israeli elementary school projects

Problem solving has been a main focus in mathematics education for several decades, yet it seems that its definition and classroom implementation are far from being consensual. We explore the views and approaches of a small community: the project leaders of five elementary mathematics curriculum development projects in Israel, working within a centralized system, which dictates the syllabus. We describe and analyze their views along six categories: What are problems? What are not problems? Classification of problems, problem solving and individual differences, the ratio of problem solving tasks to other tasks in the project, and the role of heuristics and metacognition in teaching problem solving. We describe, exemplify, interpret and discuss the (few) points of convergence and the many different approaches. Finally, we reflect on the possible role of research in settling those differences. We speculate that our analysis and results go beyond the local and the idiosyncratic.     

Electrostatic potential–density relationships in molecules

In this work, we present Hartree–Fock and density functional theory nuclear electrostatic potential–density relationships for several homonuclear diatomic molecules. The results of our calculations are encouraging with relatively low errors in the energies. Implications for the application of this work to novel molecular energy equations as well as the need for further improvement of these newly proposed relationships in molecules have been addressed. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Two algorithms for the Student-Project Allocation problem

We study the Student-Project Allocation problem (SPA), a generalisation of the classical Hospitals/Residents problem (HR). An instance of SPA involves a set of students, projects and lecturers. Each project is offered by a unique lecturer, and both projects and lecturers have capacity constraints. Students have preferences over projects, whilst lecturers have preferences over students. We present two optimal linear-time algorithms for allocating students to projects, subject to the preference and capacity constraints. In particular, each algorithm finds a stable matching of students to projects. Here, the concept of stability generalises the stability definition in the HR context. The stable matching produced by the first algorithm is simultaneously best-possible for all students, whilst the one produced by the second algorithm is simultaneously best-possible for all lecturers. We also prove some structural results concerning the set of stable matchings in a given instance of SPA. The SPA problem model that we consider is very general and has applications to a range of different contexts besides student-project allocation.     

Self‐assembly of star‐shaped polystyrene‐block‐polypeptide copolymers synthesized by the combination of atom transfer radical polymerization and ring‐opening living polymerization of α‐amino acid‐N‐carboxyanhydrides

The self‐assembling nature and phase‐transition behavior of a novel class of triarm, star‐shaped polymer–peptide block copolymers synthesized by the combination of atom transfer radical polymerization and living ring‐opening polymerization of α‐amino acid‐N‐carboxyanhydride are demonstrated. The two‐step synthesis strategy adopted here allows incorporating polypeptides into the usual synthetic polymers via an amido–amidate nickelacycle intermediate, which is used as the macroinitiator for the growth of poly(γ‐benzyl‐L ‐glutamate). The characterization data are reported from analyses using gel permeation chromatography and infrared, ¹H NMR, and ¹³C NMR spectroscopy. This synthetic scheme grants a facile way to prepare a wide range of polymer–peptide architectures with perfect microstructure control, preventing the formation of homopolypeptide contaminants. Studies regarding the supramolecular organization and phase‐transition behavior of this class of polymer‐block‐polypeptide copolymers have been accomplished with X‐ray diffraction, infrared spectroscopy, and thermal analyses. The conformational change of the peptide segment in the block copolymer has been investigated with variable‐temperature infrared spectroscopy. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2774–2783, 2006     

Salmonella-host cell interactions, changes in host cell architecture, and destruction of prostate tumor cells with genetically altered Salmonella.

Increasingly, genetically modified Salmonella are being explored as a novel treatment for cancer because Salmonella preferentially replicate within tumors and destroy cancer cells without causing the septic shock that is typically associated with wild-type S. typhimurium infections. However, the mechanisms by which genetically modified Salmonella strains preferentially invade cancer cells have not yet been addressed in cellular detail. Here we present data that show S. typhimurium strains VNP20009, LT2, and CRC1674 invasion of PC-3M prostate cancer cells. S. typhimurium-infected PC-3M human prostate cancer cells were analyzed with immunofluorescence microscopy and transmission electron microscopy (TEM) at various times after inoculation. We analyzed microfilaments, microtubules, and DNA with fluorescence and immunofluorescence microscopy. 3T3 Phi-Yellow-mitochondria mouse 3T3 cells were used to study the effects of Salmonella infestation on mitochondria distribution in live cells. Our TEM results show gradual destruction of mitochondria within the PC-3M prostate cancer cells with complete loss of cristae at 8 h after inoculation. The fluorescence intensity in YFP-mitochondria-transfected mouse 3T3 cells decreased, which indicates loss of mitochondria structure. Interestingly, the nucleus does not appear affected by Salmonella within 8 h. Our data demonstrate that genetically modified S. typhimurium destroy PC-3M prostate cancer cells, perhaps by preferential destruction of mitochondria.     

Solute-solvent interactions in micellar electrokinetic chromatography. Characterization of sodium dodecyl sulfate-Brij 35 micellar systems for quantitative structure-activity relationship modelling.

The solvation parameter model has been applied to the characterization of micellar electrokinetic chromatographic (MEKC) systems with mixtures of sodium dodecyl sulfate and Brij 35 as surfactant. The variation in MEKC surfactant composition results in changes in the coefficients of the correlation equation, which in turns leads to information on solute-solvent and solute-micelle interactions. Since the same solvation model can be used to describe many biological processes, particular MEKC surfactant compositions can be selected that model the solute-solvent interactions of some of these processes. Two different MEKC systems have been selected to model the solute-solvent interactions of two processes of biological interest (octanol-water partition and tadpole narcosis).