On an iterative method for a class of 2 point \& 3 point nonlinear SBVPs

In this article, we propose a novel modification to Quasi-Newton method, which is now a days popularly known as variation iteration method (VIM) and use it to solve the following class of nonlinear singular differential equations which arises in chemistry $-y''(x)-\frac{\alpha}{x}y''(x)=f(x,y),~x\in(0,1),$ where $\alpha\geq1$, subject to certain two point and three point boundary conditions. We compute the relaxation parameter as a function of Bessel and the modified Bessel functions. Since rate of convergence of solutions to the iterative scheme depends on the relaxation parameter, thus we can have faster convergence. We validate our results for two point and three point boundary conditions. We allow $\partial f/\partial y$ to take both positive and negative values.     

Optimal Control of Fractional Elliptic PDEs with State Constraints and Characterization of the Dual of Fractional-Order Sobolev Spaces

Journal of Optimization Theory and Applications - This paper introduces the notion of state constraints for optimal control problems governed by fractional elliptic partial differential equations....     

Design and analysis of MEMS MWCNT/epoxy strain sensor using COMSOL

Wiesenfeld and Faure investigated rotational quenching of H ₂CO by molecular hydrogen where they considered 40 rotational levels of o-H ₂CO and 41 rotational levels of p-H ₂CO. Data on energies of rotational levels of the molecule are fundamental in the investigation. We have found that the sequence of levels reported by Wiesenfeld and Faure is not as per convention of molecular physics. Their results are also available on the website: http://www.home.strw.leidenuniv.nl/~moldata/datafiles/ph2co-h2.dat, where the collisional transitions are shown even between the levels having equal energies. Data for such transitions should not be there.     

Selective debenzylation of 1-benzyloxy-4-methoxy benzene over 5-sulfosalicylic acid-functionalized ordered mesoporous silica (SBA-15/SFSA) catalyst

5-Sulfosalicylic acid (SFSA) functionalized mesoporous silica nanocomposites (SBA/APTS/SFSA) were synthesized by post grafting technique for selective debenzylation of 1-benzyloxy-4-methoxy benzene. The uniform incorporation of SFSA inside the mesoporous SBA-15 framework was confirmed by standard characterization techniques (PXRD, adsorption studies, FT-IR, etc.). Total surface area, pore size and pore volume of the SBA/APTS/SFSA catalysts decreased with increase in the concentration of SFSA confirming the uniform insertion of SFSA into mesoporous SBA-15 matrix. Catalytic activity studies showed highest conversion and selectivity of the desired product on SBA/APTS/SFSA catalyst compared to homogeneous SFSA and other solid support (Al₂O₃ and SiO₂). All the reaction parameters such as reaction time, reaction temperature and catalyst weight were optimized under environmental friendly conditions. Finally, the possible mechanism of the reaction was explained.

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Impacting the Remedial Potential of Nano Delivery-Based Flavonoids for Breast Cancer Treatment

Breast cancer persists as a diffuse source of cancer despite persistent detection and treatment. Flavonoids, a type of polyphenol, appear to be a productive option in the treatment of breast cancer, because of their capacity to regulate the tumor related functions of class of compounds. Plant polyphenols are flavonoids that appear to exhibit properties which are beneficial for breast cancer therapy. Numerous epidemiologic studies have been performed on the dynamic effect of plant polyphenols in the prevention of breast cancer. There are also subclasses of flavonoids that have antioxidant and anticarcinogenic activity. These can regulate the scavenging activity of reactive oxygen species (ROS) which help in cell cycle arrest and suppress the uncontrolled division of cancer cells. Numerous studies have also been performed at the population level, one of which reported a connection between cancer risk and intake of dietary flavonoids. Breast cancer appears to show intertumoral heterogeneity with estrogen receptor positive and negative cells. This review describes breast cancer, its various factors, and the function of flavonoids in the prevention and treatment of breast cancer, namely, how flavonoids and their subtypes are used in treatment. This review proposes that cancer risk can be reduced, and that cancer can be even cured by improving dietary intake. A large number of studies also suggested that the intake of fruit and vegetables is associated with reduced breast cancer and paper also includes the role and the use of nanodelivery of flavonoids in the healing of breast cancer. In addition, the therapeutic potential of orally administered phyto-bioactive compounds (PBCs) is narrowed because of poor stability and oral bioavailability of compounds in the gastrointestinal tract (GIT), and solubility also affects bioavailability. In recent years, creative nanotechnology-based approaches have been advised to enhance the activity of PBCs. Nanotechnology also offers the potential to become aware of disease at earlier stages, such as the detection of hidden or unconcealed metastasis colonies in patients diagnosed with lung, colon, prostate, ovarian, and breast cancer. However, nanoformulation-related effects and safety must not be overlooked. This review gives a brief discussion of nanoformulations and the effect of nanotechnology on herbal drugs.     

Thermo-oxidative degradation kinetics of grafted polypropylene films

The thermo-oxidative stability and degradation behavior of polypropylene (PP) and grafted PP have been investigated using thermogravimetric analysis. Three multiple heating rate methods, namely Kissinger, Kim–Park and Flynn–Wall have been used to calculate the activation energy as a function of the extent of degradation. The four different heating rates (5, 10, 15 and 20°C/min) were maintained in the temperature range of 30–550°C during the analysis. Fourier transform infrared spectroscopy has confirmed the presence of carboxylic group on the surface of grafted PP films. Differential scanning calorimetry has shown that the crystallinity decreased with the increase in grafting. In the air atmosphere, the thermo-oxidative degradation occurs via a pathway that involves decomposition of polymer peroxide. Thermo-oxidative stability of grafted PP films is found to increase with an increase in the degree of grafting (DG). The degradation kinetic parameters were used to predict the lifetime of PP and grafted PP films. The activation energy and lifetime of grafted PP films increased with an increase in the DG. The lifetime of PP and grafted PP decreased with an increase in degradation temperature.     

Irradiation effect of low-energy ion on polyurethane nanocoating containing metal oxide nanoparticles

Irradiation effect of low-energy ion beam has been investigated on nanocoating developed with silica, titania and silica–titania core–shell nanoparticles embedded in an organic binder for nanopaint application. In this work, we have taken polyurethane as a model organic binder. Silica nanoparticles have been prepared through sol–gel synthesis with a particle size of 85?nm. Titania and core–shell nanoparticles have been prepared through both sol–gel and peptization process. Particle sizes obtained were 107?nm for titania and 240?nm for core–shell nanoparticles prepared through sol–gel process and 75?nm for TiO₂ and 144?nm for core–shell nanoparticles prepared through peptization process. The coating formulations were developed with the above nanoparticles individually and nanoparticle concentration was varied from 1 to 6?wt% and the best performance in terms of hydrophobicity was obtained with 4?wt % of the nanoparticles in polyurethane coating formulation. All the coating formulations prepared were applied on a glass substrate and dried at 100°C. The dry film thickness obtained was around 100?µm in each case. These films dried on glass substrate were irradiated by nitrogen and argon ion beam with energy of 26?keV at fluences of 10¹⁴ to 10¹⁶?ions/cm². The anti-algal property of the irradiated samples was improved and hydrophobicity was reduced.     

Measuring microelastic properties of stratum corneum

We explore the compression moduli of a thin biological tissue through probe microscopy. The elastic modulus (E') of isolated stratum corneum is measured at varying depths through the use of an atomic force microscope (AFM) as well as a nano-indentor (Hysitron Triboscope). In addition, a nano-DMA is used to measure visco-elastic properties. Measurements on dry and hydrated stratum corneum show an order of magnitude difference in E' and the measured tandelta (E'/E') is seen to increase from approximately 0.1 to 0.25. In addition, extensive validation of the experiments is conducted with different indentation probes at different force ranges to reveal the effects of indentor geometry and indentation depth on the measured elastic modulus. The sensitivity of the measurements is tested with applying known treatments to stratum corneum and exploring their effects on biomechanical parameters.     

A class of nonpositively curved Kähler manifolds biholomorphic to the unit ball in Cn

Let $(M,g)$ be a simply connected complete Kähler manifold with nonpositive sectional curvature. Assume that g has constant negative holomorphic sectional curvature outside a compact set. We prove that M is then biholomorphic to the unit ball in ${\mathbb{C}}^n$, where ${\dim }_{\mathbb{C}}M=n$. To cite this article: H. Seshadri, K. Verma, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Monitoring phagocytic uptake of amyloid β into glial cell lysosomes in real time

Phagocytosis by glial cells is essential to regulate brain function during health and disease. Therapies for Alzheimer''s disease (AD) have primarily focused on targeting antibodies to amyloid β (Aβ) or inhibitng enzymes that make it, and while removal of Aβ by phagocytosis is protective early in AD it remains poorly understood. Impaired phagocytic function of glial cells during later stages of AD likely contributes to worsened disease outcome, but the underlying mechanisms of how this occurs remain unknown. We have developed a human Aβ_1–42 analogue (Aβ^pH) that exhibits green fluorescence upon internalization into the acidic organelles of cells but is non-fluorescent at physiological pH. This allowed us to image, for the first time, glial uptake of Aβ^pH in real time in live animals. We find that microglia phagocytose more Aβ^pH than astrocytes in culture, in brain slices and in vivo. Aβ^pH can be used to investigate the phagocytic mechanisms responsible for removing Aβ from the extracellular space, and thus could become a useful tool to study Aβ clearance at different stages of AD.

Glial cell phagocytosis of pH-dependent amyloid-β, Aβ^pH, in live and fixed cultures, brain tissue sections, retina, cortex and in live animals useful for studying function in health and disease.