July 12, 2012 Tags: DIFFERENCE equations -- Oscillation theory, DIFFERENTIAL equations, GENERALIZATION, INEQUALITIES (Mathematics), Natural, Nonlinear, NONLINEAR theories, NUMBERS, PROOF theory
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Using the fixed point method, we prove the Hypers-Ul am stability of the orthogonally additive-quadratic functional equation 2f (x + y/2) + 2f (x – y/2) = 3/2f(x) – 1/2f(-x) + 1/2f(y) + 1/2f(-y) (0.1) for all x, y with x ⊥ y, in non-Archimedean Banach spaces. Here ⊥ is the orthogonality in the sense of Rätz. [ABSTRACT FROM AUTHOR]
Read MoreJuly 12, 2012 Tags: BANACH spaces, CAUCHY problem, EQUATIONS, FIXED point theory, INEQUALITIES (Mathematics), ORTHOGONALIZATION methods, Quadratic, STABILITY
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The main purpose of this paper is to develop certain operational formula for Jacobi-Pineiro polynomials and to find some properties of these polynomials with the help of operational formulas. [ABSTRACT FROM AUTHOR]
Read MoreJuly 12, 2012 Tags: GENERALIZATION, GENERATING functions, JACOBI polynomials, MATHEMATICS -- Formulae, ORTHOGONALIZATION methods, PROOF theory, RECURRENT sequences (Mathematics)
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Nanoparticles have attracted lot of attention for their exceptional properties which are different from those of materiais in bulks. Metal oxides have shown application in many domains of science. Especially, manganese oxide has proven applications in energy storage, sensors, imaging technologies and even biomedicine. But, synthesis of ultrafine monodisperse nanoparticles that can be dispersed easily in polar or non-polar solvent is of prime importance for applications involving composites, phase change energy material, thermal management etc. We report the synthesis of ultrafine monodisperse MnO nanoparticles from manganese acetate tetrahydrate by a solvothermal method. Surfactants, oleie acid and 1-octadecene were used in suitable concentrations to yield oleie acid stabilized manganese oxide nanoparticles. The formation of manganese-oleate complex in the first step was confirmed using FTIR. X-ray diffraction spectra confirmed the formation of manganese oxide. Scanning and Transmission Electron Micrographs established the size of nanoparticles to be in the range of 15-20 nm. Crystalline nature of the nanoparticles was confirmed using selected area electron diffraction. Aging time has been found to influence the size of the nanoparticles, with layer particle sizes obtained for higher aging periods. These nanoparticles are suitable for dispersion in non-polar solvents and in thermic fluids like Therminol 55 resulting in nanofluids. [ABSTRACT FROM AUTHOR]
Read MoreJuly 12, 2012 Tags: MANGANESE acetate, MANGANESE oxides, METALLIC oxides, NANOPARTICLES, OLEIC acid, SOLVENTS
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In this paper, we show that the proof of Theorem 3.9 of the paper George and Veeramani [On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395-399.] is not true. We also correct the proof in this note. [ABSTRACT FROM AUTHOR]
Read MoreJuly 12, 2012 Tags: COMPACT spaces, Continuous, FUNCTIONS, FUZZY sets, METRIC spaces, PROOF theory, SET theory, TOPOLOGY
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Using the fixed point method, we prove the Hyers-Ulam stability of the following generalized Jensen quadratic funtional equation f ( x + y / r + sz ) + f ( x + y / r – sz ) + f ( x – y / r + sz ) + f (x – y / r – sz ) = 4 / r² f (x) + 4 / r² f (y) + 4s² f (z) in fuzzy Banach spaces. [ABSTRACT FROM AUTHOR]
Read MoreJuly 12, 2012 Tags: BANACH spaces, EQUATIONS, FIXED point theory, FUNCTIONAL equations, FUNCTIONS of complex variables, FUZZY sets, GENERALIZATION, Quadratic
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For the large sparse system of weakly nonlinear equations, based on separable property and strong dominance between the linear and the nonlinear terms and on the asymmetric Hermitian and skew-Hermitian splitting (AHSS) of the coefficient matrix, we establish two nonlinear composite iteration schemes, called Picard-AHSS and nonlinear AHSS-like methods. The advantage of these methods is that they only need to solve the linear sub-systems of constant coefficient matrices. In addition, these methods can also take full advantage of the dominance of Hermitian part. Therefore, computational workloads and computer storage may be saved in actual implementations. Theoretical analysis show that these new iteration methods are local convergent under suitable conditions. Numerical results show that both Picard-AHSS and nonlinear AHSS-like iteration methods are feasible and effective for the large scale system of weakly nonlinear equations, especially when the Hermitian part of the coefficient matrix is dominant. [ABSTRACT FROM AUTHOR]
Read MoreJuly 12, 2012 Tags: BINOMIAL coefficients, HERMITIAN operators, ITERATIVE methods (Mathematics), MATRIX inequalities, NONLINEAR models (Statistics), NONLINEAR systems, NUMERICAL analysis
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Psoriasis is a chronic inflammatory skin condition which affects 2-3% of population around the world. Psoriasis Area and Severity Index (PASI) is a gold standard to assess psoriasis severity as well as the treatment efficacy. Although a gold standard, PASI is rarely used because it is tedious and complex. In practice, PASI score is determined subjectively by dermatologists, therefore inter and intra variations of assessment are possible to happen even among expert dermatologists. This research develops an algorithm to assess psoriasis lesion for PASI scoring objectively. Focus of this research is thickness assessment as one of PASI four parameters beside area, erythema and scaliness. Psoriasis lesion thickness is measured by averaging the total elevation from lesion base to lesion surface. Thickness values of 122 3D images taken from 39 patients are grouped into 4 PASI thickness score using K-means clustering. Validation on lesion base construction is performed using twelve body curvature models and show good result with coefficient of determinant (R2) is equal to 1. [ABSTRACT FROM AUTHOR]
Read MoreJuly 12, 2012 Tags: CHRONIC diseases, DERMATOLOGISTS, IMAGE analysis, INFLAMMATION, PSORIASIS, THICKNESS measurement, TREATMENT effectiveness
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The one-dimensional fractional diffusion equation is studied systematically using the non-polynomial spline method. The Caputo fractional derivative is used for formulation. An example is solved to assess the accuracy of the method. The numerical results are obtained for different values (n) of equation. An effective and easy-to-use method for solving such equations is needed. [ABSTRACT FROM AUTHOR]
Read MoreJuly 12, 2012 Tags: EQUATIONS -- Numerical solutions, FRACTIONAL integrals, HEAT equation, NUMERICAL analysis, POLYNOMIALS, PROBLEM solving, SPLINE theory
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The article focuses on the challenges of Susan Trail, superintendent of Antietam National Battlefield, Maryland, in guiding the park during its 150th celebration in September 2012.
Read MoreJuly 12, 2012 Category: Articles No Comments