Discrete Modified Projection Methods for Urysohn Integral Equations with Green's Function Type Kernels

In the present paper we consider discrete versions of the modified projection methods for solving a Urysohn integral equation with a kernel of the type of Green's function. For $r \geq 0,$ a space of piecewise polynomials of degree $\leq r$ with respect to an uniform partition is chosen to be the approximating space. We define a discrete orthogonal projection onto this space and replace the Urysohn integral operator by a Nystr\"{o}m approximation. The order of convergence which we obtain for the discrete version indicates the choice of numerical quadrature which preserves the orders of convergence in the continuous modified projection methods. Numerical results are given for a specific example.Comment: This is the the same paper with the arXiv identifier 1904.07895, but the shortened version. A bit change in the title als

Effect of microstructure on the high temperature strength of nitride bonded silicon carbide composite

Four compositions of nitride bonded SiC were fabricated with varying particle size of SiC of ~ 9.67, ~ 13.79, ~ 60 μ and their mixture with Si of ~ 4.83 μ particle size. The green density and hence the open porosity of the shapes were varied between 1.83 to 2.09 g/cc and 33.3 to 26.8 vol.%, respectively. The effect of these parameters on room temperature and high temperature strength of the composite up to 1300°C in ambient condition were studied. The high temperature flexural strength of the composite of all compositions increased at 1200 and 1300°C because of oxidation of Si3N4 phase and blunting crack front. Formation of Si3N4 whisker was also observed. The strength of the mixture composition was maximum

Overcomplete steerable pyramid filters and rotation invariance

A given (overcomplete) discrete oriented pyramid may be converted into a steerable pyramid by interpolation. We present a technique for deriving the optimal interpolation functions (otherwise called 'steering coefficients'). The proposed scheme is demonstrated on a computationally efficient oriented pyramid, which is a variation on the Burt and Adelson (1983) pyramid. We apply the generated steerable pyramid to orientation-invariant texture analysis in order to demonstrate its excellent rotational isotropy. High classification rates and precise rotation identification are demonstrated

Long term Ultra-Violet Variability of Seyfert galaxies

Flux variability is one of the defining characteristics of Seyfert galaxies, a class of active galactic nuclei (AGN). Though these variations are observed over a wide range of wavelengths, results on their flux variability characteristics in the ultra-violet (UV) band are very limited. We present here the long term UV flux variability characteristics of a sample of fourteen Seyfert galaxies using data from the International Ultraviolet Explorer acquired between 1978 and 1995. We found that all the sources showed flux variations with no statistically significant difference in the amplitude of UV flux variation between shorter and longer wavelengths. Also, the flux variations between different near-UV (NUV, 1850 - 3300 A) and far-UV (FUV, 1150 - 2000 A) passbands in the rest frames of the objects are correlated with no time lag. The data show indications of (i) a mild negative correlation of UV variability with bolometric luminosity and (ii) weak positive correlation between UV variability and black hole mass. At FUV, about 50% of the sources show a strong correlation between spectral indices and flux variations with a hardening when brightening behaviour, while for the remaining sources the correlation is moderate. In NUV, the sources do show a harder when brighter trend, however, the correlation is either weak or moderate.Comment: Accepted by Journal of Astrophysics and Astronom

Q-Learning Induced Artificial Bee Colony for Noisy Optimization

The paper proposes a novel approach to adaptive selection of sample size for a trial solution of an evolutionary algorithm when noise of unknown distribution contaminates the objective surface. The sample size of a solution here is adapted based on the noisy fitness profile in the local surrounding of the given solution. The fitness estimate and the fitness variance of a sub-population surrounding the given solution are jointly used to signify the degree of noise contamination in its local neighborhood (LN). The adaptation of sample size based on the characteristics of the fitness landscape in the LN of a solution is realized here with the temporal difference Q-learning (TDQL). The merit of the present work lies in utilizing the reward-penalty based reinforcement learning mechanism of TDQL for sample size adaptation. This sidesteps the prerequisite setting of any specific functional form of relationship between the sample size requirement of a solution and the noisy fitness profile in its LN. Experiments undertaken reveal that the proposed algorithms, realized with artificial bee colony, significantly outperform the existing counterparts and the state-of-the-art algorithms

Implications of New Quantum Spin Perspective In Quantum Gravity

Consequences of new quantum spin perspective in quantum gravity are far-reaching. Results of this novel perspective in loop quantum gravity, i.e., the modification of the equation of geometrical operators such as the area and the volume operator are known. Using newly proposed formula from this perspective, the magnitude of fundamental constants such as the reduced Planck constant $\hbar$, the gravitational constant $G$, the speed of light $c$, the Boltzmann constant $k_{\beta}$, the fine structure constant $\alpha$, can be validated. With the aid of this perspective, we find new formulas for the fundamental Planckian quantities and the derived Planckian quantities. We also propose novel formulas for the Planck star such as the size, the curvature, the surface area and the size of black hole (for the Planck star) without modifying its significance. The relation of the quantum spin with the Planck temperature $T_{P}$ $(T_{p} \propto n^{2})$, the Planck mass $m_{P}$ $(m_{P} \propto n^{2})$, the Planck length $l_{P}$ $(l_{P} \propto n)$ are also proposed using this novel perspectiveComment: 13 page