Emergence of Cosmic Space and Minimal Length in Quantum Gravity

An emergence of cosmic space has been suggested by Padmanabhan in [arXiv:1206.4916]. This new interesting approach argues that the expansion of the universe is due to the difference between the number of degrees of freedom on a holographic surface and the one in the emerged bulk. In this paper, we derive, using emergence of cosmic space framework, the general dynamical equation of FRW universe filled with a perfect fluid by considering a generic form of the entropy as a function of area. Our derivation is considered as a generalization of emergence of cosmic space with a general form of entropy. We apply our equation with higher dimensional spacetime and derive modified Friedmann equation in Gauss-Bonnet gravity. We then apply our derived equation with the corrected entropy-area law that follows from Generalized Uncertainty Principle (GUP) and derive a modified Friedmann equations due to the GUP. We then derive the modified Raychaudhuri equation due to GUP in emergence of cosmic space framework and investigate it using fixed point method. Studying this modified Raychaudhuri equation leads to non-singular solutions which may resolve singularities in FRW universe.Comment: 10 pages, revtex4, 1 figure, to match published version in PL

Curvatures of the Melnikov type, Hausdorff dimension, rectifiability, and singular integrals on R-n

One of the most fundamental steps leading to the solution of the analytic capacity problem ( for 1-sets) was the discovery by Melnikov of an identity relating the sum of permutations of products of the Cauchy kernel to the three-point Menger curvature. We here undertake the study of analogues of this so-called Menger-Melnikov curvature, as a nonnegative function defined on certain copies of R-n, in relation to some natural singular integral operators on subsets of R-n of various Hausdorff dimensions. In recent work we proved that the Riesz kernels x\x\(-m-1) (m is an element of N\ {1}) do not admit identities like that of Melnikov in any L-k norm (k is an element of N). In this paper we extend these investigations in various ways. Mainly, we replace the Euclidean norm \.\ by equivalent metrics delta(., .) and we consider all possible k, m, n, delta(., .). We do this in hopes of finding better algebraic properties which may allow extending the ideas to higher dimensional sets. On the one hand, we show that for m > 1 no such identities are admissible at least when is a norm that is invariant under reflections and permutations of the coordinates. On the other hand, for m = 1, we show that for each choice of metric, one gets an identity and a curvature like those of Melnikov. This allows us to generalize those parts of the recent singular integral and recti ability theories for the Cauchy kernel that depend on curvature to these much more general kernels, and provides a more general framework for the curvature approach

Hybrid fuzzy- proportionl integral derivative controller (F-PID-C) for control of speed brushless direct curren motor (BLDCM)

Hybrid Fuzzy proportional-integral-derivative (PID) controllers (F-PID-C) is designed and analyzed for controlling speed of brushless DC (BLDC) motor. A simulation investigation of the controller for controlling the speed of BLDC motors is performed to beat the presence of nonlinearities and uncertainties in the system. The fuzzy logic controller (FLC) is designed according to fuzzy rules so that the systems are fundamentally robust. There are 49 fuzzy rules for each parameter of FUZZY-PID controller. Fuzzy Logic is used to tune each parameter of the proportional, integral and derivative ( kp,ki,kd) gains, respectively of the PID controller. The FLC has two inputs i.e., i) the motor speed error between the reference and actual speed and ii) the change in speed of error (rate of change error). The three outputs of the FLC are the proportional gain, kp, integral gain ki and derivative gain kd, gains to be used as the parameters of PID controller in order to control the speed of the BLDC motor. Various types of membership functions have been used in this project i.e., gaussian, trapezoidal and triangular are assessed in the fuzzy control and these membership functions are used in FUZZY PID for comparative analysis. The membership functions and the rules have been defined using fuzzy system editor given in MATLAB. Two distinct situations are simulated, which are start response, step response with load and without load. The FUZZY-PID controller has been tuned by trial and error and performance parameters are rise time, settling time and overshoot. The findings show that the trapezoidal membership function give good results of short rise time, fast settling time and minimum overshoot compared to others for speed control of the BLDC motor

A novel disparity-assisted block matching-based approach for super-resolution of light field images

Currently, available plenoptic imaging technology has limited resolution. That makes it challenging to use this technology in applications, where sharpness is essential, such as film industry. Previous attempts aimed at enhancing the spatial resolution of plenoptic light field (LF) images were based on block and patch matching inherited from classical image super-resolution, where multiple views were considered as separate frames. By contrast to these approaches, a novel super-resolution technique is proposed in this paper with a focus on exploiting estimated disparity information to reduce the matching area in the super-resolution process. We estimate the disparity information from the interpolated LR view point images (VPs). We denote our method as light field block matching super-resolution. We additionally combine our novel super-resolution method with directionally adaptive image interpolation from [1] to preserve sharpness of the high-resolution images. We prove a steady gain in the PSNR and SSIM quality of the super-resolved images for the resolution enhancement factor 8x8 as compared to the recent approaches and also to our previous work [2]