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

Black Hole with Quantum Potential

In this work, we investigate black hole (BH) physics in the context of quantum corrections. These quantum corrections were introduced recently by replacing classical geodesics with quantal (Bohmian) trajectories and hence form a quantum Raychaudhuri equation (QRE). From the QRE, we derive a modified Schwarzschild metric, and use that metric to investigate BH singularity and thermodynamics. We find that these quantum corrections change the picture of Hawking radiation greatly when the size of BH approaches the Planck scale. They prevent the BH from total evaporation, predicting the existence of a quantum BH remnant, which may introduce a possible resolution for the catastrophic behavior of Hawking radiation as the BH mass approaches zero. Those corrections also turn the spacelike singularity of the black hole to be timelike, and hence this may ameliorate the information loss problem.Comment: 16 pages, 6 figures; Accepted in Nucl.Phys.

Hard Decision Cooperative Spectrum Sensing Based on Estimating the Noise Uncertainty Factor

Spectrum Sensing (SS) is one of the most challenging issues in Cognitive Radio (CR) systems. Cooperative Spectrum Sensing (CSS) is proposed to enhance the detection reliability of a Primary User (PU) in fading environments. In this paper, we propose a hard decision based CSS algorithm using energy detection with taking into account the noise uncertainty effect. In the proposed algorithm, two dynamic thresholds are toggled based on predicting the current PU activity, which can be successfully expected using a simple successive averaging process with time. Also, their values are evaluated using an estimated value of the noise uncertainty factor. These dynamic thresholds are used to compensate the noise uncertainty effect and increase (decrease) the probability of detection (false alarm), respectively. Theoretical analysis is performed on the proposed algorithm to deduce its enhanced false alarm and detection probabilities compared to the conventional hard decision CSS. Moreover, simulation analysis is used to confirm the theoretical claims and prove the high performance of the proposed scheme compared to the conventional CSS using different fusion rules.Comment: 5 pages, 4 figures, IEEE International Conference on Computer Engineering and Systems (ICCES 2015). arXiv admin note: text overlap with arXiv:1505.0558

A Proposal for Testing Gravity's Rainbow

Various approaches to quantum gravity such as string theory, loop quantum gravity and Horava-Lifshitz gravity predict modifications of the energy-momentum dispersion relation. Magueijo and Smolin incorporated the modified dispersion relation (MDR) with the general theory of relativity to yield a theory of gravity's rainbow. In this paper, we investigate the Schwarzschild metric in the context of gravity's rainbow. We investigate rainbow functions from three known modified dispersion relations that were introduced by Amelino-Camelia, et el. in [arXiv:hep-th/9605211, arXiv:0806.0339v2, arXiv:astro-ph/9712103] and by Magueijo-Smolin in [arXiv:hep-th/0112090]. We study the effect of the rainbow functions on the deflection of light, photon time delay, gravitational red-shift, and the weak equivalence principle. We compare our results with experiments to obtain upper bounds on the parameters of the rainbow functions.Comment: 6 pages, no figures, to appear in Europhysics Letter

Bivalirudin versus unfractionated heparin: a meta-analysis of patients receiving percutaneous coronary intervention for acute coronary syndromes

OBJECTIVE: Acute coronary syndrome (ACS) encompasses ST segment elevation myocardial infarction (STEMI), with generally high thrombus burden and non-ST segment elevation ACS (NSTE-ACS), with lower thrombus burden. In the setting of percutaneous coronary intervention (PCI) for ACS, bivalirudin appears superior to unfractionated heparin (UFH), driven by reduced major bleeding. Recent trials suggest that the benefit of bivalirudin may be reduced with use of transradial access and evolution in antiplatelet therapy. Moreover, a differential role of bivalirudin in ACS cohorts is unknown. METHODS: A meta-analysis of randomised trials comparing bivalirudin and UFH in patients with ACS receiving PCI, with separate analyses in STEMI and NSTE-ACS groups. Overall estimates of treatment effect were calculated with random-effects model. RESULTS: In 5 trials of STEMI (10 358 patients), bivalirudin increased the risk of acute stent thrombosis (ST) (OR 3.62; CI 1.95 to 6.74; p<0.0001) compared with UFH. Bivalirudin reduced the risk of major bleeding only when compared with UFH plus planned glycoprotein IIb/IIIa inhibitors (GPI) (OR 0.49; CI 0.36 to 0.67; p<0.00001). In 14 NSTE-ACS trials (25 238 patients), there was no difference between bivalirudin and UFH in death, myocardial infarction or ST. However, bivalirudin reduced the risk of major bleeding compared with UFH plus planned GPI (OR 0.52; CI 0.43 to 0.62; p<0.00001), or UFH plus provisional GPI (OR 0.68; CI 0.46 to 1.01; p=0.05). The reduction in major bleeding with bivalirudin was not related to vascular access site. CONCLUSIONS: Bivalirudin increases the risk of acute ST in STEMI, but may confer an advantage over UFH in NSTE-ACS while undergoing PCI, reducing major bleeding without an increase in ST

Remnant for all Black Objects due to Gravity's Rainbow

We argue that a remnant is formed for all black objects in gravity's rainbow. This will be based on the observation that a remnant depends critically on the structure of the rainbow functions, and this dependence is a model independent phenomena. We thus propose general relations for the modified temperature and entropy of all black objects in gravity's rainbow. We explicitly check this to be the case for Kerr, Kerr-Newman-dS, charged-AdS, and higher dimensional Kerr-AdS black holes. We also try to argue that a remnant should form for black Saturn in gravity's rainbow. This work extends our previous results on remnants of Schwarzschild black holes [ arXiv:1402.5320] and black rings [arXiv:1409.5745].Comment: 21 pages, 13 figures, Accepted in Nucl.Phys.

Remnants of Black Rings from Gravity's Rainbow

In this paper, we investigate a spinning black ring and a charged black ring in the context of gravity's rainbow. By incorporating rainbow functions proposed by Amelino-Camelia, et al. in [arXiv:hep-th/9605211, arXiv:0806.0339v2] in the metric of the black rings, a considerable modification happens to their thermodynamical properties. We calculate corrections to the temperature, entropy and heat capacity of the black rings. These calculations demonstrate that the behavior of Hawking radiation changes considerably near the Planck scale in gravity's rainbow, where it is shown that black rings do not evaporate completely and a remnant is left as the black rings evaporate down to Planck scale.Comment: 14 pages, 6 figure

A Gradient-Type Optimization Technique for the Optimal Control for Schrodinger Equations

In this paper, we are considered with the optimal control of a schrodinger equation. Based on the formulation for the variation of the cost functional, a gradient-type optimization technique utilizing the finite difference method is then developed to solve the constrained optimization problem. Finally, a numerical example is given and the results show that the method of solution is robust