Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments

We discuss the existence of positive solutions to a class of fractional boundary value problem with changing sign nonlinearity and advanced arguments Dαx(t)+μh(t)f(x(a(t)))=0,t∈(0,1),20,x(0)=x′(0)=0,x(1)=βx(η)+λ[x],β>0, and  η∈(0,1), where Dα is the standard Riemann-Liouville derivative, f:[0,∞)→[0,∞) is continuous, f(0)>0, h :[0,1]→(−∞,+∞), and a(t) is the advanced argument. Our analysis relies on a nonlinear alternative of Leray-Schauder type. An example is given to illustrate our results

Causal association between adiposity and hemorrhoids: a Mendelian randomization study

BackgroundHemorrhoids are a very common anorectal disorder affecting a large number of individuals throughout the world. This study aimed to evaluate the causal effects of four adiposity traits including body mass index (BMI), body fat percentage, waist circumference, and waist-to-hip ratio on hemorrhoids by Mendelian randomization (MR).MethodsWe used summary statistics of BMI (N = 461,460), body fat percentage (N = 454,633), waist circumference (N = 462,166), waist-to-hip ratio (N = 212,244), and hemorrhoids (N = 337,199) from large-scale genome wide association studies of European ancestry. Univariable and multivariable MR were carried out to infer causality. The MR Steiger directionality test was used to test the causal direction.ResultsThe primary MR analysis using the inverse variance weighted (IVW) method showed that there were positive effects of genetically determined BMI [odds ratio (OR) = 1.005, 95% confidence interval (CI): 1.003–1.008, per standard deviation (SD), p = 7.801 × 10−5], body fat percentage (OR = 1.005, 95% CI: 1.001–1.008, per SD, p = 0.008), waist circumference (OR = 1.008, 95% CI: 1.005–1.011, per SD, p = 1.051 × 10−6), and waist-to-hip ratio (OR = 1.010, 95% CI: 1.003–1.017, per SD, p = 0.003) on hemorrhoids. These findings were robust in multivariable MR adjusting for physical activity. The Steiger directionality test showed evidence against reverse causation.ConclusionOur MR study supports a causal role of adiposity in the development of hemorrhoids. Adiposity prevention may be an important strategy for reducing hemorrhoids risk

Thermodynamic properties of higher-dimensional dS black holes in dRGT massive gravity

On the basis of the state parameter of de Sitter space-time satisfying the first law of thermodynamics,we can derive some effective thermodynamic quantities.When the temperature of the black hole horizon is equal to that of the cosmological horizon, we think that the effective temperature of the space-time should have the same value. Using this condition, we obtain a differential equation of the entropy of the de Sitter black hole in the higherdimensional de Rham, Gabadadze and Tolley (dRGT) massive gravity. Solving the differential equation, we obtain the corrected entropy and effective thermodynamic quantities of the de Sitter black hole. The results show that for multiparameter black holes, the entropy satisfied differential equation is invariable with different independent state parameters. Therefore, the entropy of higher-dimensional dS black holes in dRGT massive gravity is only a function of the position of the black hole horizon, and is independent of other state parameters. It is consistent with the corresponding entropy of the black hole horizon and the cosmological horizon. The thermodynamic quantities of self-consistent de Sitter spacetime are given theoretically, and the equivalent thermodynamic quantities have the second-order phase transformation similar to AdS black hole, but unlike AdS black hole, the equivalent temperature of de Sitter space-time has a maximum value. By satisfying the requirement of thermodynamic equilibrium and stability of space-time, the conditions for the existence of dS black holes in the universe are obtained.Comment: 11 pages, 6 figure

Two-Tier Prediction of Solar Power Generation with Limited Sensing Resource

This paper considers a typical solar installations scenario with limited sensing resources. In the literature, there exist either day-ahead solar generation prediction methods with limited accuracy, or high accuracy short timescale methods that are not suitable for applications requiring longer term prediction. We propose a two-tier (global-tier and local-tier) prediction method to improve accuracy for long term (24 hour) solar generation prediction using only the historical power data. In global-tier, we examine two popular heuristic methods: weighted k-Nearest Neighbors (k-NN) and Neural Network (NN). In local-tier, the global-tier results are adaptively updated using real-time analytical residual analysis. The proposed method is validated using the UCLA Microgrid with 35kW of solar generation capacity. Experimental results show that the proposed two-tier prediction method achieves higher accuracy compared to day-ahead predictions while providing the same prediction length. The difference in the overall prediction performance using either weighted k-NN based or NN based in the global-tier are carefully discussed and reasoned. Case studies with a typical sunny day and a cloudy day are carried out to demonstrate the effectiveness of the proposed two-tier predictions

Parameter Setting Strategy for the Controller of the DFIG Wind Turbine Considering the Small-Signal Stability of Power Grids

Due to the increasing penetration of the wind generation, the stability, especially the small-signal stability, of the power grid is much related to it. Currently, few studies considered the impact of the parameter settings of the wind turbine controller on the small-signal stability of the grid under the full range of wind conditions. In this paper, we propose a framework for deriving a set of controller parameters by interiorizing their impact on the power system stability, based on an analytic model of a 15th-order single DFIG-infinite grid connection under all wind speeds. The study results on a real wind turbine show that the controller parameters optimized for a specific wind speed may not feasible for other operational conditions yet the proposed framework can obtain a set of parameters guaranteeing the power system stability under all wind speeds