M-fractional derivative under interval uncertainty: theory, properties and applications

In the recent years some efforts were made to propose simple and well-behaved fractional derivatives that inherit the classical properties from the first order derivative. In this regards, the truncated M-fractional derivative for α-differentiable function was recently introduced that is a generalization of four fractional derivatives presented in the literature and has their important features. In this research, we aim to generalize this novel and effective derivative under interval uncertainty. The concept of interval truncated M-fractional derivative is introduced and some of the distinguished properties of this interesting fractional derivative such as Rolle’s and mean value theorems, are developed for the interval functions. In addition, the existence and uniqueness conditions of the solution for the interval fractional differential equations (IFDEs) based on this new derivative are also investigated. Finally, we present the applicability of this novel interval fractional derivative for IFDEs based on the notion of w-increasing (w-decreasing) by solving a number of test problems

A Gradient Weighted Moving Finite-Element Method with Polynomial Approximation of Any Degree

A gradient weighted moving finite element method (GWMFE) based on piecewise polynomial of any degree is developed to solve time-dependent problems in two space dimensions. Numerical experiments are employed to test the accuracy and effciency of the proposed method with nonlinear Burger equation

Acoustic phonon scattering in a low density, high mobility AlGaN/GaN field effect transistor

We report on the temperature dependence of the mobility, $\mu$, of the two-dimensional electron gas in a variable density AlGaN/GaN field effect transistor, with carrier densities ranging from 0.4$\times10^{12}$ cm$^{-2}$ to 3.0$\times10^{12}$ cm$^{-2}$ and a peak mobility of 80,000 cm$^{2}$/Vs. Between 20 K and 50 K we observe a linear dependence $\mu_{ac}^{-1} = \alpha$T indicating that acoustic phonon scattering dominates the temperature dependence of the mobility, with $\alpha$ being a monotonically increasing function of decreasing 2D electron density. This behavior is contrary to predictions of scattering in a degenerate electron gas, but consistent with calculations which account for thermal broadening and the temperature dependence of the electron screening. Our data imply a deformation potential D = 12-15 eV.Comment: 3 pages, 2 figures, RevTeX. Submitted to Appl Phys Let

Differences in maladaptive schemas between patients suffering from chronic and acute posttraumatic stress disorder and healthy controls

War, as a stressor event, has a variety of acute and chronic negative consequences, such as posttraumatic stress disorder (PTSD). In this context, early maladaptive schema-based problems in PTSD have recently become an important research area. The aim of this study was to assess early maladaptive schemas in patients with acute and chronic PTSD.; Using available sampling methods and diagnostic criteria, 30 patients with chronic PTSD, 30 patients with acute PTSD, and 30 normal military personnel who were matched in terms of age and wartime experience were selected and assessed with the Young Schema Questionnaire-Long Form, Beck Depression Inventory second version (BDI-II), the Beck Anxiety Inventory (BAI), and the Impact of Events Scale (IES).; Both acute and chronic PTSD patients, when compared with normal military personnel, had higher scores for all early maladaptive schemas. Additionally, veterans suffering from chronic PTSD, as compared with veterans suffering from acute PTSD and veterans without PTSD, reported more impaired schemas related, for instance, to Self-Control, Social Isolation, and Vulnerability to Harm and Illness.; The results of the present study have significant preventative, diagnostic, clinical, research, and educational implications with respect to PTSD

Developing a Local Neurofuzzy Model for Short-Term Wind Power Forecasting

Large scale integration of wind generation capacity into power systems introduces operational challenges due to wind power uncertainty and variability. Therefore, accurate wind power forecast is important for reliable and economic operation of the power systems. Complexities and nonlinearities exhibited by wind power time series necessitate use of elaborative and sophisticated approaches for wind power forecasting. In this paper, a local neurofuzzy (LNF) approach, trained by the polynomial model tree (POLYMOT) learning algorithm, is proposed for short-term wind power forecasting. The LNF approach is constructed based on the contribution of local polynomial models which can efficiently model wind power generation. Data from Sotavento wind farm in Spain was used to validate the proposed LNF approach. Comparison between performance of the proposed approach and several recently published approaches illustrates capability of the LNF model for accurate wind power forecasting

On new solutions of linear system of first -order fuzzy differential equations with fuzzy coefficient

In this paper, we firstly introduce system of first order fuzzy differential equations. Then, we convert the problem to two crisp systems of first order differential equations. For numerical aspects, we apply exponentially fitted Runge Kutta method to solve the fuzzy problems. We solve some well-known examples in order to demonstrate the applicability and accuracy of results

Tau method for the numerical solution of a fuzzy fractional kinetic model and its application to the oil palm frond as a promising source of xylose

The Oil Palm Frond (a lignocellulosic material) is a high-yielding energy crop that can be utilized as a promising source of xylose. It holds the potential as a feedstock for bioethanol production due to being free and inexpensive in terms of collection, storage and cropping practices. The aim of the paper is to calculate the concentration and yield of xylose from the acid hydrolysis of the Oil Palm Frond through a fuzzy fractional kinetic model. The approximate solution of the derived fuzzy fractional model is achieved by using a tau method based on the fuzzy operational matrix of the generalized Laguerre polynomials. The results validate the effectiveness and applicability of the proposed solution method for solving this type of fuzzy kinetic model

Better Guarantees for k-Means and Euclidean k-Median by Primal-Dual Algorithms

bibsource: dblp computer science bibliography, http://dblp.org biburl: http://dblp.org/rec/bib/conf/focs/AhmadianNSW17 timestamp: Thu, 16 Nov 2017 15:01:42 +0100 bdsk-url-1: https://doi.org/10.1109/FOCS.2017.15 bdsk-url-2: http://dx.doi.org/10.1109/FOCS.2017.15bibsource: dblp computer science bibliography, http://dblp.org biburl: http://dblp.org/rec/bib/conf/focs/AhmadianNSW17 timestamp: Thu, 16 Nov 2017 15:01:42 +0100 bdsk-url-1: https://doi.org/10.1109/FOCS.2017.15 bdsk-url-2: http://dx.doi.org/10.1109/FOCS.2017.1

Uncertain viscoelastic models with fractional order: a new spectral tau method to study the numerical simulations of the solution

The analysis of the behaviors of physical phenomena is important to discover significant features of the character and the structure of mathematical models. Frequently the unknown parameters involve in the models are assumed to be unvarying over time. In reality, some of them are uncertain and implicitly depend on several factors. In this study, to consider such uncertainty in variables of the models, they are characterized based on the fuzzy notion. We propose here a new model based on fractional calculus to deal with the Kelvin–Voigt (KV) equation and non-Newtonian fluid behavior model with fuzzy parameters. A new and accurate numerical algorithm using a spectral tau technique based on the generalized fractional Legendre polynomials (GFLPs) is developed to solve those problems under uncertainty. Numerical simulations are carried out and the analysis of the results highlights the significant features of the new technique in comparison with the previous findings. A detailed error analysis is also carried out and discussed