On initial value and terminal value problems for subdiffusive stochastic Rayleigh-Stokes equation

In this paper, we study two stochastic problems for time-fractional RayleighStokes equation including the initial value problem and the terminal value problem. Here, two problems are perturbed by Wiener process, the fractional derivative are taken in the sense of Riemann-Liouville, the source function and the time-spatial noise are nonlinear and satisfy the globally Lipschitz conditions. We attempt to give some existence results and regularity properties for the mild solution of each problem

On stochastic nonclassical diffusion equation with standard and fractional Brownian motion

This paper is concerned with the mathematical analysis of terminal value problems for a stochastic non-classical diffusion equation, where the source is assumed to be driven by classical and fractional Brownian motions. Our two problems are to study in the sense of well-posedness and ill-posedness meanings. Here, a terminal value problem is a problem of determining the statistical properties of the initial data from the final time data. In the case 0 < β ≤ 1, where β is the fractional order of a Laplace operator, we show that these are well-posed under certain assumptions. We state a definition of ill-posedness and obtain the ill-poseness results for the problems when β > 1. The major analysis tools in this paper are based on properties of stochastic integrals with respect to the fractional Brownian motion

On Throughput for UAV Relay Assisted for Use in Disaster Communications

In this paper, the system performance of an energy harvesting (EH) unmanned aerial vehicle (UAV) system for use in disasters was investigated. The communication protocol was divided into two phases. In the first phase, a UAV relay (UR) harvested energy from a power beacon (PB). In the second phase, a base station (BS) transmitted the signal to the UR using non-orthogonal multiple access (NOMA); then, the UR used its harvested energy from the first phase to transfer the signal to two sensor clusters, i.e., low-priority and high-priority clusters, via the decode-and-forward (DF) technique. A closed-form expression for the throughput of the cluster heads of these clusters was derived to analyze the system performance. Monte Carlo simulations were employed to verify our approach

On terminal value problems for bi-parabolic equations driven by Wiener process and fractional Brownian motions

In this paper, we study two terminal value problems (TVPs) for stochastic bi-parabolic equations perturbed by standard Brownian motion and fractional Brownian motion with Hurst parameter h ∈ ( 1/2 , 1) separately. For each problem, we provide a representation for the mild solution and find the space where the existence of the solution is guaranteed. Additionally, we show clearly that the solution of each problem is not stable, which leads to the ill-posedness of each problem. Finally, we propose two regularization results for both considered problems by using the filter regularization method

Forced nonlinear vibration of shallow shell and application to technical diagnosis

This paper presents direct and inverse problems of forced nonlinear vibration of shallow shell. From that the method of establishment and solution of technical diagnosis for shallow shell under the vibrated load is proposed. The diagnosis criterion is the minimum of the difference between the square of experimental and theoretical data. The diagnosed parameters are the external loads and the reactions arose at the boundaries

Building a Model of Organizational Activities Experience in Natural Sciences under Stem Education Orientation

STEM educational-oriented Natural Science experience activities are learner-oriented activities Taking learners as the center in all natural science research activities applying engineering technology and mathematics STEM in solving practical problems Based on theoretical research on experiential activities STEM education and the characteristics of Natural Sciences the article studies the educational forces inside and outside the school From there it is proposed to build a model of organizational structure for experiential activities in Natural Sciences oriented toward STEM education The results of this research are meaningful in helping principals see the importance and significance of coordinating educational forces inside and outside the school in organizing experiential activities in Natural Sciences according to orientation STEM education for student

A simple, effective, green method for regioselective 3-acylation of unprotected indoles

A fast and green method is developed for regioselective acylation of indoles in the 3-position without the need for protection of the NH position. The method is based on Friedel-Crafts acylation using acid anhydrides. The method has been optimized, and Y(OTf)3 in catalytic amounts is found to be the best catalyst together with the commercially available ionic liquid [BMI]BF4 (1-butyl-3-methylimidazolium tetrafluoro-borate) as solvent. The reaction is completed in a very short time using monomode microwave irradiation. The catalyst can be reused up to four times without significant loss of activity. A range of substituted indoles are investigated as substrates, and thirteen new compounds have been synthesized