Exp-function Method for Wick-type Stochastic Combined KdV-mKdV Equations

Exp-function method is proposed to present soliton and periodic wave solutions for variable coefficients combined KdV- mKdV equation. By means of Hermite transform and white noise analysis, we consider the variable coefficients and Wick-type stochastic combined KdV-mKdV equations. As a result, we can construct new and more general formal solutions. These solutions include exact stochastic soliton and periodic wave solutions.Keywords: combined KdV-mKdV equation, Exp-function method, Wick product, Hermite transform, White noise

COVID-19 Prediction Using LSTM Algorithm: GCC case study

Coronavirus-19 (COVID-19) is the black swan of 2020. Still, the human response to restrain the virus is also creating massive ripples through different systems, such as health, economy, education, and tourism. This paper focuses on research and applying Artificial Intelligence (AI) algorithms to predict COVID-19 propagation using the available time-series data and study the effect of the quality of life, the number of tests performed, and the awareness of citizens on the virus in the Gulf Cooperation Council (GCC) countries at the Gulf area. So we focused on cases in the Kingdom of Saudi Arabia (KSA), United Arab of Emirates (UAE), Kuwait, Bahrain, Oman, and Qatar. For this aim, we accessed the time-series real-datasets collected from Johns Hopkins University Center for Systems Science and Engineering (JHU CSSE). The timeline of our data is from January 22, 2020 to January 25, 2021. We have implemented the proposed model based on Long Short-Term Memory (LSTM) with ten hidden units (neurons) to predict COVID-19 confirmed and death cases. From the experimental results, we confirmed that KSA and Qatar would take the most extended period to recover from the COVID-19 virus, and the situation will be controllable in the second half of March 2021 in UAE, Kuwait, Oman, and Bahrain. Also, we calculated the root mean square error (RMSE) between the actual and predicted values of each country for confirmed and death cases, and we found that the best values for both confirmed and death cases are 320.79 and 1.84, respectively, and both are related to Bahrain. While the worst values are 1768.35 and 21.78, respectively, and both are related to KSA. On the other hand, we also calculated the mean absolute relative errors (MARE) between the actual and predicted values of each country for confirmed and death cases, and we found that the best values for both confirmed and deaths cases are 37.76 and 0.30, and these are related to Kuwait and Qatar respectively. While the worst values are 71.45 and 1.33, respectively, and both are related to KSA

Generalized Solutions of Wick-type Stochastic KdV-Burgers Equations Using Exp-function Method

Variable coefficients and Wick-type stochastic KdV-Burgers equations are researched. Expfunction method is proposed to present soliton and periodic wave solutions for variable coefficients KdVBurgers equation. Generalized white noise functional solutions for Wick-type stochastic KdV-Burgersequations are showed via Hermite transform and white noise analysis.Keywords: KdV-Burgers equation; Exp-function method; Wick product; Hermite transform; White noise

The Moment Problem in Hypercomplex Systems

This paper is devoted to give the necessary and sufficient conditions guarantees that the product of two generalized moment functions defined in a hypercomplex system L1(Q,m) is also generalized moment function in L1(Q,m) . Also, we prove that a bounded continuous function  in a hypercomplex system L1(Q,m) is conditionally positive definite if and only if is generalized moment functions defined in L1(Q,m) . Moreover, we will give the integral representations of a generalized moment functions defined in L1 (Q, m)

2-Amino-4-phenyl-4H,10H-1,3,5-triazino[1,2-a]benzimidazol-3-ium chloride

2-Guanidinobenzimidazole condenses with benzaldehyde in the presence of hydro­chloric acid to form 2-amino-3,4-dihydro-4-phenyl-1,3,5-triazino[1,2-a]benzimidazole, which was isolated as its hydro­chloride, C15H14N5 +·Cl−. The positive charge of the cation is formally placed on the double-bonded N atom of the dihydro­triazine ring. The six-membered dihydro­triazine that is fused with the benzimidazole ring system is relatively flat (r.m.s. deviation = 0.106 Å), with the methine C atom deviating most [0.164 (1) Å] from the mean-square plane. The phenyl ring connected to the methine C atom is disordered over two positions in a 0.558 (1):0.442 (1) ratio; the two orientations are aligned at 85.1 (1) and 89.6 (1)° with respect to the dihydro­triazine ring. In the crystal, adjacent cations and anions are linked by N—H⋯N and N—H⋯Cl hydrogen bonds, generating a double chain running along the b axis

SELF-GRAVITATING ELECTRODYNAMIC STABILITY OF ACCELERATING STREAMING FLUID CYLINDERS IN SELF-GRAVITATING TENUOUS MEDIUM

ABSTRACT The stability of electrodynamic self-gravitational of accelerating streaming fluid cylinder surrounded by tenuous medium has been studied for all axisymmetric and non-axisymmetric perturbation modes. The dispersion relation is derived, discussed and some reported works are recovered as limiting cases from it. The electro-dynamic forces interior and exterior the fluid cylinder are destabilizing. The self-gravitating forces are destabilizing for small axisymmetric domain while they are stabilizing in all other domains. The accelerating (periodic) streaming has a stabilizing tendency. The self-gravitating electrodynamic stable domains are enlarged due to the resonance of the periodic streaming and could overcome the instability character of the model, if it is so strong

Non-Gaussian White Noise Functional Solutions of χ -Wick-Type Stochastic KdV Equations

In this paper, KdV equations with variable coefficients and Wick-type stochastic KdV equations are investigated. White noise functional solutions are shown by Hermite transform, homogeneous balance principle and F-expansion method. By means of the direct connection between the theory of hypercomplex systems and white noise analysis, we setup a full framework to study the stochastic partial differential equations with non-Gaussian parameters. Using this framework and F-expansion method, we present multiple families of exact and stochastic travelling wave solutions for the variable coefficients KdV equations and the stochastic KdV equations with non-Gaussian parameters, respectively. These solutions include functional solutions of Jacobi elliptic functions (JEFs), trigonometric and hyperbolic types

4-(4-Chlorobenzyl)-5-methyl-2-phenyl-1H-pyrazol-3(2H)-one

The five-membered ring of the title compound, C17H15ClN2O, is almost planar (r.m.s. deviation = 0.008 Å), and its phenyl subsitutent is aligned at 34.9 (1)° with respect to this ring. The angle at the methylene C atom is opened to 116.4 (2)°. In the crystal, adjacent molecules are linked by an N—H...O hydrogen bond, generating a linear chain along the a axis