Coronaviruses are enveloped RNA viruses from the Coronaviridae family affecting neurological, gastrointestinal, hepatic and respiratory systems. In late 2019 a new member of this family belonging to the Betacoronavirus genera (referred to as COVID-19) originated and spread quickly across the world calling for strict containment plans and policies. In most countries in the world, the outbreak of the disease has been serious and the number of confirmed COVID-19 cases has increased daily, while, fortunately the recovered COVID-19 cases have also increased. Clearly, forecasting the "confirmed" and "recovered" COVID-19 cases helps planning to control the disease and plan for utilization of health care resources. Time series models based on statistical methodology are useful to model time-indexed data and for forecasting. Autoregressive time series models based on two-piece scale mixture normal distributions, called TP-SMN-AR models, is a flexible family of models involving many classical symmetric/asymmetric and light/heavy tailed autoregressive models. In this paper, we use this family of models to analyze the real world time series data of confirmed and recovered COVID-19 cases.

A dynamic model for the electric field-dependent steady-state vibrational response of a rectangular sandwich plate with a tunable electrorheological fluid (ERF) interlayer, subjected to a general harmonic transverse excitation, is developed. Hamilton's principle and the classical thin plate theory are applied to derive a set of fully coupled dynamic equations of motion along with the associated general boundary conditions. Assuming simply-supported edge conditions, the displacement components of the ERF-based sandwich plate are postulated by means of generalized double Fourier series with frequency-dependent coefficients. The natural frequencies and modal loss factors are subsequently determined by solving a complex eigenvalue problem. Analytical solutions are also obtained for the forced vibration characteristics of the adaptive structure under different external transverse excitations of varying frequency (0-300 Hz) and applied electric field strength (0-3.5 kV mm −1 ). Primary attention is focused on the effects of electric field magnitude, geometric aspect ratio, loading type, and ER core layer thickness on the dynamic characteristics of the sandwich plate. In addition, an effort is made to find the optimal electric field which yields minimized vibration amplitude for each excitation frequency. Limiting cases are considered and good agreements with the numerical solutions available in the literature are obtained.

Coronaviruses are a huge family of viruses that affect neurological, gastrointestinal, hepatic and respiratory systems. The numbers of confirmed cases are increased daily in different countries, especially in Unites State America, Spain, Italy, Germany, China, Iran, South Korea and others. The spread of the COVID-19 has many dangers and needs strict special plans and policies. Therefore, to consider the plans and policies, the predicting and forecasting the future confirmed cases are critical. The time series models are useful to model data that are gathered and indexed by time. Symmetry of error's distribution is an essential condition in classical time series. But there exist cases in the real practical world that assumption of symmetric distribution of the error terms is not satisfactory. In our methodology, the distribution of the error has been considered to be two-piece scale mixtures of normal ( TP – SMN ). The proposed time series models works well than ordinary Gaussian and symmetry models (especially for COVID-19 datasets), and were fitted initially to the historical COVID-19 datasets. Then, the time series that has the best fit to each of the dataset is selected. Finally, the selected models are applied to predict the number of confirmed cases and the death rate of COVID-19 in the world.

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Motivated by experimental and numerical studies revealing that discoidal high-density lipoprotein (HDL) particles may adopt flat elliptical and nonplanar saddle-like configurations, it is hypothesized that these might represent stabilized configurations of initially unstable flat circular particles. A variational description is developed to explore the stability of a flat circular discoidal HDL particle. While the lipid bilayer is modeled as two-dimensional fluid film endowed with surface tension and bending elasticity, the apoA-I belt is modeled as one-dimensional inextensible twist-free chain endowed with bending elasticity. Stability is investigated using the second variation of the underlying energy functional. Various planar and nonplanar instability modes are predicted and corresponding nondimensional critical values of salient dimensionless parameters are obtained. The results predict that the first planar and nonplanar unstable modes occur due to in-plane elliptical and transverse saddle-like perturbations. Based on available data, detailed stability diagrams indicate the range of input parameters for which a flat circular discoidal HDL particle is linearly stable or unstable.