Mathematical Epidemiological Model of the Propagation and Prevention of Infectious Diseases Considering COVID-19 Vaccination

The duration of the necessity of current restrictions and preventive countermeasures against the COVID-19 pandemic is of great concern. While several previous epidemiological studies have discussed controlling the course of the epidemic with regard to social distancing, vaccination, care capacities, and future scenarios, we adopt an alternative approach to provide insights into the time scale of epidemic propagation in human populations. We show that the reproduction number modified by preventive countermeasures Rm implies a threshold R~m to reach the herd immunity level at time Th. While Th varies moderately for large Rm, it increases sharply around Rm=R~m, and Th is infinite below Rm=R~m. The transition region for this increase is minute, demonstrating that prevention of infectious diseases must consider the relatively asymptotic nature of their propagation, which varies unpredictably between steady transmission and explosive outbreaks. These results suggest the continuation of preventive countermeasures to suppress the transmission of COVID-19 for many years; if they were discontinued or reduced such that Rm exceeded R~m, the disease would be transmitted throughout the considered community, and the required herd immunity level would be reached within 250 days if Rm > 1.6. However, the implementation of vaccination programs could drastically alter this dynamic.

Variability of newly identified B-type stars observed by Kepler

ABSTRACT Recent re-determination of stellar atmospheric parameters for a sample of stars observed during the Kepler mission allowed to enlarge the number of Kepler B-type stars. We present the detailed frequency analysis for all these objects. All stars exhibit pulsational variability with maximum amplitudes at frequencies corresponding to high-order g modes. Peaks that could be identified with low-order p/g modes are also extracted for a few stars. We identified some patters in the oscillation spectra that can be associated with the period spacings that can results from the asymptotic nature of the detected pulsational modes. We also tentatively confront the observed oscillation characteristics with predictions from linear non-adiabatic computations of stellar pulsations. For high-order g modes the traditional approximation was employed to include the effects of rotation on the frequency values and mode instability.

An Upper Bound of the Bias of Nadaraya-Watson Kernel Regression under Lipschitz Assumptions

The Nadaraya-Watson kernel estimator is among the most popular nonparameteric regression technique thanks to its simplicity. Its asymptotic bias has been studied by Rosenblatt in 1969 and has been reported in several related literature. However, given its asymptotic nature, it gives no access to a hard bound. The increasing popularity of predictive tools for automated decision-making surges the need for hard (non-probabilistic) guarantees. To alleviate this issue, we propose an upper bound of the bias which holds for finite bandwidths using Lipschitz assumptions and mitigating some of the prerequisites of Rosenblatt’s analysis. Our bound has potential applications in fields like surgical robots or self-driving cars, where some hard guarantees on the prediction-error are needed.

Характеристики аэрозольного облака, образующегося при микровзрывном разрушении двухжидкостной капли

The results of experimental studies of micro-explosion of two-fluid (water and rapeseed oil) droplets during heating in an air flow with a temperature of 250 to 450 oC are presented. As a result of video registration, an information database was obtained on the external surface area of the emerging aerosol cloud and the free surface of the liquid in comparison with the similar parameters of the initial drop. The dependences of these parameters on the heating temperature and the relative concentration (10–90 vol.%) of the combustible component in the droplet are established. The conditions for obtaining the asymptotic nature of these dependencies are determined.

Existence of Ψ-bounded Solutions for System of Linear Dynamic equations on Time Scales

In this work, we develop the criteria for existence of Ψ- bounded solutions of system of linear dynamic equations on time scales. The advantage of results in this dynamical system is it unifies discrete as well as continuous systems. Initially, we develop if and only if conditions for the existence of at least one Ψ-bounded solution for linear dynamic equation y∆(τ ) = P (τ )y +g(τ ), for each Ψ- delta integrable Lebesgue function g, on time scale T +. Later, we obtain asymptotic nature of Ψ-bounded solutions of dynamical system. Also we provided the examples for supporting the results.AMS Subject Classification: 74H20, 34N05, 34C11

On the relation between pole and running heavy quark masses beyond the four-loop approximation

The effective charges motivated method is applied to the relation between pole and M̅S̅-scheme heavy quark masses to study high order perturbative QCD corrections in the observable quantities proportional to the running quark masses. The non-calculated five- and six-loop perturbative QCD coefficients are estimated. This approach predicts for these terms the sign-alternating expansion in powers of number of lighter flavors nl, while the analyzed recently infrared renormalon asymptotic expressions do not reproduce the same behavior. We emphasize that coefficients of the quark mass relation contain proportional to π2 effects, which result from analytical continuation from the Euclidean region, where the scales of the running masses and QCD coupling constant are initially fixed, to the Minkowskian region, where the pole masses and the running QCD parameters are determined. For the t-quark the asymptotic nature of the non-resummed PT mass relation does not manifest itself at six-loops, while for the b-quark the minimal PT term appears at the probed by direct calculations four-loop level. The recent infrared renormalon based studies support these conclusions.