A Method of Joining Piecewise Functions to Produce Continuous Functions of Difficult Data

This article describes a method of modelling data that involves splitting the curve into two (or more) and creating separate piecewise functions for each part; these functions are then concatenated via a linking function to create one overall continuous function that better describes the original data than is otherwise achievable. The linking function is able to do this by separating the original two (or more) subfunctions so that they are each active in only the relevant portion of the overall curve without the use of dummy variables. The final result is a continuous function in which it is straightforward to smooth the transition at the knot between the piecewise subfunctions. In addition, the piecewise subfunctions do not need to align at the knot since the degree of smoothing is readily controlled. All types of functions may be concatenated so that the method is flexible and relatively simple to apply.

A Method of Joining Piecewise Functions to Produce Continuous Functions of Difficult Data

This article describes a method of modelling data that involves splitting the curve into two (or more) and creating separate piecewise functions for each part; these functions are then concatenated via a linking function to create one overall continuous function that better describes the original data than is otherwise achievable. The linking function is able to do this by separating the original two (or more) subfunctions so that they are each active in only the relevant portion of the overall curve without the use of dummy variables. The final result is a continuous function in which it is straightforward to smooth the transition at the knot between the piecewise subfunctions. In addition, the piecewise subfunctions do not need to align at the knot since the degree of smoothing is readily controlled. All types of functions may be concatenated so that the method is flexible and relatively simple to apply.

Long-Term Predictions of COVID-19 in Some Countries by the SIRD Model

As COVID-19 in some countries has increasingly become more severe, there have been significant efforts to develop models that forecast its evolution there. These models can help to control and prevent the outbreak of these infections. In this paper, we make long-term predictions based on the number of current confirmed cases, accumulative recovered cases, and dead cases of COVID-19 in some countries by the modeling approach. We use the SIRD (S: susceptible, I: infected, R: recovered, D: dead) epidemic model which is a nonautonomous dynamic system with incubation time delay to study the evolution of COVID-19 in some countries. From the analysis of the recent data, we find that the cure and death rates may not be constant and, in some countries, they are piecewise functions. They can be estimated from the delayed SIRD model by the finite difference method. According to the recent data and its subsequent cure and death rates, we can accurately estimate the parameters of the model and then predict the evolution of COVID-19 there. Through the predicted results, we can obtain the turning points, the plateau period, and the maximum number of COVID-19 cases. The predicted results suggest that the epidemic situation in some countries is very serious. It is advisable for the governments of these countries to take more stringent and scientific containment measures. Finally, we studied the impact of the infection rate β on COVID-19. We find that when the infection rate β decreases, the cumulative number of confirmed cases and the maximum number of currently infected cases will greatly decrease. The results further affirm that the containment techniques taken by these countries to curb the spread of COVID-19 should be strengthened further.

A method of joining piecewise functions to produce continuous functions of difficult data

This article describes a method of modelling data that involves splitting the curve into two (or more) and creating separate piecewise functions for each part; these functions are then concatenated via a linking function to create one overall continuous function that better describes the original data than is otherwise achievable. The linking function is able to do this by separating the original two (or more) subfunctions so that they are each active in only the relevant portion of the overall curve without the use of dummy variables. The final result is a continuous function in which it is straightforward to smooth the transition at the knot between the piecewise subfunctions. In addition, the piecewise subfunctions do not need to align at the knot since the degree of smoothing is very readily controlled. All types of functions may be concatenated so that the method is flexible and relatively simple to apply.

Algorithms for analysis of stability and dynamic characteristics of signal generators at the physical level in FANET networks

To ensure the reliability of the physical level of Flying Ad Hoc Networks (FANET), the article substantiates the relevance of the study of stability and dynamic processes of signal formation and processing paths in the terminal and intermediate network equipment. The limitations of the known methods of the theory of automatic control, which make it difficult to perform the analysis of essentially nonlinear high-order signal generators, are shown. To analyze the stability of such formations proposed algorithm based on the use of the Nyquist criterion and approximation of the characteristic polynomial of a device by continuous piecewise functions; to analyze the dynamic characteristics of the algorithm based on spectral method of the input signal approximation and the frequency characteristics of a device by continuous piecewise functions.

Discontinuous generalized double-almost-periodic functions on almost-complete-closed time scales

In this paper, we introduce the concept of almost-complete-closed time scales (ACCTS) that allows independent variables of functions to possess almost-periodicity under translations. For this new type of time scale, a class of piecewise functions with double-almost-periodicity is proposed and studied. Based on these, concepts of weighted pseudo-double-almost-periodic functions (WPDAP) in Banach spaces and a translation-almost-closed set are introduced. Further, we prove that the function space WPDAP0 affiliated to WPDAP is a translation-almost-closed set. Then, by introducing the concept of almost-uniform convergence for piecewise functions on ACCTS and using measure theory on time scales, some composition theorems of WPDAP and the completeness of the function space are proved.