Abstract: The existence of sine and cosine series as a Fourier
series, their L1-convergence seems to be one of the difficult question
in theory of convergence of trigonometric series in L1-metric norm.
In the literature so far available, various authors have studied the
L1-convergence of cosine and sine trigonometric series with special
coefficients. In this paper, we present a modified cosine and sine sums
and criterion for L1-convergence of these modified sums is obtained.
Also, a necessary and sufficient condition for the L1-convergence of
the cosine and sine series is deduced as corollaries.
Abstract: The present study focuses on the environmental performance of the companies in the electricity-producing sector and its relationship with their financial performance. We will review the major studies that examined the relationship between the environmental and financial performance of firms in various industries. While the classical economic debates consider the environmental friendly activities costly and harmful to a firm’s profitability, it is claimed that firms will be rewarded with higher profitability in long run through the investments in environmental friendly activities. In this context, prior studies have examined the relationship between the environmental and financial performance of firms operating in different industry sectors. Our study will employ an environmental indicator to increase the accuracy of the results and be employed as an independent variable in our developed econometric model to evaluate the impact of the financial performance of the firms on their environmental friendly activities in the context of companies operating in the Australian electricity-producing sector. As a result, we expect our methodology to contribute to the literature and the findings of the study will help us to provide recommendations and policy implications to the electricity producers.
Abstract: This paper proposes and analyzes an SIRS epidemic model incorporating the effects of the awareness programs driven by the media. Media and media driven awareness programs play a promising role in disseminating the information about outbreak of any disease across the globe. This motivates people to take precautionary measures and guides the infected individuals to get hospitalized. Timely hospitalization helps to reduce diagnostic delays and hence results in fast recovery of infected individuals. The aim of this study is to investigate the impact of the media on the spread and control of infectious diseases. This model is analyzed using stability theory of differential equations. The sensitivity of parameters has been discussed and it has been found that the awareness programs driven by the media have positive impact in reducing the infection prevalence of the infective population in the region under consideration.