This article mainly divides into two parts. In the first part, We find a new system by using the plane wave transform and self-similar transform, then we give the exact solution by using the Cardan formula. In the second part, assuming the original equation exist weak solution, when γ→1, it will tend to the weak solution of the limit equation, that is to say the original equation has the limiting behavior.
A new dynamic model for the malaria disease has been developed for areas where the whole populace is at risk and exposure to the malaria infection is continuous throughout the year. In this model, the two vulnerable groups that is, infectious people those under 5years and pregnant women have been given separate compartments. The model has two equilibria, that is, disease-free and endemic equilibrium points. The basic reproduction number ( R0 )for the model has been derived using the next-generation matrix approach. The local stability of two equilibria is investigated using matrix elementary row operations. However, global stability of disease-free equilibrium is investigated using theorem by Castillo-Chavez et.al (2002) and that of the endemic equilibrium is also investigated using Lyapunov’s function. It is proven that disease-free equilibrium is locally asymptotically stable if R0 < 1 and the endemic equilibrium exists if R0 > 1. The endemic equilibrium is locally asymptotically stable when and E17E19 > E16E20. Sensitivity analysis has proved that malaria can be controlled or eliminated if the following parameters such as biting rates, recruitment rate and density-dependent natural mortality rate for mosquitoes and clinical recovery rates for humans are controlled.
Successfully understanding of social media conversation growth, dissemination and extinction is a challenging task that relies on identifying groups, group influence, diffusion models, forecast models, social dynamics and text analytics. In this problem, we concentrate on the description of a novel approach for identifying drivers of the direction and momentum of social conversations, including the spread of mood, sentiment and issues. The approach first groups potential drivers of conversation based on variability. The primary driver in each group is then selected. Finally, the relationship between the selected drivers and the topic outcome is calculated and displayed visually. This enables the quick identification of the form and structure of the conversation and allows us to predict momentum, direction, contagion risks, potential responses and interventions.
There is a huge amount of data in the form of text available today in the internet across various channels – social media, news articles, blogs, e-commerce websites. Most of this data is a part of some “conversation” or the other where real-world entities discuss, analyze, comment, exchange information in the form of written expressions in textual format. Driver Modeling on textual data can be useful in observing the key drivers which are driving the “conversation” coupled with the associated sentiments and mood states for the observed key drivers. These insights about the key conversational drivers are often used in a variety of domains such as tracking news cycles, stock movements, legislation developments, brand image, viral breakouts and much more.
This research paper proposes a fully implicit five-quarters computational algorithms of order five for Numerical Approximation of Second order IVPs in ODEs. The method is consistent, convergent, zero stable and A-stable. The method solved second order ordinary differential equations efficiently and accurately. It has a low error constant and gives better approximation than some existing methods.
In this paper we de ne pairwise L-closed spaces and study their properties, we obtain several results concerning pairwise L-closed spaces, and some product theorems. Some examples dealing with pairwise L-closed spaces are discussed.