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s The movement of positive people Coronavirus Disease that was discovered in 2019 (Covid-19), written 2019-nCoV, from one location to another has a great opportunity to transmit the virus to more people. High-risk locations for transmission of the virus are public transportations, one of which is the train, because many people take turns in or together inside. One of the policies of the government is physical distancing, then followed by large-scale social restrictions. The keys to the policy are distance and movement. The most famous transportation used for the movement of people among provinces on Java is train. Here a Generalized Space Time Autoregressive (GSTAR) model is applied to forecast infected case of 2019-nCoV for 6 provinces in Java. The specialty of this model is the weight matrix as a tool to see spatial dependence. Here, the modified Inverse Distance Weight matrix is proposed as a combination of the population ratio factor with the average distance of an inter-provincial train on the island of Java. The GSTAR model (1; 1) can capture the pattern of daily cases increase in 2019-nCoV, evidenced by representative results, especially in East Java, where the increase in cases is strongly influenced by other provinces on the island of Java. Based on the Mean Squares of Residuals, it is obtained that the modified matrix gives better result in both estimating (in-sample) and forecasting (out-sample) compare with the ordinary matrix.

In this expository article we introduce a diagrammatic scheme to represent reverse classes of weights and some of their properties.Comment: 32 pages, 43 figures. Minor typos fixed. To appear in Expositiones Mathematica

Computers and Internet play a key role in the processes of data transaction, data exchange and data storage in a business. Malicious software or computer viruses is one of the biggest threats that can attack computer networks and cause huge losses due to loss of data and information. As a way to transfer risk, cyber insurance requires precise and appropriate calculations even though many challenges are faced including the effects of differences in network structure. Standards of cyber insurance that have not been established as in the mortality table for life insurance open the possibility to set a standard calculation based on network structure by determining cyber insurance rates. This study uses a general susceptible-infectious-susceptible model with Markovian property to simulate the process of spreading computer virus and calculate the total loss for each computer. Rate making will consider the number of infected neighbours on a node as an exposure to set insurance rates on regular network topology. The simulation process shows that the rates at each node are affected by the probability of initial infection, the degree of each node on the network, and the parameters of infection or recovery.

The purpose of this paper is to give a convergence analysis of the iterative scheme:where T := K * K, T a := T + aI, q ∈ (0, 1), a n := α 0 q n , α 0 > 0, with finite-dimensional approximations of T and K * for solving stably Fredholm integral equations of the first kind with noisy data. MSC: 15A12; 47A52; 65F05; 65F22Keywords: Fredholm integral equations of the first kind, iterative regularization, variational regularization; discrepancy principle; Dynamical Systems Method (DSM) Biographical notes: Professor Alexander G. Ramm is an author of more than 580 papers, 2 patents, 12 monographs, an editor of 3 books, and an associate editor of several mathematics and computational mathematics Journals. He gave more than

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A quadratic inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be applied to the study of global existence of solutions to nonlinear PDE.