On the regularization of solution of an inverse ultraparabolic equation associated with perturbed final data

In this paper, we study the inverse problem for a class of abstract ultraparabolic equations which is well-known to be ill-posed. We employ some elementary results of semi-group theory to present the formula of solution, then show the instability cause. Since the solution exhibits unstable dependence on the given data functions, we propose a new regularization method to stabilize the solution. then obtain the error estimate. A numerical example shows that the method is efficient and feasible. This work slightly extends to the earlier results in Zouyed et al. \cite{key-9} (2014).Comment: 19 pages, 4 figures, 1 tabl

Foreign Ownership and Stock Return Volatility in Vietnam: the Destabilizing Role of Firm Size

This study aims to examine the relevance of foreign ownership to stock return volatility in the Vietnam stock market over ten years (2008 - 2017). After applying the fixed effects regressions and the extended instrumental variable regressions with fixed effects, we find that foreign ownership decreases the volatility of stock returns. However, the stabilizing impact of foreign ownership on stock return volatility becomes weaker in large firms since the coeffcient of the interaction term between firm size and foreign ownership turns out to be significantly positive. The estimated results remain robust when we use the future one-year volatility, other than the current one, as an alternative measure of the dependent variable

MODELING USING 2-D AREAS OF IDEAL CROSS-POINT REGIONS FOR LOSSLESS IMAGES COMPRESSION

This paper presents 2-D areas of ideal cross-point regions which are the new part in the theory of cross-point regions. Actually for using cross-point regions we need an algorithm for determining cross-point maps; this takes a long time and a big space for storing these maps, and brings about not high compression ratio when using one dimensional cross-point regions because many coordinates of data points need to be saved for decoding. When these 2-D areas are used, the scheme of 2-DICRIC (2-D Ideal Cross-point Regions for lossless Image Compression) for losslessly encoding and decoding images with the optimization of probability of cross points which are neighbor to the points of grey levels 2n is improved to get higher compression ratio. The base idea of this method is the effect of Gray coding on cross points, and there are many cross-point regions. Before Gray coding data sets of cross points are determined, they are called the ideal cross point regions (ICRs). After Gray coding these regions always contain only 1 bits or 0 bits depending on the number of bit plane after the operation of bit plane decomposition. This is the characteristic of images, the data do not change much in a specific area, especially in medical images which have many regions with the approximate grey levels. So, the way to determine 2-D areas of cross-point regions so that the cross-point maps are small is important for the theory. The theory with these 2-D areas has important effects on the compression ratio when encoding and decoding processes of lossless image compression for data transmission are proceeded