On the proof of some theorem on locally nilpotent subgroups in division rings

In Hai-Thin (2009), there is a theorem, stating that every locally nilpotent subnormal subgroup in a division ring $D$ is central (see Hai-Thin (2009, Th. 2.2)). Unfortunately, there is some mistake in the proof of this theorem. In this note we give the another proof of this theorem.Comment: 3 page

Convolution for the transform induced by Fourier integral transform and its inverse

Joint Research on Environmental Science and Technology for the Eart

Rough Standard Neutrosophic Sets: An Application on Standard Neutrosophic Information Systems

A rough fuzzy set is the result of the approximation of a fuzzy set with respect to a crisp approximation space. It is a mathematical tool for the knowledge discovery in the fuzzy information systems. In this paper, we introduce the concepts of rough standard neutrosophic sets and standard neutrosophic information system, and give some results of the knowledge discovery on standard neutrosophic information system based on rough standard neutrosophic sets

Asymptotically almost periodic solutions to parabolic equations on the real hyperbolic manifold

In this work we study the existence and the asymptotic behaviour of the asymptotically almost periodic mild solutions of the vectorial parabolic equations on the real hyperbolic manifold $\mathbb{H}^d(\mathbb{R})$ ($d \geqslant 2$). We will consider the vectorial laplace operator in the sense of Ebin-Marsden's laplace operator. Our method is based on certain dispertive and smoothing estimates of the semigroup generated by the linearized vectorial heat equation and the fixed point argument. First, we prove the existence and the uniqueness of the asymptotically almost periodic mild solution for the linearized equations. Next, using the fixed point argument, we can pass from linearized equations to semilinear equations to prove the existence, uniqueness, exponential decay and stability of the solutions. Our abstract results will be applied to the incompressible Navier-Stokes equation and the semilinear vectorial heat equation.Comment: 20 pages. arXiv admin note: text overlap with arXiv:2101.0330

Correlation between Resilient Modulus MR and Deviator Stress for Subgrade soils of northern provinces in Vietnam

Recently, Resilient Modulus is applied in pavement structural design in Vietnam. The resilient modulus of subgrade soil is an essential input parameter for a flexible pavement design. The resilient modulus depends on soil properties, stress state, and soil type.  However, there is limited research on resilient modulus of soils and models to estimate resilient modulus in Vietnam. Therefore, in this study, soil samples were collected from two provinces in northern Vietnam, namely Bac Giang province and Ninh Binh province, and then physical and mechanical tests were conducted for these samples. In addition, a series of cyclic triaxial tests also conducted according to AASHTO T307 specification to obtain resilient modulus of these soils.  The results showed that the resilient modulus decreased with the increase of deviator stress for Bac Giang samples and increased with the increase of deviator stress in the case of Ninh Binh samples. Simple deviator stress models have developed to estimate a resilient modulus of soils in the area