Distinct distances on regular varieties over finite fields

In this paper we study some generalized versions of a recent result due to Covert, Koh, and Pi (2015). More precisely, we prove that if a subset $\mathcal{E}$ in a regular variety satisfies $|\mathcal{E}|\gg q^{\frac{d-1}{2}+\frac{1}{k-1}}$, then $\Delta_{k, F}(\mathcal{E})\supseteq \mathbb{F}_q\setminus \{0\}$ for some certain families of polynomials $F(\mathbf{x})\in \mathbb{F}_q[x_1, \ldots, x_d]$

Buckling and postbuckling of axially-loaded CNT-reinforced composite cylindrical shell surrounded by an elastic medium in thermal environment

Buckling and postbuckling behaviors of nanocomposite cylindrical shells reinforced by single walled carbon nanotubes (SWCNTs), surrounded by an elastic medium, exposed to a thermal environment and subjected to uniform axial compression are investigated in this paper. Material properties of carbon nanotubes (CNTs) and isotropic matrix are assumed to be temperature dependent, and effective properties of nanocomposite are estimated by extended rule of mixture. The CNTs are embedded into matrix via uniform distribution (UD) or functionally graded (FG) distribution along the thickness direction. Governing equations are based on Donnell’s classical shell theory taking into account von Karman-Donnell nonlinear terms and interaction between the shell and surrounding elastic medium. Three-term form of deflection and stress function are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain load-deflection relation from which buckling and postbuckling behaviors are analyzed. Numerical examples are carried out to analyze the effects of CNT volume fraction and distribution types, geometrical ratios, environment temperature and surrounding elastic foundation on the buckling loads and postbuckling strength of CNTRC cylindrical shells

A Study on Employment for Rural Laborers in the Process of Industrialization and Modernization of Vietnam

Employment and job creation are global socio-economic issues and concern every country in the world and Vietnam is no exception. Today, the concept of development is comprehensively understood and economic growth is associated with progress, social justice, poverty reduction, on the basis of creating sustainable jobs for workers. At different times, employments for workers also have different characteristics. In the dimension of this study, employment for rural laborers with the case study of Nam Dinh of Vietnam have been investigated, then some recommendations are proposed for creating more jobs for rural people. Keywords: Employment, job creation, rural employment, rural labor. DOI: 10.7176/EJBM/12-21-13 Publication date:July 31st 202

Multi-step algorithms for solving EPs

The paper introduces and analysizes the convergence of two multi-step proximal-like algorithms for pseudomonotone and Lipschitz-type continuous equilibrium problems in a real Hilbert space. The algorithms are combinations between the multi-step proximal-like method and Mann or Halpern iterations. The weakly and strongly convergent theorems are established with the prior knowledge of two Lipschitz-type continuous constants. Moreover, by choosing two sequences of suitable stepsizes, we also show that the multi-step proximal-like algorithm for strongly pseudomonotone and Lipschitz-type continuous equilibrium problems where the construction of solution approximations and the establishing of its convergence do not require the prior knowledge of strongly pseudomonotone and Lipschitz-type continuous constants of bifunctions. Finally, several numerical examples are reported to illustrate the convergence and the performance of the proposed algorithms over classical extragradient-like algorithms

On the Dynamical Symmetry Breaking of the Electroweak Interactions by the Top Quark

We discuss the electroweak gauge symmetry breaking triggered by a new strong attractive interaction to condensate fermion-antifermion, and topcolor is a prototype. To deal with the fermion pairing, a general method based on the Hubbard-Stratonovich transformation in the functional integral approach is used. We derive a formula which relates the $W^\pm$, $Z^0$ weak boson masses to that of the condensated fermion, thus generalizing the Pagels-Stokar formula obtained in QCD. The custodial SU(2) electroweak symmetry turns out to be systematically violated, the deviation of $\rho\equiv M_W^2/(M_Z^2\cos^2\theta_W)$ from unity is related to the new physics scale $\Lambda$. Some phenomenological consequences of the top-pair condensation models are discussed. Distinctive signatures of the $\bar{t}t$ scalar bound state, a Higgs boson like denoted by $H_t$, are the dominant decay modes $H_t\to \Upsilon +\gamma ,$ $H_t\to \Upsilon +Z^0$, and $H_t \to B^* +\bar{B}^*$.Comment: Latex2e 9 pages, 2 postscript figures, 1 postscript log