Bounds for eigenvalue ratios of the Laplacian

For a bounded domain $\Omega$ with a piecewise smooth boundary in an $n$-dimensional Euclidean space $\mathbf{R}^{n}$, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. First we give a general inequality for eigenvalues of the Laplacian. As an application, we study lower order eigenvalues of the Laplacian and derive the ratios of lower order eigenvalues of the Laplacian.Comment: 14 page

Surface plasmon polaritons in topological insulator

We study surface plasmon polaritons on topological insulator-vacuum interface. When the time-reversal symmetry is broken due to ferromagnetic coupling, the surface states exhibit magneto-optical Kerr effect. This effect gives rise to a novel transverse type surface plasmon polariton, besides the longitudinal type. In specific, these two types contain three different channels, corresponding to the pole of determinant of Fresnel reflection matrix. All three channels of surface plasmon polaritons display tight confinement, long lifetime and show strong light-matter coupling with a dipole emitter.Comment: 6 pages, 4 figure

Thermodynamics of the Mg-B system: Implications for the deposition of MgB2 thin films

We have studied thermodynamics of the Mg-B system with the modeling technique CALPHAD using a computerized optimization procedure. Temperature-composition, pressure-composition, and pressure-temperature phase diagrams under different conditions are obtained. The results provide helpful insights into appropriate processing conditions for thin films of the superconducting phase, MgB2, including the identification of the pressure/temperature region for adsorption-controlled growth. Due to the high volatility of Mg, MgB2 is thermodynamically stable only under fairly high Mg overpressures for likely growth temperatures. This constraint places severe temperature constraints on deposition techniques employing high vacuum conditions

Isovector channel of quark-meson-coupling model and its effect on symmetry energy

The non-relativistic approximation of the quark-meson-coupling model has been discussed and compared with the Skyrme-Hartree-Fock model which includes spin exchanges. Calculations show that the spin-exchange interaction has important effect on the descriptions of finite nuclei and nuclear matter through the Fock exchange. Also in the quark-meson-coupling model, it is the Fock exchange that leads to a nonlinear density-dependent isovector channel and changes the density-dependent behavior of the symmetry energy.Comment: 20 pages, 9 figures and 1 table, accepted for publication in Nuclear Physics

Pre processing of social media remarks for forensics

The Internet's rapid growth has led to a surge in social network users, resulting in an increase in extreme emotional and hate speech online. This study focuses on the security of public opinion in cyber security by analyzing Twitter data. The goal is to develop a model that can detect both sentiment and hate speech in user texts, aiding in the identification of content that may violate laws and regulations. The study involves pre processing the acquired forensic data, including tasks like lowercasing, stop word removal, and stemming, to obtain clear and effective data. This paper contributes to the field of public opinion security by linking forensic data with machine learning techniques, showcasing the potential for detecting and analyzing Twitter text data

On the Application of Gluon to Heavy Quarkonium Fragmentation Functions

We analyze the uncertainties induced by different definitions of the momentum fraction $z$ in the application of gluon to heavy quarkonium fragmentation function. We numerically calculate the initial $g \to J / \psi$ fragmentation functions by using the non-covariant definitions of $z$ with finite gluon momentum and find that these fragmentation functions have strong dependence on the gluon momentum $\vec{k}$. As $| \vec{k} | \to \infty$, these fragmentation functions approach to the fragmentation function in the light-cone definition. Our numerical results show that large uncertainties remains while the non-covariant definitions of $z$ are employed in the application of the fragmentation functions. We present for the first time the polarized gluon to $J/\psi$ fragmentation functions, which are fitted by the scheme exploited in this work.Comment: 11 pages, 7 figures;added reference for sec.