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

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

Some integral inequalities on time scales

In this paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales.Comment: 8 page

Modeling Vocal Fold Motion with a New Hydrodynamic Semi-Continuum Model

Vocal fold (VF) motion is a fundamental process in voice production, and is also a challenging problem for direct numerical computation because the VF dynamics depend on nonlinear coupling of air flow with the response of elastic channels (VF), which undergo opening and closing, and induce internal flow separation. A traditional modeling approach makes use of steady flow approximation or Bernoulli's law which is known to be invalid during VF opening. We present a new hydrodynamic semi-continuum system for VF motion. The airflow is modeled by a quasi-one dimensional continuum aerodynamic system, and the VF by a classical lumped two mass system. The reduced flow system contains the Bernoulli's law as a special case, and is derivable from the two dimensional compressible Navier-Stokes equations. Since we do not make steady flow approximation, we are able to capture transients and rapid changes of solutions, e.g. the double pressure peaks at opening and closing stages of VF motion consistent with experimental data. We demonstrate numerically that our system is robust, and models in-vivo VF oscillation more physically. It is also much simpler than a full two-dimensional Navier-Stokes system.Comment: 27 pages,6 figure

Topological aspect of graphene physics

Topological aspects of graphene are reviewed focusing on the massless Dirac fermions with/without magnetic field. Doubled Dirac cones of graphene are topologically protected by the chiral symmetry. The quantum Hall effect of the graphene is described by the Berry connection of a manybody state by the filled Landau levels which naturally possesses non-Abelian gauge structures. A generic principle of the topologically non trivial states as the bulk-edge correspondence is applied for graphene with/without magnetic field and explain some of the characteristic boundary phenomena of graphene.Comment: 12 pages, 8 figures. Proceedings for HMF-1

A new class of (2+1)(2+1)-d topological superconductor with Z8\mathbb{Z}_8 topological classification

The classification of topological states of matter depends on spatial dimension and symmetry class. For non-interacting topological insulators and superconductors the topological classification is obtained systematically and nontrivial topological insulators are classified by either integer or $Z_2$. The classification of interacting topological states of matter is much more complicated and only special cases are understood. In this paper we study a new class of topological superconductors in $(2+1)$ dimensions which has time-reversal symmetry and a $\mathbb{Z}_2$ spin conservation symmetry. We demonstrate that the superconductors in this class is classified by $\mathbb{Z}_8$ when electron interaction is considered, while the classification is $\mathbb{Z}$ without interaction.Comment: 5 pages main text and 3 pages appendix. 1 figur

Minimizing the Average Delay at Intersections via Presignals and Speed Control

© 2018 Mina Ghanbarikarekani et al. Urban intersections have been well recognized as bottlenecks of urban transport systems. It is thus important to propose and implement strategies for increasing the efficiency of public and private transportation systems as a whole. In order to achieve this goal, an additional signal could be set up near the intersection to give priority to buses through stopping vehicles in advance of the main intersection as a presignal. It has been increasingly popular in urban cities. While presignals indeed reduce the average delay per traveler, they cause extra stops of private vehicles, which might compromise the overall efficiency, safety, and sustainability. This paper aims to propose a model to improve presignals by reducing the vehicles' number of stops behind the presignals. By applying the method, vehicles would be able to adjust their speed based on traffic conditions as well as buses' speed and approach. Numerical analyses have been conducted to determine the conditions required for implementing this method