Geometry of Evolving Plane Curves Problem via Lie Group Analysis

The purpose of the present work is to construct new geometrical models for motion of plane curves. We have obtained nonlinear partial differential equations and have discussed the solutions of these equations using symmetry groups methods. Also, geometric interpretation for these solutions are given through the Gaussian and mean curvatures to the soliton surfaces attached to the solution of the evolving problem. Key Words: Motion of curve; Symmetry groups; Monge for

Weingarten timelike tube surfaces around a spacelike curve,

Abstract The subject of this paper is the study of a timelike tube surface around the spacelike curve with timelike and spacelike binormal vectors in a three-dimensional Minkowski space E 3 1 . Moreover, we have discussed Weingarten and linear Weingarten conditions for this surface with respect to their curvatures; the mean curvature H , Gaussian curvature K and the second Gaussian curvature K II

On Dual Curves of DAW(k)-Type and Their Evolutes

In this paper, we study to express the theory of curves including a wide section of Euclidean geometry in terms of dual vector calculus which has an important place in the three -dimensional dual space $\mathbb{D}^{3}$. In other words, we study $DAW(k)$-type curves $\left( 1\leq k\leq 3\right)$ by using Bishop frame defined as alternatively of these curves and give some of their properties in $\mathbb{D}^{3}$. \ Moreover, we define the notion of evolutes of dual spherical curves for ruled surfaces. Finally, we give some examples to illustrate our findings

Some Properties of Special Magnetic Curves

In the theory of curves, a magnetic field generates a magnetic flow whose trajectories are curves called magnetic curves. This paper aims at studying some properties for these curves which corresponding to the Killing magnetic fields in the 3-dimensional Euclidean space. We investigate the trajectories of the magnetic fields called $T$-magnetic and $e$-magnetic curves, also we give some characterizations of these curves. In addition, we determine all magnetic curves for new spherical images of a spherical curve and finally, we defray some examples to confirm our main results

The Quark-Gluon Plasma in a Finite Volume

The statistical mechanics of quarks and gluons are investigated within the context of the canonical ensemble. Recursive techniques are developed which enforce the exact conservation of baryon number, total isospin, electric charge, strangeness, and color. Bose and Fermi-Dirac statistics are also accounted for to all orders. The energy, entropy and particle number densities are shown to be significantly reduced for volumes less than 5 cubic fm.Comment: 8 pages, 3 figure