Uniqueness of Asymptotically Conical Higher Codimension Self-Shrinkers and Self-Expanders

Let $C$ be an $m$-dimensional cone immersed in $\mathbb{R}^{n+m}$. In this paper, we show that if $F:M^m \rightarrow \mathbb{R}^{n+m}$ is a properly immersed mean curvature flow self-shrinker which is smoothly asymptotic to $C$, then it is unique and converges to $C$ with unit multiplicity. Furthermore, if $F_1$ and $F_2$ are self-expanders that both converge to $C$ smoothly asymptotically and their separation decreases faster than $\rho^{-m-1}e^{-\rho^2/4}$ in the Hausdorff metric, then the images of $F_1$ and $F_2$ coincide.Comment: 37 pages. A few typos have been corrected and a redundant topological condition has been droppe

Historical Overview of Language Politics in Post-Colonial India

One of the main political issues in Indian politics is connected to language problem After India s independence the government decided that the official language of India will be Hindi In this paper I have attempted to take a look at study of politics of languages in late colonial India A set of languages used by political operators in the Indian scenario where the diverse political scenarios play a vital role in the linguistic matters viz organization of languages language policies and planning minority and majority languages The motive of this paper is to present the historical overview of language politics in India and its impact on the documentation and organization of languages How the political concern influences the up gradation and degradation of the status of a language It further illustrates how the government policies used for the development of majority languages causing a threat to minority language

The structure of translating surfaces with finite total curvature

In this paper, we prove that any mean curvature flow translator Σ2 ⊂ R3 with finite total curvature and one end must be a plane. We also prove that if the translator Σ has multiple ends, they are asymptotic to a plane Π containing the direction of translation and can be written as graphs over Π. Finally, we determine that the ends of Σ are strongly asymptotic to Π and obtain quantitative estimates for their asymptotic behavior

Herlyn-Werner-Wunderlich syndrome : a rare genitourinary anomaly in females : a series of four cases

We present case series of four patients with an important syndrome known as Herlyn-Werner-Wunderlich syndrome. Herlyn-Werner-Wunderlich syndrome is a rare congenital anomaly characterised by uterus didelphys with blind hemivagina and ipsilateral renal agenesis. It usually presents after menarche with progressive pelvic pain during menses secondary to haematocolpos. Awareness is necessary to diagnose and treat this disorder properly before complications occur. Magnetic resonance imaging is the preferred modality for the delineation of uterine malformation. When renal anomalies are encountered, a screening should also be made for congenital abnormalities of the reproductive tract and vice versa

Three dimensional printed degradable and conductive polymer scaffolds promote chondrogenic differentiation of chondroprogenitor cells

Degradable and electroactive polymers have been widely used for various biomedical applications including biosensors, tissue engineering and regenerative medicine. However, the poor processability of these polymers hinders the fabrication of electroactive polymer structures into complex desirable geometries. Herein, a block copolymer of tetraaniline (TA) and PCL, tetraaniline-b-polycaprolactone-b-tetraaniline (TPT) (possessing ~33% TA content), was synthesised and fabricated for the first time into a 3D printed electroactive biodegradable scaffold by direct-ink writing. This printable polymer ink was further formulated by the blending of TPT with high molecular weight PCL and directly 3D printed to generate a mechanically robust electroactive scaffold. The presence of TA content at 2.5% and 5% weight in relation to total PCL weight rendered the scaffold surface electrically and biologically active, in which fibronectin absorption and chondrogenic differentiation of chondroprogenitor cells over 28 days were enhanced, when compared to 0% TA. Our work demonstrates the formulation of a poorly processible materials (i.e., conductive polymers) into bio-inks able to produce 3D printed scaffolds and highlights the potential use of degradable and electroactive materials for cartilage tissue regeneration

MHD free convection flow over an inclined plate that applies arbitrary shear stress to the fluid

An exact analysis of heat transfer past an infinite inclined plate that applies arbitrary shear stress to the fluid with Newtonian heating is presented, The fluid is considered electrically conducting and passing through a porous medium, The influence of thermal radiation in the enerh'Y equations is also considered, General solutions of the problem are obtained in closed form using the Laplace transform technique, They satisfy the governing equations, initial and boundary conditions and can set up a huge number of exact solutions correlatives to various fluid motions, The effects of various parameters on velocity and temperature profiles are shown graphically and discussed in details