Abstract:
: This article is based on the study on the model written texts provided in the Senior High School English textbooks. It is aimed at finding out whether those models are written by considering the English two contexts, cultural and situational, which encircle them. The data are all written texts provided in the six recommended English textbooks published by six different publishers. The results reveal that only eleven out of 115 model written texts tend to be incompatible with the two contexts encircling them, this implies that 104 of them (93.43%) are likely to be compatible and can be used as model texts.

Abstract:
In a rapidly developing nation like India, the prime aspect of growth is development of private projects to cater to the need for generating revenue. Land is developed for closed housing communities, industrial and IT parks and areas for the private sector. Even though, open spaces may be provided inside and along the developments, they are used by a restricted clientele, since the spaces are not open to all tiers of the society and for public use. As a result, even with the generation of enough open spaces, there is no realization of a public realm in most of the urban zones. Since there are several conflicting demands from different participatory bodies in a development project, the resolution of this conflict is not possible, but selection of the best solution is within the human abilities of the decision-making bodies. The City of Arts and Sciences in Valencia of Spain by architect Santiago Calatrava is a good example of providing urban space from an architectural project, with infrastructural planning and integration with the environment involving public participation and creating a successful public realm through celebrating modernity of structure-oriented bio mimicry architecture applied to the project area. The paper aims to study the effect of a government-initiated urban renewal project in the development of a degraded urban space and the urban design elements applied in the conceptual stage in order to realize an attractive public realm. The integrated approach towards the planning disciplines is encouraged in a plural society like India where all development aspects are fragmented, with a special emphasis on the creation of open spaces for public use for all tiers of the society.

Abstract:
In this paper we consider a dimensional reduction of slightly modified Seiberg-Witten equations, the modification being a different choice of the Pauli matrices which go into defining the equations. We get interesting equations with a Higgs field, spinors and a connection. We show interesting solutions of these equations. Then we go on to show a family of symplectic structures on the moduli space of these equations which can be geometrically prequantized using the Quillen determinant line bundle.

Abstract:
Let $h$ be a complete metric of Gaussian curvature $K_0$ on a punctured Riemann surface of genus $g \geq 1$ (or the sphere with at least three punctures). Given a smooth negative function $K$ with $K=K_0$ in neighbourhoods of the punctures we prove that there exists a metric conformal to $h$ which attains this function as its Gaussian curvature for the punctured Riemann surface. We do so by minimizing an appropriate functional using elementary analysis.

Abstract:
Hitchin has shown that the moduli space ${\mathcal M}$ of the dimensionally reduced self-dual Yang-Mills equations has a hyperK\"{a}hler structure. In this paper we first explicitly show the hyperK\"{a}hler structure, the details of which is missing in Hitchin's paper. We show here that ${\mathcal M}$ admits three pre-quantum line bundles, corresponding to the three symplectic forms. We use Quillen's determinant line bundle construction and show that the Quillen curvatures of these prequantum line bundles are proportional to each of the symplectic forms mentioned above. The prequantum line bundles are holomorphic with respect to their respective complex structures. We show how these prequantum line bundles can be derived from cocycle line bundles of Chern-Simons gauge theory with complex gauge group in the case when the moduli space is smooth.

Abstract:
The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact K\"{a}hler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact, K\"{a}hler) structures $\Omega_{\Psi_0}$ on the moduli space, parametrised by $\Psi_0$, a section of a line bundle on the Riemann surface. Next we show that corresponding to these there is a family of prequantum line bundles ${\mathcal P}_{\Psi_0} $on the moduli space whose curvature is proportional to the symplectic forms $\Omega_{\Psi_0}$.

Abstract:
The self-duality equations on a Riemann surface arise as dimensional reduction of self-dual Yang-Mills equations. Hitchin had showed that the moduli space ${\mathcal M}$ of solutions of the self-duality equations on a compact Riemann surface of genus $g >1$ has a hyperK\"{a}hler structure. In particular ${\mathcal M}$ is a symplectic manifold. In this paper we elaborate on one of the symplectic structures, the details of which is missing in Hitchin's paper. Next we apply Quillen's determinant line bundle construction to show that ${\mathcal M}$ admits a prequantum line bundle. The Quillen curvature is shown to be proportional to the symplectic form mentioned above. We do it in two ways, one of them is a bit unnatural (published in R.O.M.P.) and a second way which is more natural.

Abstract:
In this paper we obtain the general solution to the minimal surface equation, namely its local Weierstrass-Enneper representation, by using a system of hodographic coordinates. This is done by using the method of solving the Born-Infeld equations by Whitham. We directly compute conformal coordinates on the minimal surface which give the Weierstrass-Enneper representation. From this we derive the hodographic coordinate $\rho \in D \subset {\CC}$ and $\sigma $ its complex conjugate which enables us to write the Weierstrass-Enneper representation in a new way.

Abstract:
This paper is about interpolating minimal surfaces between two real analytic curves, a and b, each of which are simple real analytic curves, using the Bj\"{o}rling-Schwarz formula in the domain where it is valid, changing the normal distributions on inital curves. We insert curves $l_1,...l_L$ at specific locations and claim that there exists piecewise minimal surfaces interpolating between $a$ to $l_1$,$l_2$ to $l_3$, ...$l_L$ to $b

Abstract:
Using Ramanujan's identities and the Weierstrass-Enneper representation of minimal surfaces and the analogue for Born-Infeld solitons, we derive further non-trivial identities.