Retrospective Conversion of Ancient Knowledge, Issues and Challenges: A Case Study of Central Library, Banaras Hindu University, India

The paper outlines the efforts of Sayaji Rao Gaekwad Library, which belongs to Asia \u27s largest university system, Banaras Hindu University (BHU), to make their rich collection of manuscripts available to the world of scholars. It also includes an elaboration of the National Mission for Manuscripts of India and the affiliation of Central Library, BHU with it. A detailed account of the Central Library, BHU as Manuscript Conservation Centre is provided. The issues and future targets for the library pertaining to preservation of manuscripts are described. The paper is first to report the gradual evolution of Central Library, BHU as an essential part of the National Mission for Manuscripts, a National initiative by Ministry of Culture, Government of India

Achieving Millennium Development Goals and India Vision 2020: Evidences from slums of Varanasi City

The objective of this paper is to examine the achievements of Millennium Development Goals (MDGs) and India Vision 2020 in the context of the slums of Varanasi city. India has been facing the problem of growing urban poverty due to rapid urbanisation. According to the Census of India 2011, about 65 million people live in urban slums, which are overcrowded, polluted, unhygienic, and deprived of basic services. This paper compares the goals and targets of UN MDGs and India Vision 2020 with the status of the slum dwellers of Varanasi city. The study is based on primary data, which includes survey of 150 households of five different slums of Varanasi city. The study reveals that more than 70% people are illiterate, less than 35% of population access government health facilities, only 36% household use tap water, etc. This comparison portrays a pathetic picture of slums and the inabilities to achieve both MDGs and national goals.Key words:MDGs, India Vision 2020, Slums, Poverty, Quality of life, Varanasi City, Indi

Nehari manifold approach for fractional Kirchhoff problems with extremal value of the parameter

In this work we study the following nonlocal problem \begin{equation*} \left\{ \begin{aligned} M(\|u\|^2_X)(-\Delta)^s u&= \lambda {f(x)}|u|^{\gamma-2}u+{g(x)}|u|^{p-2}u &&\mbox{in}\ \ \Omega, u&=0 &&\mbox{on}\ \ \mathbb R^N\setminus \Omega, \end{aligned} \right. \end{equation*} where $\Omega\subset \mathbb R^N$ is open and bounded with smooth boundary, $N>2s, s\in (0, 1), M(t)=a+bt^{\theta-1},\;t\geq0$ with $\theta>1, a\geq 0$ and $b>0$. The exponents satisfy $1<\gamma<2<{2\theta<p<2^*_{s}=2N/(N-2s)}$ (when $a\neq 0$) and $2<\gamma<2\theta<p<2^*_{s}$ (when $a=0$). The parameter $\lambda$ involved in the problem is real and positive. The problem under consideration has nonlocal behaviour due to the presence of nonlocal fractional Laplacian operator as well as the nonlocal Kirchhoff term $M(\|u\|^2_X)$, where $\|u\|^{2}_{X}=\iint_{\mathbb R^{2N}} \frac{|u(x)-u(y)|^2}{\left|x-y\right|^{N+2s}}dxdy$. The weight functions $f, g:\Omega\to \mathbb R$ are continuous, $f$ is positive while $g$ is allowed to change sign. In this paper an extremal value of the parameter, a threshold to apply Nehari manifold method, is characterized variationally for both degenerate and non-degenerate Kirchhoff cases to show an existence of at least two positive solutions even when $\lambda$ crosses the extremal parameter value by executing fine analysis based on fibering maps and Nehari manifold