Solutions of cubic equations in quadratic fields

Let K be any quadratic field with O-K its ring of integers. We study the solutions of cubic equations, which represent elliptic curves defined over Q, in quadratic fields and prove some interesting results regarding the solutions by using elementary tools. As an application we consider the Diophantine equation r + s + t = rst = 1 in O-K. This Diophantine equation gives an elliptic curve defined over Q with finite Mordell-Weil group. Using our study of the solutions of cubic equations in quadratic fields we present a simple proof of the fact that except for the ring of integers of Q(i) and Q(root 2), this Diophantine equation is not solvable in the ring of integers of any other quadratic fields, which is already proved in [4].

New Ventures’ influence on the Growth of SME Employment, Production and Exports in India: Does Institutional Credit matter?

New ventures are considered to be a major source of small firm growth. In Indian context the contribution of new ventures in terms of new employment, production and exports has largely remained unexplored. It is equally important and unexplored, the significance of the contribution of bank credit to the growth of new ventures in India. This paper is an attempt to throw light on these two aspects. The research is based on secondary data of the liberalized period provided by Ministry of Micro, Small and Medium Enterprises, Government of India and Reserve Bank of India. To analyze the influence of bank credit growth on new ventures and the influence of new ventures on growth of additional employment, additional production and additional exports, we used a Bi-Variate Vector Auto Regression. Based on the model generated, Granger causality tests are conducted to obtain the results. The study found that rate of growth of bank credit causes the number of new ventures, implying any increase in the rate of growth of bank credit will be beneficial to the growth of new ventures. The study also concluded that new ventures are not causing the growth of additional employment or additional production. However new ventures cause the growth of additional exports. This is reasonable as entrepreneurs start their new ventures with minimum possible employment and relatively low rate of capacity utilization and they come up to take advantage of the process of globalization by catering to the international market.

Modern energy access to all in rural India: An integrated implementation strategy

Expanding energy access to the rural population of India presents a critical challenge for its government. The presence of 364 million people without access to electricity and 726 million who rely on biomass for cooking indicate both the failure of past policies and programs, and the need for a radical redesign of the current system. We propose an integrated implementation framework with recommendations for adopting business principles with innovative institutional, regulatory, financing and delivery mechanisms. The framework entails establishment of rural energy access authorities and energy access funds, both at the national and regional levels, to be empowered with enabling regulatory policies, capital resources and the support of multi-stakeholder partnership. These institutions are expected to design, lead, manage and monitor the rural energy interventions. At the other end, trained entrepreneurs would be expected to establish bioenergy-based micro-enterprises that will produce and distribute energy carriers to rural households at an affordable cost. The ESCOs will function as intermediaries between these enterprises and the international carbon market both in aggregating carbon credits and in trading them under CDM. If implemented, such a program could address the challenges of rural energy empowerment by creating access to modern energy carriers and climate change mitigation. (C) 2011 Elsevier Ltd. All rights reserved.

On isometries of the Kobayashi and Caratheodory metrics

This article considers C-1-smooth isometries of the Kobayashi and Caratheodory metrics on domains in C-n and the extent to which they behave like holomorphic mappings. First we provide an example which suggests that B-n cannot be mapped isometrically onto a product domain. In addition, we prove several results on continuous extension of C-0-isometries f : D-1 -> D-2 to the closures under purely local assumptions on the boundaries. As an application, we show that there is no C-0-isometry between a strongly pseudoconvex domain in C-2 and certain classes of weakly pseudoconvex finite type domains in C-2.

Achieving universal rural energy access in india: A low carbon pathway

India's energy challenges are three pronged: presence of majority energy poor lacking access to modern energy; need for expanding energy system to bridge this access gap as well as to meet the requirements of fast-growing economy; and the desire to partner with global economies in mitigating the threat of climate change. The presence of 364 million people without access to electricity and 726 million relying on biomass for cooking out of a total rural population of 809 million indicate the seriousness of challenge. In this paper, we discuss an innovative approach to address this challenge, which intends to take advantage of recent global developments and untapped capabilities possessed by India. Intention is to use climate change mitigation imperative as a stimulus and adopt a public-private-partnership-driven ‘business model' with innovative institutional, regulatory, financing, and delivery mechanisms. Some of the innovations are: creation of rural energy access authorities within the government system as leadership institutions; establishment of energy access funds to enable transitions from the regime of "investment/fuel subsidies" to "incentive-linked" delivery of energy services; integration of business principles to facilitate affordable and equitable energy sales and carbon trade; and treatment of entrepreneurs as implementation targets. This proposal targets 100% access to modern energy carriers by 2030 through a judicious mix of conventional and biomass energy systems with an investment of US$35 billion over 20 years. The estimated annual cost of universal energy access is about US$9 billion for a GHG mitigation potential of 213Tg CO2e at an abatement cost of US$41/tCO2e. It is a win-win situation for all stakeholders. Households benefit from modern energy carriers at affordable cost; entrepreneurs run profitable energy enterprises; carbon markets have access to CERs; the government has the satisfaction of securing energy access to rural people; and globally, there is a benefit of climate change mitigation.

Evaluating competing theories of street entrepreneurship

Conventionally, street entrepreneurs were either seen as a residue from a pre-modern era that is gradually disappearing (modernisation theory), or an endeavour into which marginalised populations are driven out of necessity in the absence of alternative ways of securing a livelihood (structuralist theory). In recent years, however, participa-tioninstreetentrepreneurshiphas beenre-read eitherasa rationaleconomicchoice(neo-liberal theory) or as conducted for cultural reasons (post-modern theory). The aim of this paper is to evaluate critically these competing explanations for participation in street entrepreneurship. To do this, face-to-face interviews were conducted with 871 street entrepreneurs in the Indian city of Bangalore during 2010 concerning their reasons for participation in street entrepreneurship. The finding is that no one explanation suffices. Some 12 % explain their participation in street entrepreneurship as necessity-driven, 15 % as traditional ancestral activity, 56 % as a rational economic choice and 17 % as pursued for social or lifestyle reasons. The outcome is a call to combine these previously rival explanations in order to develop a richer and more nuanced theorisation of the multifarious motives for street entrepreneurship in emerging market economies.

External support and innovation performance of SMEs in Bangalore: Role of firm level factors

This paper probes the role of internal factors in SMEs in obtaining external support and achieving innovation performance in the context of auto component, electronics and machine tool industries of Bangalore in India. Using step-wise logistic regression analysis, the study found that only if SMEs have internal technical competence in terms of technically qualified entrepreneur, an exclusive design centre, and innovate more frequently, they will be able to obtain external support. Further using step-wise multiple regression the study concluded that SMEs which have come up to implement innovative ideas or exploit market opportunities and which have obtained external support with technically qualified entrepreneurs are able to exhibit better innovation performance.

Variation of Electrical Resistivity with High Pressure in Ge-Te-Sn Glasses: A Composition Dependent Study

The variation of normalized electrical resistivity in the system of glasses Ge15Te85-xSnx with (1 <= x <= 5) has been studied as a function of high pressure for pressures up to 9.5 GPa. It is found that with the increase in pressure, the resistivity decreases initially and shows an abrupt fall at a particular pressure, indicating the phase transition from semiconductor to near metallic at these pressures, which lie in the range 1.5-2.5 GPa, and then continues being metallic up to 9.5 GPa. This transition pressure is seen to decrease with the increase in the percentage content of tin due to increasing metallicity of tin. The semiconductor to near metallic transition is exactly reversible and may have its origin in a reduction of the band gap due to high pressure.