Diagonal property of the symmetric product of a smooth curve

Let $C$ be an irreducible smooth projective curve defined over an algebraically closed field. We prove that the symmetric product ${\rm Sym}^d(C)$ has the diagonal property for all $d \geq 1$. For any positive integers $n$ and $r$, let ${\mathcal Q}_{{\mathcal O}^{\oplus n}_C}(nr)$ be the Quot scheme parametrizing all the torsion quotients of ${\mathcal O}^{\oplus n}_C$ of degree $nr$. We prove that ${\mathcal Q}_{{\mathcal O}^{\oplus n}_C}(nr)$ has the weak point property.Comment: Final versio

Urban transport in India: issues, challenges, and the way forward

Cities and towns play a vital role in promoting economic growth and prosperity. Although less than one-third of India’s people live in cities and towns, these areas generate over two-third of the country’s income and account for 90% of government revenues. In the coming years, as India becomes more and more urbanized, urban areas will play a critical role in sustaining high rates of economic growth. But, economic growth momentum can be sustained if and only if cities function efficiently - that their resources are used to maximize the cities’ contribution to national income. City efficiency largely depends upon the effectiveness of its transport systems, that is, efficacy with which people and goods are moved throughout the city. Poor transport systems stifle economic growth and development, and the net effect may be a loss of competitiveness in both domestic as well as international markets. Although Indian cities have lower vehicle ownership rate, number of vehicles per capita, than their counterparts in developed countries, they suffer from worse congestion, delay, pollution, and accidents than cities in the industrialized world. This paper provides an overview of urban transport issues and challenges in India. Rather than covering every aspect of urban transportation, it primarily focuses on those areas that are important from policy point of view. The paper first reviews the trends of vehicular growth and availability of transport infrastructure in Indian cities. This is followed by a discussion on the nature and magnitude of urban transport problems such as congestion, pollution and road accidents. Building on this background, the paper proposes policy measures to improve urban transportation in India

Economic Analysis of Menthol Mint Cultivation in Uttar Pradesh: A Case Study of Barabanki District

The present study has been carried out in the Barabanki district of Uttar Pradesh on economic analysis of menthol mint cultivation in the year 2010. The economics has been worked out by comparing costs and returns at different stages by the conventional method. The linear production function has been fitted to evaluate the resources-use efficiency in the production of menthol mint. The study has shown that the major portion of operational cost is shared by hired labour, interculture operations, distillation charges, irrigation and machine / tractor charge. The overall benefit-cost ratio has been found to be 2.55, which indicates a higher profit for farmers on less investment in mint cultivation. The independent variables like human labour, machinery, manures and fertilizer, irrigation charges and intercultural operations have shown a positive and significant impact on the returns of mentha crop in the study area. The major problems faced by the farmers are high input cost, erratic supply of electricity, lack of adequate information, infrastructural facilities, regulated markets and energy-efficient distillation units.Menthol mint, Medicinal and aromatic plants, Mentha crop, Barabanki district, Economic analysis, Agricultural and Food Policy, Q 12, Q 18,

The demand for road-based passenger mobility in India: 1950-2030 and relevance for developing and developed countries

The main aim of the paper is to estimate the demand for road-based passenger mobility in India and subsequently project the energy demand and CO2 emissions resulting from the same. Based on a data set of the four major motorized modes of transport – buses, cars (including jeeps and taxis), two-wheelers, and auto-rickshaws from 1950-51 to 2000-01, long-term trends in motorized traffic volume and modal split are projected up to the year 2030-31. It is found that the road-based traffic volume in India will increase from 3079 billion passenger-kilometers in 2000-01 to 12546 billion passenger-kilometers in 2030-31. Between 2000-01 and 2030-31, the aggregate share of private- and para-transit modes is projected to increase from 24.3% to 55.3% whereas the share of public transport mode is estimated to decrease from 75.7% to 44.7%. Based on the projected values of aggregate traffic volume, modal split, and modal intensities for energy demand and CO2 emissions, the paper then estimated the level of energy demand and CO2 emission from the road-based passenger transport sector in India. If there is no reduction in modal intensities, energy demand is projected to increase from 954 peta joules in 2000-01 to 5897 peta joules in 2030- 31 whereas CO2 emission is estimated to increase from 17.27 to 93.22 million metric tons of carbon equivalent during the same period. Even when we assume a reduction of 1% per year in energy and CO2 intensity of all modes of transport, energy demand and CO2 emission is projected to increase by a 4.6- and 4.0-fold respectively from 2000-01 to 2030-31

Bifurcation in cell cycle dynamics regulated by p53

We study the regulating mechanism of p53 on the properties of cell cycle dynamics in the light of the proposed model of interacting p53 and cell cycle networks via p53. Irradiation (IR) introduce to p53 compel p53 dynamics to suffer different phases, namely oscillating and oscillation death (stabilized) phases. The IR induced p53 dynamics undergo collapse of oscillation with collapse time \Delta t which depends on IR strength. The stress p53 via IR drive cell cycle molecular species MPF and cyclin dynamics to different states, namely, oscillation death, oscillations of periods, chaotic and sustain oscillation in their bifurcation diagram. We predict that there could be a critical \Delta t_c induced by p53 via IR_c, where, if \Delta t < \Delta t_c the cell cycle may come back to normal state, otherwise it will go to cell cycle arrest (apoptosis)