A Note On Transversals

Let $G$ be a finite group and $H$ a core-free subgroup of $G$. We will show that if there exists a solvable, generating transversal of $H$ in $G$, then $G$ is a solvable group. Further, if $S$ is a generating transversal of $H$ in $G$ and $S$ has order 2 invariant sub right loop $T$ such that the quotient $S/T$ is a group. Then $H$ is an elementary abelian 2-group.Comment: 7 page

Comparing symmetry restoration trends for meson masses and mixing angles in the QCD-like three quark flavor models

We are computing the modifications for the scalar and pseudoscalar meson masses and mixing angles due to the proper accounting of fermionic vacuum fluctuation in the framework of the generalized 2+1 flavor quark meson model and the Polyakov loop augmented quark meson model(PQM). The renormalized contribution of the divergent fermionic vacuum fluctuation at one loop level makes these models effective QCD-like models. It has been explicitly shown that analytical expressions for the model parameters, meson masses, and mixing angles do not depend on any arbitrary renormalization scale. We have investigated how the incorporation of fermionic vacuum fluctuation in quark meson and PQM models qualitatively and quantitatively affects the convergence in the masses of the chiral partners in pseudoscalar ($\pi$, $\eta$, $\eta'$, $K$) and scalar ($\sigma$, $a_0$, $f_0$, $\kappa$) meson nonets as the temperature is varied on the reduced temperature scale. Comparison of present results in the quark meson model with vacuum term and PQM model with vacuum term with the already existing calculations in the bare 2+1 quark meson and PQM models, shows that the restoration of chiral symmetry becomes smoother due to the influence of the fermionic vacuum term. We find that the melting of the strange condensate registers a significant increase in the presence of the fermionic vacuum term and its highest melting is found in the PQM model with vacuum term. The role of the $U_A(1)$ anomaly in determining the isoscalar masses and mixing angles for the pseudoscalar ($\eta$ and $\eta'$) and scalar ($\sigma$ and $f_0$) meson complex has also been significantly modified due to the fermionic vacuum correction. In its influence, the interplay of chiral symmetry restoration and the setting up of the $U_A(1)$ restoration trends have also been shown to be significantly modified.Comment: 21 Pages, 9 captioned figures (18 .eps figure files). arXiv admin note: substantial text overlap with arXiv:0911.246

Solvable and Nilpotent Right Loops

In this paper the notion of nilpotent right transversal and solvable right transversal has been defined. Further, it is proved that if a core-free subgroup has a generating solvable transversal or a generating nilpotent transversal, then the whole group is solvable.Comment: arXiv admin note: substantial text overlap with arXiv:1307.539

Pattern Identification of Land use and Resource use efficiencies in Agriculture in Jhabua Tribal district in Madhya Pradesh

In the fifties and sixties of 20th century, the regional economists identified a regional process of circular and cumulative causation of under- development of resource-rich but backward regions (Myrdal) and core-periphery relation of developed industrial regions with resource hinterland regions (Friedman). In the seventies, environment and development conflicts were identified leading to ecological and socio-economic degradation in the resource regions. In the regional framework, the tribal regions as sub-national regions have come under serious anthropogenic impacts due to increasing demands for resource materials for trade and industries. Growing awareness of environmental degradation and depletion, the policy makers, planners, environmentalist and economists have focused their attention to examine the efficiencies of land use and the resource use in agriculture, identifying the ecological and economic efficiencies of the resource use pattern. Agriculture, being an organic economic activity, has a close relation with the natural resources like land and water. The tribal ecology is changing and the tribes have gradually adapted to agriculture activities and a distinct agro-ecosystem has grown in tribal areas. The tribes are trying to diversify the resource use for their ecological and economic sustenance. The government is also influencing resource use and land use as development strategy in the tribal region. It is necessary to examine the land use and the resource use efficiencies in the agricultural areas in regional and temporal framework. Land use and resource use efficiencies have been measured to evaluate ecologic and economic efficiency and growth in agriculture. Since, agriculture operates in system dynamic framework in which agriculture has close relation with other uses like forestry in ecological landscape in eco-regional framework and is affected by climatic change and other anthropogenic impacts resulting from industrialization and urbanization. it is necessary to identify the land use and resource use efficiencies in agriculture in the tribal eco-system. Along with land, other natural resources like water are important in agriculture. The efficiency of irrigation may be an indicator to identify the use of water resource and its efficiency in agriculture. The land use and irrigation intensity are used as an indicators for measuring land use and resource use efficiency in this study. In this paper, the land use intensity has been measured by (1) Analysis of the land use extension in agriculture in different tahsils of Jhabua district to identify the level of resource use in different regions. (2) The land use and irrigation intensity has been used as measure of resource use intensity and efficiency in different tahsils in study area (3) The agricultural land use efficiency has been measured using standard coefficient, which is a modified Kendall’s Ranking Coefficient method for agricultural land use zoning based on land use efficienciesPattern identification, land use and resource use efficiency, Kendall's Ranking coefficient

Agricultural development and regional carrying capacity measurement of agro-ecosystem in Jhabua tribal district in Madhya Pradesh

The agro-ecosystem is a system composed of population, natural resources and economic activities related in a dynamic interaction in terms of socio-ecological and socio-economic relations conditioned by endogenous and exogenous factors. With time, the agro-ecosystem undergoes changes. By analysing the agro-ecosystem dynamics over a period of time, we can plan the agro-ecosystem for higher level of production and productivity, achieving higher level of resource use and environmental efficiency and maximise food security as well as livelihood security. Due to the control of forest area by the government, the tribes are largely depending on agriculture. Jhabua district is tribal dominated with almost 86.84 percent tribal population of approximately 14 lakhs by 2001 Census. The geographical area of the district is 6793 sq. km. The net cultivated area is in the district is 64 percent to the total geographical area. The Jhabua district is located in the western part of Madhya Pradesh on the spur of the Vindhyas and along the western boundry of the Malwa plateau. It adjoins by Banswara district of Rajasthan in Northwest, by Panchmahal and Barodra district of Gujrat in the west, Dhulia district of Maharastra and West Nimar district of Madhya Pradesh in south, Dhar district in the east and Rutlam in the west. The Carrying capacity of agricultural ecosystem may be measured by taking production, productivity and socio-ecologic criteria. Food security, production and food availability and population and employment are used as indicators for measuring the carrying capacity of any agro-ecosystem. The carrying capacity measurement is important to check the capacity of the agro-ecosystem to support the population, the productivity changes of the ecosystem and food availability and other measures. In this paper, an attempt is made to analyse the adaptation of tribal population to agriculture and changes taking place in the agro-ecosystem and its productivity. It is necessary to identify population change, its density and spread, changes taking place in habitat in terms of land use changes and population and agro-ecosystem linkages in terms of landholding, population carrying capacity, food security, employment condition etc. Such an analysis would help to undertake agricultural development food security and employment security in the tribal regions with the objectives of eco-restoration, conservation and development.Population carrying capacity, ecosystem productivity, food security