Necessary and sufficient condition for hydrostatic equilibrium in general relativity

We present explicit examples to show that the `compatibility criterion' is capable of providing a {\em necessary} and {\em sufficient} condition for any regular configuration to be compatible with the state of hydrostatic equilibrium. This conclusion is drawn on the basis of the finding that the $M-R$ relation gives the necessary and sufficient condition for dynamical stability of equilibrium configurations only when the compatibility criterion for these configurations is appropriately satisfied. In this regard, we construct an appropriate sequence composed of core-envelope models on the basis of compatibility criterion, such that each member of this sequence satisfies the extreme case of causality condition $v = c = 1$ at the centre. The maximum stable value of $u \simeq 0.3389$ (which occurs for the model corresponding to the maximum value of mass in the mass-radius relation) and the corresponding central value of the local adiabatic index, $(\Gamma_1)_0 \simeq 2.5911$, of this model are found fully consistent with those of the corresponding {\em absolute} values, $u_{\rm max} \leq 0.3406$, and $(\Gamma_1)_0 \leq 2.5946$, which impose strong constraints on these parameters of such models. In addition to this example, we also study dynamical stability of pure adiabatic polytropic configurations on the basis of variational method for the choice of the `trial function', $\xi =re^{\nu/4}$, as well as the mass-central density relation, since the compatibility criterion is appropriately satisfied for these models. The results of this example provide additional proof in favour of the statement regarding compatibility criterion mentioned above.Comment: 31 pages (double-spaced) revtex style, 1 figure in `ps' forma

Hydrostatic equilibrium of insular, static, spherically symmetric, perfect fluid solutions in general relativity

An analysis of insular solutions of Einstein's field equations for static, spherically symmetric, source mass, on the basis of exterior Schwarzschild solution is presented. Following the analysis, we demonstrate that the {\em regular} solutions governed by a self-bound (that is, the surface density does not vanish together with pressure) equation of state (EOS) or density variation can not exist in the state of hydrostatic equilibrium, because the source mass which belongs to them, does not represent the `actual mass' appears in the exterior Schwarzschild solution. The only configuration which could exist in this regard is governed by the homogeneous density distribution (that is, the interior Schwarzschild solution). Other structures which naturally fulfill the requirement of the source mass, set up by exterior Schwarzschild solution (and, therefore, can exist in hydrostatic equilibrium) are either governed by gravitationally-bound regular solutions (that is, the surface density also vanishes together with pressure), or self-bound singular solutions (that is, the pressure and density both become infinity at the centre).Comment: 16 pages (including 1 table); added section 5; accepted for publication in Modern Physics Letters

Service quality attributes affecting passengers’ satisfaction with HIGER city bus

Service quality and customer satisfaction are the growing concerns for business organizations throughout the world, and customer satisfaction studies have been proven to be essential tools in trying to optimize services provided to users. For transit agencies, as in other service industries, increase in customer satisfaction translates into retained markets, increased use of the system, newly attracted customers, and a more positive public image. To accomplish these ends, public transport needs reliable and efficient methods of identifying the determinants of service quality from the customers’ perspective. The study is an attempt to identify the factors determining quality in city bus transit, by using a modified SERVPERF approach, and examines passengers’ overall satisfaction with HIGER city bus services. Therefore, a model depicting overall service quality was developed and tested empirically among the bus passengers. Factor and reliability (Cronbach Alpha coefficients) analyses were carried out to determine the validity and unidimensionality of the construct. Furthermore, associations between the passengers’ satisfaction and service quality attributes were explored, and found to be statistically significant. While the dimension of ‘reliability and complaint handling’ emerged as the largest contributor in estimating overall service quality, overall satisfaction was contributed significantly by overall service quality.Keywords: Service Quality, SERVPERF, Customer Satisfaction, HIGER Bus Service, Ethiopia

Tumačenja oktonionske valne jednadžbe

The interpretations of octonion wave equations in eight-dimensional space-time is studied. We made an attempt to consider the octonion field equation as the equation of motion for particles carrying simultaneously electric and magnetic charges (i.e. dyons) in external and internal spaces. It has been concluded that the component of octonion potential wave equations behaves neither as the generalized electromagnetic fields of monopoles nor of the dyons. Rather, it has a mixed behaviour of electromagnetic fields associated with the electric and magnetic charges in external and internal spaces. We have also made an attempt to investigate the split octonion wave equation and its interpretation in classical electrodynamics, and accordingly the consistent and compact forms of eight-dimensional potential and current equation of dyons are obtained in terms of Zorn\u27s vector matrix realization of split octonions. Visualizing the external four-space as the localization space for tachyons, it is shown that the split octonion wave equation reduces to the Maxwell\u27s equation (field equation) for bradyons in R4-space as well as that for tachyons in T4- space in the absence of other.Raspravljamo tumačenja oktonionske valne jednadžbe u osmodimenzijskom prostoru-vremenu. Pokušavamo raspraviti oktonionsku jednadžbu polja kao jednadžbu za gibanje čestica koje istovremeno nose električan i magnetski naboj (tj. diona) u vanjskom i unutarnjem prostoru. Zaključujemo da komponenta oktonionskog potencijala nema svojstva kako poopćenog elektromagnetskog polja, tako i diona. Zapravo, ona ima miješana svojstva elektromagnetskih polja pridruženih vanjskom i unutarnjim prostorima. Također, smo pokušali istražiti podvojenu oktonionsku jednadžbu i njeno tumačenje u klasičnoj elektrodinamici, te smo izveli skladne i sažete oblike osmodimenzijskog potencijala i jednadžbe za struju za dione koje smo izveli preko Zornove vektorske matrice za podvojene oktonione. Predstavljajući vanjski četveroprostor kao prostor za smještaj tahiona, pokazujemo da se podvojena oktonionska jednadžba svodi na Maxwellovu jednadžbu (jednadžbu polja) za bradione u R4 -prostoru, a u odsustvu ovih za tahione u T 4 -prostoru

Diversity, Distribution, Use Pattern and Evaluation of Wild Edible Plants of Uttarakhand, India

Wild edible plants are crucial not only for their role as a source of food and nutrition but are also integral part of culture and traditions of the Himalayan societies. Because of availability of diverse altitudinal, topographical and microclimatic conditions, the state of Uttarakhand supports a huge diversity of wild edible plants. Most of the species of wild edible plants in Uttarakhand are primarily consumed as a food by the local communities residing in remote hilly regions. However, several other species are consumed for their medicinal and health promoting benefits. The availability of enormous diversity of wild edible plants in the region has attracted attention of researchers. Consequently, research has been carried out on different aspects of wild edible plants. These include studies on distribution and use pattern, development of propagation protocols and bioprospecting and biochemical evaluation. As a result of this, some of the species are being utilized at commercial scale, and thus are considered capable of providing alternate options of livelihood for marginal communities residing in far flung areas of the state. However, there are several other promising species of wild fruits in the region, which need attention for conducting research on various aspects so that their optimum nutritional and economic potentials could be harnessed in sustainable manner

Analysis of MAGSAT data of the Indian region

Progress in the development of software for reading MAGSAT data tapes and for the reduction of anomaly data, and in the preparation of data for magnetic anomaly maps is reported

Octonion Quantum Chromodynamics

Starting with the usual definitions of octonions, an attempt has been made to establish the relations between octonion basis elements and Gell-Mann \lambda matrices of SU(3)symmetry on comparing the multiplication tables for Gell-Mann \lambda matrices of SU(3)symmetry and octonion basis elements. Consequently, the quantum chromo dynamics (QCD) has been reformulated and it is shown that the theory of strong interactions could be explained better in terms of non-associative octonion algebra. Further, the octonion automorphism group SU(3) has been suitably handled with split basis of octonion algebra showing that the SU(3)_{C}gauge theory of colored quarks carries two real gauge fields which are responsible for the existence of two gauge potentials respectively associated with electric charge and magnetic monopole and supports well the idea that the colored quarks are dyons