Distance Product of Graphs

In graph theory, different types of product of two graphs have been studied, e.g. Cartesian product, Tensor product, Strong product, etc. Later on, Cartesian product and Tensor product have been generalized by 2-Cartesian product and 2-Tensor product. In this paper, we give one more generalize form, distance product of two graphs. Mainly we discuss the connectedness, bipartiteness and Eulerian property in this product

Type IIA Orientifold Limit of M-Theory on Compact Joyce 8-Manifold of Spin(7)-Holonomy

We show that M-theory compactified on a compact Joyce 8-manifold of $Spin(7)$-holonomy, which yields an effective theory in $D = 3$ with $\N$ = 1 supersymmetry, admits at some special points in it moduli space a description in terms of type IIA theory on an orientifold of compact Joyce 7-manifold of $G_2$-holonomy. We find the evidence in favour of this duality by computing the massless spectra on both M-thory side and type IIA side. For the latter, we compute the massless spectra by going to the orbifold limit of the Joyce 7-manifold.Comment: 26 pages, 2 eps figures, Latex file, two references and one footnote added, corrected some typo

A RANDOMISED DOUBLE-BLIND CLINICAL STUDY TO EVALUATE AND COMPARE THE EFFECTS OF VRIDDADARU RASAYANA WITH BHARGAVAPROKTA RASAYANA ON AGEING IN APPARENTLY HEALTHY ELDERLY SUBJECTS

According to estimation, India currently has 6.7% over 65 years of age, which is expected to increase to 20% by the year 2050. As growing old is a part of the life cycle, the effect of time is bound to happen and is unavoidable. The Kalajajara is a Swabhavika vyadhi, wherein, it is clearly mentioned that Swabhava balapravritta vyadhis being Yapya, can be managed through Bhojana, Paana, and Rasayana. Vriddadaru Rasayana is one such Rasayana mentioned in Gadanigraha especially for the elderly to promote healthy ageing and helping to prevent old age problems. Aims and objectives: To assess the effect of Vriddadaru Rasayana in improving the general body health and quality of life in the apparently healthy elderly subjects. Methodology– A Randomized double blind clinical study where 20 healthy elderly subjects were administered with Vriddadaru Rasayana for a period of 12 weeks. Observations and Results- Vriddadaru rasayana showed improvement in Ayurvedic parameters like Twakparushata, Slataasti, Slata sandhi, Utasahahani and Parakramahani but when compared with regard to objective parameters Vriddadaru rasayana showed significant values in DHEAS levels and 6MWT. Conclusion: Vriddadaru does Vatashamana, balancing the Doshas, increasing the Utsaha and Parakrama and helps in improving the Agni thus helping in Dhatuposhana in the elderly

G(2) quivers

We present, in explicit matrix representation and a modernity befitting the community, the classification of the finite discrete subgroups of G2 and compute the McKay quivers arising therefrom. Of physical interest are the classes of Script N = 1 gauge theories descending from M-theory and of mathematical interest are possible steps toward a systematic study of crepant resolutions to smooth G2 manifolds as well as generalised McKay Correspondences. This writing is a companion monograph to hep-th/9811183 and hep-th/9905212, wherein the analogues for Calabi-Yau three- and four-folds were considered

Occurrence of Unapproved Pesticides and their Ecotoxicological Significance for an Agriculturally Influenced Reservoir and its Tributaries in Nepal

Many catchments in Nepal are affected by intensive agricultural activities, leading to extensive pesticide usages. This study aimed to assess pesticide abundance in concurrently collected water, sediment and fish samples for the first time in intensively cultivated catchment (Indra Sarowar) located in the mid-hill region of Nepal during the rice and vegetables growing season. A total of 75 pesticides were analysed, of which 4 pesticides (alachlor, diuron, metalaxyl and pyrimethanil) were present in water with detection frequency (DF) > 40%, with alachlor (0.62 – 2.68 µg L−1) being ubiquitous. In the sediment of tributaries, the pesticides p,p′-DDT, β-HCH, alachlor and diuron were detected with DF exceeding 40%, where β-HCH was commonly observed (DF = 92%) with concentration ranging from 6.29 – 99.22 µg kg−1. The ecotoxicological risk indicated that herbicides (alachlor and diuron) posed a high risk to aquatic organisms in both tributaries and reservoir water. Such risk in sediment was even more pronounced, with alachlor and diuron showing up to 2.3 and 53.7 times higher risk respectively compared to water samples. However, none of these herbicides were detected in fish muscles. Among the fish species studied, pyrimethanil was the only quantified pesticide in edible tissue of both cage cultured (0.35 – 1.80 µg g−1 ww) and open stock fishes (0.06 – 1.12 µg g−1 ww). The consumer risk assessment showed very low human health risk associated with fish consumption (HQ < 0.2). Nonetheless, long-term consumption of contaminated fish may pose some risk that cannot be ignored. Overall, this study generated the benchmark data highlighting pervasive presence of banned (DDT, endosulfan, HCH) and unapproved (alachlor, diuron, pyrimethanil) pesticides in the environmental compartments in the mid-hill’s streams of Nepal

On the upper bound of the electronic kinetic energy in terms of density functionals

We propose a simple density functional expression for the upper bound of the kinetic energy for electronic systems. Such a functional is valid in the limit of slowly varying density, its validity outside this regime is discussed by making a comparison with upper bounds obtained in previous work. The advantages of the functional proposed for applications to realistic systems is briefly discussed.Comment: 10 pages, no figure

On the equivalence of N=1 brane worlds and geometric singularities with flux

We consider Kaluza Klein reductions of M-theory on the Z_N orbifold of the spin bundle over S^3 along two different U(1) isometries. The first one gives rise to the familiar ``large N duality'' of the N=1 SU(N) gauge theory in which the UV is realized as the world-volume theory of N D6-branes wrapped on S^3, whereas the IR involves N units of RR flux through an S^2. The second reduction gives an equivalent version of this duality in which the UV is realized geometrically in terms of an S^2 of A_{N-1} singularities, with one unit of RR flux through the S^2. The IR is reached via a geometric transition and involves a single D6 brane on a lens space S^3/Z_N or, alternatively, a singular background (S^2\times R^4)/Z_N, with one unit of RR flux through S^2 and, localized at the singularities, an action of their stabilizer group in the U(1) RR gauge bundle, so that no massless twisted states occur. We also consider linear sigma-model descriptions of these backgrounds.Comment: 25 pages, LaTeX; v2: one reference added, published versio

Scherk-Schwarz reduction of M-theory on G2-manifolds with fluxes

We analyse the 4-dimensional effective supergravity theories obtained from the Scherk--Schwarz reduction of M-theory on twisted 7-tori in the presence of 4-form fluxes. We implement the appropriate orbifold projection that preserves a G2-structure on the internal 7-manifold and truncates the effective field theory to an N=1, D=4 supergravity. We provide a detailed account of the effective supergravity with explicit expressions for the Kaehler potential and the superpotential in terms of the fluxes and of the geometrical data of the internal manifold. Subsequently, we explore the landscape of vacua of M-theory compactifications on twisted tori, where we emphasize the role of geometric fluxes and discuss the validity of the bottom-up approach. Finally, by reducing along isometries of the internal 7-manifold, we obtain superpotentials for the corresponding type IIA backgrounds.Comment: 43 pages, Latex; v3 typos corrected, one reference added, JHEP versio