Pinning down neutrino oscillation parameters in the 2–3 sector with a magnetised atmospheric neutrino detector: a new study

We determine the sensitivity to neutrino oscillation parameters from a study of atmospheric neutrinos in a magnetised detector such as the ICAL at the proposed India-based Neutrino Observatory. In such a detector, which can separately count \(\nu _\mu \) and \(\overline{\nu }_\mu \)-induced events, the relatively smaller (about 5%) uncertainties on the neutrino–antineutrino flux ratios translate to a constraint in the \(\chi ^2\) analysis that results in a significant improvement in the precision with which neutrino oscillation parameters such as \(\sin ^2\theta _{23}\) can be determined. Such an effect is unique to all magnetisable detectors and constitutes a great advantage in determining neutrino oscillation parameters using such detectors. Such a study has been performed for the first time here. Along with an increase in the kinematic range compared to earlier analyses, this results in sensitivities to oscillation parameters in the 2–3 sector that are comparable to or better than those from accelerator experiments where the fluxes are significantly higher. For example, the \(1\sigma \) precisions on \(\sin ^2\theta _{23}\) and \(|\Delta {m^2_{32(31)}}|\) achievable for 500 kton year exposure of ICAL are \({\sim }9\) and \({\sim }2.5\)%, respectively, for both normal and inverted hierarchies. The mass hierarchy sensitivity achievable with this combination when the true hierarchy is normal (inverted) for the same exposure is \(\Delta \chi ^2\approx 8.5\) (\(\Delta \chi ^2\approx 9.5\)).     

Decomposition of involutions on inertially split division algebras

Let F be a Henselian valued field with , and let S be an inertially splitF}-central division algebra with involution $\sigma ^{\ast }$ that is trivial on an inertial lift in S of the field . We prove necessary and sufficient conditions for S to contain a -stable quaternion {\it F}-subalgebra, and for to decompose into a tensor product of quaternion algebras. These conditions are in terms of decomposability of an associated residue central simple algebra that arises from a Brauer group decomposition of S. Received February 1, 1999; in final form August 26, 1999 / Published online July 3, 2000     

Etching and dielectric studies on L‐lysine monohydrochloride dihydrate single crystal

The nonlinear optical single crystals of L‐Lysine monohydrochloride dihydrate (L‐LMHCl) have been grown and examined by High‐resolution X‐ray diffraction and etching studies for their perfection. The vibrational frequencies have been identified by the micro‐Raman studies and the dielectric behaviour has been studied and the results are presented in detail. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Proximinal subspaces of finite codimension in direct sum spaces

We give a necessary and sufficient condition for proximinality of a closed subspace of finite codimension in c₀-direct sum of Banach spaces.     

Spin dependent gluon densities from largeP T photon and dimuon production

We investigate spin asymmetries in highp _T photon and dimuon production and show that the spin dependent gluon density can be extracted reliably frompp collisions with these final states. The statement remains true even when the balancing jet is not observed. Hence fixed target experiments can be used to measure the spin dependent gluon density. We also compute the asymmetries in \(p\bar p\) collisions, and show that the EMC measurement of the spin structure function can be verified and the spin dependent gluon density can be extracted from these experiments.     

Review of recent results in deep inelastic scattering

This talk gives a summary of recent results in deep inelastic lepton hadron scattering. This includes structure functions from inclusive measurements as well as fragmentation in semi-inclusive processes, mainly with respect to data from colliders such as HERA at DESY, and their associated phenomenology.     

Decompositions of complete graphs and complete bipartite graphs into isomorphic supersubdivision graphs

A graph H is called a supersubdivison of a graph G if H is obtained from G by replacing every edge uv of G by a complete bipartite graph K_2,m (m may vary for each edge) by identifying u and v with the two vertices in K_2,m that form one of the two partite sets. We denote the set of all such supersubdivision graphs by SS(G). Then, we prove the following results.

1. Each non-trivial connected graph G and each supersubdivision graph HSS(G) admits an α-valuation. Consequently, due to the results of Rosa (in: Theory of Graphs, International Symposium, Rome, July 1966, Gordon and Breach, New York, Dunod, Paris, 1967, p. 349) and El-Zanati and Vanden Eynden (J. Combin. Designs 4 (1996) 51), it follows that complete graphs K_2cq+1 and complete bipartite graphs K_mq,nq can be decomposed into edge disjoined copies of HSS(G), for all positive integers m,n and c, where q=|E(H)|.

2. Each connected graph G and each supersubdivision graph in SS(G) is strongly n-elegant, where n=|V(G)| and felicitous.

3. Each supersubdivision graph in EASS(G), the set of all even arbitrary supersubdivision graphs of any graph G, is cordial.

Further, we discuss a related open problem.     

Piperidone derivative from Dalbergia sympathetica

An alcoholic extract of Dalbergia sympathetica, on column chromatography, yielded a compound which analyzed for C(6)H(11)NO(3) (M(+) 145). The IR spectrum of the compound showed the presence of carbonyl and hydroxyl groups. PMR, (13)C and DEPT NMR spectral studies of the compound showed the presence of one N-methyl, two methine and two methylene groups. A quaternary carbon signal at delta 172.88 ppm was assigned to C-2 carbonyl of the compound. From all the above observations and also from the HMQC 2D NMR spectrum, the compound was identified as 3, 6-dihydroxy-N-methyl-2-piperidone. This is the first report of the natural occurrence of this compound from plant sources.     

Mononuclear transition metal complexes with sterically hindered carboxylate ligands: Synthesis, structural and spectral properties

The metal coordination geometry in the active site of metalloproteins are very different from the one of small inorganic complexes, due to the inflexibility of the ligand set from amino acid side chains different from freely moving ligand set in synthesis. Using the sterically hindered 2,6-di-(p-fluorophenyl)benzoate(L) ligand, a series of mononuclear Co(II), Ni(II) and Cu(II) complexes of general formula [M(L)₂(Hdmpz)₂] (where, Hdmpz = 3,5-dimethyl pyrazole) have been synthesized and characterized by the variety of spectroscopic methods. A distorted octahedral geometry in case of nickel, tetrahedral geometry for cobalt and square pyramidal in copper was observed in the X-ray studies, which also revealed that the uncoordinated oxygen atom of the carboxylate group forms intramolecular hydrogen bonding with the N-H group of the coordinated 3,5-dimethylpyrazole in case of cobalt and copper.