On sparse spanners of weighted graphs

Given a graphG, a subgraphG' is at-spanner ofG if, for everyu,v V, the distance fromu tov inG' is at mostt times longer than the distance inG. In this paper we give a simple algorithm for constructing sparse spanners for arbitrary weighted graphs. We then apply this algorithm to obtain specific results for planar graphs and Euclidean graphs. We discuss the optimality of our results and present several nearly matching lower bounds.The work of G. Das and D. Joseph was supported by NSF PYI Grant DCR-8402375. The work of D. Dobkin was supported by NSF Grant CCR-8700917. The work of J. Soares was supported by CNPq proc 203039/87.4 (Brazil) and NSF Grant CCR-9014562. This research was accomplished while G. Das was a student at the University of Wisconsin-Madison. A preliminary version was presented at the Second Scandinavian Workshop on Algorithm Theory, Bergen, Norway, 1990, under the title Generating Sparse Spanners for Weighted Graphs, and proceedings appear in the series Lecture Notes in Computer Science, Springer-Verlag. The preliminary version also appears as Princeton University Technical Report CS-TR-261-90, and as University of Wisconsin-Madison Computer Sciences Technical Report 882.     

Lauricella hypergeometric series $$F_A^{(n)}$$ F A ( n ) over finite fields

The Ramanujan Journal - In this paper, we develop a finite field analogue for one of the Lauricella series, $$F^{(n)}_A$$ . Extending results of Greene, a finite field analogue for the multinomial...     

Beyond the standard model: Working group report

This report summarises the work done in the ‘Beyond the Standard Model’ working group of the Sixth Workshop on High Energy Physics Phenomenology (WHEPP-6) held at the Institute of Mathematical Sciences, Chennai, Jan 3–15, 2000. The participants in this working group were: R Adhikari, B Ananthanarayan, K P S Balaji, Gour Bhattacharya, Gautam Bhattacharyya, Chao-Hsi Chang (Zhang). D Choudhury, Amitava Datta, Anindya Datta, Asesh K Datta, A Dighe, N Gaur, D Ghosh, A Goyal, K Kar, S F King, Anirban Kundu, U Mahanta, R N Mohapatra, B Mukhopadhyaya, S Pakvasa, P N Pandita, M K Parida, P Poulose, G Raffelt, G Rajasekaran, S Rakshit, Asim K Ray, A Raychaudhuri, S Raychaudhuri, D P Roy, P Roy, S Roy, K Sridhar and S Vempati.     

Form I of desloratadine,a tricyclic anti­histamine

The title compound [systematic name: 8‐chloro‐11‐(piperidin‐4‐yl­idene)‐6,11‐dihydro‐5H‐benzo[4,5]cyclo­hepta­[2,1‐b]pyridine], C₁₉H₁₉ClN₂, was crystallized from ethyl acetate. The inter­esting feature of the reported structure is that it does not contain any strong hydrogen bonds, although the mol­ecule contains a secondary NH group, which is a good hydrogen‐bond donor.     

Charge-transfer-induced twisting of the nitro group

Excited-state relaxation dynamics of 2-amino-7-nitrofluorene (ANF) and 2-dimethylamino-7-nitrofluorene (DMANF) has been investigated in two aprotic solvents, namely acetonitrile and DMSO using femtosecond transient absorption spectroscopic technique. Following photoexcitation to the highly dipolar excited singlet (S1) state, ANF and DMANF undergo mainly two concomitant relaxation processes, namely dipolar solvation and conformational relaxation via twisting of the nitro group to an orthogonal configuration with respect to the aromatic plane. Viscosity dependence of the relaxation dynamics of the S1 states of both ANF and DMANF suggests no involvement of the twisting motion of the amino or dimethylamino group in the charge-transfer process. The twisting of the nitro group is found to be a friction affected diffusive motion, which does not associate with any further charge transfer. The results presented in this paper resolve experimentally the dynamics of the twisting motion of the nitro group for the first time.     

Synthesis and spectroscopic characterization of transition metal complexes of a 12-membered tetraaza [N<Subscript>4</Subscript>] macrocyclic ligand and their biological activity

Cobalt(II), nickel(II) and copper(II) complexes are synthesized with 1,3,7,9-tetraaza- 4,6,10,12-tetraphenyl-2,8-dithiacyclododecane, a tetradentate ligand (L) and characterized by elemental analysis, molar conductance measurements, magnetic susceptibitity measurements, mass, i.r., electronic and e.p.r. spectral studies. All the complexes are non-electrolytes so they may be formulated as [M(L)X₂] [where, M = Co(II), Ni(II) and Cu(II) and X = Cl⁻ and NO ₃ ⁻ ]. All the complexes are of high spin type. On the basis of i.r., electronic and e.p.r. spectral studies an octahedral geometry has been assigned for Co(II) and Ni(II) complexes and tetragonal geometry for Cu(II) complexes. The antimicrobial activities of the ligand and its complexes, as growth inhibiting agents, have been screened in vitro against two different species of bacteria and plant pathogenic fungi.     

Non-fouling microfluidic chip produced by radio frequency tetraglyme plasma deposition

This Technical Note presents the direct surface modification of a glass/PTFE hybrid microfluidic chip, via radio frequency glow discharge plasma polymerisation of tetraethlylene glycol dimethylether (tetraglyme), to produce hydrophilic, non-fouling, PEO-like surfaces. We use several techniques including X-ray photoelectron spectroscopy (XPS), direct enzyme-linked immunosorbent assays (ELISA) and immunofluorescent imaging to investigate the channel coatings. Our results indicate the successful deposition of a PEO-like coating onto microchannel surfaces that has both solution and shelf stability (>3 months) and is capable of preventing fibrinogen adsorption to the microchannel surfaces.