Interplay between four conjectures on certain zero-sum problems

In this paper, we explore the interplay of four different conjectures on certain zero-sum problems in Z_p Z_p. This study of the inter-relations between these conjectures leads to the conclusion that determining the structure of minimal zero sequences (see below for the precise definition) is crucial. Also, we study the analogous situation in Z_n.     

Development and investigation of perovskite (ABO3)-type oxides for power generation

Critical problems of the present approach of electrolytes for Solid Oxide Fuel Cells (SOFCs) for commercialization are discussed. Major progress is expected from the development of materials based on the “SEA (Single Element Arrangement)” concept. The galvanic cell consists in this case basically of a single chemically homogeneous compound, which functions as electrodes at high and low activity and as electrolyte at intermediate activities of the electroactive component. In view of the large structural flexibility of the chemical nature of the constitutents, we explored perovskite (ABO₃)-type compounds to be used as SEAs for SOFCs. Results of studies on Pr-substituted LSGM and Fe-substituted SrSnO₃ perovskite-type oxides are presented. For instance, SrSn_1-xFe_xO_3-δ with x=0.1 exhibits p and n-type electronic conduction at the cathode and anode sides of the SOFC, respectively, while oxide ion conduction prevails at intermediate oxygen partial pressures. The SEA concept is also applicable for other devices in the field of Ionics.     

Ruthenium(II) carbonyl complexes containing tridentate Schiff bases

New ruthenium(II) complexes, [Ru(CO)(B)(LL)(PPh₃)] (where, LL = tridentate Schiff bases; B = PPh₃, pyridine, piperidine or morpholine) have been prepared by reacting [RuHCl(CO)(PPh₃)₃] or [RuHCl(CO)(PPh₃)₂(B)] with Schiff bases containing donor groups (O, N, X) viz., salicylaldehyde thiosemicarbazone (X = S), salicylaldehyde semicarbazone (X = O), o-hydroxyacetophenone thiosemicarbazone (X = S) and o-hydroxyacetophenone semicarbazone (X = O). The new complexes were characterised by elemental analysis, spectral (i.r., ¹H- and ³¹P-n.m.r.), data.     

Biomolecular docking,antimicrobial and cytotoxic studies on new bidentate schiff base ligand derived metal (II) complexes

Three new metal complexes [Cu(L)₂] (1), [Co(L)₂] (2) and [Zn(L)₂] (3) have been prepared by the reaction of hydrated salts of metal (II) acetate with new Schiff base ligand HL, [2‐((4‐(dimethylamino)phenylimino)methyl)‐4,6‐di‐t‐butylphenol] and characterized by different physico‐chemical analyses such as elemental analysis, single XRD, ¹H NMR, FTIR and UV–Vis spectroscopic techniques. Their biomolecular docking, antimicrobial and cytotoxicity studies have also been demonstrated. The proposed structure of Schiff base ligand HL and complex 2 are confirmed by Single crystal X‐ray crystallography study. This analysis revealed that metal (II) complexes remain in distorted tetrahedral coordination environments. The electronic properties such as HOMO and LUMO energies are carried out by gaseous phase DFT/B3LYP calculations using Gaussian 09 program. Complex 1 showed a good binding propensity to the DNA and HSA, during the assessment of docking studies. Schiff base ligand HL and its metal (II) complexes, 1–3 screened for their in vitro antimicrobial activities using the disc diffusion method against selected microbes. Complex 1 shows higher antimicrobial activity than complexes 2, 3 and Schiff base ligand HL. According to the results obtained from the cytotoxic studies, Schiff base ligand HL and its metal (II) complexes 1–3 have better cytotoxicity against MCF‐7 cell lines with potency higher than the currently used chemotherapeutic agent cyclophosphamide.     

Tailoring ceramics for specific applications: A case study of the development of all-solid-state lithium batteries

Metal oxides with the nominal chemical compositions Li₅La₃M₂O₁₂ (M=Nb, Ta), possessing a garnet-like structure, exhibit ionic bulk conductivities of the order of magnitude of ∼10⁻⁶ S/cm at 25 °C. Partial substitution of La by alkaline earth elements (Ca, Sr, Ba) in Li₅La₃M₂O₁₂ yields new members of compounds with garnet-like structure with the composition Li₆ALa₂M₂O₁₂ (A=Ca, Sr, Ba). Among the investigated compounds, so far, the Ba-compound Li₆BaLa₂Ta₂O₁₂ exhibits the highest bulk conductivity of 4.0×10⁻⁵ S/cm at 22 °C with an activation energy of 0.40 eV. All Ta-members were found to be stable against chemical reaction with molten elemental lithium. Li₆ALa₂Ta₂O₁₂ (A=Sr, Ba) exhibit also high electrochemical stability of ∼6 V vs. lithium and chemical stability against reaction with LiCoO₂ cathode material. A novel high voltage thin-film battery was constructed using spinel-type Li₂MMn₃O₈ (M=Co, Fe) as positive electrode, LiPON as electrolyte and Al as negative electrode material. Li₂MMn₃O₈ (M=Fe, Co) electrodes show two reversible plateaus during the charging and discharging cycle at ∼4 and ∼5 V vs. Li. The former plateau is due to the valence change of Mn³⁺ to Mn⁴⁺ and the latter one is due to the oxidation of M³⁺ to M⁴⁺. The chemical diffusion coefficient ( ) was found to be in the range 10⁻¹³–10⁻¹² cm²/sec for any composition x of Li_2−xMMn₃O₈ (M=Fe, Co) in the range from 0.1 to 1.6 by employing the galvanostatic intermittent titration technique (GITT). AC impedance studies revealed an electrolyte-electrode charge transfer resistance of 260–290 Θ and an electrode double layer capacity of ∼45–70 μF for an electrode area of 6.7 cm² at room temperature. The chemical diffusion coefficient of the Al,LiAl negative electrode is about three orders of magnitude higher than that of the positive electrode materials. Accordingly, we believe that the diffusion of Li into and out of the cathode material is the rate determining process. Paper presented at the Patras Conference on Solid State Ionics - Transport Properties, Patras, Greece, Sept. 14 – 18, 2004.     

High Pressure effects on electrical resistivity and dielectric properties of nanocrystalline SnO2

Nanocrystalline tin oxide (SnO₂) was prepared by chemical precipitation method with different grain sizes. The X-ray diffraction studies showed the structural stability of nanocrystalline SnO₂ under high-pressure. Electrical and dielectric properties were studied on these samples using complex impedance spectroscopy under different hydrostatic pressures. Electrical resistivity and dielectric studies showed a transition in nanocrystalline SnO₂ when it was subjected to high-pressure. The transition pressures obtained from both the resistivity and dielectric measurements agree with each other. The transition pressures were found to increase considerably with the decrease in grain size. Dielectric constant was found to decrease with the reduction of grain size. In order to find whether the transition with pressure is structure- related or not, Raman spectroscopy was done at normal temperature and pressure (NTP) and as a function of pressure at room temperature. Raman modes at NTP showed lines which correspond to tetragonal rutile structure of SnO₂. In situ high-pressure Raman measurements were carried out up to 3.38 GPa. No structural change was found with pressure.     

Monolithic electrochromic devices using lithium ion conducting perovskite-type oxides

The electrical conductivities of several perovskite-type lithium ion conductors in the Li-Sr-Nb-Ta-Ti-O system have been investigated. The Li⁺-ion conductivities of the Ta-compounds were found to be higher than those of the corresponding Nb-compounds, i.e., Li_0.3Sr_0.6Ta_0.5Ti_0.5O₃ exhibits a bulk ionic conductivity of 1.7×10⁻⁴ S/cm at 30 °C, while Li_0.3Sr_0.6Nb_0.5Ti_0.5O₃ shows a value of 5.4×10⁻⁶ S/cm at the same temperature. Substitution of Fe in Li_0.3Sr_0.6Ta_0.5Ti_0.5O₃ decreases the Li⁺-ion conductivity slightly. The operation of a monolithic (single element) electrochromic devices was demonstrated using perovskite-type Li_0.3Sr_0.6B_0.5Ti_0.5O₃ (B=Nb, Ta). The tantalum compound exhibited the largest coloration at the positive electrode side by the application of a voltage of 1.5 V and was bleached under short-circuit conditions at 350 °C. Paper presented at the 9th EuroConference on Ionics, Ixia, Rhodes, Greece, Sept. 15–21, 2002.     

A note on a conjecture of Borwein and Choi

A polynomial P(X) with coefficients {ǃ} of odd degree N - 1 is cyclotomic if and only if¶¶P(X) = ±F_p1 (±X)F_p2(±X^p1) ?F_pr(±X^{p1 p2 ?p_r-1}) P(X) = \pm \Phi_{p1} (\pm X)\Phi_{p2}(\pm X^{p1}) \cdots \Phi_{p_r}(\pm X^{p1 p2 \cdots p_r-1}) ¶where N = p₁ p₂ · · · p_r and the p_i are primes, not necessarily distinct, and where F_p(X) : = (X^p - 1) / (X - 1) \Phi_{p}(X) := (X^{p} - 1) / (X - 1) is the p-th cyclotomic polynomial. This is a conjecture of Borwein and Choi [1]. We prove this conjecture for a class of polynomials of degree N - 1 = 2^r p^l - 1 N - 1 = 2^{r} p^{\ell} - 1 for any odd prime p and for integers r, l\geqq 1 r, \ell \geqq 1 .     

Recent study of nanomaterials prepared by inert gas condensation using ultra high vacuum chamber

The ultra high vacuum chamber was developed in the Department of Nuclear Physics, University of Madras with the funding from DST, India. This UHV chamber is used to prepare nanocrystalline materials by inert gas condensation technique (IGCT). Nanocrystalline materials such as PbF₂, Mn²⁺-doped PbF₂, Sn-doped In₂O₃ (ITO), ZnO, Al₂O₃, Ag₂O, CdO, CuO, ZnSe:ZnO etc., were prepared by this technique and characterized. Results of some of these materials will be presented in this paper. In solid-state²⁰⁷Pb NMR on PbF₂ a separate signal due to the presence of grain boundary has been observed. The structural phase transition pressure during the phase transformation from the cubic phase to orthorhombic phase under high pressure shows an increase with the decrease in grain size. Presence of electronic centres in nanocrystalline PbF₂ is observed from Raman studies and the same has been confirmed by photoluminescence studies. Al₂O₃ was prepared and⁵⁶Fe ions were implanted. After implantation segregation of⁵⁶Fe ions was examined by SEM. The oxidation properties of ITO were studied by HRTEM. As against the expectation of oxide coating on individual nanograins of In-Sn alloy, ITO nanograins grew into faceted nanograins on heat treatment in air and O₂ atmosphere. The growth of ITO under O₂ atmosphere showed pentagon symmetry. The PMN was initially prepared by solid-state reaction. Further, this PMN relaxor material will be used to convert into nanocrystalline PMN by IGCT with sputtering and will be studied