The Implication Problem for Functional and Multivalued Dependencies

Computation of the dependency basis is the fundamental step in solving the implication problem for MVDs in relational database theory. We examine this problem from an algebraic perspective. We introduce the notion of the inference basis of a set M of MVDs and show that it contains the maximum information about the logical consequences of M. We propose the notion of an MVD-lattice and develop an algebraic characterization of the inference basis using simple notions from lattice theory. We also establish several properties of MVD-lattices related to the implication problem. Founded on our characterization, we synthesize efficient algorithms for (a) computing the inference basis of a given set M of MVDs; (b) computing the dependency basis of a given attribute set w.r.t. M; and (c) solving the implication problem for MVDs. Finally, we show that our results naturally extend to incorporate FDs also in a way that enables the solution of the implication problem for both FDs and MVDs put together.

Action of Transition Metal Oxides on Composite Solid Propellants

The catalytic effects of Fe2O3, Ni2O3, MnO2, and Co2O3 transition metal oxides (TMO) on the combustion of polystyrene and carboxyl-terminated polybutadiene were investigated. The order of activity of TMO's was explained by the presence of Co and absence of Fe and Ni in their lattice systems along with a reduced electron-transfer process; in systems which induce the metal ions to enter the lattice, the electron transfer process is much greater. The thermal decomposition of ammonium perchlorate propellants was enhanced to a greater extent by Co2O3 and MnO2 than by Fe2O3 and Ni2O3.

Using lead sulphate instead of lead oxide in flux growth of yttrium iron garnet(YIG) crystals

Crystal growth of YIG from fluxes containing lead sulphate in place of lead oxide in the usual lead oxide-lead fluoride-boron oxide flux system has been tried. Lead sulphate decomposes during crystal growth giving lead oxide and sulphur trioxide. Due to the influence of sulphur trioxide in the system the yield of crystals almost doubles. There is no change either in the morphology of the crystals or their lattice parameter. It is possible that solubility of YIG is different in the new flux and the changed solubility causes the increase in yield of crystals.

Adsorption isotherms for neutral organic compounds-A hierarchy in modelling: Part II

A two-state model allowing for size disparity between the solvent and the adsorbate is analysed to derive the adsorption isotherm for electrosorption of organic compounds. Explicity, the organic adsorbate is assumed to occupy "n" lattice sites at the interface as compared to "one" by the solvent. The model parameters are the respective permanent and induced dipole moments apart from the nearest neighbour distance. The coulombic interactions due to permanent and induced dipole moments, discreteness of charge effects, and short-range and specific substrate interactions have all been incorporated. The adsorption isotherm is then derived using mean field approximation (MFA) and is found to be more general than the earlier multi-site versions of Bockris and Swinkels, Mohilner et al., and Bennes, as far as the entropy contributions are concerned. The role of electrostatic forces is explicity reflected in the adsorption isotherm via the Gibbs energy of adsorption term which itself is a quadratic function of the electrode charge-density. The approximation implicit in the adsorption isotherm of Mohilner et al. or Bennes is indicated briefly.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Adsorption isitherms for neutral organic compounds-A hierarchy in modelling: Part IV. Charge of maximum adsorption-Statistical mechanical basis

The charge at which adsorption of orgamc compounds attains a maximum ( \sigma MAX M) at an electrochenucal interface is analysed using several multi-state models in a hierarchical manner The analysis is based on statistical mechamcal results for the following models (A) two-state site parity, (B) two-state muhl-slte, and (C) three-state site parity The coulombic interactions due to permanent and reduced dipole effects (using mean field approximation), electrostatic field effects and specific substrate interactions have been taken into account. The simplest model in the hierarchy (two-state site parity) yields the exphcit dependence of ( \sigma MAX M) on the permanent dipole moment, polarizability of the solvent and the adsorbate, lattice spacing, effective coordination number, etc Other models in the baerarchy bring to hght the influence of the solvent structure and the role of substrate interactions, etc As a result of this approach, the "composition" of oM.x m terms of the fundamental molecular constants becomes clear. With a view to use these molecular results to maxamum advantage, the derived results for ( \sigma MAX M) have been converted into those involving experimentally observable parameters lake Co, C 1, E N, etc Wherever possible, some of the earlier phenomenologlcal relations reported for ( \sigma MAX M), notably by Parsons, Damaskm and Frumkln, and Trasattl, are shown to have a certain molecular basis, vlz a simple two-state sate panty model.As a corollary to the hxerarcbacal modelling, \sigma MAX M and the potential corresponding to at (Emax) are shown to be constants independent of 0max or Corg for all models The lmphcatlon of our analysis f o r OmMa x with respect to that predicted by the generalized surface layer equation (which postulates Om~ and Ema x varlaUon with 0) is discussed in detail Finally we discuss an passing o M. and the electrosorptlon valency an this context.

Adsorption isotherms-Microscopic modelling: Part II

A lattice formahsm using "spin variables" is employed to analyse multi-state models for the adsorption of neutral dipoles.In particular, a spin-1/2 (two-state) model incorporating permanent and reduced dipole moments of the solvent and the organic adsorbate,substrate interactions, and &screteness of charge effects is analysed The resulting Generalized Islng Hamaltonian is solved under mean field approximation (MFA) in order to derive the adsorption isotherm for organic molecules A few spin-1 (three-state) models are also analysed under MFA to describe the competitive adsorption of multi-state solvent and organic dipoles, and the appropriate equilibrium relations are derived The unification and isomorphism existing at the Hamlltonlan level for several diverse realizations, such as adsorption of ions and solvent/orgamc molecules, is indicated The possibility of analysing phase transitions using this generalized approach is briefly indicated.

Low-temperature and high-pressure Raman and x-ray studies of pyrochlore Tb2Ti2O7: Phonon anomalies and possible phase transition

We have carried out temperature- and pressure-dependent Raman and x-ray measurements on single crystals of Tb2Ti2O7. We attribute the observed anomalous temperature dependence of phonons to phonon-phonon anharmonic interactions. The quasiharmonic and anharmonic contributions to the temperature-dependent changes in phonon frequencies are estimated quantitatively using mode Grüneisen parameters derived from pressure-dependent Raman experiments and bulk modulus from high-pressure x-ray measurements. Further, our Raman and x-ray data suggest a subtle structural deformation of the pyrochlore lattice at ~9 GPa. We discuss possible implications of our results on the spin-liquid behavior of Tb2Ti2O7.

Watson-Crick pairing, the Heisenberg group and Milnor invariants

We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenber invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict allosteric structures for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson-Crick pairs found.

Studies of Phosphazenes. Part 13.' Thermal Rearrangement Reactions of Some Met hoxycyclo phosp hazenes

The methoxycyclophosphazenes [NP(OMe),], (n = 3-6) rearrange on heating to give oxocyclophosphazanes, [N(Me)PO(OMe)],. Isomeric products are formed when n = 4-6. The lH, ,lP, and 13C n.m.r. data for the starting materials and the products are presented. The ethoxy- and n-propoxy-derivatives N,P,( OR)* do not undergo the above rearrangement. The geminal derivatives N,P,R,(OMe), (R = Ph or NHBut) on heating yield both fully and partially rearranged products, namely dioxophosphaz-1 -enes and oxophosphazadienes, as shown by 270- MHz lH n.m.r. spectroscopy. The non-geminal derivative N,P,( NMe,),(OMe), gives only the fully rearranged product N,Me,P,(NMe,),O,(OMe), whose structure has been established from its lH and 31P n.m.r. spectra.

Studies in Nonlinear Optical Materials: Structure of Methyl 2-(4-Ethyl-5-methyl- 2-thioxo-2,3-dihydro-l,3-thiazol- 3-yl) propionate

CIoH15NO282, Mr=245"0, orthorhombic, P21212 ~, a = 6.639 (2), b = 8.205 (2), c = 22.528(6)A, V= I227.2(6)A 3, z=4, Dm= 1.315, Dx= 1.326gem -3, MoKa, 2=0.7107A, 12= 3.63 cm -1, F(000) = 520, T= 293 K, R = 0.037 for 1115 significant reflections. The second-harmonicgeneration (SHG) efficiency of this compound is only 1/10th of the urea standard. The observed low second-order nonlinear response may be attributed to the unfavourable packing of the molecules in the crystal lattice.

Depth profile composition studies of thin film CdS: Cu,S solar cells using XPS and AES

Surface composition and depth profile studies of hemiplated thin film CdS:CuzS solar cells have been carried out using x-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) techniques. These studies indicate that the junction is fairly diffused in the as-prepared cell. However, heat treatment of the cell at 210°C in air relatively sharpens the junction and improves the cell performance. Using the Cu(2p3p)/S(2p) ratio as well as the Cu(LVV)/(LMM) Auger intensity ratio, it can be inferred that the nominal valency of copper in the layers above the junction is Cut and it is essentially in the CUSS form. Copper signals are observed from layers deep down in the cell. These seem to appear mostly from the grain boundary region. From the observed concentration of Cd, Cu and S in these deeper layers and the Cu(LVV)/(LMM) ratio it appears that the signals from copper essentially originate partly from copper in CuS and partly from Cu2t trapped in the lattice. It is significant to note that the nominal valence state of copper changes rather abruptly from Cut to Cuz+ across the junction.

Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations.

Effect of pressure on the electrical resistivity of indium sulphide

Indium sulphide (INS) is a III-VI compound semiconductor and crystallizes in the orthorhombic structure with a space group D~(Pmnn). The lattice parameters at room temperature and atmospheric pressure are: a = 3.944 A, b = 4.447 A and c= 10.648#, [1, 2]. The crystal structure comprises an ethane-like SalnlnS3 atomic arrangement;the SalnInS3 groups are mutually linked by sharing S corners and form a three-dimensional network.