Cationic complexes of chelated bis(η-cyclopentadienyl)titanium(IV) with halometallates of gallium(III), indium(III) and thallium(III)

Summary Eight complexes of the chelated bis(-cyclopenta-dienyl)titanium(IV) cation. [-Cp₂TiL][MX₄] (L = acetyl-acetone, M = Ga^III, In^III or Ti^III: X = Cl, Br or I) have been isolated from aqueous solution and characterised by elemental analyses and i.r. data. Their ionic nature has been confirmed by conductance measurements.     

Gauss sums forF q [T]

The purpose of this paper is to define Gauss sums taking values in function fields of one variable over a finite field and to prove analogues of various classical and recent results. These results include Stickelberger's theorem, the Hasse-Davenport theorem, Weil's theorem on Jacobi sums as Hecke characters and the Gross-Koblitz theorem. For comparison, the reader may consult [G-K] and references given there.In this paper we deal only with the simplest case, where the base ringA is the polynomial ringF _q [T] and where we use the Carlitz module; i.e., the simplest rank one Drinfeld module. (See section I). The general case, which has a quite different flavour, will be presented elsewhere. These results formed a part of the author's thesis, Gamma functions and Gauss sums for function fields and periods of Drinfeld modules (Harvard 1987). But the new presentation here is due to a suggestion by Professor Tate. It is my pleasure to thank him.Supported in part by NSF grant DMS 8610730C2     

Fuzzy optimization approach to component selection of fault-tolerant software system

In developing software systems, a manager’s goal is to design software using limited resources and meet the user requirements. One of the important user requirements concerns the reliability of the software. The decision to choose the right software modules (components) becomes extremely difficult because of the number of parameters to be considered while making the decision. If suitable components are not available, then the decision process is further complicated with build versus buy decisions. In this paper, we have formulated a fuzzy multi-objective approach to optimal decision “build-or-buy” for component selection for a fault-tolerant modular software system under the consensus recovery block scheme. A joint optimization model is formulated where the two objectives are maximization of system reliability and minimization of the system cost with a constraint on delivery time. An example of developing a retail system for small-and-medium-size enterprises is used to illustrate the proposed methodology.     

On Bohr's Inequality

Bohr's inequality says that if is a bounded analytic function on the closed unit disc, then for 0 leq r 1/3 and that1/3 is sharp. In this paper we give an operator-theoretic proofof Bohr's inequality that is based on von Neumann's inequality.Since our proof is operator-theoretic, our methods extend toseveral complex variables and to non-commutative situations. We obtain Bohr type inequalities for the algebras of boundedanalytic functions and the multiplier algebras of reproducingkernel Hilbert spaces on various higher-dimensional domains,for the non-commutative disc algebra A_n, and for the reduced(respectively full) group C*-algebra of the free group on ngenerators. We also include an application to Banach algebras. We provethat every Banach algebra has an equivalent norm in which itsatisfies a non-unital version of von Neumann's inequality. 2000 Mathematical Subject Classification: 47A20, 47A56.     

Stability of a bubble expanding and translating through an inviscid liquid

A bubble expands adiabatically and translates in an incompressible and inviscid liquid. We investigate the number of equilibrium points of the bubble and the nature of stability of the bubble at these points. We find that there is only one equilibrium point and the bubble is stable there.     

A laminate-based framework for switching and microstructure evolution in polycrystalline ferroelectrics

This contribution deals with the numerical modelling of polycrystalline ferroelectric materials considering a sequential laminate-based approach established for tetragonal single-crystal ferroelectrics. The particular model [1] is considered and extended to predict the material behaviour of poly-crystal tetragonal ferroelectric ceramics. The derived laminate-based model is implemented in a finite element environment to simulate the time-dependent domain evolution and switching response of a bulk polycrystalline ferroelectric ceramic. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Behavior prediction of washing system in a paper industry using GA and fuzzy lambda–tau technique

Availability analysis has been an important issue in the design field of any Industrial system as the system structure has become more complicated. Also, the system availability is affected by many factors such as design, manufacturing, installation, etc., and so it may be extremely difficult to model, analyze and predict the failure behavior of the system. The purpose of this paper is to develop a new approach for computing various performance measures, namely reliability, availability, MTBF (mean time between failures), ENOF (expected number of failures), failure rate and repair time, for any industrial system. In the proposed approach, the failure rates and repair times of all constituent components are obtained using genetic algorithms and then various performance measures are computed using fuzzy lambda–tau methodology. Washing system, the major part of paper industry is the subject of study. The interactions among the working components are modeled using Petri nets. Failure and repair rates are represented using triangular fuzzy numbers as they allow expert opinion, linguistic variables, operating conditions, uncertainty and imprecision in reliability information to be incorporated into system model. Based on calculated reliability parameters, a structured framework has been developed that may help the maintenance engineers to analyze and predict the system behavior.     

Single cell discretization of O(kh2 + h4) for the estimates of ${\partial u}\over{\partial n}$ for the two‐space dimensional quasi‐linear parabolic equation

In this article, new stable two‐level explicit difference methods of O(kh² + h⁴) for the estimates of for the two‐space dimensional quasi‐linear parabolic equation are derived, where k > 0 and h > 0 are grid sizes in time and space directions, respectively. We use a single computational cell for the methods, which are applicable to the problems both in cartesian and polar coordinates. The proposed methods have the simplicity in nature and employ the same marching type technique of solution. Numerical results obtained by the proposed methods for several different problems were compared with the exact solutions. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 250–261, 2001     

Effect of post annealing temperature on structural and optical properties of ZnCdO thin films deposited by sol–gel method

Ternary ZnCdO thin films oriented along c-axis have been successfully deposited on p-Si (1 0 0) substrates using sol–gel spin coating route. To optimize most suitable annealing temperature for the Zn_1−xCd_xO thin films; these films with selected cadmium content x = 0.10 were treated at annealing temperatures from 300 °C up to 800 °C in oxygen ambient after deposition. The structural and optical properties of deposited thin films have been characterized by X-ray diffraction, energy dispersive spectroscopy, atomic force microscopy, UV–Vis spectroscopy, and photoluminescence spectra. The results show that the obtained films possess high crystallinity with wurtzite structure. The crystallite size, lattice parameters, lattice strain and stress in the deposited films are determined from X-ray diffraction analysis. The band gap energy increased as a function of annealing temperatures as observed from optical reflectance spectra of samples. The presence of Cd in the deposited films is confirmed by energy dispersive spectrum and it is observed that Cd re-evaporate from the lattice with annealing. The photoluminescence measurements as performed at room temperature did not exhibit any luminescence related to oxygen vacancies defects for lower annealing temperatures, as normally displayed by ZnO films. The green yellow luminescence associated to these defects was observed at higher annealing temperatures (≥700 °C).     

Structural and electrical transport properties of ZnxFe3−xO4 thin film deposited on Si (1 1 1) by pulsed-laser deposition

Polycrystalline thin films of Fe_3−xZn_xO₄ (x = 0.0, 0.01 and 0.02) were prepared by pulsed-laser deposition technique on Si (1 1 1) substrate. X-ray diffraction studies of parent as well as Zn doped magnetite show the spinel cubic structure of film with (1 1 1) orientation. The order–disorder transition temperature for Fe₃O₄ thin film with thickness of 150 nm are at 123 K (Si). Zn doping leads to enhancement of resistivity by Zn²⁺ substitution originates from a decrease of the carrier concentration, which do not show the Verwey transition. The Raman spectra for parent Fe₃O₄ on Si (1 1 1) substrate shows all Raman active modes for thin films at energies of T_2g¹, T_2g³, T_2g², and A_1g at 193, 304, 531 and 668 cm⁻¹. It is noticed that the frequency positions of the strongest A_1g mode are at 668.3 cm⁻¹, for all parent Fe₃O₄ thin film shifted at lower wave number as 663.7 for Fe_2.98Zn_0.02O₄ thin film on Si (1 1 1) substrate. The integral intensity at 668 cm⁻¹ increased significantly with decreasing doping concentration and highest for the parent sample, which is due to residual stress stored in the surface.