Efficient algorithms on distributive lattices

We present several efficient algorithms on distributive lattices. They are based on a compact representation of the lattice, called the ideal tree. This allows us to exploit regularities in the structure of distributive lattices. The algorithms include a linear-time algorithm to reconstruct the covering graph of a distributive lattice from its ideal tree, a linear-time incremental algorithm for building the ideal lattice of a poset and a new incremental algorithm for listing the ideals of a poset in a combinatorial Gray code manner (in an code.)     

On Morse Conjecture for Flows on Closed Surfaces

Let M be a closed orientable surface and let ϕ be a C¹‐flow on M with set of singularities compact countable. In this paper, we prove the Morse conjecture for ϕ: if ϕ is topologically transitive then it is metrically transitive.     

An integral equation method for the electromagnetic scattering from cavities

Consider a time‐harmonic electromagnetic plane wave incident on a cavity in a ground plane. The physical process is modelled by Maxwell's equations. In this paper, integral representations of the solutions to the model problem in both fundamental polarizations are derived and studied. Existence and uniqueness of the solutions for the integral equations are established. The integral equations approach forms a basis for numerical solution of the model problem. In particular, for each fundamental polarization, an integral formulation with Gårding‐type estimates is derived. These formulations provide a basis for variational boundary element methods for solving the cavity problem. The Gårding‐type estimates imply convergence results for conforming boundary element methods. Copyright © 2000 John Wiley & Sons, Ltd     

Effect of SnSb Particle Size on Creep Behaviour under Power Law Regime of Sn-10%Sb Alloy

Sn-10 %Sb alloy was casted from the liquid state, drawn into wires of 0.55 mm in diameter or rolled into sheet of 0.2 mm thick. The as received as well as the heat treated specimens were examined by metallurgical microscope. Room temperature creep tests at constant loads were also carried out. The results obtained show that increasing annealing temperature, T_a, affects the structure and properties of the alloy. The increase of T_a leads to smaller SnSb particle size, therefore results in increasing its mechanical strength as measured by the decrease in steady state creep rate of specimen. The stress exponent parameter (m) calculated from the equation ϵ_S= A s_m was found to have higher values than usual and to decrease by increasing annealing temperature which was related to the associated decrease of the SnSb particle size.     

The Hydrothermal Synthesis of Petalite Mineral Phases and their Morphological Changing by Increasing of Temperature

In this investigation the Petalite minerals were synthesized hydrothermally at different temperatures from a glass with the composition Li₂CO₃:Al₂O₃: SiO₂ and the relation 1: 1: 8. On that occasion the following mineral phases arised:

• at low temperatures (410°C) α-petalite (unit cell å = 11.737 Å/b̊ = 5.17 Å/c̊ = 7.63 Å, space group P₂/a);
• At 490 °C α-petalite was splitted to quartz and an orthorhombic β₁-petalite (unit cell å = 18.24 Å/c̊ = 10.54 Å/c̊ = 10.57 Å, space group P_mC_n). β₁-petalite could be observated until 1000 °C.
• at 560 °C tetragonal β₂-petalite (unit cell å = 7.50 Å/c̊ = 9.07 Å, space group P 4₃2₁2) in parallel with β₁-petalite;
• Behind 750 °C β₂-petalite was not observed.
• Behind 900 °C a pseudohexagonal mineral phase developed from β₁-petalite. May be it is possible to indicate this phase as hexagonal (unit cell å = 5.217 Å/c̊ = 5.464 Å, space group P 6₂22 or P 6₄22). The author suggests to denote this phase as β₃-petalite.

     

Novel experimental design paradigm for development of eco-friendly gradient chromatographic method for simultaneous determination of metronidazole and spiramycin

This work describes the innovative experimental design-assisted development of a green gradient chromatographic method for concomitant analysis of metronidazole (MTR) and spiramycin (SPR). Two different designs including fractional factorial and Box-Behnken designs were implemented for screening and optimization steps, respectively. The optimum chromatographic conditions involved a mobile phase consisting of ethanol and 20 mM sodium dihydrogen phosphate solution (pH adjusted to 2.5) in the ratio 2:98 (v/v) for 2 min then the ratio changed to 30:70 (v/v). The flow rate was 1.3 mL/minute. Separation and analysis were performed on X-bridge C18 (150 mm × 4.6 mm × 3.5 μm) column with diode array detector set at 230 nm. Column oven temperature was 40°C. A linear response was acquired over the range of 5–125 μg/mL for both drugs. Detection and quantitation limits were 0.86 and 2.62 μg/mL for MTR and 0.92 and 2.83 μg/mL for SPR, respectively. The method was implemented for determination of both drugs in three tablet formulations. The method was proved to be green as evaluated by three assessment tools. The application of experimental designs assists in development of a robust green chromatographic method in gradient elution mode for determination of both drugs within reasonable time.     

The Hydrothermal Effect on Crystal Development and Electrical Conductivity of Li2CO3

Lithiumcarbonat was treated hydrothermally in the range of temperature from 80 °C to 600 °C. The Li₂CO₃-crystals of the starting material were monoclinic with the unit cell a = 8.39 Å, b = 5.00 Å, c = 6.21 Å, β = 114.5° and the space group C2/c (Zemann). During the increase of temperature the habit of the Li₂CO₃-crystals changed in the ranges of higher temperatures that they could be described as pseudocubic. In parallel with this development the electrical conductivity of the crystals also changed.