p-Median theorems for competitive locations

In competitive location theory, one wishes to optimally choose the locations ofr facilities to compete againstp existing facilities for providing service (or goods) to the customers who are at given discrete points (or nodes). One normally assumes that: (a) the level of demand of each customer is fixed (i.e. this demand is not a function of how far a customer is from a facility), and (b) the customer always uses the closest available facility. In this paper we study competitive locations when one or both of the above assumptions have been relaxed. In particular, we show that for each case and under certain assumptions, there exists a set of optimal locations which consists entirely of nodes.This work was supported by a National Science Foundation Grant ECS-8121741.     

Microstructure and optical properties of ZnO nanoparticles prepared by a simple method

In this investigation, ZnO nanoparticles were prepared by a simple and rapid method. This method is based on the short time solid state milling and calcinations of zinc acetate and citric acid powders. The samples were characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM), Fourier transform infrared (FTIR) spectroscopy, photoluminescence and UV-vis spectroscopy. It was shown that the calcination temperature significantly affected the particle size and optical properties of the synthesized ZnO nanoparticles. Calculation based on the XRD data shows that the average sizes of ZnO particles are in agreement with those from TEM images and the size of the particles increases on increasing the calcination temperature. Also the band gap of samples decreased from 3.29 to 3.23 eV on increasing the calcination temperature from 350 to 600 °C. Photoluminescence analyses show that many defects such as interstitial zinc, zinc vacancy and oxygen vacancy are responsible for the observed optical properties.     

A generalization of edge-coloring in graphs

Bounds are given on the number of colors required to color the edges of a graph (multigraph) such that each color appears at each vertex v at most m(ν) times. The known results and proofs generalize in natural ways. Certain new edge-coloring problems, which have no counterparts when m(ν) = 1 for all ν ? V, are studied.     

Numerical simulation of cavitating flow in 2D and 3D inducer geometries

A computational method is proposed to simulate 3D unsteady cavitating flows in spatial turbopump inducers. It is based on the code FineTurbo, adapted to take into account two‐phase flow phenomena. The initial model is a time‐marching algorithm devoted to compressible flow, associated with a low‐speed preconditioner to treat low Mach number flows. The presented work covers the 3D implementation of a physical model developed in LEGI for several years to simulate 2D unsteady cavitating flows. It is based on a barotropic state law that relates the fluid density to the pressure variations. A modification of the preconditioner is proposed to treat efficiently as well highly compressible two‐phase flow areas as weakly compressible single‐phase flow conditions. The numerical model is applied to time‐accurate simulations of cavitating flow in spatial turbopump inducers. The first geometry is a 2D Venturi type section designed to simulate an inducer blade suction side. Results obtained with this simple test case, including the study of its general cavitating behaviour, numerical tests, and precise comparisons with previous experimental measurements inside the cavity, lead to a satisfactory validation of the model. A complete three‐dimensional rotating inducer geometry is then considered, and its quasi‐static behaviour in cavitating conditions is investigated. Numerical results are compared to experimental measurements and visualizations, and a promising agreement is obtained. Copyright © 2004 John Wiley & Sons, Ltd.     

An adaptive algorithm for system level diagnosis

Consider a system of n units, at most t of which are faulty. An adaptive diagnosis algorithm is presented which uses a sequence of tests to identify a fault-free unit. The algorithm requires at most 2t − ν(t) tests, where ν(t) is the number of 1's in the binary representation of t. Moreover, many of the tests can be performed simultaneously. The previously best algorithms for the same purpose required 2t − 1 tests, none of which could be performed simultaneously.     

Graphs with given odd sets and the least number of vertices

This note presents a solution to the following problem posed by Chen, Schelp, and Šoltés: find a simple graph with the least number of vertices for which only the degrees of the vertices that appear an odd number of times are given. © 1997 John Wiley & Sons, Inc.     

Improved iodine-125 removal in anionic form of iodate by column method using laterite soil

Soil column experiments have been conducted to treat liquid wastes from hospitals containing¹²⁵I. Three sorbent samples of laterite clay materials with different contents of iron oxides (goethite, -FeOOH) and hydroxides were used to sorb anionic iodate. Post-treatment on effluent wastes with sodium hypochlorite (redox reagent) oxidized the iodide to the desirable iodate ion. Effluent pH after treatment ranges between 4.8 to 5.8, which does not vary much from the initial effluent pH of 4.5 before treatment. Results show that 90 to 97% sorption of iodine radionuclides with a decontamination factor ranges between 10–32 was obtained after the first two hours of experiments. Concentration has decreased from the initial 10 Bq/ml to concentration ranges of 0.3 to 0.9 Bq/ml. Batch experiments conducted using different sorbent masses of soils, show that there was a drop in sorption as the mass of soils fell below approximately 0 to 0.25 g. The sorption remains constant with the soil mass above 0.25 g. Another batch experiment using a different concentration shows that the adsorption capacity of the laterite soil was 1.1 Ci/g. The adsorption is about 96% with a distribution coefficient of 1170.     

Synthesis,Characterization and Crystal Structure of a Silver(I) Complex containing AMTT (AMTT = 4‐amino‐5‐methyl‐2H‐1,2,4‐triazole‐3(4H)‐thione)

The reaction of 4‐amino‐5‐methyl‐2H‐1,2,4‐triazole‐3(4H)‐thione with AgNO₃ in methanol led to the complex [Ag(ATT)₂]NO₃ ( 2 ). 2 was characterized by elemental analyses, IR, ¹HNMR and Raman spectroscopy as well as single‐crystal X‐ray diffraction. Crystal data for 2 at ?70 °C: space group P2₁/n with a = 1356.7(12), b = 770.4(7), c = 1475.2(12) pm, β = 111.730(15)°, Z = 4, R₁ = 0.0402.     

Reaction of 2‐[(2‐aminoethyl)amino]ethanol with pyridine‐2‐carbaldehyde and complexation of the products with CuII and CdII along with docking studies

The reaction between 2‐[2‐(aminoethyl)amino]ethanol and pyridine‐2‐carbaldehyde in a 1:2 molar ratio affords a mixture containing 2‐({2‐[(pyridin‐2‐ylmethylidene)amino]ethyl}amino)ethanol (PMAE) and 2‐[2‐(pyridin‐2‐yl)oxazolidin‐3‐yl]‐N‐(pyridin‐2‐ylmethylidene)ethanamine (POPME). Treatment of this mixture with copper(II) chloride or cadmium(II) chloride gave trichlorido[(2‐hydroxyethyl)({2‐[(pyridin‐2‐ylmethylidene)amino]ethyl})azanium]copper(II) monohydrate, [Cu(C₁₀H₁₆N₃O)Cl₃]·H₂O or [Cu(HPMAE)Cl₃]·H₂O, 1 , and dichlorido{2‐[2‐(pyridin‐2‐yl)oxazolidin‐3‐yl]‐N‐(pyridin‐2‐ylmethylidene)ethanamine}cadmium(II), [CdCl₂(C₁₆H₁₈N₄O)] or [CdCl₂(POPME)], 2 , which were characterized by elemental analysis, FT–IR, Raman and ¹H NMR spectroscopy and single‐crystal X‐ray diffraction. PMAE is potentially a tetradentate N₃O‐donor ligand but coordinates to copper here as an N₂ donor. In the structure of 1 , the geometry around the Cu atom is distorted square pyramidal. In 2 , the Cd atom has a distorted octahedral geometry. In addition to the hydrogen bonds, there are π–π stacking interactions between the pyridine rings in the crystal packing of 1 and 2 . The ability of PMAE, POPME and 1 to interact with ten selected biomolecules (BRAF kinase, CatB, DNA gyrase, HDAC7, rHA, RNR, TrxR, TS, Top II and B‐DNA) was investigated by docking studies and compared with doxorubicin.