A note on primality tests forN=h·2 n −1

Using only the most simple properties of the finite field , we give a short proof of Riesel's primality test for integers of the formN=h·2 ⁿ –1.     

Robustness of minimax controllers to nonlinear perturbations

We study the robustness of minimax controllers, originally designed for nominal linear or nonlinear systems, to unknown static nonlinear perturbations in the state dynamics, measurement equation, and performance index. When the nominal system is linear, we consider both perfect state measurements and general imperfect state measurements; in the case of nominally nonlinear systems, we consider perfect state measurements only. Using a differential game theoretic approach, we show for the former class that, as the perturbation parameter (say, >0) approaches zero, the optimal disturbance attenuation level for the overall system converges to the optimal disturbance attenuation level for the nominal system if the nonlinear structural uncertainties satisfy certain prescribed growth conditions. We also show that anH -controller, designed based on a chosen performance level for the nominal linear system, achieves the same performance level when the parameter is smaller than a computable threshold, except for the finite-horizon imperfect state measurements case. For that case, we show that the design of the nominal controller must be based on a decreased confidence level of the initial data, and a controller thus designed again achieves a desired performance level in the face of nonlinear perturbations satisfying a computable norm bound. In the case of nominally nonlinear systems, and assuming that the nominal system is solvable, we obtain sufficient conditions such that the nominal controller achieves a desired performance in the face of perturbations satisfying computable norm bounds. In this way, we provide a characterization of the class of uncertainties that are tolerable for a controller designed based on the nominal system. The paper also presents two numerical examples; in one of these, the nominal system is linear; in the other one, it is nonlinear.This research was supported in part by the US Department of Energy, Grant DE-FG-02-88-ER-13939 and in part by the National Science Foundation, Grant ECS-91-13153.An abridged version was presented at the 32nd IEEE Conference on Decision and Control, San Antonio, Texas, December 15–17, 1993, and it appeared in the Conference Proceedings.     

Simulation modeling for emergency bed requirement planning

Due to its highly stochastic nature and complex interaction between services involved, health care has been a demanding area of application for computer simulation. This paper includes details and results of a simulation study realized in the Surgical Emergency Department at Istanbul University School of Medicine. The purpose is to suggest new bed capacities to improve the current system, and also to provide the management with guidelines for their expansion plans. For this aim, arrival rates, treatment procedures, inpatient admittance, and service durations have been carefully analyzed and modeled. The model, coded in SLAM-II simulation language, has been run under several bed capacity scenarios, and resulting queueing and waiting patterns have been discussed in detail.Dedictated to Professor Nusret Fiek     

Synthesis and electrochemical properties of phthalocyanines with four 8-quinolinoxy-substituents

A metal-free phthalocyanine and its cobalt(II) and copper(II) phthalocyanate complexes were prepared by cyclotetramerization of 4-(8-quinolinoxy)phthalonitrile. The new compounds were characterized by elemental analyses, ¹H-n.m.r., i.r. and u.v.–vis. spectral data. Electrochemical measurements indicated that CoPc had two metal based and two ligand based redox couples, while H₂Pc and CuPc showed four ligand based redox couples. For all complexes, linear variation of the peak current of the first reduction peak (I _pc) with scan rate () indicated the adsorption of the complexes to the electrode surface.     

Liquid-liquid interfaces as potentiometric ion-sensors-I The n-butanol-water interface as indicating sensor for the potentiometric titration of some acids and bases

The property that liquid-liquid interfaces modify their electrical charge as a function of the composition of the two phases in contact has been used to detect the end-points in a series of acid-base titrations in the aqueous phase. Although the titration curves are not classical in shape, the equivalence points can be located if the solutions are not too dilute. Good results for concentrations down to 10(-3)N have been obtained. The electrode has a fast response. The influence of surface-active substances on the titration has also been investigated.     

Benzaldehyde lyase-catalyzed enantioselective carboligation of aromatic aldehydes with mono- and dimethoxy acetaldehyde

[reaction: see text] Benzaldehyde lyase from the Pseudomonas fluorescens catalyzes the reaction of aromatic aldehydes with methoxy and dimethoxy acetaldehyde and furnishes (R)-2-hydroxy-3-methoxy-1-arylpropan-1-one and (R)-2-hydroxy-3,3-dimethoxy-1-arylpropan-1-one in high yields and enantiomeric excess via acyloin linkage. Aromatic aldehydes and benzoins are converted into enamine-carbanion-like intermediates prior to carboligation.     

A novel method for the spectrophotometric determination of nitrite in water

A rapid, simple, selective and sensitive method for the spectrophotometric determination of nitrite in water has been developed and optimum reaction conditions along with other analytical parameters have been evaluated. Nitrite reacts with barbituric acid in acidic solution to give the nitroso derivative, violuric acid. At analytical wavelength of 310 nm, Beer's law is obeyed over the concentration range 0.00–3.22 ppm of nitrite. The molar absorptivity is 15330 ± 259.7 (95%) with pooled standard deviation of 355.57 and R.S.D. of 2.32%. As well as the method is sensitive (2.99 × 10⁻³ μg NO₂ cm⁻²) and selective, it tolerates most of the potential interferents. It has been successfully applied to nitrite determination in natural waters by use of a calibration graph with determination limit of 1.66 μg NO₂ in 100 mL working solution corresponding to minimum 9.5 ppb NO₂–N in water samples. Lower concentrations of nitrite (3.0 μg NO₂/L sample) is precisely analyzed by using the method of dilution with sample, with R.S.D. of lower than 0.5%. The results were compared with standard N-(1-naphtyl)ethylenediamine dihydrochloride method and very good agreement between the data was observed. The method can easily be applied in the field.     

Mixed-ligand Copper(II) Complexes: Investigation of their Spectroscopic, Catalysis, Antimicrobial and Potentiometric Properties

Schiff base ligands HL¹–HL⁶ have been prepared from the reaction of 2,6-diformyl-4-t-butylphenol and 2,6-di-formyl-4-methylphenol with various aromatic amines in ethanolic solution. The Schiff base ligands 2,2′-dipyridine (dp) mixed-ligand Cu^II complexes have been obtained. Mixed-ligand Cu^II complexes containing the dp ligand have ionic nature and they conduct the electricity in solution media. The complexes have been obtained in two different forms: one of them is [Cu₂(Lⁿ)Cl₃] (n: 1, 2, 3, 4, 5 and 6) and other complexes have the general formula [Cu₂(Lⁿ)(dp)₂]3Cl. Ligands and their complexes have been characterized by elemental analyses, FT-IR, electronic spectra, molar conductance, ¹H(¹³C)-n.m.r. and mass spectral data. Their stoichiometric protonation constants have been determined potentiometrically in dioxan using a combined pH electrode at 25 °C, under a nitrogen atmosphere. For the calculation of the protonation constants, PKAS computer programme has been used. The effects of the substituents on the protonation constants and the additivities of these effects are discussed. The antimicrobial activity studies of the ligands and their complexes have been studied against the Bacillus megaterium, Micrococcus luteus, Corynebavterium xenosis, Enterococcuc faecalis, bacteria and Saccoramyces cerevisia, yeast. The catalytic properties of the complexes have been studied on the ascorbic acid, catechol and 2,6-di-t-butylphenol substrates. Thermal behaviour of the complexes has been studied by thermal techniques.     

Strong fluorescence enhancement of 2-bromo-3-(1H-indol-3-yl)maleimide upon coordination to a Lewis-acidic metal complex

The emission intensity of an indolyl maleimide derivative increases approximately 80-fold by reversible coordination to (1,4,7,11-tetraazacyclododecane)zinc(II), which makes the system a promising new signalling motif for molecular sensors.     

Measurement of K shell fluorescence cross sections and K shell fluorescence yields for the atomic region 22≤Z≤64 by 59.5 keV photons

A new method has been developed to determine K shell fluorescence cross section and K shell fluorescence yields. This method is based on simultaneous measurement of fluorescence radiation and scattered radiation, thus avoiding problems with measuring the source strength and source-to-detector solid angle. The K shell fluorescence cross section and K shell fluorescence yield for 21 elements in the atomic range 22£Z£64 have been measured by using a Si(Li) detector. The obtained results are compared with the other experimental, theoretical and fit values.