Montgomery Multiplication in GF(2k)

We show that the multiplication operation c=a · b · r^-1 in the field GF(2^k can be implemented significantly faster in software than the standard multiplication, where r is a special fixed element of the field. This operation is the finite field analogue of the Montgomery multiplication for modular multiplication of integers. We give the bit-level and word-level algorithms for computing the product, perform a thorough performance analysis, and compare the algorithm to the standard multiplication algorithm in GF(2^k. The Montgomery multiplication can be used to obtain fast software implementations of the discrete exponentiation operation, and is particularly suitable for cryptographic applications where k is large.     

A locally computed suboptimal control strategy for a class of interconnected systems

In this paper, a locally computed suboptimal control strategy for a class of interconnected systems is introduced. First, optimal statefeedback control equations are derived for a finite-horizon quadratic cost. Then, the control for each subsystem is separated into two portions. The first portion stabilizes the isolated subsystem, and the second portion corresponds to the interactions. To achieve a locally calculable control, an approximation to the optimal control equations is introduced, and two iterative suboptimal control algorithms are developed. In the first algorithm, the initial conditions of subsystems are assumed to be known; in the second algorithm, this information is replaced by statistical distributions. The orders of errors in the iterations of the algorithm and in the suboptimality are given in terms of interconnections. An example with comparisons is also included to show the performance of the approach.     

Fracture strength of class II slot cavities restored with polymerizable restorative materials

This study compared the fracture strength of Class II slot cavities restored with polymerizable restorative materials. Sixty, caries-free, posterior teeth were divided into five groups of 12 teeth. The Class II slot cavities were prepared. The teeth were restored with two packable composites (Filtek P60, Surefil), a microhybrid composite (Filtek Z250)and two ormocer (Definite, Admira). The restorations were then subjected to fracture resistance tests. The marginal ridges of the restorations were loaded at an angle of 13.5° to the long axis of the tooth in an Universal Testing Machine until failure. Analysis of mean forces indicated that, Filtek P60, Surefil and Filtek Z250 exhibited better performance than Definite and Admira. The tested resin composites differed in their mechanical properties. This study suggested that fracture behavior were highly influenced by the filler system. Overall, Filtek P60, Surefil, Filtek Z250, demonstrated good fracture resistance. Copyright © 2003 John Wiley & Sons, Ltd.     

Effect of operating parameters on selective separation of heavy metals from binary mixtures via polymer enhanced ultrafiltration

Performance of continuous polymer enhanced ultrafiltration (PEUF) method was investigated for removal of mercury and cadmium from binary mixtures. This method includes the addition of polyethyleneimine (PEI) as a water soluble polymer to bind the metals, which was followed by ultrafiltration operation performed on both laboratory and pilot scale systems. The influence of various operating parameters such as temperature, metal/polymer ratio, presence of calcium ions and pH on retention of metals and permeate flux was investigated. To investigate the possibility of selective separation of mercury and cadmium, experiments were conducted for binary solutions at different pH and loading ratios. It was seen that the retention of mercury decreased and permeate flux increased when the temperature increased. The increased pH and decreased metal/polymer ratio, loading (L), resulted in higher retention of both metals. Shapes of retention vs. pH or L curves were very similar for both metals. Retentions stay almost constant at a value very close to unity until a critical L or pH value was reached, then, R decreases almost linearly with L or pH. However, retention of cadmium was affected more than that of mercury as the pH decreased and L increased. This leads to the selective separation of mercury and cadmium. At low pH values (about 5) and at high L values (about 0.3), mercury was removed by ultrafiltration operation while almost all cadmium passed through the membrane. At pH 5.5 and cadmium/polymer ratio about 0.35 and mercury/polymer ratio about 0.39, the highest separation factor was obtained as 49.     

Determination of bismuth, indium and lead in geological samples by electrothermal AAS Part 2. Comparative study of palladium and molybdenum containing chemical modifiers*

A comparative and systematic study has been carried out of the effects of palladium and molybdenum containing chemical modifiers, such as Pd + Rh, Pd + Pt, Pd + Ru, Pd + Rh + Pt, Pd + Rh + Ru, Mo + Pd, Mo + Rh, Mo + Ru and Mo + Pt and additionally tartaric acid (TA) as a reducing agent together with mixed modifiers for the thermal stabilization of Bi, In and Pb in a Zeeman electrothermal atomic absorption spectrometer (ETAAS). The effect of the mass ratios of the mixed modifier components on the maximum pretreatment temperature for the analytes has been determined. The modifier mixtures of Pd + Rh + Pt, Mo + Pd + TA and Mo + Pt + TA were found to be especially powerful for the determination of Bi, In and Pb. These mixed modifiers could increase the ashing temperatures of the analytes up to 1250–1400° C. They were applied to the determination of Bi and Pb in dissolved geological reference samples and accuracy and precision of the method were thereby enhanced. The percent relative error was decreased from 20.0 to 0.4 for Bi and from 10.5 to 0.3 for Pb, depending on the sample type. Received: 9 May 1997 / Revised: 19 August 1997 / Accepted: 20 August 1997     

Establishment of a quality system for nuclear analytical laboratories

Comprehensive Quality Control (QC) and Quality Assurance (QA) Program is stated on the quality policy, organization, methods and records for nuclear analytical laboratories which are necessary for improvement of productivity, to upgrade the performance, credibility and reputation. The proper and complete identification of quality elements for management and technical requirements are being written in Quality Manual as well as analytical and organizational procedures and working instructions according to ISO 17025 standard. Technical ability of gamma, X-ray and a/b laboratories in the Center has been checked by participation in proficiency test, critical technical variables, and quality results. Performance of quality system has been controlled by external audit inspection, progress reports and service to clients. The present study is a framework of the model project of IAEA, coded RER/2/004, which has resulted self-sustainable accreditation from the national body, TURKAK. This revised version was published online in August 2006 with corrections to the Cover Date.     

Synthesis of linear and starlike polymers from poly(propylene glycol) methacrylate using controlled radical polymerization

The copper‐catalyzed atom transfer radical polymerization (ATRP) of poly(propylene glycol) methacrylate (PPGM) in solution to produce linear and starlike polymers is reported, using methylethyl ketone as the solvent and a temperature of 80 °C. The ATRP system used was efficient for polymerization of the functionalized monomer without protecting hydroxyl end groups of monomer. The polymerizations were consistent with “living” or controlled processes, as revealed by the linear evolution of molecular weight with conversion. Increasing the [M]₀:[I]₀ ratio resulted in increasing molecular weights, whereas the polydispersity indices remained low (M_w/M_n < 1.4) even at high conversion. Decreasing the [CuBr]₀:[I]₀ ratio resulted in lower conversions, slightly larger polydispersities, and decreased molecular weights, likely resulting from a lower initiation efficiency. Polymers were characterized by ¹H and ¹³C NMR; molecular weights of polymers with low degrees of polymerization were estimated by end‐group analysis from ¹³C NMR spectra obtained using distortionless enhancement by polarization transfer and the gated decoupling techniques. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 40: 334–343, 2002     

Determination of Lead, Chromium, Manganese and Zinc in Slurries of Botanical and Biological Samples by Electrothermal Atomic Absorption Spectrometry Using Tungsten-Containing Chemical Modifiers

Lead, Cr, Mn and Zn in slurries of botanic and biological samples were determined by electrothermal atomic absorption spectrometry (ETAAS) using W, Ir, NH₄H₂PO₄, W and NH₄H₂PO₄, Ir and NH₄H₂PO₄, W and Ir, and W + Ir + NH₄H₂PO₄ chemical modifiers in an 0.2% (v/v) Triton X-100 plus 0.2% (v/v) nitric acid mixture. Zeeman effect background correction was performed and platforms inserted into graphite tubes were used. Comprehensive comparative studies were carried out with respect to pyrolysis and atomization temperatures, atomization and background absorption profiles, characteristic masses, detection limits and accuracy of the determinations in the presence and absence of modifiers. The mixture of W + Ir + NH₄H₂PO₄ was found to be preferable for the determination of Pb, Cr, Mn and Zn in slurry samples. The pyrolysis temperatures of the analytes were increased up to 1250 °C for Pb, 1000 °C for Zn, 1400 °C for Cr and Mn by using W + Ir + NH₄H₂PO₄ with an 0.2% (v/v) Triton X-100 plus 0.2% (v/v) nitric acid mixture used as diluent solution. The optimum masses of the mixed modifier components were found to be 20 µg W + 4 µg Ir + 50 µg NH₄H₂PO₄. The characteristic masses of Pb, Cr, Mn and Zn obtained are 16.3, 5.6, 0.1 and 1.1 pg, respectively. The detection limits of Pb, Cr, Mn and Zn based on integrated absorbance for 0.5% (m v⁻¹) slurries were found to be 0.14, 0.06, 0.02 and 0.01 µg g⁻¹, respectively. The slurries of botanic and biological certified and standard reference materials were analyzed with and without the modifiers. Depending on the sample type, the percent recoveries increased from 63 up to 104% for analytes when using the proposed modifier mixture.