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191.
Let be an integer and let be the set of integers that includes zero and the odd integers with absolute value less than . Every integer can be represented as a finite sum of the form , with , such that of any consecutive 's at most one is nonzero. Such representations are called width- nonadjacent forms (-NAFs). When these representations use the digits and coincide with the well-known nonadjacent forms. Width- nonadjacent forms are useful in efficiently implementing elliptic curve arithmetic for cryptographic applications. We provide some new results on the -NAF. We show that -NAFs have a minimal number of nonzero digits and we also give a new characterization of the -NAF in terms of a (right-to-left) lexicographical ordering. We also generalize a result on -NAFs and show that any base 2 representation of an integer, with digits in , that has a minimal number of nonzero digits is at most one digit longer than its binary representation.
192.
Konstantinos A. Draziotis. 《Mathematics of Computation》2006,75(255):1493-1505
We completely solve diophantine equations of the form where is a positive integer, using a reduction to some quartic elliptic equations, which can be solved with well known methods.
193.
We study the attractors of a finite system of planar contraction similarities S
j
(j=1,...,n) satisfying the coupling condition: for a set {x
0,...,x
n} of points and a binary vector (s
1,...,s
n
), called the signature, the mapping S
j
takes the pair {x
0,x
n} either into the pair {x
j-1,x
j
} (if s
j
=0) or into the pair {x
j
, x
j-1} (if s
j
=1). We describe the situations in which the Jordan property of such attractor implies that the attractor has bounded turning, i.e., is a quasiconformal image of an interval of the real axis. 相似文献
194.
María J. Culzoni Agustina V. Schenone Natalia E. Llamas Mariano Garrido Maria S. Di Nezio Beatriz S. Fernández Band Héctor C. Goicoechea 《Journal of chromatography. A》2009,1216(42):7063-7070
A fast chromatographic methodology is presented for the analysis of three synthetic dyes in non-alcoholic beverages: amaranth (E123), sunset yellow FCF (E110) and tartrazine (E102). Seven soft drinks (purchased from a local supermarket) were homogenized, filtered and injected into the chromatographic system. Second order data were obtained by a rapid LC separation and DAD detection. A comparative study of the performance of two second order algorithms (MCR-ALS and U-PLS/RBL) applied to model the data, is presented. Interestingly, the data present time shift between different chromatograms and cannot be conveniently corrected to determine the above-mentioned dyes in beverage samples. This fact originates the lack of trilinearity that cannot be conveniently pre-processed and can hardly be modelled by using U-PLS/RBL algorithm. On the contrary, MCR-ALS has shown to be an excellent tool for modelling this kind of data allowing to reach acceptable figures of merit. Recovery values ranged between 97% and 105% when analyzing artificial and real samples were indicative of the good performance of the method. In contrast with the complete separation, which consumes 10 mL of methanol and 3 mL of 0.08 mol L−1 ammonium acetate, the proposed fast chromatography method requires only 0.46 mL of methanol and 1.54 mL of 0.08 mol L−1 ammonium acetate. Consequently, analysis time could be reduced up to 14.2% of the necessary time to perform the complete separation allowing saving both solvents and time, which are related to a reduction of both the costs per analysis and environmental impact. 相似文献
195.
Nano-mechanical mapping by atomic force microscopy has been developed as an useful application to measure mechanical properties of soft materials at nanometer scale. To date, the Hertzian theory was used for analyzing force-distance curves as the simplest model among several contact mechanics between elastic bodies. However, the preexisting methods based on this theory do not consider the adhesive interaction in principle, which cannot be neglected in the ambient condition. A new analytical method was introduced to estimate the elasticity and the adhesive energy simultaneously by means of the JKR theory, describing adhesive contact between elastic materials. Poly(dimethylsiloxane) (PDMS) and isobutylene-co-isoprene rubber (IIR) were analyzed to verify the applicable limit of the JKR analysis. For elastic samples such as PDMS, the force-deformation plots obtained experimentally were consistent with JKR theoretical curves. Meanwhile, for viscoelastic samples, especially for IIR, the experimental plots revealed large deviations from JKR curves depending on scanning velocity and maximum loading force. Some nano-rheological arguments were employed based on the difference between these specimens. 相似文献
196.
Summary The concept of a diffusion-averaged molecular weight, Md is presented, and Md is defined for polydisperse samples. It is shown via oligostyrene mixtures that Md can be determined in 20 minutes with common chromatographic equipment. If Md is measured and Mn or Mw is known, the polydispersity can be obtained. 相似文献
197.
An equation for a polarization curve of a hydrophobized electrode is proposed for electrosynthesis of a soluble electroactive product in an inner-kinetic mode. The equation contains the concentration of the target product (TP) in an explicit form. The shape of the curve depends on the biquadratic root of the TP concentration and the square root of the ratio between exchange currents of the side and target reactions. 相似文献
198.
The factors influencing the electrochemical behaviour of a supercapacitor have been partly examined in this work. The effects
of so-called intrinsic parameters, i.e. exchange current density, unit cell length and double layer (DL) capacitance; as well
as the so-called application parameters, i.e. cell current, on the cell potential discharge time have been considered. The
contributions of each type of capacitors, DL capacitor and faradaic supercapacitor under various states of operation and material
have been analyzed, and the competing (compensating) effects of the two types of capacitors as regards to the discharge and
power characteristics manifested by current–potential and energy–power (Ragone plots) are elucidated. 相似文献
199.
200.
Proportionally spaced cubicB-splines are an appropriate function system for the approximation of titration curves and other sigmoidal functions. They give a smooth weighted leastsquares fit without instability problems. The degree of smoothing depends only on the number of spline function which can be chosen by the user. The equivalence points of titration curves can be estimated with high accuracy from the zeros of the second derivative.The method gives good approximation curves even in the case of empty data regions, i. e. there are no artefacts in subranges where no data points exist. The routine has been tested successfully with large series of simulated and experimental data. 相似文献