Order Of Log Research Articles

The design and evaluation of the Simple Self-Similar Sequences Generator

This paper describes a new algorithm for the generation of pseudo random numbers with approximate self-similar structure. The Simple Self-Similar Sequences Generator ( 4SG) elaborates on an intuitive approach to obtain a fast and accurate procedure, capable of reproducing series of points exhibiting the property of persistence and anti-persistence. 4SG has a computational complexity of O ( n ) and memory requirements of the order of log 2 ( N ) , where N is the number of points to be generated. The accuracy of the algorithm is evaluated by means of computer-based simulations, recurring to several Hurst parameter estimators, namely Variance Time (VT) and the Wavelets-based estimator. The Hosking and the Wavelets-based methods for the generation of self-similar series were submitted to the same tests the 4SG was analysed with, providing for a basis for comparison of several performance aspects of the algorithm. Results show that the proposal embodies a good candidate not only for on-demand emulation of arbitrarily long self-similar sequences, but also for fast and efficient online simulations.

Asymptotic analysis of SDMA systems with near-orthogonal user scheduling (NEOUS) under imperfect CSIT

In this paper, we focus on the asymptotic cross layer analysis of multi-antenna systems with transmit MMSE (Tx- MMSE) beamforming, near orthogonal scheduling and outdated CSIT. To capture the effect of the potential packet outage, we introduce the average system goodput, which measures the average b/s/Hz delivered to the mobiles successfully, as the system performance objective. We derive closed-form expressions for the optimal power and rate allocations as well as a low complexity near orthogonal user scheduling (NEOUS) algorithm to solve the cross-layer optimization problem.We derive the asymptotic order of growth in system goodput for general CSIT error variance σ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and found that for sufficiently large nT (number of antennas at the base station) and K (number of users) where K = g <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> (nT) for some strictly increasing function g(x) = o(x), the the system goodput grows in the order of nT log[(1-σ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) logK] when σ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> < 1. This is the same order of growth as the optimal order of growth in broadcast channels with perfect CSIT and hence, the NEOUS is order-optimal. On the other hand, we need exponentially larger K to compensate for the penalty in multiuser diversity gain due to CSIT errors.

Thermal transpiration for the linearized Boltzmann equation

AbstractThe phenomena of thermal transpiration due to the boundary temperature gradient is studied on the level of the linearized Boltzmann equation for the hard‐sphere model. We construct such a flow for a highly rarefied gas between two plates and also in a circular pipe. It is shown that the flow velocity parallel to the plates is proportional to the boundary temperature gradient. For a highly rarefied gas, that is, for a sufficiently large Knudsen number κ, the flow velocity between two plates is of the order of log κ, and the flow velocity in a pipe is of finite order. Our analysis is based on certain pointwise estimates of the solutions of the linearized Boltzmann equation. © 2006 Wiley Periodicals, Inc.

SCATTERING MECHANISM OF HIGH ENERGY STRONG INTERACTION SOFT PROCESSES

Starting from the viewpoint that the constituent quark has its own structure and incorporating the hypothesis of maximum nonperturbative strong interaction reaction (MNSIR), which should be obeyed in high energy strong soft processes, we modified the field theory for soft Pomeron (ℙ) of Landshoff and Nachtmann and proposed a new structure model for the soft Pomeron ℙ and Reggeon ℝ. In this model a pair of constituent quarks coming from colliding hadron in strong soft processes are first disaggregated into a valance quark with a nonperturbative gluon cloud G wrapped about, or, according to the case, into a nonperturbative gluon wrapped by spinor cloud. Corresponding to such mechanism, the relevant structure of soft Pomeron ℙ or Region ℝ is represented by the sum of a series of cut ladder diagrams. In the multi-Regge region, where the energy of the system is very large and the momentum transfer |t| is very small, and in the approximation where only the leading order of log s is preserved, we calculated the [Formula: see text] scattering amplitude and its total cross-section from the sum of such ladder diagrams. The Regge-behavior factor in the form of an exponential power law of s does arise. We also get compact formulas for the trajectories of soft ℙ and ℝ. As example of application, an alternative mechanism of J/Ψ nonquarkonic-hadron decay is proposed.

Synthesis and Binding Properties of Dendritic Oxybathophenanthroline Ligands towards Copper(II)

AbstractDendritic oxybathophenanthroline ligands (generation 0 to 3) have been synthesized by treatment of 4,7‐bis(4′‐hydroxyphenyl)‐1,10‐phenanthroline with the corresponding Fréchet‐type dendrons carrying a benzylic bromide function at the focal point. The complexation of copper(II) has been studied by liquid–liquid extraction using the radioisotope 64Cu and time‐resolved laser‐induced fluorescence spectroscopy (TRLFS) in organic media indicating the formation of 1:3 complexes (Cu:dendritic ligand). Electronic and EPR spectroscopy were used to characterize the copper(II) chromophore, which is shown to have the expected distorted square‐planar geometry with two phenanthroline donors coordinated to the copper(II) center. The third dendritic ligand therefore is proposed to be bound by secondary interactions. The stability constants of the 1:3 complexes were found to be in the order of log K ≈ 16 in CHCl3. On the other hand, increasing generation of the dendritic Fréchet‐type branches leads to enhanced shielding of the copper ion from the environment. Additional information about this behaviour was obtained by the fluorescence lifetimes, which are much less influenced upon addition of copper(II) salt to solutions of the higher generation ligands. (© Wiley‐VCH Verlag GmbH &amp; Co. KGaA, 69451 Weinheim, Germany, 2005)

Anion Binding by a Tetradipicolylamine-Substituted Resorcinarene Cavitand

Anion binding has been achieved with a resorcinarene substituted with four 2,2'-dipicolylamine moieties on the upper rim. The four dipicolylamine groups reside in proximity on one rim of the cavitand. The dipicolylamine groups were protonated with triflic acid to provide the cationic ammonium sites for anion binding. This anion receptor binds strongly to anions of different geometries, such as H(2)PO(4)(-), Cl(-), F(-), CH(3)CO(2)(-), HSO(4)(-), and NO(3)(-). The association constants for binding these anions are large, on the order of log K = 5 in CD(3)CN, a solvent of intermediate dielectric constant. These values represent significant binding compared to other cavitands with nitrogen pendant groups. Evidence suggests that the cavitand provides two identical receptor sites formed by two dipicolylamine groups, facilitating the simultaneous binding of two anions. Intramolecular binding of anions between two protonated dipicolylamine groups is indicated on the basis of the comparison to a structurally similar monomeric analogue and by semiempirical PM3 molecular modeling. Titrations with the analogue result in much weaker anion association, even at high concentrations, indicating the importance of proximity and preorganization of sites on the cavitand upper rim.

The use of novel water-in-oil microemulsions in microemulsion electrokinetic chromatography.

We describe the novel use of water-in-oil (W/O) microemulsions to achieve unique separations in microemulsion electrokinetic chromatography (MEEKC). The choice and concentration of the buffer type, surfactant and co-surfactant were all examined and optimized. Separations of a range of neutral and acidic analytes was shown to be markedly different to that obtained by (oil-in-water) O/W MEEKC. Neutral solutes are separated by virtue of their solubility (log P) values in O/W MEEKC with the more water-insoluble solutes migrating last. This separation process does not occur in W/O, as neutral solutes are not separated in order of log P.

Photochemical degradation of organic iron complexing ligands in seawater

It has been shown by a number of investigators that greater than 99% of the Fe in the open ocean is complexed with organic ligands having conditional stability constants on the order of log K = 10–12. Some of these studies have shown evidence for the presence of 2 distinct ligand classes. It is hypothesized that the strong ligand class is produced by plankton while the weaker ligand is a result of decomposition of the strong ligand. Photochemical degradation in the surface ocean (upper 1–5 m) is one possible mechanism for this decomposition. Data from 2 cruises to the Gulf of Mexico demonstrate the importance of this photochemical reaction. The photodegradation of ligands appears to occur in a ligand that is less than 1 kDa in size and is ubiquitous throughout the Gulf of Mexico. This reaction may be responsible for controlling surface water Fe concentrations throughout the ocean and will help to further refine biogeochemical models of primary production.

Application of a nonuniform spectral resampling transform in Fourier-transform spectrometry.

We describe a nonuniform spectral resampling transform (NUSRT) that resamples a frequency-scaled spectrum that has been measured by a Fourier-transform spectrometer (FTS). Frequency scaling of a spectrum can arise from measurements made with off-axis detectors and Doppler shift induced by motion of a spaceborne FTS relative to an input radiation source. In addition, a spectrum may need to be rescaled in frequency to match spectral lines for applications such as the retrieval of atmospheric state parameters. The NUSRT is cast as a linear algebraic expression that relates a nonuniformly sampled interferogram to an input spectrum. A polynomial approximation is applied to this expression that reduces the inverse of the NUSRT to a series of Fourier transforms that can be implemented as fast Fourier transforms (FFTs). We show that this NUSRT algorithm requires on the order of 6N log N flops, which reduces the computational cost of rescaling by more than 1 order of magnitude compared with conventional FFT-based Shannon interpolation techniques while comparable accuracy is maintained.

Molecular Hydrogen in High-Velocity Clouds

We present Far Ultraviolet Spectroscopic Explorer observations of interstellar molecular hydrogen (H2) in two Galactic high-velocity clouds (HVCs). Molecular hydrogen absorption is detected in the Magellanic Stream (abundance ~0.3 solar) toward the Seyfert galaxy Fairall 9 in the lowest three rotational states (J = 0-2) at vLSR = +190 km s-1, yielding a total H2 column density of log N(H2) = 16.40. In contrast, no H2 absorption is seen in the HVC Complex C (abundance ~0.1 solar) toward the quasar PG 1259+593 [log N(H2) ≤ 13.96 at vLSR = -130 km s-1], although both HVCs have similar H I column densities on the order of log N(H I) ≈ 20. Weak H2 absorption is detected in the Intermediate-Velocity Arch (IV Arch; abundance ~1.0 solar) toward PG 1259+593 [log N(H2) = 14.10 at vLSR = -55 km s-1 and log N(H I) = 19.5]. It thus appears that metal- and dust-poor halo clouds like Complex C are not able to form and maintain widely distributed H2, whereas metal- and dust-rich halo clouds like the IV Arch can maintain H2 even at low H I column densities.

Trace metals, arsenic and lead isotopes in dissolved and particulate phases of North Australian coastal and estuarine seawater

Total dissolved ( m) metal concentrations (Cd, Co, Cu, Fe, Pb, Ni and Zn), analysed by an ammonium pyrrolidine dithiocarbamate (APDC) solvent extraction/Hg exchange back-extraction method, arsenic concentrations and lead isotope ratios (Pb-208/Pb-206 and Pb-207/Pb-206), were determined on seawater samples from nine tropical north Australian estuarine and coastal areas. The low metal concentrations (e.g. av. Zn 38-154 ng/1 and Pb 3.9-13.3 ng/1) and low molar Zn/Cd ratios (av. 17-65) were at near-pristine levels. There were only few strong element/salinity and inter-element correlations, which is attributed mainly to the restricted salinity range sampled (91% of samples had salinity > 20). Metal (APDC-extractable) and arsenic concentrations and lead isotope ratios were also determined on unfiltered samples (dissolved plus particulate phases). The APDC-extractable metals method provided a measure of labile metals in the particulate phase. There were strong positive correlations between suspended particulate matter (SPM) and unfiltered metal concentrations, except for Cd. The slopes of the trendlines approximated the average labile metal concentration in the SPM. In the shallow Bynoe and Norman Rivers' estuaries, which have extensive depositional banks of fine-grained sediments, SPM consisted mainly of re-suspended local bottom sediments. In these estuaries, the ratio of labile metal concentration in SPM to acid extracted total metal concentration in the m grain size fraction of bottom sediments was in the order Pb > Cu > Zn approximate to Ni. A more direct measure of metal lability was obtained from the South Alligator and Adelaide Rivers' estuaries by comparing APDC-extractable concentrations in SPM with total concentrations derived by analysis of acid-digested SPM retained on 0.45 mum membrane filters. The order of lability in these estuaries was Pb > Zn > Cu approximate to Ni. Distribution coefficients (K-D) for metals between the particulate (> 0.45 mum) and dissolved ( m) phases showed a general order of log K-D values for all sites of Fe > Pb > Zn > Ni approximate to Cd approximate to Cu. This is in contrast to the order Cu > Cd > Zn > Ni commonly reported in polluted estuaries and rivers. The north Australian data showed strong log K-D versus SPM correlations for Fe and Cu. The Pb isotopic composition of both filtered and unfiltered samples was similar to previously recorded values for oceanic seawater (Pb-208/Pb-206 = 2.02-2.10). In contrast, the Pb-208/Pb-206 ratios of Pb-Zn ores in the region range from 2.21 to 2.25 allowing the use of Pb isotope data as sensitive indicator of any future impacts from mining developments. Variations in the Pb isotope ratios of unfiltered samples (dominated by Pb in SPM) between some estuaries were found to reflect different compositions of geological units in their catchments. (C) 2001 Elsevier Science BY. All rights reserved.

Scaling of accuracy in extremely large phylogenetic trees.

The accuracy of phylogenetic inference was examined in simulated data sets up to nearly 10,000 taxa, the size of the largest set of homologous genes in existing molecular sequence databases. Even with a simple search algorithm (maximum parsimony without branch swapping), the number of characters needed to estimate 80% of a tree correctly can scale remarkably well at optimal substitution rates (on the order of log N, where N is the number of taxa). In other words, the number of taxa in an analysis can be doubled and only an arithmetic increase in the number of characters is required to maintain the same level of accuracy. Even substitution rates that are much higher than normally used in phylogenetic studies did not affect the scaling too adversely. However, scaling is usually worse than log N for more stringent levels of accuracy. Moreover, errors are not distributed randomly throughout the tree. Shallow nodes are remarkably easy to reconstruct and display favourable log-linear scaling. The deepest nodes are extremely difficult to reconstruct accurately, even with branch swapping, and the scaling is poor. Therefore, the strategy of sequencing large numbers of homologous genes may not always provide global solutions to extreme phylogenetic problems and alternative strategies may be required.

Evaluation of Novel Local Structural Parameters of Acids and Bases for 1 : 1 Hydrogen-Bond Complexation I. OH-, NH-Acids and Phosphorus Bases in Carbon Tetrachloride

Abstract Novel local structural parameters, η° and ω°, representing the nature of the functional group and the residual moiety (supporting group) of acid and base molecules, respectively, have been evaluated for the first time for the 1 : 1 hydrogen-bond complexation of nine OH- or NH-acids and five phosphorus bases in CCl4. An evaluation of η° and ω° was carried out by making use of convergent linear relationships among the log K values and by introducing three numerical criteria. For acid-base complexation, all of the 180 log K values at 288.15—318.15 K and 45 ΔHf° values were reproduced from the η and ω values within the experimental error. The reversals in the order of log K and ΔHf° observed in the system could be reasonably explained by applying the η° and ω° scales.

Iron hydrolysis and solubility revisited: observations and comments on iron hydrolysis characterizations

Abstract This work describes and evaluates previous hydrolysis characterizations relevant to the behavior of iron in natural solutions, with special emphasis given to the physical chemistry of iron in seawater. New potentiometric data are used in this work to extend FeOH 2+ hydrolysis constant characterizations to 6 M ionic strength. These results obtained in NaClO 4 are in excellent agreement with previous spectrophotometric characterizations over the range of conditions of those previous works. The enthalpy for the first Fe 3+ hydrolysis step (Δ H 1 *) is 10.2 kcal mol −1 and the molal scale hydrolysis constant appropriate to the first hydrolysis step ( β 1 *=[FeOH 2+ ][H + ][Fe 3+ ] −1 ) is log β 1 *=−2.71±0.03 at 25°C and the ionic strength of seawater. Recalculations of previous data, as well as new experimental analyses in this work indicate that Fe(OH) 2 + hydrolysis constants ( β 2 *=[Fe(OH) 2 + ][H + ] 2 [Fe 3+ ] −1 ) for ionic strengths between 0.7 and 3.0 M are on the order of log β 2 *≤−7. This constant is, like β 1 *, expected to be strongly temperature-dependent (Δ H 2 *≅16.9 kcal mol −1 ). Previous estimates for β 3 * derived from solubility analyses are operationally defined and model-dependent. At 25°C and the ionic strength of seawater β 3 * is estimated as log β 3 *≤−13.6. Enthalpy estimates appropriate to β 3 * (Δ H 3 *≅23.9 kcal mol −1 ) indicate that this upper bound decreases strongly with decreasing temperature. Our current understanding of the pH dependence of Fe III solubility behavior is closely tied to assumptions about the form of Fe(OH) 3(s) solubility products in aqueous solution. Evidence is presented which indicates that the Fe(OH) 3(s) solubility product, K so *=[Fe 3+ ][H + ] − n , should be written with n

A rigorous derivation of a free-boundary problem arising in superconductivity

We study the Ginzburg–Landau energy of superconductors submitted to a possibly non-uniform magnetic field, in the limit of a large Ginzburg–Landau parameter κ . We prove that the induced magnetic fields associated to minimizers of the energy-functional converge as κ→+∞ to the solution of a free-boundary problem. This free-boundary problem has a nontrivial solution only when the applied magnetic field is of the order of the “first critical field”, i.e. of the order of log κ . In other cases, our results are contained in those we had previously obtained [15, 16, 14]. We also derive a convergence result for the density of vortices.

New Techniques for the Computation of Linear Recurrence Coefficients

The n coefficients of a fixed linear recurrence can be expressed through its m≤2n terms or, equivalently, the coefficients of a polynomial of a degree n can be expressed via the power sums of its zeros—by means of a polynomial equation known as the key equation for decoding the BCH error-correcting codes. The same problem arises in sparse multivariate polynomial interpolation and in various fundamental computations with sparse matrices in finite fields. Berlekamp's algorithm of 1968 solves the key equation by using order of n2 operations in a fixed field. Several algorithms of 1975–1980 rely on the extended Euclidean algorithm and computing Padé approximation, which yields a solution in O(n(log n)2 log log n) operations, though a considerable overhead constant is hidden in the “O” notation. We show algorithms (depending on the characteristic c of the ground field of the allowed constants) that simplify the solution and lead to further improvements of the latter bound, by factors ranging from order of log n, for c=0 and c>n (in which case the overhead constant drops dramatically), to order of min (c, log n), for 2≤c≤n; the algorithms use Las Vegas type randomization in the case of 2<c≤n.

Use of the supremum distribution of Gaussian Processes in queueing analysis with long-range Dependence and self-similarity

In this paper we study the supremum distribution of a general class of Gaussian processes with stationary increments. This distribution is directly related to the steady state queue length distribution of a queueing system. Hence, its study is also important for different queueing applications such as delay analysis in communication networks. Our study is based on Extreme Value Theory and we show that asymptotically grows at most (on the order of) log x, where mx is the reciprocal of the maximum (normalized) variance of Xt This result is considerably stronger than the existing results in the literature based on Large Deviation Theory. We further show that this improvement can be critical in characterizing the asymptotic behavior of . Our results cover a large class of self-similar, short range dependent, and long-range dependent Gaussian processes

Ionophores based on 1,3-dithiole-2-thione-4,5-dithiolate (DMIT) as potentiometric silver sensors

A range of acyclic compounds based on 1,3-dithiole-2-thione-4,5-dithiolate (DMIT), functionalised with a silver binding chain and an alkyl chain, were synthesised and assessed as silver ionophores suitable for incorporation into potentiometric ion-selective electrodes as sensors for silver ions in photographic emulsions. The new ionophores were compared with a commercially available ionophore and a 14-crown-4-based ionophore. The membrane compositions were optimised for silver ion selectivity over a range of ions of relevance in the photographic process. 4-(Butylsulfanyl)-5-(phenylmethylthioethylsulfanyl)-1,3-dithiole-2-one was shown to be the most suitable ionophore in plasticised membrane electrodes, with a Nernstian response in the range 10−1–10−6 mol dm−3 and selectivity coefficients of the order of log KPOTAg/M ≤ −4.0.

BTEX Sorption by Montmorillonite Organo-Clays: TMPA, Adam, HDTMA

Organo-clay can be utilized for the containment of environmentalpollutants originating from waste sites or accidental spills. Abatch study was conducted using organo-clays produced from aWyoming montmorillonite (SWy) and three organic cations(trimethylphenylammonium (TMPA), trimethylammonium adamantane(Adam), and hexadecyltrimethylammonium (HDTMA)) to characterizeBTEX (benzene, toluene, ethylbenzene, o-, m-, p-xylene) sorption. Sorption data were fitted to two models,with Freundlich resulting in greater correlations of the datathan the Langmuir model (R2 at P ≤0.001-0.05). The Freundlich conditional index (nf),which describes the experimental sorption characteristics,decreased curvilinearly with organic-cation molecular weights,thus suggesting organo-clays with smaller cations had greaterhydrocarbon retention. Sorption of BTEX followed the order ofTMPA > Adam > HDTMA organo-clays. A similar sequence in themagnitudes of log Kd and log Komsupportedthis finding. Positive log Kom/Kow valuesfor TMPA and Adam derivatives indicated there was a greaterretention of BTEX by these organo-clays than octanol. The orderof log Kom for SWy-HDTMA, although concentration-dependent, was analogous to the log Kow order,indicating partitioning was the dominant sorption mechanism forthe HDTMA-clay. Isotherms for SWy-TMPA and SWy-Adam followed aconvex up pattern. In contract, a concave up curvature, notedfor SWy-HDTMA isotherms, was probably caused by a cosorptiveenhancement process resulting from an effective increase in organic matter content of the organo-clay due to furtherhydrocarbon sorption,in concurrence with a decrease inadsorbate activity coefficients. Values of binding affinityconstant, Kf, for SWy-TMPA were consistently higherthan SWy-Adam. The Kf values determined for totalBTEX sorption by TMPA and Adam derivatives were higher thanthose for the individual hydrocarbons. With SWy-HDTMA, the same order was observed for benzene and toluene; however, ethylbenzene and xylenes had greater Kf values thanthat for the BTEX mixture, possibly due to higher partitioningaffinity of the larger alkylbenzenes. With SWy-HDTM, thesequence of Kf values was: ethylbenzene > m-xylene > p-xylene > o-xylene > toluene >benzene. Trends for SWy-TMPA and SWy-Adam were in contrast tothat of the partitioning order, suggesting that adsorption, ratherthan partitioning, was the primary sorption mechanism for thesetwo organo-clays. With respect to the equilibriumconcentrations, the sorbed amounts for total BTEX mixture weregenerally higher than those for the individual compounds. Ascompared to benzene and toluene, the large-size alkylbenzenesshowed greater partitioning affinity due to their high hydrophobicity.

Viscosity of fluoride glasses near the fiber drawing temperature region

The temperature–viscosity dependence of ZrF 4-, InF 3- and CdF 2-based fluoride glasses was obtained by two methods. The first method uses a predictive relation based on differential scanning calorimetric (DSC) data based on the width of the glass transition region i.e. T g and T g ′, the beginning and end temperatures of the glass transition. We defined the factor, G=( T g ′/ T g)( T g ′− T g), in the relation which determines the viscosity at the temperature ( T− T g ′). The slope of the calculated log η versus T decreased in the order: fluorozirconate glass (0.085 K −1) > fluoroindate glasses (0.067 K −1) > cadmium fluorochloride glass (0.047 K −1). The second method was by measurement using the parallel-plate technique. The same order of ( log η(T)) slope was observed in the measured results, e.g. 0.12±0.02, 0.09±0.02 and 0.08±0.02 K −1 , respectively, for the tetravalent, the trivalent, and the divalent fluoride glasses. The Arrhenius activation energies of the shear viscosity are 115±10 kJ/mol for PGICdZn and 64±10 kJ/mol for CdFCl. These differences in activation energy affect the fiber drawing ability, because a larger activation energy corresponds to a drawing temperature closer to T g.