Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations

The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent “accurately” harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in “accurate” reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Padé approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.

Invariance of brain-wave representations of simple visual images and their names

In two experiments, electric brain waves of 14 subjects were recorded under several different conditions to study the invariance of brain-wave representations of simple patches of colors and simple visual shapes and their names, the words blue, circle, etc. As in our earlier work, the analysis consisted of averaging over trials to create prototypes and test samples, to both of which Fourier transforms were applied, followed by filtering and an inverse transformation to the time domain. A least-squares criterion of fit between prototypes and test samples was used for classification. The most significant results were these. By averaging over different subjects, as well as trials, we created prototypes from brain waves evoked by simple visual images and test samples from brain waves evoked by auditory or visual words naming the visual images. We correctly recognized from 60% to 75% of the test-sample brain waves. The general conclusion is that simple shapes such as circles and single-color displays generate brain waves surprisingly similar to those generated by their verbal names. These results, taken together with extensive psychological studies of auditory and visual memory, strongly support the solution proposed for visual shapes, by Bishop Berkeley and David Hume in the 18th century, to the long-standing problem of how the mind represents simple abstract ideas.

Young children's understanding of oddity: reducing complexity by simple oddity and "most different" strategies

Children aged between 3 and 7 years were taught simple and dimension-abstracted oddity discrimination using learning-set training techniques, in which isomorphic problems with varying content were presented with verbal explanation and feedback. Following the training phase, simple oddity (SO), dimension-abstracted oddity with one or two irrelevant dimensions, and non-oddity (NO) tasks were presented (without feedback) to determine the basis of solution. Although dimension-abstracted oddity requires discrimination based on a stimulus that is different from the others, which are all the same as each other on the relevant dimension, this was not the major strategy. The data were more consistent with use of a simple oddity strategy by 3- to 4-year-olds, and a most different strategy by 6- to 7-year-olds. These strategies are interpreted as reducing task complexity. (C) 2002 Elsevier Science Inc. All rights reserved.

SCC initiation for X65 pipeline steel in the "high" pH carbonate/bicarbonate solution

The initiation of stress corrosion cracking (SCC) was studied using scanning electron microscope observations of linearly increasing stress test specimens. SCC initiation from the following surfaces was studied: (i) initiation from the commercial pipe surface covered by the Zn coating, (ii) initiation from a mechanically polished surface with a deformed layer, and (iii) initiation from an electro-polished surface. SCC initiation involved different features for these surfaces as follows. (i) For the Zn coated commercial pipe surface, a crack in the Zn coating led to the dissolution of the deformed layer and when the deformed layer was penetrated, intergranular SCC initiation became possible. (ii) For a mechanically polished surface with a deformed layer, cracks in the surface oxide concentrated the anodic dissolution to such an extent that there was transgranular SCC in the deformed layer. SCC was intergranular when the deformed layer had been penetrated. Transgranular stress corrosion cracks were stopped at ferrite grain boundaries (GBs) oriented perpendicular to the SCC propagation direction. (iii) For an electro-polished surface, the surface oxide film was cracked at many locations, but intergranular SCC only propagated into the steel when the oxide crack corresponded to a GB. An oxide crack away from a GB is expected to be healed. The observed SCC initiation mechanism was not associated with simple preferential chemical attack of the ferrite GBs. (C) 2003 Elsevier Ltd. All rights reserved.

An Analytical Solution for the Elastic Lateral-Distortional Buckling of I-section Beams

Lateral-distortional buckling may occur in I-section beams with slender webs and stocky flanges. A computationally efficient method is presented in this paper to study this phenomenon. Previous studies on distortional buckling have been on the use of 3(rd) and 5(th) order polynomials to model the displacements. The present study provides an alternative way, using Fourier Series, to model the behaviour. Beams of different cross-sectional dimensions, load cases and restraint conditions are examined and compared. The accuracy and versatility of the method are verified by calibrating against the results of other published studies. The present method is believed to be a simple and efficient way of determining the buckling load and mode shapes of I-section beams that are susceptible to lateral-distortional buckling modes.

Similarity solution of axisymmetric flow in porous media

Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate. (c) 2005 Elsevier Ltd. All rights reserved.

Facile synthesis of rhodamine esters using acetyl chloride in alcohol solution

The rhodamines are a highly fluorescent class of compound used in many different fields of research, from the lasing medium in dye lasers to biological stains and markers for cellular drug resistance. In this study, esters (2-7) of rhodamine 110 (1) were conveniently prepared via the addition of acetyl chloride to a solution of the free acid (1) in the appropriate alcohol. This method conferred several advantages over previous preparations, namely that for low boiling alcohols, simple evaporation of the solution afforded the ester in quantitative yield with no need for purification. For higher boiling point alcohols, a method has been developed which allows the separation of longer chain esters from the alcohol solvent.

A simple method to localise pleiotropic susceptibility loci using univariate linkage analyses of correlated traits

Univariate linkage analysis is used routinely to localise genes for human complex traits. Often, many traits are analysed but the significance of linkage for each trait is not corrected for multiple trait testing, which increases the experiment-wise type-I error rate. In addition, univariate analyses do not realise the full power provided by multivariate data sets. Multivariate linkage is the ideal solution but it is computationally intensive, so genome-wide analysis and evaluation of empirical significance are often prohibitive. We describe two simple methods that efficiently alleviate these caveats by combining P-values from multiple univariate linkage analyses. The first method estimates empirical pointwise and genome-wide significance between one trait and one marker when multiple traits have been tested. It is as robust as an appropriate Bonferroni adjustment, with the advantage that no assumptions are required about the number of independent tests performed. The second method estimates the significance of linkage between multiple traits and one marker and, therefore, it can be used to localise regions that harbour pleiotropic quantitative trait loci (QTL). We show that this method has greater power than individual univariate analyses to detect a pleiotropic QTL across different situations. In addition, when traits are moderately correlated and the QTL influences all traits, it can outperform formal multivariate VC analysis. This approach is computationally feasible for any number of traits and was not affected by the residual correlation between traits. We illustrate the utility of our approach with a genome scan of three asthma traits measured in families with a twin proband.

A D-optimal designed population pharmacokinetic study of itraconazole capsules and solution in adults with cystic fibrosis

Background: Oral itraconazole (ITRA) is used for the treatment of allergic bronchopulmonary aspergillosis in patients with cystic fibrosis (CF) because of its antifungal activity against Aspergillus species. ITRA has an active hydroxy-metabolite (OH-ITRA) which has similar antifungal activity. ITRA is a highly lipophilic drug which is available in two different oral formulations, a capsule and an oral solution. It is reported that the oral solution has a 60% higher relative bioavailability. The influence of altered gastric physiology associated with CF on the pharmacokinetics (PK) of ITRA and its metabolite has not been previously evaluated. Objectives: 1) To estimate the population (pop) PK parameters for ITRA and its active metabolite OH-ITRA including relative bioavailability of the parent after administration of the parent by both capsule and solution and 2) to assess the performance of the optimal design. Methods: The study was a cross-over design in which 30 patients received the capsule on the first occasion and 3 days later the solution formulation. The design was constrained to have a maximum of 4 blood samples per occasion for estimation of the popPK of both ITRA and OH-ITRA. The sampling times for the population model were optimized previously using POPT v.2.0.[1] POPT is a series of applications that run under MATLAB and provide an evaluation of the information matrix for a nonlinear mixed effects model given a particular design. In addition it can be used to optimize the design based on evaluation of the determinant of the information matrix. The model details for the design were based on prior information obtained from the literature, which suggested that ITRA may have either linear or non-linear elimination. The optimal sampling times were evaluated to provide information for both competing models for the parent and metabolite and for both capsule and solution simultaneously. Blood samples were assayed by validated HPLC.[2] PopPK modelling was performed using FOCE with interaction under NONMEM, version 5 (level 1.1; GloboMax LLC, Hanover, MD, USA). The PK of ITRA and OH‑ITRA was modelled simultaneously using ADVAN 5. Subsequently three methods were assessed for modelling concentrations less than the LOD (limit of detection). These methods (corresponding to methods 5, 6 & 4 from Beal[3], respectively) were (a) where all values less than LOD were assigned to half of LOD, (b) where the closest missing value that is less than LOD was assigned to half the LOD and all previous (if during absorption) or subsequent (if during elimination) missing samples were deleted, and (c) where the contribution of the expectation of each missing concentration to the likelihood is estimated. The LOD was 0.04 mg/L. The final model evaluation was performed via bootstrap with re-sampling and a visual predictive check. The optimal design and the sampling windows of the study were evaluated for execution errors and for agreement between the observed and predicted standard errors. Dosing regimens were simulated for the capsules and the oral solution to assess their ability to achieve ITRA target trough concentration (Cmin,ss of 0.5-2 mg/L) or a combined Cmin,ss for ITRA and OH-ITRA above 1.5mg/L. Results and Discussion: A total of 241 blood samples were collected and analysed, 94% of them were taken within the defined optimal sampling windows, of which 31% where taken within 5 min of the exact optimal times. Forty six per cent of the ITRA values and 28% of the OH-ITRA values were below LOD. The entire profile after administration of the capsule for five patients was below LOD and therefore the data from this occasion was omitted from estimation. A 2-compartment model with 1st order absorption and elimination best described ITRA PK, with 1st order metabolism of the parent to OH-ITRA. For ITRA the clearance (ClItra/F) was 31.5 L/h; apparent volumes of central and peripheral compartments were 56.7 L and 2090 L, respectively. Absorption rate constants for capsule (kacap) and solution (kasol) were 0.0315 h-1 and 0.125 h-1, respectively. Comparative bioavailability of the capsule was 0.82. There was no evidence of nonlinearity in the popPK of ITRA. No screened covariate significantly improved the fit to the data. The results of the parameter estimates from the final model were comparable between the different methods for accounting for missing data, (M4,5,6)[3] and provided similar parameter estimates. The prospective application of an optimal design was found to be successful. Due to the sampling windows, most of the samples could be collected within the daily hospital routine, but still at times that were near optimal for estimating the popPK parameters. The final model was one of the potential competing models considered in the original design. The asymptotic standard errors provided by NONMEM for the final model and empirical values from bootstrap were similar in magnitude to those predicted from the Fisher Information matrix associated with the D-optimal design. Simulations from the final model showed that the current dosing regimen of 200 mg twice daily (bd) would provide a target Cmin,ss (0.5-2 mg/L) for only 35% of patients when administered as the solution and 31% when administered as capsules. The optimal dosing schedule was 500mg bd for both formulations. The target success for this dosing regimen was 87% for the solution with an NNT=4 compared to capsules. This means, for every 4 patients treated with the solution one additional patient will achieve a target success compared to capsule but at an additional cost of AUD $220 per day. The therapeutic target however is still doubtful and potential risks of these dosing schedules need to be assessed on an individual basis. Conclusion: A model was developed which described the popPK of ITRA and its main active metabolite OH-ITRA in adult CF after administration of both capsule and solution. The relative bioavailability of ITRA from the capsule was 82% that of the solution, but considerably more variable. To incorporate missing data, using the simple Beal method 5 (using half LOD for all samples below LOD) provided comparable results to the more complex but theoretically better Beal method 4 (integration method). The optimal sparse design performed well for estimation of model parameters and provided a good fit to the data.

The dynamics of a genetic algorithm for a simple learning problem

A formalism for describing the dynamics of Genetic Algorithms (GAs) using method s from statistical mechanics is applied to the problem of generalization in a perceptron with binary weights. The dynamics are solved for the case where a new batch of training patterns is presented to each population member each generation, which considerably simplifies the calculation. The theory is shown to agree closely to simulations of a real GA averaged over many runs, accurately predicting the mean best solution found. For weak selection and large problem size the difference equations describing the dynamics can be expressed analytically and we find that the effects of noise due to the finite size of each training batch can be removed by increasing the population size appropriately. If this population resizing is used, one can deduce the most computationally efficient size of training batch each generation. For independent patterns this choice also gives the minimum total number of training patterns used. Although using independent patterns is a very inefficient use of training patterns in general, this work may also prove useful for determining the optimum batch size in the case where patterns are recycled.

Passive mode-locked lasing by injecting a carbon nanotube-solution in the core of an optical fiber

In this paper, we propose a saturable absorber (SA) device consisting on an in-fiber micro-slot inscribed by femtosecond laser micro fabrication, filled by a dispersion of Carbon Nanotubes (CNT). Due to the flexibility of the fabrication method, efficient and simple integration of the mode-locking device directly into the optical fiber is achieved. Furthermore, the fabrication process offers a high level of control over the dimensions and location of the micro-slots. We apply this fabrication flexibility to extend the interaction length between the CNT and the propagating optical field along the optical fiber, hence enhancing the nonlinearity of the device. Furthermore, the method allows the fabrication of devices that operate by either a direct field interaction (when the central peak of the propagating optical mode passes through the nonlinear media) or an evanescent field interaction (only a fraction of the optical mode interacts with the CNT). In this paper, several devices with different interaction lengths and interaction regimes are investigated. Self-starting passively modelocked laser operation with an enhanced nonlinear interaction is observed using CNT-based SAs in both interaction regimes. This method constitutes a simple and suitable approach to integrate the CNT into the optical system as well as enhancing the optical nonlinearity of CNT-based photonic devices.

A general route to synthesize supported isolated oxide and mixed-oxide nanoclusters at sizes below 5 nm

A simple and efficient route to prepare supported nanocrystalline oxides is presented. The synthesis procedure, i.e. in situ autocombustion of a glycine complex, allows the production of nanocrystals in a porous matrix presenting larger pore size. An example of successful formation of 2-5 nm nanocrystals is given for a single oxide (Fe2O3), a mixed-oxide structure (LaCoO3 perovskite-type) and a nickel-doped oxide. © 2011 The Royal Society of Chemistry.

Electrocoating of carbon fibres:a route for interface control in carbon fibre reinforced poly methylmethacrylate?

A simple method of creating defined PMMA and poly (MMA-co-Cz) electrocoatings on carbon fibres is described. The electrodeposition of poly methylmethacrylate (PMMA) onto unsized, unmodified carbon fibres was performed by simple constant current electrolyses of methylmethacrylate (MMA) monomer in dimethylformamide (DMF) solutions and the 'pur' liquid monomer using sodium nitrate and lithium perchlorate as supporting electrolytes. The presence of polymeric coatings successfully attached to the carbon fibres was verified by scanning electron microscopy and photoelectron spectroscopy (XPS). Performing the electrolysis in dilute MMA in DMF solutions ([MMA]

Hydrothermal saline promoted grafting:a route to sulfonic acid SBA-15 silica with ultra-high acid site loading for biodiesel synthesis

A simple grafting protocol is reported which affords a ten-fold enhancement in acid site density of mesoporous sulfonic acid silicas compared to conventional syntheses, offering improved process efficiency and new opportunities for tailored supported solid acids in sustainable chemistry. This journal is

Characterizations of the Solution Sets of Generalized Convex Minimization Problems

2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20.