Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15

Rolle's Theorem for Complex Polynomials with Real Coefficients

Let p(z) be an algebraic polynomial of degree n ¸ 2 with real coefficients and p(i) = p(¡i). According to Grace-Heawood Theorem, at least one zero of the derivative p0(z) is on the disk with center in the origin and radius cot(¼=n). In this paper is found the smallest domain containing at leas one zero of the derivative p0(z).

Extention of Apolarity and Grace Theorem

MSC 2010: 30C10

Gas chromatographic enantiomer separation on single and mixed cyclodextrin derivative chiral stationary phases

Capillary gas chromatographic enantiomer separation of some polar compounds, including alpha-phenylethylamine, styrene oxide, pyrethroid insecticides and other carboxylates, was investigated on modified cyclodextrin (CD) chiral stationary phases. The chiral stationary phases studied included permethylated beta-CD (PMBCD), heptakis (2,6-di-O-butyl-3-O-butyryl)-beta-CD (DBBBCD), heptakis (2,6-di-O-nonyl-3-O-trifluoroacetyl)-beta-CD (DNTBCD), the mixture of PMBCD and DBBBCD, and the mixture of PMBCD and DNTBCD. On the mixed chiral stationary phases containing the mixtures of derivatized cyclodextrins, enantiomer separation was improved significantly for some compounds as compared to the single cyclodextrin derivative chiral stationary phases, and synergistic effects were observed for some compounds on the mixed cyclodextrin derivative chiral stationary phases.

Chemical profile of the polar extract of Paepalanthus microphyllus (Guill.) Kunth (Eriocaulaceae)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A Benzaldehyde Derivative as a Chelating Ligand: Helical Manganese(II) Coordination Polymers Assembling into a Porous Solid

A molecular, porous crystalline material constructed from neutral helical coordination polymers incorporating manganese(II) ions and two types of bridging ligands, namely the deprotonated form of 2-hydroxy-5-methoxy-3-nitrobenzaldehyde (HL) and isobutyrate (iB−), has been obtained and structurally characterized. Structural analysis reveals that within the coordination polymer each benzaldehyde derivative ligates two manganese ions in 6-membered chelating rings, and the isobutyrate ligands cooperatively chelate either two or three manganese ions. The solid state assembly of the resulting polymeric chains of formula [Mn4(L)2(iB)6]n (1), described in the polar space group R3c, is associated with tubular channels occupied by MeCN solvent molecules (1·xMeCN; x ≤ 9). TGA profiles and PXRD measurements demonstrate that the crystallinity of the solid remains intact in its fully desolvated form, and its stability and crystallinity are ensured up to a temperature of 190 °C. Gas adsorption properties of desolvated crystals were probed, but no remarkable sorption capacity of N2 and only a limited one for CO2 could be observed. Magnetic susceptibility data reveal an antiferromagnetic type of coupling between adjacent manganese(II) ions along the helical chains with energy parameters J1 = −5.9(6) cm−1 and J2 = −1.8(9) cm−1.

Osteryoung square wave voltammetric determination of lactose in food samples by a derivative procedure

A method for determination of lactose in food samples by Osteryoung square wave voltammetry (OSWV) was developed. It was based on the nucleophilic addition reaction between lactose and aqua ammonia. The carbonyl group of lactose can be changed into imido group, and this increases the electrochemical activity in reduction and the sensitivity. The optimal condition for the nucleophilic addition reaction was investigated and it was found that in NH4Cl–NH3 buffer of pH 10.1, the linear range between the peak current and the concentration of lactose was 0.6–8.4 mg L−1, and the detection limits was 0.44 mg L−1. The proposed method was applied to the determination of lactose in food samples and satisfactory results were obtained.

Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

Combining Cartesian and polar coordinates in IBVS

Image-based visual servo (IBVS) is a simple, efficient and robust technique for vision-based control. Although technically a local method in practice it demonstrates almost global convergence. However IBVS performs very poorly for cases that involve large rotations about the optical axis. It is well known that re-parameterizing the problem by using polar, instead of Cartesian coordinates, of feature points overcomes this limitation. First, simulation and experimental results are presented to show the complementarity of these two parameter-izations. We then describe a new hybrid visual servo strategy based on combining polar and Cartesian image Jacobians. © 2009 IEEE.

Non-invasive assessment of tear film surface quality

The tear film plays an important role preserving the health of the ocular surface and maintaining the optimal refractive power of the cornea. Moreover dry eye syndrome is one of the most commonly reported eye health problems. This syndrome is caused by abnormalities in the properties of the tear film. Current clinical tools to assess the tear film properties have shown certain limitations. The traditional invasive methods for the assessment of tear film quality, which are used by most clinicians, have been criticized for the lack of reliability and/or repeatability. A range of non-invasive methods of tear assessment have been investigated, but also present limitations. Hence no “gold standard” test is currently available to assess the tear film integrity. Therefore, improving techniques for the assessment of the tear film quality is of clinical significance and the main motivation for the work described in this thesis. In this study the tear film surface quality (TFSQ) changes were investigated by means of high-speed videokeratoscopy (HSV). In this technique, a set of concentric rings formed in an illuminated cone or a bowl is projected on the anterior cornea and their reflection from the ocular surface imaged on a charge-coupled device (CCD). The reflection of the light is produced in the outer most layer of the cornea, the tear film. Hence, when the tear film is smooth the reflected image presents a well structure pattern. In contrast, when the tear film surface presents irregularities, the pattern also becomes irregular due to the light scatter and deviation of the reflected light. The videokeratoscope provides an estimate of the corneal topography associated with each Placido disk image. Topographical estimates, which have been used in the past to quantify tear film changes, may not always be suitable for the evaluation of all the dynamic phases of the tear film. However the Placido disk image itself, which contains the reflected pattern, may be more appropriate to assess the tear film dynamics. A set of novel routines have been purposely developed to quantify the changes of the reflected pattern and to extract a time series estimate of the TFSQ from the video recording. The routine extracts from each frame of the video recording a maximized area of analysis. In this area a metric of the TFSQ is calculated. Initially two metrics based on the Gabor filter and Gaussian gradient-based techniques, were used to quantify the consistency of the pattern’s local orientation as a metric of TFSQ. These metrics have helped to demonstrate the applicability of HSV to assess the tear film, and the influence of contact lens wear on TFSQ. The results suggest that the dynamic-area analysis method of HSV was able to distinguish and quantify the subtle, but systematic degradation of tear film surface quality in the inter-blink interval in contact lens wear. It was also able to clearly show a difference between bare eye and contact lens wearing conditions. Thus, the HSV method appears to be a useful technique for quantitatively investigating the effects of contact lens wear on the TFSQ. Subsequently a larger clinical study was conducted to perform a comparison between HSV and two other non-invasive techniques, lateral shearing interferometry (LSI) and dynamic wavefront sensing (DWS). Of these non-invasive techniques, the HSV appeared to be the most precise method for measuring TFSQ, by virtue of its lower coefficient of variation. While the LSI appears to be the most sensitive method for analyzing the tear build-up time (TBUT). The capability of each of the non-invasive methods to discriminate dry eye from normal subjects was also investigated. The receiver operating characteristic (ROC) curves were calculated to assess the ability of each method to predict dry eye syndrome. The LSI technique gave the best results under both natural blinking conditions and in suppressed blinking conditions, which was closely followed by HSV. The DWS did not perform as well as LSI or HSV. The main limitation of the HSV technique, which was identified during the former clinical study, was the lack of the sensitivity to quantify the build-up/formation phase of the tear film cycle. For that reason an extra metric based on image transformation and block processing was proposed. In this metric, the area of analysis was transformed from Cartesian to Polar coordinates, converting the concentric circles pattern into a quasi-straight lines image in which a block statistics value was extracted. This metric has shown better sensitivity under low pattern disturbance as well as has improved the performance of the ROC curves. Additionally a theoretical study, based on ray-tracing techniques and topographical models of the tear film, was proposed to fully comprehend the HSV measurement and the instrument’s potential limitations. Of special interested was the assessment of the instrument’s sensitivity under subtle topographic changes. The theoretical simulations have helped to provide some understanding on the tear film dynamics, for instance the model extracted for the build-up phase has helped to provide some insight into the dynamics during this initial phase. Finally some aspects of the mathematical modeling of TFSQ time series have been reported in this thesis. Over the years, different functions have been used to model the time series as well as to extract the key clinical parameters (i.e., timing). Unfortunately those techniques to model the tear film time series do not simultaneously consider the underlying physiological mechanism and the parameter extraction methods. A set of guidelines are proposed to meet both criteria. Special attention was given to a commonly used fit, the polynomial function, and considerations to select the appropriate model order to ensure the true derivative of the signal is accurately represented. The work described in this thesis has shown the potential of using high-speed videokeratoscopy to assess tear film surface quality. A set of novel image and signal processing techniques have been proposed to quantify different aspects of the tear film assessment, analysis and modeling. The dynamic-area HSV has shown good performance in a broad range of conditions (i.e., contact lens, normal and dry eye subjects). As a result, this technique could be a useful clinical tool to assess tear film surface quality in the future.

The application of the statutory derivative action in Pt 2F.1A of the Corporations Act to companies in liquidation under Ch 5 : Well oiled machine or is Pt 2F.1A in need of a tune up?

The statutory derivative action was introduced in Australia in 2000. This right of action has been debated in the literature and introduced in a number of other jurisdictions as well. However, it is by no means clear that all issues have been resolved despite its operation in Australia for over 10 years. This article considers the application of Pt 2F.1A of the Corporations Act to companies in liquidation under Ch 5. It demonstrates that the application involves consideration of not only proper statutory interpretation but also policy matters around the role and the supervision by the court of a liquidator once a company has entered liquidation.