Regioregular poly(3-hexyl-thiophene) helical self-organization on carbon nanotubes

Mixtures of Regioregular Poly(3-hexyl-thiophene) (rrP3HT) and multi wall carbon nanotubes have been investigated by Scanning Tunneling Microscopy in Ultra High Vacuum. Carbon nanotubes covered by rrP3HT have been imaged and analyzed, providing a clear evidence that this polymer self assembles on the nanotube surface following geometrical constraints and adapting its equilibrium chain-to-chain distance. Largely spaced covered nanotubes have been analyzed to investigate the role played by nanotube chirality in the polymer wrapping, evidencing strong rrP3HT interactions along well defined directions.

Synthesis and Raman spectroscopic study of Mg/Al,Fe hydrotalcites with variable cationic ratios

Hydrotalcites of formula Mg6 (Fe,Al)2(OH)16(CO3).4H2O formed by intercalation with the carbonate anion as a function of divalent/trivalent cationic ratio have been successfully synthesised. The XRD patterns show variation in the d-spacing attributed to the size of the cation. Raman and infrared bands in the OH stretching region are assigned to (a) brucite layer OH stretching vibrations (b) water stretching bands and (c) water strongly hydrogen bonded to the carbonate anion. Multiple (CO3)2- symmetric stretching bands suggest that different types of (CO3)2- exist in the hydrotalcite interlayer. Increasing the cation ratio (Mg/Al,Fe) resulted in an increase in the combined intensity of the 2 Raman bands at around 3600 cm-1, attributed to Mg-OH stretching modes, and a shift of the overall band profile to higher wavenumbers. These observations are believed to be a result of the increase in magnesium in the structure. Raman spectroscopy shows a reduction in the symmetry of the carbonate, leading to the conclusion that the anions are bonded to the brucite-like hydroxyl surface and to the water in the interlayer. Water bending modes are identified in the infrared spectra at positions greater than 1630 cm-1, indicating the water is strongly hydrogen bonded to both the interlayer anions and the brucite-like surface.

Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

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.

New insights into appetite, inflammation and the use of fish oil in hemodialysis patients

Protein-energy wasting (PEW) is commonly seen in patients with chronic kidney disease (CKD). The condition is characterised by chronic, systemic low-grade inflammation which affects nutritional status by a variety of mechanisms including reducing appetite and food intake and increasing muscle catabolism. PEW is linked with co-morbidities such as cardiovascular disease, and is associated with lower quality of life, increased hospitalisations and a 6-fold increase in risk of death1. Significant gender differences have been found in the severity and effects of several markers of PEW. There have been limited studies testing the ability of anti-inflammatory agents or nutritional interventions to reduce the effects of PEW in dialysis patients. This thesis makes a significant contribution to the understanding of PEW in dialysis patients. It advances understanding of measurement techniques for two of the key components, appetite and inflammation, and explores the effect of fish oil, an anti-inflammatory agent, on markers of PEW in dialysis patients. The first part of the thesis consists of two methodological studies conducted using baseline data. The first study aims to validate retrospective ratings of hunger, desire to eat and fullness on visual analog scales (VAS) (paper and pen and electronic) as a new method of measuring appetite in dialysis patients. The second methodological study aims to assess the ability of a variety of methods available in routine practice to detect the presence of inflammation. The second part of the thesis aims to explore the effect of 12 weeks supplementation with 2g per day of Eicosapentaenoic Acid (EPA), a longchain fatty acid found in fish oil, on markers of PEW. A combination of biomarkers and psychomarkers of appetite and inflammation are the main outcomes being explored, with nutritional status, dietary intake and quality of life included as secondary outcomes. A lead in phase of 3 months prior to baseline was used so that each person acts as their own historical control. The study also examines whether there are gender differences in response to the treatment. Being an exploratory study, an important part of the work is to test the feasibility of the intervention, thus the level of adherence and factors associated with adherence are also presented. The studies were conducted at the hemodialysis unit of the Wesley Hospital. Participants met the following criteria: adult, stage 5 CKD on hemodialysis for at least 3 months, not expected to receive a transplant or switch to another dialysis modality during the study, absence of intellectual impairment or mental illness impairing ability to follow instructions or complete the intervention. A range of intermediate, clinical and patient-centred outcome measures were collected at baseline and 12 weeks. Inflammation was measured using five biomarkers: c-reactive protein (CRP), interleukin-6 (IL6), intercellular adhesion molecule (sICAM-1), vascular cell adhesion molecule (sVCAM-1) and white cell count (WCC). Subjective appetite was measured using the first question from the Appetite and Dietary Assessment (ADAT) tool and VAS for measurements of hunger, desire to eat and fullness. A novel feature of the study was the assessment of the appetite peptides leptin, ghrelin and peptide YY as biomarkers of appetite. Nutritional status/inflammation was assessed using the Malnutrition-Inflammation Score (MIS) and the Patient-Generated Subjective Global Assessment (PG-SGA). Dietary intake was measured using 3-day records. Quality of life was measured using the Kidney Disease Quality of Life Short Form version 1.3 (KDQOL-SF™ v1.3 © RAND University), which combines the Short-Form 36 (SF36) with a kidney-disease specific module2. A smaller range of these variables was available for analysis during the control phase (CRP, ADAT, dietary intake and nutritional status). Statistical analysis was carried out using SPSS version 14 (SPSS Inc, Chicago IL, USA). Analysis of the first part of the thesis involved descriptive and bivariate statistics, as well as Bland-Altman plots to assess agreement between methods, and sensitivity analysis/ROC curves to test the ability of methods to predict the presence of inflammation. The unadjusted (paired ttests) and adjusted (linear mixed model) change over time is presented for the main outcome variables of inflammation and appetite. Results are shown for the whole group followed by analyses according to gender and adherence to treatment. Due to the exploratory nature of the study, trends and clinical significance were considered as important as statistical significance. Twenty-eight patients (mean age 61±17y, 50% male, dialysis vintage 19.5 (4- 101) months) underwent baseline assessment. Seven out of 28 patients (25%) reported sub-optimal appetite (self-reported as fair, poor or very poor) despite all being well nourished (100% SGA A). Using the VAS, ratings of hunger, but not desire to eat or fullness, were significantly (p<0.05) associated with a range of relevant clinical variables including age (r=-0.376), comorbidities (r=-0.380) nutritional status (PG-SGA score, r=-0.451), inflammatory markers (CRP r=-0.383; sICAM-1 r=-0.387) and seven domains of quality of life. Patients expressed a preference for the paper and pen method of administering VAS. None of the tools (appetite, MIS, PG-SGA, albumin or iron) showed an acceptable ability to detect patients who are inflamed. It is recommended that CRP should be tested more frequently as a matter of course rather than seeking alternative methods of measuring inflammation. 27 patients completed the 12 week intervention. 20 patients were considered adherent based on changes in % plasma EPA, which rose from 1.3 (0.94)% to 5.2 (1.1)%, p<0.001, in this group. The major barriers to adherence were forgetting to take the tablets as well as their size. At 12 weeks, inflammatory markers remained steady apart from the white cell count which decreased (7.6(2.5) vs 7.0(2.2) x109/L, p=0.058) and sVCAM-1 which increased (1685(654) vs 2249(925) ng/mL, p=0.001). Subjective appetite using VAS increased (51mm to 57mm, +12%) and there was a trend towards reduction in peptide YY (660(31) vs 600(30) pg/mL, p=0.078). There were some gender differences apparent, with the following adjusted change between baseline and week 12: CRP (males -3% vs females +17%, p=0.19), IL6 (males +17% vs females +48%, p=0.77), sICAM-1 (males -5% vs females +11%, p=0.07), sVCAM-1 (males +54% vs females +19%, p=0.08) and hunger ratings (males 20% vs females -5%, p=0.18). On balance, males experienced a maintainence or reduction in three inflammatory markers and an improvement in hunger ratings, and therefore appeared to have responded better to the intervention. Compared to those who didn’t adhere, adherent patients maintained weight (mean(SE) change: +0.5(1.6) vs - 0.8(1.2) kg, p=0.052) and fat-free mass (-0.1 (1.6) vs -1.8 (1.8) kg, p=0.045). There was no difference in change between the intervention and control phase for CRP, appetite, nutritional status or dietary intake. The thesis makes a significant contribution to the evidence base for understanding of PEW in dialysis patients. It has advanced knowledge of methods of assessing inflammation and appetite. Retrospective ratings of hunger on a VAS appear to be a valid method of assessing appetite although samples which include patients with very poor appetite are required to confirm this. Supplementation with fish oil appeared to improve subjective appetite and dampen the inflammatory response. The effectiveness of the intervention is influenced by gender and adherence. Males appear to be more responsive to the primary outcome variables than females, and the quality of response is improved with better adherence. These results provide evidence to support future interventions aimed at reducing the effects of PEW in dialysis patients.

Infrared spectroscopic investigation of the effects of titania photocatalyst on the degradation of linear low density polyethylene film for commercial applications

There is a need in industry for a commodity polyethylene film with controllable degradation properties that will degrade in an environmentally neutral way, for applications such as shopping bags and packaging film. Additives such as starch have been shown to accelerate the degradation of plastic films, however control of degradation is required so that the film will retain its mechanical properties during storage and use, and then degrade when no longer required. By the addition of a photocatalyst it is hoped that polymer film will breakdown with exposure to sunlight. Furthermore, it is desired that the polymer film will degrade in the dark, after a short initial exposure to sunlight. Research has been undertaken into the photo- and thermo-oxidative degradation processes of 25 ìm thick LLDPE (linear low density polyethylene) film containing titania from different manufacturers. Films were aged in a suntest or in an oven at 50 °C, and the oxidation product formation was followed using IR spectroscopy. Degussa P25, Kronos 1002, and various organic-modified and doped titanias of the types Satchleben Hombitan and Hunstsman Tioxide incorporated into LLDPE films were assessed for photoactivity. Degussa P25 was found to be the most photoactive with UVA and UVC exposure. Surface modification of titania was found to reduce photoactivity. Crystal phase is thought to be among the most important factors when assessing the photoactivity of titania as a photocatalyst for degradation. Pre-irradiation with UVA or UVC for 24 hours of the film containing 3% Degussa P25 titania prior to aging in an oven resulted in embrittlement in ca. 200 days. The multivariate data analysis technique PCA (principal component analysis) was used as an exploratory tool to investigate the IR spectral data. Oxidation products formed in similar relative concentrations across all samples, confirming that titania was catalysing the oxidation of the LLDPE film without changing the oxidation pathway. PCA was also employed to compare rates of degradation in different films. PCA enabled the discovery of water vapour trapped inside cavities formed by oxidation by titania particles. Imaging ATR/FTIR spectroscopy with high lateral resolution was used in a novel experiment to examine the heterogeneous nature of oxidation of a model polymer compound caused by the presence of titania particles. A model polymer containing Degussa P25 titania was solvent cast onto the internal reflection element of the imaging ATR/FTIR and the oxidation under UVC was examined over time. Sensitisation of 5 ìm domains by titania resulted in areas of relatively high oxidation product concentration. The suitability of transmission IR with a synchrotron light source to the study of polymer film oxidation was assessed as the Australian Synchrotron in Melbourne, Australia. Challenges such as interference fringes and poor signal-to-noise ratio need to be addressed before this can become a routine technique.

An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation

Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.

Prandial subcutaneous injections of glucagon-like peptide-1 cause weight loss in obese human subjects

Recombinant glucagon-like peptide-1 (7–36)amide (rGLP-1) was recently shown to cause significant weight loss in type 2 diabetics when administered for 6 weeks as a continuous subcutaneous infusion. The mechanisms responsible for the weight loss are not clarified. In the present study, rGLP-1 was given for 5d by prandial subcutaneous injections (PSI) (76nmol 30min before meals, four times daily; a total of 302·4nmol/24h) or by continuous subcutaneous infusion (CSI) (12·7nmol/h; a total of 304·8nmol/24h). This was performed in nineteen healthy obese subjects (mean age 44·2 (sem 2·5) years; BMI 39·0 (sem 1·2)kg/m2) in a prospective randomised, double-blind, placebo-controlled, cross-over study. Compared with the placebo, rGLP-1 administered as PSI and by CSI generated a 15% reduction in mean food intake per meal (P=0·02) after 5d treatment. A weight loss of 0·55 (sem 0·2) kg (P<0·05) was registered after 5d with PSI of rGLP-1. Gastric emptying rate was reduced during both PSI (P<0·001) and CSI (P<0·05) treatment, but more rapidly and to a greater extent with PSI of rGLP-1. To conclude, a 5d treatment of rGLP-1 at high doses by PSI, but not CSI, promptly slowed gastric emptying as a probable mechanism of action of increased satiety, decreased hunger and, hence, reduced food intake with an ensuing weight loss.

Analysis of linear relationships in block ciphers

This thesis is devoted to the study of linear relationships in symmetric block ciphers. A block cipher is designed so that the ciphertext is produced as a nonlinear function of the plaintext and secret master key. However, linear relationships within the cipher can still exist if the texts and components of the cipher are manipulated in a number of ways, as shown in this thesis. There are four main contributions of this thesis. The first contribution is the extension of the applicability of integral attacks from word-based to bitbased block ciphers. Integral attacks exploit the linear relationship between texts at intermediate stages of encryption. This relationship can be used to recover subkey bits in a key recovery attack. In principle, integral attacks can be applied to bit-based block ciphers. However, specific tools to define the attack on these ciphers are not available. This problem is addressed in this thesis by introducing a refined set of notations to describe the attack. The bit patternbased integral attack is successfully demonstrated on reduced-round variants of the block ciphers Noekeon, Present and Serpent. The second contribution is the discovery of a very small system of equations that describe the LEX-AES stream cipher. LEX-AES is based heavily on the 128-bit-key (16-byte) Advanced Encryption Standard (AES) block cipher. In one instance, the system contains 21 equations and 17 unknown bytes. This is very close to the upper limit for an exhaustive key search, which is 16 bytes. One only needs to acquire 36 bytes of keystream to generate the equations. Therefore, the security of this cipher depends on the difficulty of solving this small system of equations. The third contribution is the proposal of an alternative method to measure diffusion in the linear transformation of Substitution-Permutation-Network (SPN) block ciphers. Currently, the branch number is widely used for this purpose. It is useful for estimating the possible success of differential and linear attacks on a particular SPN cipher. However, the measure does not give information on the number of input bits that are left unchanged by the transformation when producing the output bits. The new measure introduced in this thesis is intended to complement the current branch number technique. The measure is based on fixed points and simple linear relationships between the input and output words of the linear transformation. The measure represents the average fraction of input words to a linear diffusion transformation that are not effectively changed by the transformation. This measure is applied to the block ciphers AES, ARIA, Serpent and Present. It is shown that except for Serpent, the linear transformations used in the block ciphers examined do not behave as expected for a random linear transformation. The fourth contribution is the identification of linear paths in the nonlinear round function of the SMS4 block cipher. The SMS4 block cipher is used as a standard in the Chinese Wireless LAN Wired Authentication and Privacy Infrastructure (WAPI) and hence, the round function should exhibit a high level of nonlinearity. However, the findings in this thesis on the existence of linear relationships show that this is not the case. It is shown that in some exceptional cases, the first four rounds of SMS4 are effectively linear. In these cases, the effective number of rounds for SMS4 is reduced by four, from 32 to 28. The findings raise questions about the security provided by SMS4, and might provide clues on the existence of a flaw in the design of the cipher.