A Fredholm-type theory for third-kind linear integral equations

The third-kind linear integral equation Image where g(t) vanishes at a finite number of points in (a, b), is considered. In general, the Fredholm Alternative theory [[5.]] does not hold good for this type of integral equation. However, imposing certain conditions on g(t) and K(t, t′), the above integral equation was shown [[1.], 49–57] to obey a Fredholm-type theory, except for a certain class of kernels for which the question was left open. In this note a theory is presented for the equation under consideration with some additional assumptions on such kernels.

On the Solution of Certain Simultaneous Pairs of Dual Integral Equations

Mit einer direkten Methode, bei der der Erdelyi-Kober- und der modifizierte Hankel-Operator Anwendung finden, werden gewisse Systeme aus zwei bzw. drei Paaren dualer Integralgleichungen mit Bessel-Kernen in geschlossener Form gelöst. Für bestimmte Funktionenklassen und Ordnungen der Bessel-Funktionen ist die Vorgehensweise angebrachter und geeigneter als die bereits existierenden Methoden.

Fast FIR Algorithms for the Continuous Wavelet Transform From Constrained Least Squares

New algorithms for the continuous wavelet transform are developed that are easy to apply, each consisting of a single-pass finite impulse response (FIR) filter, and several times faster than the fastest existing algorithms. The single-pass filter, named WT-FIR-1, is made possible by applying constraint equations to least-squares estimation of filter coefficients, which removes the need for separate low-pass and high-pass filters. Non-dyadic two-scale relations are developed and it is shown that filters based on them can work more efficiently than dyadic ones. Example applications to the Mexican hat wavelet are presented.

A novel method for the age estimation of Saddletail snapper (Lutjanus malabaricus) using Fourier Transform-near infrared (FT-NIR) spectroscopy

Near infrared (NIR) spectroscopy was investigated as a potential rapid method of estimating fish age from whole otoliths of Saddletail snapper (Lutjanus malabaricus). Whole otoliths from 209 Saddletail snapper were extracted and the NIR spectral characteristics were acquired over a spectral range of 800–2780 nm. Partial least-squares models (PLS) were developed from the diffuse reflectance spectra and reference-validated age estimates (based on traditional sectioned otolith increments) to predict age for independent otolith samples. Predictive models developed for a specific season and geographical location performed poorly against a different season and geographical location. However, overall PLS regression statistics for predicting a combined population incorporating both geographic location and season variables were: coefficient of determination (R2) = 0.94, root mean square error of prediction (RMSEP) = 1.54 for age estimation, indicating that Saddletail age could be predicted within 1.5 increment counts. This level of accuracy suggests the method warrants further development for Saddletail snapper and may have potential for other fish species. A rapid method of fish age estimation could have the potential to reduce greatly both costs of time and materials in the assessment and management of commercial fisheries.

Determination of integral fringe order in photoelasticity

The paper describes a method to determine the integral fringe order associated with a fractional fringe value that is measured using Tardy or other similar compensators. The method makes use of two different wavelengths of light to determine the fractional fringe values. Further, it does not assume the independence of the material fringe constant on the wavelength of light used. From these measured fractional fringe values, the associated integral fringe order is determined. A method to construct a ready-reckoner table is also described which helps to identify the integral fringe order from any two measured fractional fringe values.

Boundedness of weakly singular integral operators on domains

The monograph dissertation deals with kernel integral operators and their mapping properties on Euclidean domains. The associated kernels are weakly singular and examples of such are given by Green functions of certain elliptic partial differential equations. It is well known that mapping properties of the corresponding Green operators can be used to deduce a priori estimates for the solutions of these equations. In the dissertation, natural size- and cancellation conditions are quantified for kernels defined in domains. These kernels induce integral operators which are then composed with any partial differential operator of prescribed order, depending on the size of the kernel. The main object of study in this dissertation being the boundedness properties of such compositions, the main result is the characterization of their Lp-boundedness on suitably regular domains. In case the aforementioned kernels are defined in the whole Euclidean space, their partial derivatives of prescribed order turn out to be so called standard kernels that arise in connection with singular integral operators. The Lp-boundedness of singular integrals is characterized by the T1 theorem, which is originally due to David and Journé and was published in 1984 (Ann. of Math. 120). The main result in the dissertation can be interpreted as a T1 theorem for weakly singular integral operators. The dissertation deals also with special convolution type weakly singular integral operators that are defined on Euclidean spaces.

Integral Transformations of Volterra Gaussian Processes

We study integral representations of Gaussian processes with a pre-specified law in terms of other Gaussian processes. The dissertation consists of an introduction and of four research articles. In the introduction, we provide an overview about Volterra Gaussian processes in general, and fractional Brownian motion in particular. In the first article, we derive a finite interval integral transformation, which changes fractional Brownian motion with a given Hurst index into fractional Brownian motion with an other Hurst index. Based on this transformation, we construct a prelimit which formally converges to an analogous, infinite interval integral transformation. In the second article, we prove this convergence rigorously and show that the infinite interval transformation is a direct consequence of the finite interval transformation. In the third article, we consider general Volterra Gaussian processes. We derive measure-preserving transformations of these processes and their inherently related bridges. Also, as a related result, we obtain a Fourier-Laguerre series expansion for the first Wiener chaos of a Gaussian martingale. In the fourth article, we derive a class of ergodic transformations of self-similar Volterra Gaussian processes.

Integral isobaric heat of vaporization of benzene-1,2-dichloroethane system

Abstract is not available.

R U there yet? using virtual classrooms to transform teaching practice

Access to quality higher education is challenging for many Western Australians that live outside the metropolitan area. In 2010, the School of Education moved to flexible delivery of a fully online Bachelor of Education degree for their non -metropolitan students. The new model of delivery allows access for students from any location provided they have a computer and an internet connection. A number of academic staff had previously used an asynchronous environment to deliver learning modules housed within a learning management system (LMS) but had not used synchronous software with their students. To enhance the learning environment and to provide high quality learning experiences to students learning at a distance, the adoption of synchronous software (Elluminate Live) was introduced. This software is a real-time virtual classroom environment that allows for communication through Voice over Internet Protocol (VoIP) and videoconferencing, along with a large number of collaboration tools to engage learners. This research paper reports on the integration of a live e-learning solution into the current LMS environment. Qualitative data were collected from academic staff through informal interviews and participant observation. The findings discuss (i) perceived level of support; (ii) identification of strategies used to create an effective online teacher presence; (iii) the perceived impact on the students' learning outcomes; and (iv) guidelines for professional development to enhance pedagogy within the live e-learning environment.

Fourier transform of the collagen triple-helical structure and its significance

The Fourier transforms of the collagen molecular structure have been calculated taking into consideration various side chain atoms, as well as the presence of bound water molecules. There is no significant change in the calculated intensity distribution on including the side chain atoms of non-imino-acid residues. Taking into account the presence of about two bound water molecules per tripeptide unit, the agreement with the observed x-ray pattern is slightly improved. Fourier transforms have also been calculated for the detailed molecular geometries proposed from other laboratories. It is found that there are no major differences between them, as compared to our structure, either in the positions of peak intensity or in the intensity distribution. Hence it is not possible to judge the relative merits of the various molecular geometries for the collagen triple helix from a comparison of the calculated transforms with the meagre data available from its x-ray fibre pattern. It is also concluded that the collagen molecular structure should be regarded as a somewhat flexible chain structure, capable of adapting itself to the requirements of the different side groups which occur in each local region.

Two Stage Transform Vector Quantization of LSFs for Wideband Speech Coding

We investigate the use of a two stage transform vector quantizer (TSTVQ) for coding of line spectral frequency (LSF) parameters in wideband speech coding. The first stage quantizer of TSTVQ, provides better matching of source distribution and the second stage quantizer provides additional coding gain through using an individual cluster specific decorrelating transform and variance normalization. Further coding gain is shown to be achieved by exploiting the slow time-varying nature of speech spectra and thus using inter-frame cluster continuity (ICC) property in the first stage of TSTVQ method. The proposed method saves 3-4 bits and reduces the computational complexity by 58-66%, compared to the traditional split vector quantizer (SVQ), but at the expense of 1.5-2.5 times of memory.

Review of continuum, finite element and hybrid techniques in the analysis of stress concentrations in structures

When a uniform flow of any nature is interrupted, the readjustment of the flow results in concentrations and rare-factions, so that the peak value of the flow parameter will be higher than that which an elementary computation would suggest. When stress flow in a structure is interrupted, there are stress concentrations. These are generally localized and often large, in relation to the values indicated by simple equilibrium calculations. With the advent of the industrial revolution, dynamic and repeated loading of materials had become commonplace in engine parts and fast moving vehicles of locomotion. This led to serious fatigue failures arising from stress concentrations. Also, many metal forming processes, fabrication techniques and weak-link type safety systems benefit substantially from the intelligent use or avoidance, as appropriate, of stress concentrations. As a result, in the last 80 years, the study and and evaluation of stress concentrations has been a primary objective in the study of solid mechanics. Exact mathematical analysis of stress concentrations in finite bodies presents considerable difficulty for all but a few problems of infinite fields, concentric annuli and the like, treated under the presumption of small deformation, linear elasticity. A whole series of techniques have been developed to deal with different classes of shapes and domains, causes and sources of concentration, material behaviour, phenomenological formulation, etc. These include real and complex functions, conformal mapping, transform techniques, integral equations, finite differences and relaxation, and, more recently, the finite element methods. With the advent of large high speed computers, development of finite element concepts and a good understanding of functional analysis, it is now, in principle, possible to obtain with economy satisfactory solutions to a whole range of concentration problems by intelligently combining theory and computer application. An example is the hybridization of continuum concepts with computer based finite element formulations. This new situation also makes possible a more direct approach to the problem of design which is the primary purpose of most engineering analyses. The trend would appear to be clear: the computer will shape the theory, analysis and design.

Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.