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.

Assessment of functional forms of crop yield loss models of invasive plant species applied in decision support tools and bioeconomic modelling

AbstractObjectives Decision support tools (DSTs) for invasive species management have had limited success in producing convincing results and meeting users' expectations. The problems could be linked to the functional form of model which represents the dynamic relationship between the invasive species and crop yield loss in the DSTs. The objectives of this study were: a) to compile and review the models tested on field experiments and applied to DSTs; and b) to do an empirical evaluation of some popular models and alternatives. Design and methods This study surveyed the literature and documented strengths and weaknesses of the functional forms of yield loss models. Some widely used models (linear, relative yield and hyperbolic models) and two potentially useful models (the double-scaled and density-scaled models) were evaluated for a wide range of weed densities, maximum potential yield loss and maximum yield loss per weed. Results Popular functional forms include hyperbolic, sigmoid, linear, quadratic and inverse models. Many basic models were modified to account for the effect of important factors (weather, tillage and growth stage of crop at weed emergence) influencing weed–crop interaction and to improve prediction accuracy. This limited their applicability for use in DSTs as they became less generalized in nature and often were applicable to a much narrower range of conditions than would be encountered in the use of DSTs. These factors' effects could be better accounted by using other techniques. Among the model empirically assessed, the linear model is a very simple model which appears to work well at sparse weed densities, but it produces unrealistic behaviour at high densities. The relative-yield model exhibits expected behaviour at high densities and high levels of maximum yield loss per weed but probably underestimates yield loss at low to intermediate densities. The hyperbolic model demonstrated reasonable behaviour at lower weed densities, but produced biologically unreasonable behaviour at low rates of loss per weed and high yield loss at the maximum weed density. The density-scaled model is not sensitive to the yield loss at maximum weed density in terms of the number of weeds that will produce a certain proportion of that maximum yield loss. The double-scaled model appeared to produce more robust estimates of the impact of weeds under a wide range of conditions. Conclusions Previously tested functional forms exhibit problems for use in DSTs for crop yield loss modelling. Of the models evaluated, the double-scaled model exhibits desirable qualitative behaviour under most circumstances.

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

Abstract is not available.

Germination Biology and Occurrence of Polyembryony in Two Forms of Cats Claw Creeper Vine, Dolichandra unguis-cati (Bignoniaceae): Implications for Its Invasiveness and Management

Cat’s claw creeper vine, Dolichandra unguis-cati (L.) Lohmann (syn. Macfadyena unguis-cati (L.) Gentry), is a major environmental weed in Australia. Two forms of the weed with distinctive leaf morphology and reproductive traits, including varying fruit size, occur in Queensland, Australia. The long pod form occurs in a few localities in Queensland, while the short pod form is widely distributed in Queensland and northern part of New South Wales. This investigation aimed to evaluate germination behavior and occurrence of polyembryony (production of multiple seedlings from a single seed) in the two forms of the weed. Seeds were germinated in growth chambers set to 10/20°C, 15/25°C, 20/30°C, 30/45°C and 25°C, representing ambient temperature conditions of the region. Germination and polyembryony were monitored over a period of 12 weeks. For all the treatments in this study, seeds from short pod plants exhibited significantly higher germination rates and higher occurrence of polyembryony than those from long pod plants. Seeds from long pod plants did not germinate at the lowest temperature of 10/20°C; in contrast, those of the short pod form germinated under this condition, albeit at a lower rate (reaching a maximum 45% germination at week 12). Results from this study could explain why the short pod form of D. unguis-cati is the more widely distributed plants in Australia, while the long pod is confined to a few localities. The results have implication in predicting future range of both forms of the invasive D. unguis-cati, as well as inform management decisions for control of the weed.

Reed-Muller Canonical Forms in Multivalued Logic

Canonical forms for m-valued functions referred to as m-Reed-Muller canonical (m-RMC) forms that are a generalization of RMC forms of two-valued functions are proposed. m-RMC forms are based on the operations ?m (addition mod m) and .m (multiplication mod m) and do not, as in the cases of the generalizations proposed in the literature, require an m-valued function for m not a power of a prime, to be expressed by a canonical form for M-valued functions, where M > m is a power of a prime. Methods of obtaining the m-RMC forms from the truth vector or the sum of products representation of an m-valued function are discussed. Using a generalization of the Boolean difference to m-valued logic, series expansions for m-valued functions are derived.

Two forms of methionyl-transfer RNA synthetase from Mycobacterium Smegmatis

Two methionyl-transfer RNA synthetases (A and B forms) have been isolated from Image . The homogeneous preparations of the enzymes showed 1500 fold increase in specific activity in aminoacylation of methionine specific tRNA. The A and B forms differed in their specificity of aminoacylation of tRNAmMet and tRNAfMet; enzyme B exhibited much higher specificity for tRNAfMet. The molecular activities of A and B enzymes for aminoacid and tRNA were identical. The turnover number for aminoacid was 27 fold greater than that for tRNA, while the Km values for tRNA were lower by a factor of 106 as compared to the aminoacid. Both the enzymes catalysed ATP-pyrophosphate exchange reaction to the same extent.

Relation between Chandrasekhar's X-function and the eigenvalues of integral operators with difference kernels

Abstract is not available.

Polyvanadate-stimulated NADH oxidation by plasma membranes-The need for a mixture of deca and meta forms of vanadate

Polyvanadate solutions obtained by extracting vanadium pentoxide with dilute alkali over a period of several hours contained increasing amounts of decavanadate as characterized by NMR and ir spectra. Those solutions having a metavanadate:decavanadate ratio in the range of 1-5 showed maximum stimulation of NADH oxidation by rat liver plasma membranes. Reduction of decavanadate, but not metavanadate, was obtained only in the presence of the plasma membrane enzyme system. High simulation of activity of NADH oxidation was obtained with a mixture of the two forms of vanadate and this further increased on lowering the pH. Addition of increasing concentrations of decavanadate to metavanadate and vice versa increased the stimulatory activity, reaching a maximum when the metavanadate:decavanadate ratio was in the range of 1-5. Increased stimulatory activity can also be obtained by reaching these ratios by conversion of decavanadate to metavanadate by alkaline phosphate degradation, and of metavanadate to decavanadate by acidification. These studies show for the first time that both deca and meta forms of vanadate present in polyvanadate solutions are needed for maximum activity of NADH oxidation.