On Games on Non-Wellfounded Sets and Stationary Sets

In this thesis we study a few games related to non-wellfounded and stationary sets. Games have turned out to be an important tool in mathematical logic ranging from semantic games defining the truth of a sentence in a given logic to for example games on real numbers whose determinacies have important effects on the consistency of certain large cardinal assumptions. The equality of non-wellfounded sets can be determined by a so called bisimulation game already used to identify processes in theoretical computer science and possible world models for modal logic. Here we present a game to classify non-wellfounded sets according to their branching structure. We also study games on stationary sets moving back to classical wellfounded set theory. We also describe a way to approximate non-wellfounded sets with hereditarily finite wellfounded sets. The framework used to do this is domain theory. In the Banach-Mazur game, also called the ideal game, the players play a descending sequence of stationary sets and the second player tries to keep their intersection stationary. The game is connected to precipitousness of the corresponding ideal. In the pressing down game first player plays regressive functions defined on stationary sets and the second player responds with a stationary set where the function is constant trying to keep the intersection stationary. This game has applications in model theory to the determinacy of the Ehrenfeucht-Fraisse game. We show that it is consistent that these games are not equivalent.

Radiation induced depinning of a charge density wave system

The frequency-dependent response of a pinned charge density wave is considered in terms of forced vibration of an oscillator held in an anharmonic well. It is shown that the effective pinning-frequency can be reduced by applying a d.c. field. If a strong a.c. field, superposed on a d.c. field is applied on such a system “jumps” can be observed in the frequency dependent response of the system. The conditions at which these “jumps” occur are investigated with reference to NbSe3. The possibility of observing such phenomena in other systems like superionic conductors, non-linear dielectrics like ferroelectrics is pointed out. The characteristics are expressed in terms of some “scaled variables” — in terms of which the characteristics show a universal behaviour

An evaluation of the components of a proposed perimeter baiting system for cucumber fly, Bactrocera cucumis

Management of cucumber fly (Bactrocera cucumis) has relied heavily on cover sprays of broad spectrum insecticides such as dimethoate and fenthion. Long term access to these insecticides is uncertain, and their use can disrupt integrated pest management programs for other pests such as whitefly, aphids and mites. Application of a protein bait spray for fruit fly control is common practice in tree crops. However, vegetable crops present different challenges as fruit flies are thought to enter these crops only to oviposit, spending the majority of their time in roosting sites outside of the cropping area. Perimeter baiting of non-crop vegetation was developed overseas as a technique for control of melon fly (B. cucurbitae) in cucurbits in Hawaii. More recent work has refined the technique further, with certain types of perimeter vegetation proving more attractive to melon fly than the sorghum or corn crops which are commonly utilised. Trials were performed to investigate the potential of developing a similar system for cucumber fly. Commercially available fruit fly baits were compared for attractiveness to cucumber fly. Eight plant species were evaluated for their relative attractiveness to cucumber flies as roosting sites. Differences were observed in the number of flies feeding at protein bait applied to each of the plants. Results are discussed in the context of the development of a perimeter baiting system for cucumber fly in cucurbit crops.

The mating system of the true fruit fly Bactrocera tryoniand its sister-species,Bactrocera neohumeralis

The frugivorous ‘true’ fruit fly, Bactrocera tryoni (Queensland fruit fly), is presumed to have a non-resourced-based lek mating system. This is largely untested, and contrary data exists to suggest Bactrocera tryoni may have a resource-based mating system focused on fruiting host plants. We tested the mating system of Bactrocera tryoni, and its close sibling Bactrocera neohumeralis, in large field cages using laboratory reared flies. We used observational experiments that allowed us to determine if: (i) mating pairs were aggregated or non-aggregated; (ii) mating system was resource or non-resource based; (iii) flies utilised possible landmarks (tall trees over short) as mate-rendezvous sites; and (iv) males called females from male-dominated leks. We recorded nearly 250 Bactrocera tryoni mating pairs across all experiments, revealing that: (i) mating pairs were aggregated; (ii) mating nearly always occurred in tall trees over short; (iii) mating was non-resource based; and (iv) that males and females arrived at the mate-rendezvous site together with no evidence that males preceded females. Bactrocera neohumeralis copulations were much more infrequent (only 30 mating pairs in total), but for those pairs there was a similar preference for tall trees and no evidence of a resource-based mating system. Some aspects of Bactrocera tryoni mating behaviour align with theoretical expectations of a lekking system, but others do not. Until evidence for unequivocal female choice can be provided (as predicted under a true lek), the mating system of Bactrocera tryoni is best described as a non-resource based, aggregation system for which we also have evidence that land-marking may be involved. This article is protected by copyright. All rights reserved

Assessing the integrated sustainability of a public rental housing project from the perspective of complex eco-system

Public rental housing (PRH) projects are the mainstream of China's new affordable housing policies, and their integrated sustainability has a far-reaching effect on medium-low income families' well-being and social stability. However, there are few quantitative researches on the integrated sustainability of PRH projects. Our study tries to fill this gap through proposing an assessment model of the integrated sustainability for PRH projects. First, this paper defines what the sustainability of a PRH project is. Second, after constructing the sustainable system of a PRH project from the perspective of complex eco-system, the paper explores the internal operation mechanism and the coupling mechanism among the ecological, economic and social subsystems. Third, it identifies fourteen indices to represent the sustainability system of a PRH project, including six indices of ecological subsystem, five of economic subsystem and three of social subsystem. Fourth, it qualifies the weights of three subsystems and their internal representative indices. In addition, an assessment model is established through expert surveys and analytic network process (ANP). Finally, the paper carries out an empirical research on a PRH project in Nanjing city of China, followed by suggestions to enhance the integrated sustainability. The sustainability system and its evaluation model proposed in this paper are concise and easy to understand and can provide a theoretical foundation and a scientific basis for the evaluation and optimization of PRH projects.

Transient response of coupled non-linear non-conservative systems

This paper deals with an approximate method of analysis of non-linear, non-conservative systems of two degrees of freedom. The approximate equations for amplitude and phase are obtained by a generalized averaging technique based on the ultraspherical polynomial approximation. The method is illustrated by an example of a spring-mass-damper system.

Non-linear response of a gyrostabilized platform to transient input

In this paper the response of a gyrostabilized platform subjected to a transient torque has been analyzed by deliberately introducing non-linearity into the command of the servomotor. The resulting third-order non-linear differential equation has been solved by using a transformation technique involving the displacement variable. The condition under which platform oscillations may grow with time or die with time are important from the point of view of platform stabilization. The effect of deliberate addition of non-linearity with a view to achieving the ideal response—that is, to bring the platform back to its equilibrium position with as few oscillations as possible—has been investigated. The conditions under which instability may set in on account of the small transient input and small non-linearity has also been discussed. The analysis is illustrated by means of a numerical example. The results of analysis are compared with numerical solutions obtained on a digital computer.

Construction of stability multipliers for non-linear feedback systems

This paper is concerned with the analysis of the absolute stability of a non-linear autonomous system which consists of a single non-linearity belonging to a particular class, in an otherwise linear feedback loop. It is motivated from the earlier Popovlike frequency-domain criteria using the ' multiplier ' eoncept and involves the construction of ' stability multipliers' with prescribed phase characteristics. A few computer-based methods by which this problem can be solved are indicated and it is shown that this constitutes a stop-by-step procedure for testing the stability properties of a given system.

Characterization of vitamin A transport system from goat plasma

Retinol-binding protein and its complex with prealbumin were isolated from goat serum by chromatography on DEAE-Sephadex A-50, gel filtration and immuno-affinity chromatography on antigoat-serum albumin-Sepharose 4B. The homogeneous prealbumin-retinol-binding protein complex had a molecular weight of 75 000. Both on electrophoresis and in the presence of 2 M urea, the complex dissociated into retinol-binding protein and prealbumin. The molecular weight, electrophoretic behaviour, ultraviolet and fluorescence spectra of goat retinol-binding protein were similar to those isolated from other sources. On sodium dodecyl sulphate gel electrophoresis, goat prealbumin (molecular weight ≈ 55 000) exhibited two bands corresponding to molecular weights 26 000 and 13 000. This suggests that either goat prealbumin consists of two non-identical sub-units or perhaps complete dissociation might not have occurred. Goat prealbumin was able to bind Image -thyroxine and retinol-binding protein.

Effects of 17α-ethinyl estradiol on the mating system of the sand goby (Pomatoschistus minutus)

In aquatic environments, endocrine disrupting chemicals (EDCs) that interfere with the endocrinology of males and females form a threat to the maintenance of populations. EDCs are a diverse group of natural and manmade chemicals that already at very low concentrations (at nanogram levels) can have severe effects on reproduction by individuals, e.g. complete sex reversal, feminisation of males, impaired reproduction even resulting in near extinction of populations. With regard to fish, despite the extensive literature on physiological effects of EDCs, very little is known about potential population-level effects. In this thesis, I examined how 17α-ethinyl estradiol (EE2), a synthetic estrogen used in oral contraceptive pills, affects the reproductive behaviour of a marine fish, the sand goby (Pomatoschistus minutus). The aims were fourfold. First, I investigated how exposure to EE2 affects courtship and parental care of sand goby males. Secondly, I looked at effects on the mating system and sexual selection. In the third study, I observed the effects of exposure in a social context where exposed males had to compete with non-exposed males for resources and mates. Finally, I studied the effects of exposure on male-male competition and male aggressive behaviour. This work revealed that EE2 exposure impairs the ability of males to acquire and defend a nest, as well as diminishes the attractiveness of males to females by decreasing their courtship and aggressive behaviour. These effects are harmful for a male whose reproductive success is determined by the ability to compete for limited resources and to attract mates. Furthermore, this thesis showed that selection on male size was relaxed after EE2 exposure and male size had a smaller effect on mating success. These effects can be of a profound nature as they interfere with sexual selection, and may in the long run lead to the loss of traits maintained through sexual selection. The thesis shows that an exposure to environmentally relevant levels of EE2 clearly reduces the chances of individuals to reproduce successfully. Furthermore, it strongly suggests that several types of biomarkers should be used to detect and assess the effects of EDC exposure because severe behavioural effects can sometimes be seen before effects are detectable at the molecular or morphometric level. Behavioural assays should be considered an important complementary tool for the standard ecotoxicological assays because observed behavioural changes have direct and negative effects on fitness, while the connection between changes in molecular expression and fitness may be less obvious.

Decoupling in non-linear systems with two degrees of freedom

The problem of decoupling a class of non-linear two degrees of freedom systems is studied. The coupled non-linear differential equations of motion of the system are shown to be equivalent to a pair of uncoupled equations. This equivalence is established through transformation techniques involving the transformation of both the dependent and independent variables. The sufficient conditions on the form of the non-linearity, for the case wherein the transformed equations are linear, are presented. Several particular cases of interest are also illustrated.

Non-linear systems with quadratic and cubic damping - an analytical approach

The possible equivalence of second-order non-linear systems having quadratic and cubic damping with third-order linear systems is studied in this paper. It is shown that this equivalence can be established through transformation techniques under certain constraints on the form of the non-linearity of the given system.

On the positivity and stability of non-stationary systems

The positivity of operators in Hilbert spaces is an important concept finding wide application in various branches of Mathematical System Theory. A frequency- domain condition that ensures the positivity of time-varying operators in L2 with a state-space description, is derived in this paper by using certain newly developed inequalities concerning the input-state relation of such operators. As an interesting application of these results, an L2 stability criterion for time-varying feedback systems consisting of a finite-sector non-linearity is also developed.

Theory of Non-linear Waves in Multi-dimensions: with Special Reference to Surface Water Waves

The surface water waves are "modal" waves in which the "physical space" (t, x, y, z) is the product of a propagation space (t, x, y) and a cross space, the z-axis in the vertical direction. We have derived a new set of equations for the long waves in shallow water in the propagation space. When the ratio of the amplitude of the disturbance to the depth of the water is small, these equations reduce to the equations derived by Whitham (1967) by the variational principle. Then we have derived a single equation in (t, x, y)-space which is a generalization of the fourth order Boussinesq equation for one-dimensional waves. In the neighbourhood of a wave froat, this equation reduces to the multidimensional generalization of the KdV equation derived by Shen & Keller (1973). We have also included a systematic discussion of the orders of the various non-dimensional parameters. This is followed by a presentation of a general theory of approximating a system of quasi-linear equations following one of the modes. When we apply this general method to the surface water wave equations in the propagation space, we get the Shen-Keller equation.

The non-linear response of a gyrostabilized platform: Effects of correction torque time delay and of random inputs

First, the non-linear response of a gyrostabilized platform to a small constant input torque is analyzed in respect to the effect of the time delay (inherent or deliberately introduced) in the correction torque supplied by the servomotor, which itself may be non-linear to a certain extent. The equation of motion of the platform system is a third order nonlinear non-homogeneous differential equation. An approximate analytical method of solution of this equation is utilized. The value of the delay at which the platform response becomes unstable has been calculated by using this approximate analytical method. The procedure is illustrated by means of a numerical example. Second, the non-linear response of the platform to a random input has been obtained. The effects of several types of non-linearity on reducing the level of the mean square response have been investigated, by applying the technique of equivalent linearization and solving the resulting integral equations by using laguerre or Gaussian integration techniques. The mean square responses to white noise and band limited white noise, for various values of the non-linear parameter and for different types of non-linearity function, have been obtained. For positive values of the non-linear parameter the levels of the non-linear mean square responses to both white noise and band-limited white noise are low as compared to the linear mean square response. For negative values of the non-linear parameter the level of the non-linear mean square response at first increases slowly with increasing values of the non-linear parameter and then suddenly jumps to a high level, at a certain value of the non-linearity parameter.