Ordinary differential equations of various types appear in the mathematical modelling in mechanics. Differential equations obtained are usually rather complicated nonlinear equations. However, using suitable approximations of nonlinearities, one can derive simple equations that are either well known or can be studied analytically. An example of such "approximative" equation is the so-called Duffing equation. Hence, the question on the existence of a periodic solution to the Duffing equation is closely related to the existence of periodic vibrations of the corresponding nonlinear oscillator.

This paper investigates whether East Asians are more likely than Westerners to purchase a brand presented as a best-seller given that East Asians tend to have a higher need for conformity and Westerners tend to have a higher need for uniqueness. Results show that East Asians are more likely than their Western counterparts to purchase such brands when the perceived risk is low. However, when the perceived risk is high, both East Asians and Westerners tend to prefer a brand presented as a best-seller. Results also show that, in a three-option set in which the C option is dominated by the B option but not by the A, both East Asians and Westerners are more likely to select option C when it is presented as a best-seller than when it is not. Managerial implications and the study's limitations are also discussed.

Magister Theologiae - MTh / This study begins by recognising the religiously plural context in which the Christian churches currently exist. It discusses the various forces that impel the churches towards recognition of and dialogue with those of other faiths, as well as factors that hinder this process. It mentions a variety of ways in which theology - in particular, the theological understanding of the relationship between the Christian churches and other faith communities - is influenced by its context. In an attempt to identify a model within the Judaeo-Christian tradition that will provide a basis for inter-faith dialogue, the study proposes an exploration of the relationship between Yahweh and the gods of the nations as reflected in the the prophetic writings known as Deutero- and Trito-Isaiah, writings that almost certainly emerged from two particular periods in the history of the people of lsrael: the Babylonian exile and the early post-exilic period in Palestine. The study outlines historical developments within these two periods. It explores the various religious beliefs - Babylonian, Palestinian and Persian - that together formed the multi-faith context for Deutero- and Trito-Isaiah.

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We consider the flow of nonlinear Maxwell fluids in the unsteady quasistatic case, where the effect of inertia is neglected. We study the well-posedness of the resulting PDE initial-boundary value problem. This well-posedness depends on the unique solvability of an elliptic boundary value problem. We first present results for the 3D case, locally and globally in time, with sufficiently small initial data, and for a simple shear flow problem, locally in time with arbitrary initial data; after that we extend our results to some 3D flow problems, locally in time, with large initial data. Additionally, we present results for models of White-Metzner type in 3D flow, locally and globally in time, with sufficiently small initial data. We solve our problem using an iteration between elliptic and hyperbolic linear subproblems. The limit of the iteration provides the solution of our original problem. / Ph. D.

Understanding the unequal distribution of life on earth is a fundamental goal of ecology and evolutionary biology. Past efforts to explain large-scale patterns in diversity have tended to focus on two broad classes of explanation, one invoking the importance of abiotic factors (i.e. climate and vegetation) and the other biotic (i.e. competition); but neither has proven entirely adequate. Parasites are a major but poorly understood component of life that may offer some answers. Yet despite widespread theoretical support and some empirical evidence, the role of parasites in explaining patterns in the diversity, distribution, and abundance of species remains largely untested in natural communities. In this thesis I use a mega-diverse elevation gradient of birds as a model system to study the role of avian malaria in explaining these macroecological patterns. In the first data chapter I tested the extent to which patterns of infection across species is predictable. I found that the effects of host ecology and environment were weakly related to infection prevalence and were not consistent across different malaria lineages. Instead, I show that hosts coexisting with many close phylogenetic relatives consistently experience higher infection than evolutionarily distinct host species. In the second chapter I tested if parasite sharing may help explain these observed relationships and show that parasite sharing among host pairs declines with the time since divergence. Spatial contiguity between host pairs was also positively associated with parasite sharing. In the third chapter I tested how infection prevalence varies across species ranges in accordance with expected variation in host abundance. I show that birds are more likely to be infected at the centre of their elevation range, where host abundance is expected to be highest. Intriguingly, I also found that the incidence of host infection is unrelated to the position within the geographic range of the parasite. In the fourth data chapter, I tested whether parasites may regulate diversity by limiting geographic ranges of their hosts through ‘apparent competition’ in which a non-lethal parasite in a primary host, may be lethal in a secondary host. In support of this, I found that more observed bird ranges end at parasite infection zones than would be expected by chance. Taken together, my results suggest that parasites may play a major role in shaping patterns in the distribution and diversity of species, over both ecological and evolutionary scales. This is likely to arise and be maintained by host parasite interactions in which distantly related hosts are less likely to be infected by local parasites than close relatives, thus promoting the build up of diversity locally. On the basis of my analyses, I conclude that across montane elevation gradients in birds, and across diversity gradients more generally, parasites are likely to play a crucial role in the origin and maintenance of high biological diversity.

This manuscript demonstrates the regularity and uniqueness of some geometric heat flows with critical nonlinearity. First, under the assumption of smallness of renormalized energy, several issues of the regularity and uniqueness of heat flow of harmonic maps into a unit sphere or a compact Riemannian homogeneous manifold without boundary are established. For a class of heat flow of harmonic maps to any compact Riemannian manifold without boundary, satisfying the Serrin's condition, the regularity and uniqueness is also established. As an application, the hydrodynamic flow of nematic liquid crystals in Serrin's class is proved to be regular and unique. The natural extension of all the results to the heat flow of biharmonic maps is also presented in this manuscript.

在這篇論文裡，我們利用值分佈理論來探討兩個半純函數何時會相等，進而了解兩個半純函數滿足某一函數方程時，其關係為何。最後，我們探討兩個半純函數共四個少函數且擁有少量的極點之相關性質。 / In this thesis, we use the theory of value distribution to study the uniqueness problems of two meromorphic functions and the relation of two meromorphic functions satisfying some functional equations. Also we prove some uniqueness results on two meromorphic functions with few poles sharing four small functions.

Conditions under which compositions of component systems form a well-defined system-of-systems are here formulated at a fundamental level. Statement of what defines a well-defined composition and sufficient conditions guaranteeing such a result offers insight into exemplars that can be found in special cases such as differential equation and discrete event systems. For any given global state of a composition, two requirements can be stated informally as: (1) the system can leave this state, i.e., there is at least one trajectory defined that starts from the state; and (2) the trajectory evolves over time without getting stuck at a point in time. Considered for every global state, these conditions determine whether the resultant is a well-defined system and, if so, whether it is non-deterministic or deterministic. We formulate these questions within the framework of iterative specifications for mathematical system models that are shown to be behaviorally equivalent to the Discrete Event System Specification (DEVS) formalism. This formalization supports definitions and proofs of the afore-mentioned conditions. Implications are drawn at the fundamental level of existence where the emergence of a system from an assemblage of components can be characterized. We focus on systems with feedback coupling where existence and uniqueness of solutions is problematic.