Browsing by Author "Baboolal, Deeva Lata."

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A 40,000-year record of vegetation and fire history from the Tate Vondo region, Northeastern Southpansberg, South Africa.
(2014) Baboolal, Deeva Lata.; Finch, Jemma M.
Records from the Quaternary period are used to confirm possible inferred climatic changes, reveal the responses of species to these changes, and serve as an archive against which modern environmental dynamics can be assessed. Fueled by a need to understand current climatic changes, the call for palaeoclimatic research in the southern African subregion has become more compelling. In southern Africa, such research has been largely restricted to springs and swamps as the subregion lacks natural lakes, with some exception of a few coastal lakes such as Lake Sibaya and Lake Eteza. Due to the arid and semi-arid landscapes which prevail in southern Africa, there is a paucity of suitable sedimentary deposits in the region. The highly organic peat deposit of Mutale Wetland, situated in the Tate Vondo region of the northeastern Soutpansberg presents an ideal opportunity for conducting palaeoenvironmental research. The Mutale Wetland contains relatively old sediments dating back to >30,000 cal years BP, placing this record within the late Quaternary period. Palaeoenvironmental techniques including radiocarbon, pollen and charcoal analyses were applied to produce a palaeoenvironmental reconstruction for Tate Vondo. A 302 cm sedimentary core was extracted from the Mutale Wetland. Detailed analyses show that prior to ca. 34,000 cal yr BP, conditions were fairly warm and dry. This is inferred from a dominance of open grassland vegetation. An expansion of Podocarpus forests together with an increase in fynbos elements suggest a shift to cool, subhumid conditions during the LGM. Cooler conditions persisted until ca. 12,000 cal yr BP. Thereafter, a climatic amelioration was experienced. The appearance of low charcoal concentrations throughout the late Pleistocene suggests that fire was infrequent. Between ca. 4000 – 1500 cal yr BP, conditions became warmer and drier, inferred from the development of arid savanna vegetation. The sharp increase in charcoal after ca. 4000 cal yr BP, broadly coinciding with the arrival of the first agriculturalists in the area, has implications for the history of human occupation in the Soutpansberg rather than shifts in climate. The succession from savanna to fynbos vegetation together with expanded forests implies a return to cool and moist conditions from ca. 1500 – 400 cal yr BP. Arid savanna persists from ca. 400 to the present, implying warmer and drier conditions towards the present day. Furthermore, from ca. 400 cal yr BP, the pollen and charcoal record indicate that the majority of recent changes in vegetation have been driven by anthropogenic activity. This record has contributed to an improved understanding of late Quaternary changes in climate, vegetation history and human impact in the northeastern Soutpansberg.
Completion of uniform and metric frames.
(1996) Murugan, Umesperan Goonaselan.; Baboolal, Deeva Lata.
The term "frame" was introduced by C H Dowker, who studied them in a long series of joint papers with D Papert Strauss. J R Isbell , in a path breaking paper [1972] pointed out the need to introduce separate terminology for the opposite of the category of Frames and coined the term "locale". He was the progenitor of the idea that the category of Locales is actually more convenient in many ways than the category of Frames. In fact, this proves to be the case in one of the approaches adopted in this thesis. Sublocales (quotient frames) have been studied by several authors, notably Dowker and Papert [1966] and Isbell [1972]. The term "sublocale" is due to Isbell, who also used "part " to mean approximately the same thing. The use of nuclei as a tool for studying sublocales (as is used in this thesis) and the term "nucleus" itself was initiated by H Simmons [1978] and his student D Macnab [1981]. Uniform spaces were introduced by Weil [1937]. Isbell [1958] studied algebras of uniformly continuous functions on uniform spaces. In this thesis, we introduce the concept of a uniform frame (locale) which has attracted much interest recently and here too Isbell [1972] has some results of interest. The notion of a metric frame was introduced by A Pultr [1984]. The main aim of his paper [11] was to prove metrization theorems for pointless uniformities. This thesis focuses on the construction of completions in Uniform Frames and Metric Frames. Isbell [6] showed the existence of completions using a frame of certain filters. We describe the completion of a frame L as a quotient of the uniformly regular ideals of L, as expounded by Banaschewski and Pultr[3]. Then we give a substantially more elegant construction of the completion of a uniform frame (locale) as a suitable quotient of the frame of all downsets of L. This approach is attributable to Kriz[9]. Finally, we show that every metric frame has a unique completion, as outlined by Banaschewski and Pultr[4]. In the main, this thesis is a standard exposition of known, but scattered material. Throughout the thesis, choice principles such as C.D.C (Countable Dependent Choice) are used and generally without mention. The treatment of category theory (which is used freely throughout this thesis) is not self-contained. Numbers in brackets refer to the bibliography at the end of the thesis. We will use 0 to indicate the end of proofs of lemmas, theorems and propositions. Chapter 1 covers some basic definitions on frames , which will be utilized in subsequent chapters. We will verify whatever we need in an endeavour to enhance clarity. We define the categories, Frm of frames and frame homomorphisms, and Lac the category of locales and frame morphisms. Then we explicate the adjoint situation that exists between Frm and Top , the category of topological spaces and continuous functions. This is followed by an introduction to the categories, RegFrm of all regular frames and frame homomorphisms, and KRegFrm the category of compact regular frames and their homomorphisms. We then present the proofs of two very important lemmas in these categories. Finally, we define the compactification of and a congruence on a frame. In Chapter 2 we recall some basic definitions of covers, refinements and star refinements of covers. We introduce the notion of a uniform frame and define certain mappings (morphisms) between uniform frames (locales) . In the terminology of Banaschewski and Kriz [9] we define a complete uniform frame and the completion of a uniform frame. The aim of Chapter 3 is twofold : first, to construct the compact regular coreflection of uniform frames , that is, the frame counterpart of the Samuel Compactification of uniform spaces [12] , and then to use it for a description of the completion of a uniform frame as an alternative to that previously given by Isbell[6]. The main purpose of Chapter 4 is to provide another description of uniform completion in frames (locales), which is in fact even more straightforward than the original topological construction. It simply consists of writing down generators and defining relations. We provide a detailed examination of the main result in this section, that is, a uniform frame L is complete of each uniform embedding f : (M,UM) -t (L,UL) is closed, where UM and UL denote the uniformities on the frames M and L respectively. Finally, in Chapter 5, we introduce the notions of a metric diameter and a metric frame. Using the fact that every metric frame is a uniform frame and hence has a uniform completion, we show that every metric frame L has a unique completion : CL - L.
Locally finite nearness frames.
(1998) Naidoo, Inderasan.; Baboolal, Deeva Lata.; Ori, Ramesh G.
The concept of a frame was introduced in the mid-sixties by Dowker and Papert. Since then frames have been extensively studied by several authors, including Banaschewski, Pultr and Baboolal to mention a few. The idea of a nearness was first introduced by H. Herrlich in 1972 and that of a nearness frame by Banaschewski in the late eighties. T. Dube made a fairly detailed study of the latter concept. The purpose of this thesis is to study the property of local finiteness and metacompactness in the setting of nearness frames. J. W. Carlson studied these ideas (including Lindelof and Pervin nearness structures) in the realm of nearness spaces. The first four chapters are a brief overview of frame theory culminating in results concerning regular, completely regular, normal and compact frames. In chapter five we provide the definitions for various nearness frames: Pervin, Lindelof , Locally Finite and Metacompact to mention a few. A particular locally finite nearness structure, denoted by µLF, is studied in detail. It is defined to be the nearness structure on a regular frame L generated by the family of all locally finite covers on the frame L. Also, a particular metacompact nearness structure, denoted by µPF, is studied in detail. It is defined to be the nearness structure on a regular frame L generated by the family of all point-finite covers of the frame L. Various theorems related the above nearness frames and these nearness structures are obtained.