Distribution of black nodes at various levels in a linear quadtree

The distribution of black leaf nodes at each level of a linear quadtree is of significant interest in the context of estimation of time and space complexities of linear quadtree based algorithms. The maximum number of black nodes of a given level that can be fitted in a square grid of size 2n × 2n can readily be estimated from the ratio of areas. We show that the actual value of the maximum number of nodes of a level is much less than the maximum obtained from the ratio of the areas. This is due to the fact that the number of nodes possible at a level k, 0≤k≤n − 1, should consider the sum of areas occupied by the actual number of nodes present at levels k + 1, k + 2, …, n − 1.

The paribhasas arthavadgrahane nanarthakasya, laksanapratipadoktayoh pratipadoktasyaiva grahanam and ekadesavikrtam ananyavat : Studies on some Metarules in Paninian system

In his grammatical treatise, the Astadhyayi, Panini includes sutras that state guiding rules for the right interpretation and application of his other directly grammatical sutras. These sutras are called paribhasas. In addition to these paribhasas, the various commentaries on Panini frequently invoke supplementary paribhasas which are not stated explicitly in his Astadhyayi. These paribhasas have been a subject of study since early times after Panini and have also occupied modern scholars on Panini s grammar. In regard to most of them, it remains unsettled even today whether they are used in the Astadhyayi, where they apply, what is their role, and whether they are necessary in arriving at the desired grammatical form. Some scholars go even further and argue that none of such paribhasas were intended by Panini. This study aims to settle this question by dealing with three such of these paribhasas individually considering all the information available in the commentaries in their regard and examining the cases in which, according to commentaries, the paribhasas apply. I select the paribhasas arthavadgrahane nanarthakasya, laksanapratipadoktayoh pratipadoktasyaiva grahanam and ekadesavikrtam ananyavat, which are all considered nyayasiddha or lokanyayasiddha; they express logical and obvious principles which are found in daily life. On this basis, Paniniyas explain why Panini did not mention them in the Astadhyayi. I discuss each paribhasa separately and all the issues it involves. I present and explain the cases where the specified paribhasas are invoked in the major commentaries, the Mahabhasya, the Kasika and the Siddhantakaumudi and the arguments found in the commentaries concerning these cases. If available, I supply other solutions to the difficulties for which these paribhasas are invoked. The study aims to make the issue of these paribhasas clearer, which will help us to reach a solution to the key question, that is, whether Panini has presupposed them in his Astadhyayi. My study shows that Panini has presupposed the paribhasa ekadesavikrtam ananyavat (or a similar principle). He also may have used the paribhasa arthavadgrahane nanarthakasya (or a similar principle) as this paribhasa does not lead to undesired results. As for the paribhasa laksanapratipadoktayoh pratipadoktasyaiva grahanam (or a similar principle), the original scope of this paribhasa was clearly extended by later Paniniyas. Moreover, their interpretation of this paribhasa conflicts with Panini s procedure. If Panini has used this paribhasa, he has used it in a very limited way.

Scheme of squares: Part I. Systems formalism for potentiostatic studies

The so-called “Scheme of Squares”, displaying an interconnectivity of heterogeneous electron transfer and homogeneous (e.g., proton transfer) reactions, is analysed. Explicit expressions for the various partial currents under potentiostatic conditions are given. The formalism is applicable to several electrode geometries and models (e.g., semi-infinite linear diffusion, rotating disk electrodes, spherical or cylindrical systems) and the analysis is exact. The steady-state (t→∞) expressions for the current are directly given in terms of constant matrices whereas the transients are obtained as Laplace transforms that need to be inverted by approximation of numerical methods. The methodology employs a systems approach which replaces a system of partial differential equations (governing the concentrations of the several electroactive species) by an equivalent set of difference equations obeyed by the various partial currents.

Use of S1 nuclease and formamide in combination for the reassociation studies on GC-rich DNA

The optimal parameters in the use of nuclease S1 in DNA reassociation kinetics in the presence of formamide have been determined. The conditions are especially suitable for the study of DNA rich in mole percent GC. A 10-fold dilution of the reassociation samples leading to a decrease in both NaCl and formamide concentrations, consequently resulting in a lowering of Tm by only 1.5°C, and the S1 digestion at temperatures identical to the reassociation assay in order to retain the stability of the duplex, are two important aspects of this system. Under these conditions, the kinetics of reassociation followed the theoretically predicted pattern, while the earlier reported methods have shown lower values.

Body composition studies in cystic fibrosis and myelomeningocele

One of the major considerations of improving the management of many chronic diseases has been the realisation of the importance of nutrition, and, in children, the maintenance of normal growth. Cystic Fibrosis (CF) and Myelomeningocele (MMC) are two such disease states in which nutritional status has a significant effect on morbidity.

59Co NMR studies of the spin-state equilibria in rare-earth cobaltites

Hyperfine interaction parameters reveal differences in the nature of spin-state equilibria in the lighter and heavier rare-earth cobaltites; the crystal-field parameter is lower in the lighter cobaltites. Temperature variation of the quadrupolar coupling constant is also more marked in the lighter rare-earth cobaltites, with NdCoO3 showing evidence for a structural phase transition.

Left-handed helices for DNA: studies on poly[d(I-C)]

Earlier, we showed that, for the D form (n = 8 and h = 3.03 A, where n is number of nucleotide units per turn and h is height per nucleotide unit) of poly[d(A-T)], both right- and left-handed double helical models are stereochemically satisfactory and give good agreement with the observed fiber diffraction data. It was also noted that the conformations of the right- and left-handed D-DNA models are very similar to those of the right- and left-handed B-DNA models. This observation was consistent with the D leads to B transition in the solid phase. As a continuation of our earlier studies, we have carried out similar experiments with poly[d(I-C)]. We could obtain a crystalline D-form pattern (n = 8, h = 3.13 A) of the fiber at 75% relative humidity (r.h.); the hydrated (r.h. approximately equal to 95%) form of the same fiber gave the classical B-form pattern (n = 10, h = 3.40 A). In the present report, we show that both right- and left-handed double-helical models are consistent with the fiber diffraction data of poly[d(I-C)] in the D-form. Theoretical energy calculations also suggest that the right- and left-handed B- and D-DNA models are almost equally stable. Hence, we conclude that the right- and left-handed double-helical models of poly[d(I-C)] in a given form (B or D) are equally likely and that the fiber diffraction data do not permit discrimination.

Agreement Patterns in English : Diachronic Corpus Studies on Common-Number Pronouns

This study reports a diachronic corpus investigation of common-number pronouns used to convey unknown or otherwise unspecified reference. The study charts agreement patterns in these pronouns in various diachronic and synchronic corpora. The objective is to provide base-line data on variant frequencies and distributions in the history of English, as there are no previous systematic corpus-based observations on this topic. This study seeks to answer the questions of how pronoun use is linked with the overall typological development in English and how their diachronic evolution is embedded in the linguistic and social structures in which they are used. The theoretical framework draws on corpus linguistics and historical sociolinguistics, grammaticalisation, diachronic typology, and multivariate analysis of modelling sociolinguistic variation. The method employs quantitative corpus analyses from two main electronic corpora, one from Modern English and the other from Present-day English. The Modern English material is the Corpus of Early English Correspondence, and the time frame covered is 1500-1800. The written component of the British National Corpus is used in the Present-day English investigations. In addition, the study draws supplementary data from other electronic corpora. The material is used to compare the frequencies and distributions of common-number pronouns between these two time periods. The study limits the common-number uses to two subsystems, one anaphoric to grammatically singular antecedents and one cataphoric, in which the pronoun is followed by a relative clause. Various statistical tools are used to process the data, ranging from cross-tabulations to multivariate VARBRUL analyses in which the effects of sociolinguistic and systemic parameters are assessed to model their impact on the dependent variable. This study shows how one pronoun type has extended its uses in both subsystems, an increase linked with grammaticalisation and the changes in other pronouns in English through the centuries. The variationist sociolinguistic analysis charts how grammaticalisation in the subsystems is embedded in the linguistic and social structures in which the pronouns are used. The study suggests a scale of two statistical generalisations of various sociolinguistic factors which contribute to grammaticalisation and its embedding at various stages of the process.

Abductive translation studies : The art of marshalling signs

This dissertation contributes to the fields of theoretical translation studies, semiotic translation theory, and the semiotics of translation. The aim of this work is to explore the alternative and potential which the semiotic approaches to translation entail from the viewpoint of contemporary translation studies. The overall objective is thus to show that a general semiotic translation theory, and in particular, a Peircean translation theory, are possible and indispensable. Furthermore, this study contributes to the semiotranslational approach and to its theory-building by developing the concept of abductive translation (studies). The specific theoretical frame of reference adopted in this study is provided by the semiotranslation introduced by Dinda L. Gorlée. This approach is primarily based on the semeiotic of Charles Sanders Peirce (1839 1914), and aims at a fusion of semiotics and translation studies. A more general framework is provided by the threefold background and material: the published and unpublished writings of Peirce, Peirce scholarship and Peircean-semiotic publications, as well as the translation-theoretical literature. Part One of this study concentrates on the justification, existence, and nature of the semiotic approaches to translation. This part provides a historical survey, a status report, and a discussion of this area of research, by employing the findings in a boundary-clearing that is multilayered both conceptually and terminologically. Part Two deals with Peircean semiotranslation. Here Gorlée s semiotranslational research is examined by focusing on the starting points, features, and development of semiotranslation. Attention is also paid to the state-of-the-art of semiotranslation theory and to the possibilities for future elaborations. Part Three focuses on the semiotranslational claim that translation is an abductive activity. The concept of abductive translation is based on abduction, one of Peirce s three modes of reasoning; at the same time Firstness, the category of abduction, becomes foregrounded. So abductive translation as a form of possibilistic translation receives here an extensive theoretical discussion by citing examples in which abduction manifests itself as (scientific) reasoning and as everyday contemplation. During this treatise, translation is first equated with sign action, then with interpretation and finally with reasoning. All these approaches appear to embody different facets of the same phenomenon Peirce s ubiquitous semiosis, and they all suggest that translation is inherently an intersemiotic activity in which a sign is inferred from another sign. Translation is therefore semiosis, semiosis is translation and interpretation, interpretation is reasoning, and so on ad infinitum all being manifestations of the art of marshalling signs. The three parts of this study are linked by the overall goal of abductive translation studies: investigation into abductive translation develops the theory of semiotranslation, and this enrichment of semiotranslation in turn constructs a semiotic paradigm within translation studies.

Conformational analysis of small disulfide loops. Spectroscopic and theoretical studies on a synthetic cyclic tetrapeptide containing cystine

The conformational analysis of the synthetic peptide Boc-Cys-Pro-Val-Cys-NHMe has been carried out, as a model for small disulfide loops, in biologically active polypeptides. 'H NMR studies (270 MHz) establish that the Val(3) and Cys(4) NH groups are solvent shielded, while 13C studies establish an all-trans peptide backbone. Circular dichroism and Raman spectroscopy provide evidence for a right-handed twist of the disulfide bond. Analysis of the vicinal (JaB)c oupling constants for the two Cys residues establishes that XI - *60° for Cys(4), while some flexibility is suggested at Cys( 1). Conformational energy calculations, imposing intramolecular hydrogen bonding constraints, favor a P-turn (type I) structure with Pro(2)-Va1(3) as the corner residues. Theoretical and spectroscopic results are consistent with the presence of a transannular 4 - 1 hydrogen bond between Cys( 1) CO and Cys(4) NH groups, with the Val NH being sterically shielded from the solvent environment.

Photoelastic parametric studies of mode I stress intensity factors

Results of photoelastic investigations on single edge-notch tension specimens of varying notch angle and crack length are reported. The experimental results of Mode I stress intensity factors are compared with analytical results.

Studies in Nonlinear Optical Materials: Structure of 3-Menthyl 2-[Bis(dimethylarnino)methylene]-3-oxobutyrate Hemihydrate

C 19Ha4N203.~xH 2 O, Mr= 347.5, monoclinic, C2, a = 15.473 (3), b = 6.963 (2), c = 20.708 (4) ]1, //=108.2(2) ° , V=2119(2)A 3, Z=4, Ox= 1.089 Mg m -3, ,~(Cu Ktx) = 1.5418 ]1, p = 0.523 mm -~, F(000) = 760.0, T= 293 K, R = 0.068 for 1967 unique reflections. The C=C bond length is 1-447 (6)]1, significantly longer than in ethylene, 1.336 (2)]1. The crystal structure is stabilized by O-H...O hydrogen bonding. Explanation for the observed low second-harmonic-generation efficiency (0.5 times that of urea) is provided.

Maturation studies of pecan nuts grown in Queensland

Changes in chemical composition, physical and sensory characteristics were followed in two pecan cultivars Wichita and Western Schley harvested from a commercial orchard at Gatton in Queensland seven times during 1996.Testa colour of both pecan cultivars darkened and opalescence decreased as the nuts matured. Bitterness of Western Schley pecans decreased with maturity. Colour of shuck, shell and kernel of both cultivars developed as the nuts matured. Wichita pecans were larger than Western Schley at all harvest times. Both nut-in-shell and kernel moisture decreased with maturity, whereas oil and sucrose contents increased. Both pecan cultivars had reached advanced maturation by the first harvest on March 18.

Dynamics of plant populations in Heteropogon contortus(black speargrass) pastures on a granite landscape in southern Queensland. 2. Seed production and soil seed banks of H. contortus

Seed production and soil seed hanks of H. contortus were studied in a subset of treatments within an extensive grazing study conducted in H. contortus pasture in southern Queensland between 1990 and 1996. Seed production of H. contortus in autumn ranged from 260 to 1800 seeds/m2 with much of this variation due to differences in rainfall between years. Seed production was generally higher in the silver-leaved ironbark than in the narrow-leaved ironbark land class and was also influenced by a consistent stocking rate x pasture type interaction. Inflorescence density was the main factor contributing to the variable seed production and was related to the rainfall received during February. The number of seeds per inflorescence was unaffected by seasonal rainfall, landscape position, stocking rate or legume oversowing. Seed viability was related to the rainfall received during March. Soil seed banks in spring varied from 130 to 520 seeds/m2 between 1990 and 1995 with generally more seed present in the silver-leaved ironbark than in the narrow-leaved ironbark land class. There were poor relationships between viable seed production and the size of the soil seed bank, and between the size of the soil seed bank and seedling recruitment. This study indicates that H. contortus has the potential to produce relatively large amounts of seed and showed that the seasonal pattern of rainfall plays a major role in achieving this potential

Dynamics of plant populations in Heteropogon contortus(black speargrass) pastures on a granite landscape in southern Queensland. 1. Dynamics of H. contortus populations

The dynamics of Heteropogon contortus (black speargrass) populations were measured in a subset of treatments contained within an extensive grazing study conducted between 1990 and 1996 in H. contortus pasture in southern Queensland. This subset included 2 landscape positions and 3 stocking rates in both native pasture and legume-oversown native pasture. Severe drought conditions throughout much of the study necessitated ongoing adjustments to the original stocking rates and, as a result, drought was the major influence on the dynamics of H. contortus populations. Plant density and basal area in the silver-leaved ironbark landscape were consistently higher than those in the narrow-leaved ironbark landscape. There was limited evidence of any impact by either light or moderate stocking rate but there was evidence of an impact at the heaviest stocking rate. There was minimal impact of legume oversowing. Relatively large fluctuations in plant density occurred during this study resulting from the death of existing plants, due mainly to drought, and seedling recruitment. Similarly, there were relatively large fluctuations in basal area caused mainly by changes in plant size. Rates for turnover of plant numbers were relatively high whereas plant turnover rates of basal areas were relatively low. Regular seedling recruitment appeared necessary to ensure the persistence of this species. Despite the high turnover, populations were maintained at reasonable levels indicating the overall resilience of H. contortus.