The abstract of the diploma thesis "Positive Formulas for Some Substructural Logics" by Pavel Truhlar We will examine which distributive substructural logics, as defined in the book of Restall "An Introduction to Substructural Logics" have the same positive fragment with and without the weak excluded middle axiom. The main result of this diploma thesis is that some substructural logics have this property. We repeat the basic notions as described in the Restall's book, especially the consecution, natural deduction, frame semantics, Hilbert system. We will use the soundness and completeness theorems. We also will use the equivalence of natural deduction systems and Hilbert systems. All these important theorems are in the above mentioned Restall's book. We make the proof of our main result in the next part. We will use the semantics of frames, similarly as de Jongh and Zhao in the article "Positive Formulas in Intuitionistic and Minimal Logic". We will define the top model. After, we define the construction which converts a model to the top model. We define for each formula the positive part of it; this is the formula, which behaves the same way on the top models as the original formula. We use Hilbert type calculus to formulate our main theorem. We prove our main result using the deduction theorem for certain...

This study focused on the functions of Igoru music in Okpe land. It also examined the compositional techniques of the music typology. The primary source for data collection was oral interview. Secondary sources include publications, and records. Unstructured research questions formed basis for the study. The texts of eighty seven (87) songs were transcribed and translated for this study. Fifty songs from this sample were further transcribed in staff notation, for analysis and discussion. At the end of the study, the following findings were made: <ul> <li>Igoru musicians, in their foresight, investigate, evaluate, probe, counsel, warn, and foretell future events in Okpe, to avoid painful experiences, since in traditional Okpe society, life experiences are shared.</li> <li>Most of the themes in Igoru music are derived from the sense of realism than idealism. The songs being quite topical had to be realistic than idealistic in tendency. Various sound and speech elements are put together to make communication effective. </li> <li>Igoru music praises and commends deserving members, in order to encourage those who are doing well in the society to continue in their good deeds, as well as stimulate others to emulate them.</li> <li>The musicians defend their political system, their territorial land mass, traditional religion and themselves from various attacks.</li> <li>Igoru music represents the Okpe identity, thus it was selected amongst other music typologies of the culture to represent it, both in social and political-oriented activities in Lagos and elsewhere.</li> <li>Igoru music uses the hexatonic scale system. Almost all the songs were found to be composed in compound quadruple metre. The performers involve in two-part polyphonic singing. Consecutive parallel 3rds, 4ths, and 5ths are prevalent and melodic cadences resolve upwards than downwards. Shifts of tonal centre (key), according to the convenience of performers, as well as recycling of themes are also common features. </li></ul> / Thesis (Doctor of Music (DMus))--University of Pretoria, 2007. / Music / unrestricted

In our information age, it is of the highest importance that information is easy to understand by as many members of the potential target audience as possible. The present study analyses and compares the readability of 20 newspaper articles, half from the tabloid Daily Mail and the other half from the broadsheet The Daily Telegraph. The methods used to analyse the articles are mathematic readability formulas based on sentence and word length, as well as analyses of the use of the active and the passive voice, type-token ratio, number of clauses per sentence, and linking words. The results do not completely align with each other. Three of the five methods – the readability formulas, the use of the passive voice, and clauses per sentence – suggest that the Daily Mail articles are easier to understand, whereas the type-token ratios imply the opposite, and the linking words results did not show a difference in readability.

In my research work, I study diffraction by planar periodic structures (diffraction grating). In the first chapter, I try to familiarize the importance of diffraction gratings in spectroscopy. The second chapter explains the basic principle of diffraction without involving difficult mathematical tools. In the third chapter, I deduce Fourier modal method from Maxwell equations, a modern mathematical approach used for calculating the electromagnetic response of diffraction. The most important part of my work consists of the fourth and fifth chapter. At first, I try to utilize Fourier modal method for deriving formulas involving just 0th and (-1)st diffraction orders. Because of the unreasonable difficulty of uncovered formulas, I decided to consider only a special case - so-called Littrow configuration, in which the solution can be superposed from symmetric and antisymmetric couples of rays. I further develop so-called Local modal method - very inaccurate, but mathematically fairly simple, and discuss its physical limitations. Whole work is finished by the sixth chapter, which compares accurate computations gained from simulation and derived analytical formulas for both methods.

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This study focused on multilingualism as the primary linguistic cognitive objective of investigation. An integrative approach focused on second language linguistics in order to acquire a background in the cognitive foundations of language and research methodology and theoretical models for the study of phenomena, such as language planning in multicultural societies and language and ethnic diversity. To design cognitive reading methods, a literature survey was conducted regarding the latest developments in the theories pertaining to cognitive formulas of the second language learner. A quantitative experimental study was conducted, data gathered was scrutinised and a cognitive reading programme was experimentally administered to twenty primary school learners. The responses were coded, the data captured and statistically computed. Conclusions indicated that cognitive reading materials were practical, valid and reliable. Cognitive formulas hold the potential of contributing to the understanding of cognitive reading development in second language proficiency in the Foundation Phase of schooling. / Teacher Education / M. Ed. (Didactics)