Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry

A new method to obtain trigonometry for the real spaces of constant curvature and metric of any (even degenerate) signature is presented. The method encapsulates trigonometry for all these spaces into a single basic trigonometric group equation. This brings to its logical end the idea of an absolute trigonometry, and provides equations which hold true for the nine two-dimensional spaces of constant curvature and any signature. This family of spaces includes both relativistic and non-relativistic homogeneous spacetimes; therefore a complete discussion of trigonometry in the six de Sitter, minkowskian, Newton--Hooke and galilean spacetimes follow as particular instances of the general approach. Any equation previously known for the three classical riemannian spaces also has a version for the remaining six spacetimes; in most cases these equations are new. Distinctive traits of the method are universality and self-duality: every equation is meaningful for the nine spaces at once, and displays explicitly invariance under a duality transformation relating the nine spaces. The derivation of the single basic trigonometric equation at group level, its translation to a set of equations (cosine, sine and dual cosine laws) and the natural apparition of angular and lateral excesses, area and coarea are explicitly discussed in detail. The exposition also aims to introduce the main ideas of this direct group theoretical way to trigonometry, and may well provide a path to systematically study trigonometry for any homogeneous symmetric space.Comment: 51 pages, LaTe

Recent advances in electronic structure theory and their influence on the accuracy of ab initio potential energy surfaces

Recent advances in electronic structure theory and the availability of high speed vector processors have substantially increased the accuracy of ab initio potential energy surfaces. The recently developed atomic natural orbital approach for basis set contraction has reduced both the basis set incompleteness and superposition errors in molecular calculations. Furthermore, full CI calculations can often be used to calibrate a CASSCF/MRCI approach that quantitatively accounts for the valence correlation energy. These computational advances also provide a vehicle for systematically improving the calculations and for estimating the residual error in the calculations. Calculations on selected diatomic and triatomic systems will be used to illustrate the accuracy that currently can be achieved for molecular systems. In particular, the F+H2 yields HF+H potential energy hypersurface is used to illustrate the impact of these computational advances on the calculation of potential energy surfaces

The Young Man Four-Square

In this book, ...dedicated to every young man who has an ambition to make the most of himself and his opportunities, James Vance discusses the four roles of men: business, society, politics, and religion. Vance emphasizes the importance and benefits of diligence for men in business and at work, giving advice on choosing a vocation, balancing work and other duties, and important traits for the businessman. For the young man in society, Vance warns against becoming certain types of society men, such as the blasé young man or the dishonest young man, and gives advice concerning how to take part in society. The young man in politics is to stay informed on current issues, obey the law, and vote. Finally, the young man in religion is to live like Christ and take an active role in the religious community even if he does not become a priest.https://openworks.wooster.edu/motherhomeheaven/1054/thumbnail.jp

Effect of Selection Process on Organizational Performance in the Brewery Industry of Southern Nigeria

The aim of this paper is to investigate the “Effect of Selection Process on Organizational Performance in the Brewery Industry of Southern Nigeria”.  Guided by Reflection and Attribution Theory, the research sought to: (i) ascertain the extent to which there was a positive relationship between employment tests and creativity, (ii) determine the extent to which there was a positive relationship between selection interview and profitability. Two hypotheses were formulated to guide the study. Through proportionate stratified random sampling, 328 individuals were selected from the organizations of study.  Responses from the questionnaire were complemented with personal interviews of some selected management staff.  The data obtained were analyzed using frequency tables and the values expressed in percentages. Pearson Product Moment Correlation was used for testing the hypotheses and t-test was used for testing the level of significance of correlation coefficient at 5% error and 3-degrees of freedom.  The findings of this study are: there is a positive relationship between employment tests and creativity; there is a positive relationship between selection interview and profitability. Keywords: Selection process, Organization performance, Employment tests, Selection interview

MARKETING STRATEGY AND ITS EFFECTS ON THE ORGANIZATION (A CASE STUDY OF TOWER ALUMINIUM NIGERIA PLC)

This is a summary of the entire work which seeks to investigate the marketing programme of manufacturers for products they consider successful and see if such programmes approximates to an optimal strategy.  This is because good performance is a function of good planning.  Strategy refers to the course of action towards achieving planned objectives.  Marketing strategies are therefore plans and ways in which goals and objectives of any company can be attained.  In an attempt to see how these variables are manipulated by organizations, the researcher made use of the questionnaire and interview method to gather his primary data for analysis and interpretation.  However, due to the nature of the product, it was discovered that the organization made use of direct marketing as a promotional tool for price stability though depending on the cost of production.  The researcher also found out those sales influenced by the cultural and social values of the people, and that competition in the industry is very keen.  Now, with this in mind, where every organization in the industry is trying to get a major part of the market share, what should Tower Building Products do?  It is recommended by the researcher that training scheme should be introduced; there should be continuous marketing research and that advertising should be given priority. Keywords: Marketing, Strategies, controllable variables, non- controllable variables, Macro and Micro environments

Longing for the dawn

Newspaper article with references to music

Листи Юрія Шевельова до Омеляна Пріцака

The article deals with the correspondence of the world famous Slavic Professor of Columbia University and President of Ukrainian Free Academy of Sciences (UVAN) Yurii Shevelov with the Turkologist, Ukrainianist, founder and President of the Harvard Ukrainian Research Institute (HURI) and one of the initiators of the International Association of Ukrainianists Omelian Pritsak. This correspondence includes 22 letters and it is preserved in the Library of the National University of Kyiv-Mohyla Academy. In the Introduction the compilers provide general characteristic of the archive and this correspondence. The Appendix contains a letter of Omelian Pritsak addressed to famous philanthropists Omelian and Tetiana Antonovych, initiators of the private charitable foundation that annually awards prizes to the most outstanding litterateurs, scholars and public figures.У публікації листів відомого славіста зі світовим ім’ям, професора Колумбійського університету, президента Української вільної академії наук у США Юрія Шевельова до не менш відомого тюрколога та україніста, засновника та багаторічного директора Українського наукового інституту Гарвардського університету, одного з ініціаторів створення Міжнародної асоціації україністів Омеляна Пріцака вміщено епістолярій, що зберігається у архіві останнього у Науковій бібліотеці Національного університету “Києво-Могилянська академія” (22 листи). Упорядники у вступній частині подали загальну характеристику архіву та пропонованого листування. Додатком до публікації є лист О. Пріцака до відомих меценатів – родини Омеляна та Тетяни Антоновичів, засновників приватного благодійного фонду, що щорічно нагороджує преміями найвидатніших літераторів, вчених та громадських діячів