A nonlinear generalization of the Filbert matrix and its Lucas analogue

In this paper, we present both a new generalization and an analogue of the Filbert matrix (Formula presented.) by the means of the Fibonacci and Lucas numbers whose indices are in nonlinear form (Formula presented.) for the positive integers (Formula presented.) and the integers r, s, c. This will be the first example as nonlinear generalizations of the Filbert and Lilbert matrices. Furthermore, we present q-versions of these matrices and their related results. We derive explicit formulæ for the inverse matrix, the LU-decomposition and the inverse matrices (Formula presented.), (Formula presented.) as well as we present the Cholesky decomposition for all matrices

Some aspects of quantum mechanics in chemical theory

The physics of microscopic phenomena is called quantum mechanics. When quantum mechanics is extended to the macroscopic scale, the classical macroscopic physics results. Atomic interactions such as the formation of bonds between atoms falls into the range of physics described by quantum mechanics. Because of the interest of a chemist in such interatomic effects, it seems reasonable that a chemist would be interested in quantum mechanics because it is the physics governing these effects. The point of this thesis is to present some of those aspects of quantum mechanics that are directly applicable to molecular systems and that can aid the chemist’s understanding of molecular systems. The text of this paper will be primarily qualitative and therefore necessarily very general. The purpose in writing it is to point out some possibilities of applicability to chemical conceptions, not to rigorously prove all statements made. There may, however, be some readers who are purists enough to want to know where these statements come from and what the whole basis of quantum theory is itself, not just how it is applied to chemical systems. For the satisfaction of these purists, (the author included), the appendices following the text are much more mathematically developed. However, if one is willing to accept results of the appendices, on need not understand them in order to understand the text

Liberalisation and smallholder agricultural development : a case study of coffee farms in central Kenya

Key words, Market reforms, smallholder agricultural development, prices, institutional framework, resource allocation and productivity, efficiency, policy interventionsAgricultural production and market participation by smallholder farmers in Kenya continues to decline despite the market reforms undertaken in the last one decade. This study examines the factors behind this decline. The objectives of the study are to evaluate agricultural price evolution and volatility, institutional changes, smallholder farmer's resource allocation and productivity as well as their efficiency in the advent of market reforms. The study focuses on smallholder coffee farms in Central Kenya province.Four separate but related analytical models are applied in this study. Various time series statistical methods including an ARCH (M) model are applied to analyse the price evolution and volatility for the period 1985 to 1999. Institutional changes are analysed using an exchange configuration framework, which is theoretically founded on new institutional economics. A bivariate probit selectivity model that relates household's credit and land constraints to resource allocation and farm productivity is also applied. Finally, a stochastic translog cost frontier model is applied to measure cost efficiency.The study shows that market reforms in Kenya, although of the priciest type, did not create sufficient conditions to arrest the decline in agricultural sector terms of trade and producer prices. The reforms are also associated with higher price volatility with attendant increases in price volatility costs to smallholder farmers. Institutional reforms lagged behind the market reforms, a situation that constrained access to agricultural services, supply of agricultural credit, private sector participation, while increasing transaction costs to agricultural producers. The study also shows that constraints in factor markets, high transaction costs and risks tempered resource allocation towards subsistence production with consequent declines in productivity and market participation. Smallholder farmers in Kenya are shown to have medium to high level of production efficiency that is comparable to efficiency levels in other developing countries. The study consequently concludes that smallholder-based development strategy is still an efficient mode of organising agricultural production. While there is still room for improving smallholder farmer levels of efficiency through better resource allocation and re-allocation, the highest source of growth is likely to come from technology development that shifts the production frontier outward.The conclusions points to the need for policy interventions that mainly focuses on creating institutional frameworks necessary for reducing transaction and production costs, price and institutional performance risks, increasing access to production resources, services and markets by smallholder farmers. The study also identifies and recommends specific policies to enhance private sector participation as well as the social capital of smallholder farmers. This study views these as the main challenges to be tackled in the second-generation reform programs for agricultural development, prosperity and poverty alleviation in Kenya and Sub-Saharan Africa in general. </font

Dynamics in Science-Based Markets: Two Phases of Development

This thesis analyzes the development of science-based (SB) technologies. In general, technology evolution is influenced by different factors. There are two different development phases in the SB technology cycle. The first phase is denoted as the science-push and the second as the demand-pull phase. Most studies dealing with the evolution of SB technologies are of rather descriptive nature. The aim of this thesis is the identification and quantification of the differences in the two phases

The q -Pilbert matrix

A generalized Filbert matrix is introduced, sharing properties of the Hilbert matrix and Fibonacci numbers. Explicit formulae are derived for the LU-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use q-analysis and to leave the justification of the necessary identities to the q-version of Zeilberger's celebrated algorithm. © 2012 Copyright Taylor and Francis Group, LLC

The generalized q-Pilbert matrix

A generalized q-Pilbert matrix from[KILIC, E.-PRODINGER, H.: The q-Pilbert matrix, Int. J. Comput. Math. 89 (2012), 1370-1377] is further generalized, introducing one additional parameter. Explicit formul' are derived for the LU-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use q-analysis and to leave the justification of the necessary identities to the q-version of Zeilberger's celebrated algorithm. However, the necessary identities have appeared already in disguised form in the paper referred above, so that no new computations are necessary