Orthogonal polynomials and recurrence equations, operator equations and factorization

This article surveys the classical orthogonal polynomial systems of the Hahn class, which are solutions of second-order differential, difference or q-difference equations. Orthogonal families satisfy three-term recurrence equations. Example applications of an algorithm to determine whether a three-term recurrence equation has solutions in the Hahn class - implemented in the computer algebra system Maple - are given. Modifications of these families, in particular associated orthogonal systems, satisfy fourth-order operator equations. A factorization of these equations leads to a solution basis.

Contribution of the exact Breit operator plus the electron state-dependent screening to the multiplet and fine structure of muon-electron atoms

We investigate for very general cases the multiplet and fine structure splitting of muonelectron atoms arising from the coupling of the electron and muon angular momenta, including the effect of the Breit operator plus the electron state-dependent screening. Although many conditions have to be fulfilled simultaneously to observe these effeets, it should be possible to measure them in the 6h- 5g muonic transition in the Sn region.

Factors affecting farmers’ decisions on utilization of rice straw compost in Northeastern Thailand

Rice straw is used in Northeastern Thailand as an alternative to organic fertilizer for crop production. This enables farmers to reduce the use of chemical fertilizers which leads to a decrease in production costs. In spite of the beneficial effects in agricultural production, rice straw compost cannot be produced in large amounts because the burning of rice straws is a common farming practice. The decisions of farmers who use rice straw compost have been investigated by interviewing 120 households belonging to the members of an organic fertilizer user group using a household questionnaire. The study was conducted to evaluate the factors that affect the use of rice straw compost in Khon Kaen Province in Northeastern Thailand. Results of the logit model showed that the farmers’ education, number of rice straw compost trainings in which the farmer participated, lack of knowledge about technology, insufficient labour and difficulty in making rice straw compost had a significant impact on the farmer’s decision to use rice straw compost. Difficulty in making rice straw compost appeared to be the root cause because the procedure of making rice straw compost is complex and labour intensive. Repeated trainings thus, will have a positive and significant influence on farmers’ adoption of the technology. Training provides more knowledge and will presumably change the perception of the farmers towards new technologies and the awareness of positive effects of rice straw compost utilization.

Elimination in Operator Algebras

A large class of special functions are solutions of systems of linear difference and differential equations with polynomial coefficients. For a given function, these equations considered as operator polynomials generate a left ideal in a noncommutative algebra called Ore algebra. This ideal with finitely many conditions characterizes the function uniquely so that Gröbner basis techniques can be applied. Many problems related to special functions which can be described by such ideals can be solved by performing elimination of appropriate noncommutative variables in these ideals. In this work, we mainly achieve the following: 1. We give an overview of the theoretical algebraic background as well as the algorithmic aspects of different methods using noncommutative Gröbner elimination techniques in Ore algebras in order to solve problems related to special functions. 2. We describe in detail algorithms which are based on Gröbner elimination techniques and perform the creative telescoping method for sums and integrals of special functions. 3. We investigate and compare these algorithms by illustrative examples which are performed by the computer algebra system Maple. This investigation has the objective to test how far noncommutative Gröbner elimination techniques may be efficiently applied to perform creative telescoping.

An analysis of household farm investment decisions under varying land tenure arrangements in Ghana

Land tenure insecurity is widely perceived as a disincentive for long-term land improvement investment hence the objective of this paper is to evaluate how tenure (in)security associated with different land use arrangements in Ghana influenced households’ plot level investment decisions and choices. The paper uses data from the Farmer-Based Organisations (FBO) survey. The FBO survey collected information from 2,928 households across three ecological zones of Ghana using multistaged cluster sampling. Probit and Tobit models tested the effects of land tenancy and ownership arrangements on households’ investment behaviour while controlling other factors. It was found that marginal farm size was inversely related to tenure insecurity while tenure insecurity correlate positively with value of farm land and not farm size. Individual ownership and documentation of land significantly reduced the probability of households losing uncultivated lands. Individual land ownership increased both the probability of investing and level of investments made in land improvement and irrigation probably due to increasing importance households place on land ownership. Two possible explanations for this finding are: First, that land markets and land relations have changed significantly over the last two decades with increasing money transaction and fixed agreements propelled by population growth and increasing value of land. Secondly, inclusion of irrigation investment as a long term investment in land raises the value of household investment and the time period required to reap the returns on the investments. Households take land ownership and duration of tenancy into consideration if the resource implications of land investments are relatively huge and the time dimension for harvesting returns to investments is relatively long.