The adjacency matrix of one type of graph and the Fibonacci numbers

Recently there is huge interest in graph theory and intensive study on computing integer powers of matrices. In this paper, we investigate relationships between one type of graph and well-known Fibonacci sequence. In this content, we consider the adjacency matrix of one type of graph with 2k (k=1,2,...) vertices. It is also known that for any positive integer r, the (i,j)th entry of A^{r} (A is the adjacency matrix of the graph) is just the number of walks from vertex i to vertex j, that use exactly k edges

Behind bars: Exploring the prison and post release experiences of minoritised mothers.

Academic literature concerning ‘prisons and prisoners’ generally appear to focus on solitary or at best two characteristics when exploring experiences i.e. either gender, race or class (Enos, 1998; Ginn, 2013; Mirza, 2003). It is often forgotten that individuals in fact occupy more than one social status which affects their life course. This thesis explored the prison and post release experiences of minoritised mothers in two separate studies. Study one consisted of semi structured interviews with eight women and study two was an autoethnography which was then woven into the narrative structures of study one. Using Hofstede (2011) and Crenshaw (1989) as foundational theoretical building blocks, as well as the findings from both the studies, the thesis re-conceptualised intersectionality in the form of a roundabout of oppression with numerous spokes flowing into it, but no exits. The minoritised are at the centre of the roundabout experiencing the increasing density and pressure of oppressive factors originating from each of the spurs that feed into their unique social location. The oppressive factors identified in this thesis were culture, race, ethnicity, religion, prisoner status, and motherhood. Consistent with the theoretical orientation, interpretative phenomenological analysis was utilised to gather individual biographies of women. General themes of oppressive mechanisms such as intimate partner violence, cultural and religious expectations of motherhood and womanhood, and prisoner status were identified through the narratives of the respondents in both studies. The thesis then provided empirically based recommendations for public policy for prison and probation operations. In addition, while the thesis exposed systems of oppression for minoritised women, it also generated more questions that need to be researched. Also, as a consequence of this thesis being conducted in the UK, researching women in social contexts that may eliminate one of the spokes of oppression is an important direction for further research

The effects of drip line depths and irrigation levels on yield, quality and water use characteristics of lettuce under greenhouse condition

This study was conducted to investigate the effects of different drip irrigation methods and different irrigation levels on yield, quality and water use characteristics of lettuce (Lactuca sativa var. longifolia cv. Lital) cultivated in a solar greenhouse from 07 October 2009 to 03 December 2009 in the Eastern Mediterranean region of Turkey. The irrigation methods were consisted of traditional surface drip irrigation (TDI), subsurface drip irrigation at 10 cm drip line depth (SDI10) and subsurface drip irrigation at 20 cm drip line depth (SDI20). At the treatment of irrigation levels, five irrigation treatments (I) were based on adjustment coefficients (0.25, 0.50, 0.75, 1.0 and 1.25) of Class A pan evaporation. For the yield and quality parameters of plant; marketable head weight (yield), number of marketable leaves, leaf area, plant height and diameters, plant dry weight, core diameters and firmness of head, leaf chlorophyll content, total soluble solids (TSS as °Brix), electrical conductivity (EC), pH, total dissolved solids (TDS) and salinity of leaves’ juice were determined. The yield and yield components were not affected by the irrigation methods except for core and plant diameters. Irrigation levels had significantly (p < 0.01) different effects on yield and yield components except for plant dry weight, plant height and head firmness. The results showed that the highest yield was obtained from SDI10xI100 treatment. The water use efficiency (WUE) and the irrigation water use efficiency (IWUE) increased as the irrigation was reduced.Key words: Subsurface drip irrigation, irrigation level, water use efficiency