On the Minimal Resolution Conjecture for P3

Int. J. Contemp. Math. Sciences, Vol. 3, 2008, no. 33, 1643 - 1655The Minimal Resolution Conjecture that was formulated by A Lorenzini [2] has been shown to hold true for P2, P3 [3] they made use of Quadrics, here we tackle the P3 case but making use of variant methods i.e. mainly the method of Horace (m`ethode d’Horace) to evaluate sections of fibres at given points. This was introduced by A Hirschowitz in 1984 in a letter he wrote to R Hartshorne. For a general set of points P1, . . . , Pm ∈ P3, for a positive integer m, we show that the map H0P3,ΩP3 (d + 1) −→ m i=1 ΩP3 (d + 1)|Pi is of maximal rank

Culturally Responsive Graduate Teaching Instructors: Lessons on Facilitating Classroom Dialogues on Racial, Ethnic, and Cultural Injustices

Graduate teaching instructors (GTIs) have the unique opportunity of learning to be both scholars and teachers at the same time. This juxtaposition between teacher and student presents distinctive challenges that are seldom captured in existing research. One such challenge is the task to facilitate classroom dialogues on issues of race, ethnicity, and culture. While GTIs are charged with the labor of instructing university classrooms full of diverse student populations, it is common for them to instruct these courses without ever having instructional training on culturally responsive teaching. It is also possible that GTIs are not comfortable discussing issues of race, ethnicity, and culture because they may have not critically examined their own positionalities, or the impact these positionalities can have on their instructional/classroom communication strategies and behaviors. This paper offers an autoethnographic account of the awakening of my own critical consciousness during a semester long community-based learning project at a predominantly African American high school. In reflecting on this experience, I offer suggestions for GTIs on becoming more culturally responsive teachers

Monads on multiprojective spaces and associated vector bundles

In this paper we establish the existence of monads on Cartesian products of projective spaces. We construct vector bundles associated to monads on $\mathbb{P}^{a_1}\times\mathbb{P}^{a_1}\times\mathbb{P}^{a_2}\times\mathbb{P}^{a_2}\times\cdots\times\mathbb{P}^{a_n}\times\mathbb{P}^{a_n}$. Once the monad on $X$ exists the next natural question is if the cohomology vector bundle associated to these monads are simple or not. We study these vector bundles associated to monads on $X$ and prove their stability and simplicity.Comment: 14 pages. arXiv admin note: substantial text overlap with arXiv:2202.0787

Monads on a multiprojective space, Pa × Pb

International Mathematical Forum, Vol. 7, 2012, no. 54, 2669 - 2673For all integers a, b > 0 we establish explicitly the existence of monads on a multiprojective Space Pa×Pb following the conditions established by Floystad. That is for all positive integers α, β, γ there exists a monad on the multiprojective space X = Pa × Pb whose maps A and B have entries being linear in two sets of homogeneous coordinates x0 : ... : xa and y0 : ... : yb and it takes the form: 0 Oα X(−1,−1)A Oβ X B Oγ X(1, 1) 0 where the maps A and B are matrices with B ·A = 0 and they are of maximal rank

Monads on Cartesian products of projective spaces

In this paper we establish the existence of monads on special Cartesian products of projective spaces. Special in the sense that we mimick monads on instanton bundles. We construct monads on $\mathbb{P}^1\times\cdots\times\mathbb{P}^1\times\mathbb{P}^3\times\cdots\times\mathbb{P}^3\times\mathbb{P}^5\times\cdots\times\mathbb{P}^5$. We proceed to prove stability of the kernel bundle associated to the monad and simplicity of the cohomology vector bundle. Lastly we establish the existence of monads on $\mathbb{P}^{a_1}\times\cdots\times\mathbb{P}^{a_n}$ where $a_1<a_2<\ldots<a_n$, alternating even and odd or at least $a_i$ $0<i\leq{n}$ is odd.Comment: 17 pages, the results proved follow the same trend with arXiv:2202.07876, arXiv:2301.0493

Knowledge management in a competitive economy: the Knowledge Management Readiness Score (KMRS)

Conference paper presented at Polytechnic of Namibia (Namibia's University of Science and Technology) 5th international conference in Windhoek.Knowledge Management has been touted the ultimate solution to most organizations’ competitiveness in this era that is the knowledge edge. The knowledge possessed and used by an organization’s personnel could be the difference between its survival or collapse at these times when competition is cut-throat and when today’s market leaders could as well be part of the story of the dearly departed if they do not put their acts together. Organizational competition has grown from having the muscle to build new factories and plants or flexing financial or liquidity muscles to learning how an organization can capitalize from improving its processes, on a competitor’s mistake, or learning how to collaborate if outright competition will hurt the concerned organizations. But how should organizations go about knowledge management, where they start

Impacts of Multiple Stressors on Dryland Vulnerability and Land Conflict Among Border Communities

This study examines how individuals and groups respond to prevailing politico-economic and biophysical changes and how the adjustments they make influence and are influenced by their social relations and material condition in spatial and temporal terms. This dissertation comprises of three parts: The first part is a critique of the climate-conflict relationship debate and the problems associated with studies pushing for a causal relationship between climate variables and conflict. I argue that scholars lack of attention on varying institutional capacities and the focus solely on environmental factors as trigger mechanisms for conflict leads to misleading arguments about conflict distribution and frequency which may ultimately hinder the understanding of why conflicts occur, are exacerbated or resolved, recur or not. I find that as scholars focus on climatic variables in pursuit of narrow causations, they ignore known weaknesses in both theory and methodology. In addition, shifting from a human vulnerability approach to a human security one in climate conflict studies advances a functionalist conservative discourses that pay the most attention to securing the states of the global north and global capital circulation rather than helping vulnerable groups deal with risk and the impacts of climate change. The second part of the dissertation examines how social relations around land allocation and tenure in Africa have changed over time and how the existence of a dual system of tenure in many African countries produces a third system of informal land transfers. I argue that these often-unregulated informal transfers may help circumvent protections provided within law and policy. I find that, in Kenya as in many other parts of Sub-Saharan Africa, the existence of many plots of land held as freehold without title coupled with an expensive and deeply bureaucratic process of titling produces and maintains unregulated land transfers that often cement inequalities that are addressed in formal policy and law. The third part of this dissertation utilizes the concept of ecological gradient to examine the social benefit of material relations for different livelihood groups living along the Mt Kilimanjaro altitudinal gradient. I find evidence of increased diversification and interdependence between the different livelihoods that occupy the ecological zones along the gradient. Consequently, livelihood groups living within the various ecological gradients along the mountain gradient adjust to changing biophysical and politico-economic factors by extracting social benefits from increased contact with each other

Factors Affecting Quality Management in Public Institutions: A Case Study of Machakos University, Kenya

The main purpose of this study was to determine factors affecting Quality Management in public institutions, a case study of Machakos University. The specific objectives of this study were: to establish how top management commitment affect the implementation of Quality Management in public institutions, to investigate the extent to which employee’s training affect the implementation of Quality Management in public institutions, to assess the extent to which organizational culture affect implementation of Quality Management in public institutions and to determine the effect of communication on the implementation of Quality Management in public institutions. The study adopted a case study research design targeting 42 individuals. The design allowed for a wide range and generalized study covering a number of related items which is used to generalize for the same business within a given set up. The study sampled all the target population using census. Census method enhances the generalizability of the study findings since it eliminates both the sampling bias and sampling error, which are often associated with sampling. Questionnaires were used to collect data which had both closed and open ended questions. Data was analyzed qualitatively and quantitatively through descriptive statistics such as frequencies and percentage and later presented in tables, pie-charts and pie-graphs. The findings of this study revealed that top management commitment is a critical factor in implementation of Quality Management and that top management commitment positively influences implementation of Quality Management. The study also established that organizational culture is a critical factor in implementation of Quality Management and that appropriate organizational culture positively influences implementation of Quality Management as cited by 60% of the respondents. The study revealed that employee training positively affected implementation of Quality Management according to 70% of the respondents. In addition, the study concluded that Communication is an important factor with positive influence in implementation of Quality Management. The study thus recommends that top managements commit themselves in providing leadership and key resources needed in Quality Management. Secondly, the study recommends that university train its employees on Quality Management initiatives. It is also recommended that these trainings are conducted frequently and at all levels in the university. Thirdly, the study recommends that university develop group, hierarchical, developmental and rational culture so as to enhance total Quality Management. Lastly, the study recommends that quality managers and management develop appropriate, effective and flexible communication systems that allow free flow of quality information at all levels in the university. The study suggests that further research should be carried out on factors influencing the attainment of ISO certification among public institutions. Keywords: Sort, Systematize, Sweep, Standardize, Self-Discipline, International Organization for Standardization, Quality Management, Statistical Quality Control, Total Quality Managemen

The Effect of potassium dosage on selected growth parameters and yield response modeling on potatoes grown in Molo, Kenya

Abstract: The Molo region of Kenya has experienced decreased potato acreage yields over the years. This has impacted negatively economic endeavors and food security of the region and Kenya at large. A preliminary study on the physical-chemical characterization of the soils indicated that they were deficient in the amount of available potassium. This finding was very important because the majority of the farmers in the region replenish phosphorous and nitrogen but not potassium. Subsequently, the present study was undertaken to determine the effect of replenishing selected farm soils with various potassium levels on the growth and productivity of ‘Shangi’ a variety grown in Molo Sub-county and ultimately determine the soil optimum potassium dose requirement. A field experiment was conducted with seven model-based K fertilizer treatments (0, 33.3, 41.5, 55.3, 133.3, 200 and 266.7 kg K2O/ha) and three replications in Randomized Complete Block Design (RCBD). The potassium sorption study was conducted using soil samples as adsorbent while varying the K+ concentration in solution. The data obtained were treated using both linearized and non-linearized Freundlich adsorption isotherms. The optimum potassium fertilizer rate was evaluated using yield response models (Quadratic, linear-plateau, quadratic-plateau, and square root). The results of the study showed that the increase in soil potassium levels led to a significant increase in growth and yield parameters. Aerial stem number, leaf number per plant, and plant height recorded increase with an increase in K levels. The sorption data were found to fit best in linearized Freundlich isotherm based on correlation coefficient values (R2) and error function analysis. The potassium buffering capacity ranged from 13.667-46.068 with a mean of 33.6 ± 17.4mg/Kg. The quadratic model fitted the data better than other models with R2 (0.9559) and SSE (18.237). K2O fertilizer application at 200 Kg/ha maximized the potato tuber yield to 30.111 Ton/ha. The result showed clearly that there is a need to adopt the use of potassium-based fertilizer according to soil requirements in this region to realize good tuber yield