Quantum Hamiltonian reduction of W-algebras and category O

W-algebras are a class of non-commutative algebras related to the classical universal enveloping algebras. They can be defined as a subquotient of U(g) related to a choice of nilpotent element e and compatible nilpotent subalgebra m. The definition is a quantum analogue of the classical construction of Hamiltonian reduction. We define a quantum version of Hamiltonian reduction by stages and use it to construct intermediate reductions between different W-algebras U(g,e) in type A.This allows us to express the W-algebra U(g,e') as a subquotient of U(g,e) for nilpotent elements e' covering e. It also produces a collection of (U(g,e),U(g,e'))-bimodules analogous to the generalised Gel'fand-Graev modules used in the classical definition of the W-algebra; these can be used to obtain adjoint functors between the corresponding module categories. The category of modules over a W-algebra has a full subcategory defined in a parallel fashion to that of the Bernstein-Gel'fand-Gel'fand (BGG) category O; this version of category O(e) for W-algebras is equivalent to an infinitesimal block of O by an argument of Mili\v{c}i\'{c} and Soergel. We therefore construct analogues of the translation functors between the different blocks of O, in this case being functors between the categories O(e) for different W-algebras U(g,e). This follows an argument of Losev, and realises the category O(e') as equivalent to a full subcategory of the category O(e) where e' is greater than e in the refinement ordering.Comment: University of Toronto PhD thesis, defended July 2014, 57 page

Mathematics teachers' positions and practices in discourses of assessment

Mathematics teachers ’ positions and practices in discourses of assessmen

Shanghai Stock Exchange Composite Index and Bank Stock Prices in China: A Causality Analysis

This paper analyzes empirically the relationship between the Shanghai Stock Exchange (SSE) Composite Index and the indexes of 10 Chinese listed banks to test whether the listing of these banks had played a role in leading the Chinese stock market. Using daily prices from 1 June 2006 to 15 November 2007, we applied the Granger causality test and found that a uni-directional causality relationship existed either way between most bank stock prices and the market index while the bi-directional relationship only identified among five of the ten banks. This research finding is in part consistent with previous studies showing that stock markets in great China region are integrated and are strongly influenced by the psychological factors of investors. In the following co-integration test, both AEG and Johansen’s methods concluded a long-run stable equilibrium relationship between majority of the banking stock prices and the SSE Composite Index.Shanghai Stock Exchange, VAR, Johansen co-integration tests, Granger causality tests

Impact of the US Credit Crunch and Housing Market Crisis on China

There are many similarities between the US, the UK and the Chinese housing markets, including the movements of interest rates and house prices. Some Chinese banks, especially the Bank of China, have been exposed to the US mortgage securitization market. These have triggered a serious concern as to whether the US credit crunch and housing market crisis may be replicated in China. This paper shows that there are some significant differences between China and the West, especially the US and the UK. Compared with the US and other western industrialized economies, the booming house market in China has been supported by fast economic growth, rapid urbanization and high domestic savings. In addition, Chinese banks are less exposed to mortgage defaults than their western counterparts because house buyers are mainly urban and high income residents who are required to have high down payments. These Sino-Western economic and social differences suggest that the US credit crunch and housing market crisis may have some negative impacts on Chinese commercial banks and the overall economy but are unlikely to cause a similar financial and housing crisis in China despite the current struggling Chinese stock markets and a slowdown of house price growth.US credit crunch, housing market crisis, China

A Framework for Analyzing the Market and Supporting Infrastructure for Small Satellites and Associated Systems

A comprehensive, conceptual framework within which space programs, projects, and activities can be analyzed is presented. This framework consists of a number of largely functional dimensions. Most important is the division of space-based and space-oriented activity into two major segments: the space infrastructure, and space-derived products and services. The space infrastructure includes the various functions and devices which support space-oriented activity, including launch vehicles, payload and vehicle processing facilities plus those organizational and technological elements which support space-oriented activity, including the institutional support base. Space-derived products and services are those products and services which can only be produced within the space environment, or through the application of space-oriented technology, such as vantage point products (e.g., remote sensing, communications), physical environment products (e.g., materials processing), and others. Other dimensions in the framework include: (1) time and commitment (e.g., past, present, planned), (2) scope (e.g., national, international), (3) enabling factors (e.g., enabling technologies), and (4) providers and consumers

African morality: With or Without God

Traditional African societies are noted for their religiosity and so one would naturally expect that when it comes to matters of morality they will appeal to some divinities or gods for their moral jurisdiction and interpretation of their moral codes. Yet, according to Wiredu (1992) and Gyekye (1996), this is not true of traditional African societies when it comes to finding the source of their moral codes. For the two, an appeal to religion as a source of African moral values is a mistaken position. This paper challenges their position by showing the defects in their arguments and argues that the fabric of traditional African morality may tumble if God or religion is removed as either the source or part of the source

The place of African animal ethics within the welfarist and rightist debate : An interrogation of Akan ontological and ethical beliefs towards animals and the environment.

Doctorate of Philosophy in Ethics Studies. University of KwaZulu-Natal, Pietermaritzburg,2020.Scholars in the field of environmental and animal ethics have propounded theories that outline what, in their view, ought to constitute an ethical relationship between human and the environment and humans and nonhuman animals respectively. In the field of animal ethics, the contributions by Western scholars to theorize a body of animal ethics, either as an ethic in its own right or as a branch of the broader field of environmental ethics is clearly seen.Consequently, there are, notably, two main schools of thought in the field of animal ethics. These are the ‘welfarist’ and the ‘rightist’ approaches (Regan, 2006;Owoseni&Olatoye,2014). Unfortunately, a clearly concerted effort to theorize on animal ethics from an African perspective is at the minimal, although there is a lot written in African environmental ethics, broadly construed. It is within this context that this study locates an African animal ethic within the two main theories in the global animal ethics, using traditional Akan ontology and ethics particularly, those that speak to their relationship with the environment and, especially animals.Thus, using Akan ontological worldview and ethics as foundational sources, alongside learnt principles from the emerging theories in African environmental ethics, the study seeks to find the place of Akan animal ethics within the rightist and welfarist debates. Following qualitative research rubrics, the study collected primary data through one-on-one interviews and focus groups discussions from traditional Akan leaders and experts, and young Akan adults. The data was then analysed using the study’s theoretical framework (welfarism, rightism, and the ethics of interrelatedness) in comparison with the literature to find corresponding answers to the study’s research questions. The findings indicate that the Akan perspective acknowledges the existence of an interconnection between humans and the rest of nature, and that it is an important connection that ought to be sustained. It is also evident that the Akan environmental ethics is anthropocentric in approach through its conferring of instrumental or extrinsic values on nature, instrumental values that go to the benefit of humans.This notwithstanding, Akan environmental ethics is not to be considered as individualistic in nature because it does not seek the interests or rights of individual human agents but instead, the common interest of the community through its goal to ensure the continuous progress and survival of the human community. Ultimately, the study’s findings reveal that Akan animal ethics shares closer affinities with welfarism (direct) than it does with rightism

Alien Registration- Morgan, Stephen L. (Baldwin, Cumberland County)

https://digitalmaine.com/alien_docs/32977/thumbnail.jp

The Florida Governor\u27s Commission on Space: Its Impact on Space Enterprise

At the Kennedy Space Center, on 28 Her/ 1987, at the Second Briefing Meeting of the East Central Florida Space Business Roundtable, Florida Governor Bob Martlnez signed an Executive Order creating the Governor\u27s Commission on Space. This action followed the Roundtable\u27s initiative to the state dating from September, 1986, suggesting the formation of the Commission. On hand to deliver the keynote address was Dr. Gerard K. O\u27Nelll, a former member of the National Commission on Space. Dr. O\u27Neill\u27s presence was no accident, since the purpose of the Florida Commission is to define Florida\u27s role in the continued development of many of the concepts outlined In the National Commission\u27s watershed report, Pioneering the Space Frontier. The Florida Commission identified nine topical areas for further research, and its work is still in progress. A number of legislative recommendations have already been presented to the Governor, while the final report is not due until June, 1988. This Commission, and several similar efforts in other states, is indicative of the strong interest nationally in the development of space enterprise