Emergy Algebra: Improving Matrix Methods for Calculating Tranformities
Transformity is one of the core concepts in Energy Systems Theory and it is fundamental to the calculation of emergy. Accurate evaluation of transformities and other emergy per unit values is essential for the broad acceptance, application and further development of emergy method...
Set Theory Applied to Uniquely Define the Inputs to Territorial Systems in Emergy Analyses
The language of set theory can be utilized to represent the emergy involved in all processes. In this paper we use set theory in an emergy evaluation to ensure an accurate representation of the inputs to territorial systems. We consider a generic territorial system and we describ...
Emergy, Transformity, the Emergy Unit and the Emergy Baseline.
This paper addresses three important research areas subject to some disagreement within the community of emergy practitioners or to misunderstandings within the scientific community as a whole. Emergy and its sister idea, transformity, are important new concepts derived from the...
Improvements to Emergy evaluations by using Life Cycle Assessment.
Rugani, Benedetto; Benetto, Enrico
2012-05-01
Life Cycle Assessment (LCA) is a widely recognized, multicriteria and standardized tool for environmental assessment of products and processes. As an independent evaluation method, emergy assessment has shown to be a promising and relatively novel tool. The technique has gained wide recognition in the past decade but still faces methodological difficulties which prevent it from being accepted by a broader stakeholder community. This review aims to elucidate the fundamental requirements to possibly improve the Emergy evaluation by using LCA. Despite its capability to compare the amount of resources embodied in production systems, Emergy suffers from its vague accounting procedures and lacks accuracy, reproducibility, and completeness. An improvement of Emergy evaluations can be achieved via (1) technical implementation of Emergy algebra in the Life Cycle Inventory (LCI); (2) selection of consistent Unit Emergy Values (UEVs) as characterization factors for Life Cycle Impact Assessment (LCIA); and (3) expansion of the LCI system boundaries to include supporting systems usually considered by Emergy but excluded in LCA (e.g., ecosystem services and human labor). Whereas Emergy rules must be adapted to life-cycle structures, LCA should enlarge its inventory to give Emergy a broader computational framework. The matrix inversion principle used for LCAs is also proposed as an alternative to consistently account for a large number of resource UEVs. PMID:22489863
This web presentation answers basic questions about the relatively new scientific concept, emergy. It dispels some of the confusion surrounding this idea in a PowerPoint presentation. The presentation is written in common language and uses straightforward examples. Emergy indic...
Emergy is an important quantity needed for public policy analysis that is based on a complex methodology. The intent of this Environmental Research Brief is to define emergy and its importance in a manner that is accessible to everyone with at least a high school education. Emer...
The purpose of this study is to better understand the differences and similarities between emergy and nonmarket economic valuation, when both are applied to value the same policies or development alternatives. The emdollar value of a good or service often exceeds the market value...
This is the fourth in a series of papers on quantifying the emergy of human services in a manner that is essentially independent of the monetary value of the work performed. In this paper we assembled information on the education and training required to perform the major occupat...
EMERGY METHODS: VALUABLE INTEGRATED ASSESSMENT TOOLS
NHEERL's Atlantic Ecology Division is investigating emergy methods as tools for integrated assessment in several projects evaluating environmental impacts, policies, and alternatives for remediation and intervention. Emergy accounting is a methodology that provides a quantitative...
The Geobiosphere Emergy Baseline: A synthesis
Following the Eighth Biennial Emergy Conference (January, 2014), the need for revisiting the procedures and assumptions used to compute the Geobiosphere Emergy Baseline (GEB) emerged as a necessity to strengthen the method of Emergy Accounting and remove sources of ambiguity and ...
Cosmic emergy based ecological systems modelling
NASA Astrophysics Data System (ADS)
Chen, H.; Chen, G. Q.; Ji, X.
2010-09-01
Ecological systems modelling based on the unified biophysical measure of cosmic emergy in terms of embodied cosmic exergy is illustrated in this paper with ecological accounting, simulation and scenario analysis, by a case study for the regional socio-economic ecosystem associated with the municipality of Beijing. An urbanized regional ecosystem model with eight subsystems of natural support, agriculture, urban production, population, finance, land area, potential environmental impact, and culture is representatively presented in exergy circuit language with 12 state variables governing by corresponding ecodynamic equations, and 60 flows and auxiliary variables. To characterize the regional socio-economy as an ecosystem, a series of ecological indicators based on cosmic emergy are devised. For a systematic ecological account, cosmic exergy transformities are provided for various dimensions including climate flows, natural resources, industrial products, cultural products, population with educational hierarchy, and environmental emissions. For the urban ecosystem of Beijing in the period from 1990 to 2005, ecological accounting is carried out and characterized in full details. Taking 2000 as the starting point, systems modelling is realized to predict the urban evolution in a one hundred time horizon. For systems regulation, scenario analyses with essential policy-making implications are made to illustrate the long term systems effects of the expected water diversion and rise in energy price.
Emergy analysis of an industrial park: the case of Dalian, China.
Geng, Yong; Zhang, Pan; Ulgiati, Sergio; Sarkis, Joseph
2010-10-15
With the rapid development of eco-industrial park projects in China, evaluating their overall eco-efficiency is becoming an important need and a big challenge academically. Developing ecologically conscious industrial park management requires analysis of both industrial and ecological systems. Traditional evaluation methods based on neoclassical economics and embodied energy and exergy analyses have certain limitations due to their focus with environmental issues considered secondary to the maximization of economic and technical objectives. Such methods focus primarily on the environmental impact of emissions and their economic consequences. These approaches ignore the contribution of ecological products and services as well as the load placed on environmental systems and related problems of carrying capacity of economic and industrial development. This paper presents a new method, based upon emergy analysis and synthesis. Such a method links economic and ecological systems together, highlighting the internal relations among the different subsystems and components. The emergy-based method provides insight into the environmental performance and sustainability of an industrial park. This paper depicts the methodology of emergy analysis at the industrial park level and provides a series of emergy-based indices. A case study is investigated and discussed in order to show the emergy method's practical potential. Results from DEDZ (Dalian Economic Development Zone) case show us the potential of emergy synthesis method at the industrial park level for environmental policy making. Its advantages and limitations are also discussed with avenues for future research identified. PMID:20805000
CHAPTER 10: CURRENT TECHNICAL PROBLEMS IN EMERGY ANALYSIS
Technical problems related to the determination of the emergy base for self-organization in environmental systems are considered in this paper. The comparability of emergy analysis results depends on emergy analysts making similar choices in determining the emergy base for a part...
EMERGY ANALYSIS OF THE PREHISTORIC NITROGEN CYCLE
Several relationships between the specific emergy or the emergy per unit mass and the mass concentration of nitrogen were shown to exist through an analysis of the global nitrogen cycle. These observed relationships were interpreted by examining the nature of the underlying ener...
Emergy Accounting: A Unified, Comprehensive Triple Bottom Line
Development of the concept of emergy established a medium for accounting that made it possible to express environmental, economic, and social work of all kinds on a common basis as solar emjoules. Emergy accounting can be used to combine both emergy and money accounts on a single...
The Emergy Baseline of the Earth: Is it Arbitrary?
The emergy baseline for the Earth is used in determining the transformities of the products of all planetary processes and through these relationships it influences all emergy evaluations. Estimates of the emergy baseline made in the past have changed depending on the number of i...
CURRENT TECHNICAL PROBLEMS IN EMERGY ANALYSIS
: Emergy Analysis has been a rapidly evolving assessment methodology for the past 30 years. This process of development was primarily driven by the inquiring mind and ceaseless activity of its founder, H.T. Odum, his students, and colleagues. Historically, as new kinds of proble...
Emergy of the Occupations. Chapter 43
In this paper we calculated the emergy contributed to the economy of the United States in the work done by the workers of 558 occupations in 2008. We determined the empower (semj/yr) delivered by an individual engaged in each occupation, the transformity of the occupation’s work ...
Emergy of the Global Biogeochemical Cycles of Biologically Active Elements
Accurate estimates of the emergy of elemental flows are needed to accurately evaluate the far field effects of anthropogenic wastes. The transformity and specific emergy of the elements and of their different chemical species is also needed to quantify the inputs to many producti...
The Emergy Basis for Formal Education in the United States
The education system of the United States from 1870 to 2006 was evaluated using emergy methods. The system was partitioned into three subsystems, elementary, secondary, and college education and the emergy inputs required to support each subsystem were determined for each year o...
Dealing with Emergy Algebra in the Life Cycle Assessment Framework
The Life Cycle Inventory (LCI) represents one of the four steps of the Life Cycle Assessment (LCA) methodology, which is a standardized procedure (ISO 14040:2006) to estimate the environmental impacts generated by the production, use and disposal of goods and services. In this co...
Emergy Synthesis 8 ~ Emergy and environmental accounting: Theories, applications, and methodologies
With the assembly and review of the 12 research papers for this Special Issue of Ecological Modelling, our goal was to continue working with the journal to bring a strong group of papers, indicative of the forefront of emergy research, to the global energy research community and ...
Using Toulmin Analysis to Analyse an Instructor's Proof Presentation in Abstract Algebra
ERIC Educational Resources Information Center
Fukawa-Connelly, Timothy
2014-01-01
This paper provides a method for analysing undergraduate teaching of proof-based courses using Toulmin's model (1969) of argumentation. It presents a case study of one instructor's presentation of proofs. The analysis shows that the instructor presents different levels of detail in different proofs; thus, the students have an…
Emergy evaluations for constructed wetland and conventional wastewater treatments
NASA Astrophysics Data System (ADS)
Zhou, J. B.; Jiang, M. M.; Chen, B.; Chen, G. Q.
2009-04-01
Based on emergy synthesis, this study presents a comparative study on constructed wetland (CW) and conventional wastewater treatments with three representative cases in Beijing. Accounting the environmental and economic inputs and treated wastewater output based on emergy, different characteristics of two kinds of wastewater treatments are revealed. The results show that CWs are environment-benign, less energy-intensive despite the relatively low ecological waste removal efficiency (EWRE), and less cost in construction, operation and maintenance compared with the conventional wastewater treatment plants. In addition, manifested by the emergy analysis, the cyclic activated sludge system (CASS) has the merit of higher ecological waste elimination efficiency.
ERIC Educational Resources Information Center
Wawro, Megan Jean
2011-01-01
In this study, I considered the development of mathematical meaning related to the Invertible Matrix Theorem (IMT) for both a classroom community and an individual student over time. In this particular linear algebra course, the IMT was a core theorem in that it connected many concepts fundamental to linear algebra through the notion of…
Development of the concepts of emergy and transformity established a medium (emergy) for accounting that made it possible to express economic and environmental work of all kinds on a common basis as solar emjoules. Environmental accounting using emdollars, a combined emergy-monet...
Emergy evaluation perspectives of a multipurpose dam proposal in Korea.
Kang, Daeseok; Park, Seok Soon
2002-11-01
The 'emergy' concept was used to evaluate the economy of Korea and the contributions of a multipurpose dam proposal to the real wealth of the Korean economy. Emergy is defined as the available energy of one kind previously used up directly and indirectly to make a product or service. The indices for Korea calculated from the emergy evaluation were close to those of developed countries. Even though its monetary balance of payments was negative in 1997, the economy of Korea showed positive balance in trade when exports and imports were expressed in emergy. The emergy evaluation showed that the Korean economy places a large stress on its environment. Water supply and generation of electricity were the most important contributions of the proposed dam in terms of emergy; 46.5 and 45.1% of the total benefit, respectively. Flood control contributed 8.4% of the total benefit. Major costs associated with the proposed dam were from sediments (33.2% of the total cost), construction services (22.8%), and social disruption of the region (21.6%). In terms of emergy, the ratio of benefits to costs of the proposed dam was 2.78 if sediments are not included, and 1.86 if sediments are included, which result in more benefits than costs in both cases. The benefit to cost ratio of the dam was larger than that of the current system (1.42) without the dam whether sediments are included in the total cost or not. The environmental stress of the proposed dam was considerably lower than that of the Korean economy, but the dam might increase stress on local environment. PMID:12448407
A spatial emergy model for Alachua County, Florida
NASA Astrophysics Data System (ADS)
Lambert, James David
A spatial model of the distribution of energy flows and storages in Alachua County, Florida, was created and used to analyze spatial patterns of energy transformation hierarchy in relation to spatial patterns of human settlement. Emergy, the available energy of one kind previously required directly or indirectly to make a product or service, was used as a measure of the quality of the different forms of energy flows and storages. Emergy provides a common unit of measure for comparing the productive contributions of natural processes with those of economic and social processes---it is an alternative to using money for measuring value. A geographic information system was used to create a spatial model and make maps that show the distribution and magnitude of different types of energy and emergy flows and storages occurring in one-hectare land units. Energy transformities were used to convert individual energy flows and storages into emergy units. Maps of transformities were created that reveal a clear spatial pattern of energy transformation hierarchy. The maps display patterns of widely-dispersed areas with lower transformity energy flows and storages, and smaller, centrally-located areas with higher transformities. Energy signature graphs and spatial unit transformities were used to characterize and compare the types and amounts of energy being consumed and stored according to land use classification, planning unit, and neighborhood categories. Emergy ratio maps and spatial unit ratios were created by dividing the values for specific emergy flows or storages by the values for other emergy flows or storages. Spatial context analysis was used to analyze the spatial distribution patterns of mean and maximum values for emergy flows and storages. The modeling method developed for this study is general and applicable to all types of landscapes and could be applied at any scale. An advantage of this general approach is that the results of other studies using this method
Teaching Algebra without Algebra
ERIC Educational Resources Information Center
Kalman, Richard S.
2008-01-01
Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…
What is the role of a system's size in an emergy evaluation, when we have to evaluate nested systems? To answer this question, we consider a simple nested system with three levels of organization and then examine the relationships among the emergy flows at each level and among th...
Brazilian Soybean Production: Emergy Analysis with an Expanded Scope
ERIC Educational Resources Information Center
Ortega, Enrique; Cavalett, Otavio; Bonifacio, Robert; Watanabe, Marcos
2005-01-01
This article offers the results of emergy analysis used to evaluate four different soybean production systems in Brazil that were divided into two main categories: biological models (organic and ecological farms) and industrial models (green-revolution chemical farms and herbicide with no-tillage farms). The biological models show better…
Emergy Evaluation of Educational Attainment in the United States
The emergy of educational attainment in the United States was quantified over the period for which the necessary data were available, i.e., 1948 to 2006. We propose that the portion of the knowledge in educational attainment delivered by the active workforce be considered as part...
Integrating Emergy into LCA: potential added value and lingering obstacles
Emergy attempts to measure the environmental work required to generate (ecosystem) goods and services that can be used by humans. It is claimed that the use of inventory modelling principles behind the Life Cycle Assessment (LCA) method (European Commission, 2010a) may improve th...
AN EMERGY AUDIT OF WEST VIRGINIA: STRENGTHS AND VULNERABILITIES
Emergy provides a general accounting mechanism that allows us to view the economy of humanity and the economy of nature on the same income and balance sheets. In this manner we can verify the financial picture given by economic analysis by checking it against a similar represen...
Emergy evaluation of a pumping irrigation water production system in China
NASA Astrophysics Data System (ADS)
Chen, Dan; Luo, Zhaohui; Webber, Michael; Chen, Jing; Wang, Weiguang
2014-03-01
The emergy concept was used to evaluate a pumping irrigation water production system in China. A framework for emergy evaluation of the significance of irrigation water and its production process was developed. The results show that the irrigation water saved has the highest emergy value (8.73E + 05 sej·J-1), followed by the irrigation water supplied to farmlands (1.72E + 05 sej·J-1), the pumped water (4.81E + 04 sej·J-1), with the lowest value shown from water taken from the local river (3.72E + 04 sej·J-1). The major contributions to the emergy needed for production are the inputs of soil and water. This production system could contribute to the irrigated agriculture and economy, according to several calculated emergy indices: emergy yield ratio ( EYR), emergy investment ratio ( EIR), environmental load ratio ( ELR), and environmental sustainability index ( ESI). The comparative analysis shows that the emergy theory and method, different from the conventional monetary-based analysis, could be used to evaluate irrigation water and its production process in terms of the biophysical account. Additional emergy evaluations should be completed on different types of water production and irrigated agricultural systems to provide adequate guidelines for the sustainability of irrigation development.
Development of the concept of emergy established a medium for accounting that made it possible to express economic and environmental work of all kinds on a common basis as solar emjoules. Environmental accounting using emdollars, a combined emergy-monetary unit, can be used to pr...
Estimates of the emergy carried by the flows of biologically active elements (BAE) and compounds are needed to accurately evaluate the near and far field effects of anthropogenic wastes. The transformities and specific emergies of these elements and of their different chemical sp...
Emergy Evaluation of Formal Education in the United States: 1870 to 2011
We evaluated the education system of the United States from 1870 to 2011 using emergy methods. The system was partitioned into three subsystems (elementary, secondary and college education) and the emergy inputs required to support each subsystem were determined for every year ov...
Methods for Estimating the Uncertainty in Emergy Table-Form Models
Emergy studies have suffered criticism due to the lack of uncertainty analysis and this shortcoming may have directly hindered the wider application and acceptance of this methodology. Recently, to fill this gap, the sources of uncertainty in emergy analysis were described and an...
The Emergy of Money Ratio of the United States from 1990 to 2007
The emergy to money ratio of a system is a key index used in emergy evaluations, because it represents the buying power of money and it can be used as an estimator of the average value of human service. Since both the material and energy inputs to societies and the money circulat...
Using the Language of Sets to Describe Nested Systems in Emergy Evaluations
The language of set theory has been recently used to describe the emergy evaluation of a process. In this paper this mathematical language is used as a guide to evaluate the emergy of nested systems. We analyze a territorial system on multiple scales as an example of hierarchical...
Emergy synthesis of tourism-based urban ecosystem.
Lei, Kampeng; Wang, Zhishi
2008-09-01
Macao is a tourist city with a dense population, but is short on natural resources. Almost all of the life-support resources of the city depend on imports from outside. During the past 20 years, Macao has experienced an economic boom accompanied by rapid social development. The tourism industry (including gambling, hotel accommodation, restaurant dining, and shows) have become the city's main economic activity since 1991. This paper uses emergy flow analysis to investigate and characterize the urban evolution and city development that have occurred in Macao from 1983 to 2003. Macao's tourism industry has existed almost from the establishment of the city, with the legalization of gambling in Macao occurring in 1850. Tourism has become the biggest industry in Macao, contributing more than half of the city's revenues since 1995. The emergy flow related to tourism was tracked and analyzed to measure its contribution to Macao. In addition, we used statistical analysis to divide the various emergy-based indicators into three categories: positive, negative, and insensitive indicators. PMID:17566636
NASA Astrophysics Data System (ADS)
Chen, B.; Chen, Z. M.; Zhou, Y.; Zhou, J. B.; Chen, G. Q.
2009-02-01
Ecological treatment engineering has been widely accepted as an artificially designed work to deal with the deteriorating ecological environment with low energy and resource consumption. To measure the energy and resource consumption and environmental support contained in the constructed wetland as a kind of ecological treatment engineering, emergy as embodied solar energy based assessment is performed and relative emergy-based indices including emergy yield ratio (EYR), emergy load ratio (ELR), emergy sustainability index (ESI), net economic benefit index (Np), and renewable percentage index (Pr), are also modified to evaluate the local sustainability of the constructed wetland in this paper. A case study on Longdao River constructed wetland compared with those of some earlier conventional treatment systems indicate that more local renewable resources and less ecological cost are involved, thus promoting the economic benefit due to less energy and resource consumption and simultaneously lowering the environmental stress of the treatment system on the local areas.
Keeping the books for environmental systems: an emergy analysis of West Virginia.
Campbell, Daniel; Meisch, Maria; Demoss, Thomas; Pomponio, John; Bradley, M Patricia
2004-06-01
Emergy provides a general accounting mechanism that allows us to view the economy and the environment on the same income statement and balance sheet. This allows an auditor to verify the economic picture by checking it against a more complete representation of the flows and storages of real wealth as measured by emergy. In this study, we constructed emergy accounts for the state of West Virginia in 1997. The income statement showed annual production, consumption, and flows of emergy and dollars into and out of the state. The balance sheet evaluated the storage of emergy in some of the state's assets. Emergy indices were used to answer questions posed by managers and gain insight into the state's economic and environmental strengths and weaknesses. West Virginia has great wealth in nonrenewable resources (9E14 sej m-2 or 17 times the U.S. average). The investment ratio of emergy purchased outside to indigenous renewable and nonrenewable emergy was 2.2:1, which indicates a high potential for future development. However, the environmental loading ratio (14:1) was already 1.5 times higher than that found at an average location in the U.S. Twice as much emergy was exported as received and standard of living indicators showed that people have largely failed to benefit from their state's wealth. We propose that, just as in business, where decisions made using financial accounts ensure solvency; decisions governing the environment should be made based on an emergy accounting of activities, assets, and liabilities for the combined system of humanity and nature. PMID:15141457
Emergy Evaluation of a Production and Utilization Process of Irrigation Water in China
Chen, Dan; Luo, Zhao-Hui; Chen, Jing; Kong, Jun; She, Dong-Li
2013-01-01
Sustainability evaluation of the process of water abstraction, distribution, and use for irrigation can contribute to the policy of decision making in irrigation development. Emergy theory and method are used to evaluate a pumping irrigation district in China. A corresponding framework for its emergy evaluation is proposed. Its emergy evaluation shows that water is the major component of inputs into the irrigation water production and utilization systems (24.7% and 47.9% of the total inputs, resp.) and that the transformities of irrigation water and rice as the systems' products (1.72E + 05 sej/J and 1.42E + 05 sej/J, resp.; sej/J = solar emjoules per joule) represent their different emergy efficiencies. The irrigated agriculture production subsystem has a higher sustainability than the irrigation water production subsystem and the integrated production system, according to several emergy indices: renewability ratio (%R), emergy yield ratio (EYR), emergy investment ratio (EIR), environmental load ratio (ELR), and environmental sustainability index (ESI). The results show that the performance of this irrigation district could be further improved by increasing the utilization efficiencies of the main inputs in both the production and utilization process of irrigation water. PMID:24082852
Emergy and Eco-exergy Evaluation of Four Forest Restoration Modes
Four different forest restoration modes (Acacia mangium plantation, mixed-native species plantation, conifer plantation and Eucalyptus plantation) were evaluated using Energy System Theory and the emergy synthesis method. In addition, the eco-exergies of the four forest restorati...
Guan, Fa-chun; Sha, Zhi-peng; Zhang, Yu-yang; Wang, Jun-feng; Wang, Chao
2016-01-01
Home courtyard agriculture is an important model of agricultural production on the Tibetan plateau. Because of the sensitive and fragile plateau environment, it needs to have optimal performance characteristics, including high sustainability, low environmental pressure, and high economic benefit. Emergy analysis is a promising tool for evaluation of the environmental-economic performance of these production systems. In this study, emergy analysis was used to evaluate three courtyard agricultural production models: Raising Geese in Corn Fields (RGICF), Conventional Corn Planting (CCP), and Pea-Wheat Rotation (PWR). The results showed that the RGICF model produced greater economic benefits, and had higher sustainability, lower environmental pressure, and higher product safety than the CCP and PWR models. The emergy yield ratio (EYR) and emergy self-support ratio (ESR) of RGICF were 0.66 and 0.11, respectively, lower than those of the CCP production model, and 0.99 and 0.08, respectively, lower than those of the PWR production model. The impact of RGICF (1.45) on the environment was lower than that of CCP (2.26) and PWR (2.46). The emergy sustainable indices (ESIs) of RGICF were 1.07 and 1.02 times higher than those of CCP and PWR, respectively. With regard to the emergy index of product safety (EIPS), RGICF had a higher safety index than those of CCP and PWR. Overall, our results suggest that the RGICF model is advantageous and provides higher environmental benefits than the CCP and PWR systems. PMID:27487808
Guan, Fa-Chun; Sha, Zhi-Peng; Zhang, Yu-Yang; Wang, Jun-Feng; Wang, Chao
2016-08-01
Home courtyard agriculture is an important model of agricultural production on the Tibetan plateau. Because of the sensitive and fragile plateau environment, it needs to have optimal performance characteristics, including high sustainability, low environmental pressure, and high economic benefit. Emergy analysis is a promising tool for evaluation of the environmental-economic performance of these production systems. In this study, emergy analysis was used to evaluate three courtyard agricultural production models: Raising Geese in Corn Fields (RGICF), Conventional Corn Planting (CCP), and Pea-Wheat Rotation (PWR). The results showed that the RGICF model produced greater economic benefits, and had higher sustainability, lower environmental pressure, and higher product safety than the CCP and PWR models. The emergy yield ratio (EYR) and emergy self-support ratio (ESR) of RGICF were 0.66 and 0.11, respectively, lower than those of the CCP production model, and 0.99 and 0.08, respectively, lower than those of the PWR production model. The impact of RGICF (1.45) on the environment was lower than that of CCP (2.26) and PWR (2.46). The emergy sustainable indices (ESIs) of RGICF were 1.07 and 1.02 times higher than those of CCP and PWR, respectively. With regard to the emergy index of product safety (EIPS), RGICF had a higher safety index than those of CCP and PWR. Overall, our results suggest that the RGICF model is advantageous and provides higher environmental benefits than the CCP and PWR systems. PMID:27487808
NASA Astrophysics Data System (ADS)
Wang, Guodong; Dong, Shuanglin; Tian, Xiangli; Gao, Qinfeng; Wang, Fang
2015-06-01
Emergy analysis is effective for analyzing ecological economic systems. However, the accuracy of the approach is affected by the diversity of economic level, meteorological and hydrological parameters in different regions. The present study evaluated the economic benefits, environmental impact, and sustainability of indoor, semi-intensive and extensive farming systems of sea cucumber ( Apostichopus japonicus) in the same region. The results showed that A. japonicus indoor farming system was high in input and output (yield) whereas pond extensive farming system was low in input and output. The output/input ratio of indoor farming system was lower than that of pond extensive farming system, and the output/input ratio of semi-intensive farming system fell in between them. The environmental loading ratio of A. japonicus extensive farming system was lower than that of indoor farming system. In addition, the emergy yield and emergy exchange ratios, and emergy sustainability and emergy indexes for sustainable development were higher in extensive farming system than those in indoor farming system. These results indicated that the current extensive farming system exerted fewer negative influences on the environment, made more efficient use of available resources, and met more sustainable development requirements than the indoor farming system. A. japonicus farming systems showed more emergy benefits than fish farming systems. The pond farming systems of A. japonicus exploited more free local environmental resources for production, caused less potential pressure on the local environment, and achieved higher sustainability than indoor farming system.
Pulselli, Riccardo Maria
2010-11-01
This paper presents an application of an environmental accounting method, namely emergy evaluation, developed for the monitoring and assessment of environmental resource use by local communities in the Abruzzo Region (Italy). Once quantified and classified according to their origin (renewable or non-renewable, local or external), emergy flows were elaborated through a geographic information system (GIS) that allowed us to represent their spatial distribution throughout the region. Outcomes took the form of patterns in which different emergy intensities, namely empower (unit: seJ yr(-1)), were represented through a graduated grey-scale and visualized on a cartographic basis. The concentration of emergy flows, depending on the activity of local communities, showed variable levels of environmental load in different areas. In particular, spatial zones with homogeneous values of empower density (unit: seJ yr(-1) km(-2))--high, medium and low--were detected in order to identify areas with a similar "thermodynamic" nature, emergy being a thermodynamics based function. This allowed for the representation, at a glance, of a kind of geography that mirrors the behavior of a population settled in an area as additional information for investigating the effects of the use of urban structures and functions and improving our understanding of regional systems. A combined use of emergy evaluation and GIS could thus provide a complementary view of a territorial system and inform policy makers for planning specific strategies of future development. PMID:20663603
ERIC Educational Resources Information Center
Schaufele, Christopher; Zumoff, Nancy
Earth Algebra is an entry level college algebra course that incorporates the spirit of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics at the college level. The context of the course places mathematics at the center of one of the major current concerns of the world. Through…
ERIC Educational Resources Information Center
Cavanagh, Sean
2009-01-01
As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…
Brandt-Williams, Sherry; Wigand, Cathleen; Campbell, Daniel E
2013-02-01
This study evaluated the link between watershed activities and salt marsh structure, function, and condition using spatial emergy flow density (areal empower density) in the watershed and field data from 10 tidal salt marshes in Narragansett Bay, RI, USA. The field-collected data were obtained during several years of vegetation, invertebrate, soil, and water quality sampling. The use of emergy as an accounting mechanism allowed disparate factors (e.g., the amount of building construction and the consumption of electricity) to be combined into a single landscape index while retaining a uniform quantitative definition of the intensity of landscape development. It expanded upon typical land use percentage studies by weighting each category for the intensity of development. At the RI salt marsh sites, an impact index (watershed emergy flow normalized for marsh area) showed significant correlations with mudflat infauna species richness, mussel density, plant species richness, the extent and density of dominant plant species, and denitrification potential within the high salt marsh. Over the 4-year period examined, a loading index (watershed emergy flow normalized for watershed area) showed significant correlations with nitrite and nitrate concentrations, as well as with the nitrogen to phosphorus ratios in stream discharge into the marshes. Both the emergy impact and loading indices were significantly correlated with a salt marsh condition index derived from intensive field-based assessments. Comparison of the emergy indices to calculated nitrogen loading estimates for each watershed also produced significant positive correlations. These results suggest that watershed emergy flow is a robust index of human disturbance and a potential tool for rapid assessment of coastal wetland condition. PMID:22535367
Energy and resource basis of an Italian coastal resort region integrated using emergy synthesis.
Vassallo, Paolo; Paoli, Chiara; Tilley, David R; Fabiano, Mauro
2009-10-01
Sustainable development of coastal zones must balance economic development that encourages human visitation from a larger population with desires that differ from the local residents with the need to maintain opportunities for the local resident society and conserve ecological capital, which may serve as the basis for residents. We present a case study in which the sustainability level of a coastal zone (Riviera del Beigua), located along the Ligurian coast of north-western Italy, was assessed through the lens of systems ecology using emergy synthesis to integrate across economic, social and environmental sub-systems. Our purposes were (1) to quantify the environmental sustainability level of this coastal zone, (2) to evaluate the role of tourism in affecting the economy, society and environment, and (3) to compare emergy synthesis to Butler's Tourism Area Life Cycle model (TALC). Results showed that 81% of the total emergy consumption in the coastal zone was derived from external sources, indicating that this tourist-heavy community was not sustainable. Tourism, as the dominant economic sub-system, consumed 42% of the total emergy budget, while local residents used the remaining 58%. The progressive stages of the TALC model were found to parallel the dynamic changes in the ratio of external emergy inputs to local emergy inputs, suggesting that emergy synthesis could be a useful tool for detecting a tourist region's TALC stage. Use of such a quantitative tool could expedite sustainability assessment to allow administrative managers to understand the complex relationship between a region's economy, environment and resident society so sound policies can be developed to improve overall sustainability. PMID:19783358
Geng, Yong; Liu, Zuoxi; Xue, Bing; Dong, Huijuan; Fujita, Tsuyoshi; Chiu, Anthony
2014-12-01
Industrial symbiosis is the sharing of services, utility, and by-product resources among industries. This is usually made in order to add value, reduce costs, and improve the environment, and therefore has been taken as an effective approach for developing an eco-industrial park, improving resource efficiency, and reducing pollutant emission. Most conventional evaluation approaches ignored the contribution of natural ecosystem to the development of industrial symbiosis and cannot reveal the interrelations between economic development and environmental protection, leading to a need of an innovative evaluation method. Under such a circumstance, we present an emergy analysis-based evaluation method by employing a case study at Shenyang Economic and Technological Development Zone (SETDZ). Specific emergy indicators on industrial symbiosis, including emergy savings and emdollar value of total emergy savings, were developed so that the holistic picture of industrial symbiosis can be presented. Research results show that nonrenewable inputs, imported resource inputs, and associated services could be saved by 89.3, 32.51, and 15.7 %, and the ratio of emergy savings to emergy of the total energy used would be about 25.58 %, and the ratio of the emdollar value of total emergy savings to the total gross regional product (GRP) of SETDZ would be 34.38 % through the implementation of industrial symbiosis. In general, research results indicate that industrial symbiosis could effectively reduce material and energy consumption and improve the overall eco-efficiency. Such a method can provide policy insights to industrial park managers so that they can raise appropriate strategies on developing eco-industrial parks. Useful strategies include identifying more potential industrial symbiosis opportunities, optimizing energy structure, increasing industrial efficiency, recovering local ecosystems, and improving public and industrial awareness of eco-industrial park policies. PMID
Emergy evaluation of contrasting dairy systems at multiple levels.
Vigne, Mathieu; Peyraud, Jean-Louis; Lecomte, Philippe; Corson, Michael S; Wilfart, Aurélie
2013-11-15
Emergy accounting (EmA) was applied to a range of dairy systems, from low-input smallholder systems in South Mali (SM), to intermediate-input systems in two regions of France, Poitou-Charentes (PC) and Bretagne (BR), to high-input systems on Reunion Island (RI). These systems were studied at three different levels: whole-farm (dairy system and cropping system), dairy-system (dairy herd and forage land), and herd (animals only). Dairy farms in SM used the lowest total emergy at all levels and was the highest user of renewable resources. Despite the low quality of resources consumed (crop residues and natural pasture), efficiency of their use was similar to that of industrialised inputs by intensive systems in RI, PC and BR. In addition, among the systems studied, SM dairy farms lay closest to environmental sustainability, contradicting the usual image of high environmental impact of cattle production in developing countries. EmA also revealed characteristics of the three intensive systems. Systems from RI and PC had lower resource transformation efficiency and higher environmental impacts than those from BR, due mainly to feeding strategies that differed due to differing socio-climatic constraints. Application of EmA at multiple levels revealed the importance of a multi-level analysis. While the whole-farm level assesses the overall contribution of the system to its environment, the dairy-system level is suitable for comparison of multi-product systems. In contrast, the herd level focuses on herd management and bypasses debates about definition of system boundaries by excluding land management. Combining all levels highlights the contribution of livestock to the global agricultural system and identifies inefficiencies and influences of system components on the environment. PMID:23792889
Using emergy to quantify an economic hierarchy between four U.S. states - Maryland, Delaware, New Jersey and Pennsylvania
A regional emergy evaluation was completed for each of four adjacent states with differing levels and sources of economic productivity ? Maryland, Delaware...
Zhang, Ying-Cong; Du, Shou-Hu
2012-03-01
Agro-ecosystem is the most basic system for human beings survival, while the analysis of the structure and function of the system is the key to solve the problems of agro-ecological environment. In this paper, emergy theory and related economic measurement methods including data envelopment analysis, cointegration test, and error correction model were applied to quantitatively analyze the operation dynamics, environmental loading, operation efficiency, and input-output relation of the agro-ecosystems in Sichuan Province and its 21 cities in 1997-2009. In the study period, Sichuan Province was in the transition period from traditional agriculture to modern agriculture. The agricultural mechanization level of the Province improved constantly, resources utilization efficiency enhanced continually, overall structural dominant degree was better, but the over-reliance on economic emergy input caused the sustainability of the system weakened gradually. The development status of the agro-ecosystems in the Province varied among regions. Chengdu Plain and Western Sichuan Highland were either in overexploited or in underutilized, while the hilly areas were full of vitality and development potential, tended to be the important areas for the future development of Sichuan agriculture. Generally, the operation efficiency of the agro-ecosystems in the Province was relatively low, with the situation differed in different regions due to the lower technical efficiency or improper scale. There was a long-term equilibrium between the economic emergy indices and output emergy, but the short-term emergy input didn't reach the ideal output. PMID:22720632
NASA Astrophysics Data System (ADS)
Zhou, S. Y.; Zhang, B.; Cai, Z. F.
2010-05-01
This paper aims to present a biophysical understanding of the agricultural ecological engineering by emergy analysis for a farm biogas project in China as a representative case. Accounting for the resource inputs into and accumulation within the project, as well as the outputs to the social system, emergy analysis provides an empirical study in the biophysical dimension of the agricultural ecological engineering. Economic benefits and ecological economic benefits of the farm biogas project indicated by market value and emergy monetary value are discussed, respectively. Relative emergy-based indices such as renewability (R%), emergy yield ratio (EYR), environmental load ratio (ELR) and environmental sustainability index (ESI) are calculated to evaluate the environmental load and local sustainability of the concerned biogas project. The results show that the farm biogas project has more reliance on the local renewable resources input, less environmental pressure and higher sustainability compared with other typical agricultural systems. In addition, holistic evaluation and its policy implications for better operation and management of the biogas project are presented.
[Evaluation of ecosystem service and emergy of Wanshan Waters in Zhuhai, Guangdong Province, China].
Qin, Chuan-xin; Chen, Pi-mao; Zhang, An-kai; Yuan, Hua; Li, Guo-ying; Shu, Li-ming; Zhou, Yan-bo; Li, Xiao-guo
2015-06-01
The method for monetary value and emergy value analysis of ecosystem service was used in this paper to analyze the change in value of marine ecosystem service of Wanshan District, Zhuhai from 2007 to 2012. The result showed that the monetary value and emergy value of marine ecosystem service of Wanshan District, Zhuhai rose to 11512840000 yuan and 1.97 x 10(22) sej from 7721630000 yuan and 1.04 x 10(22) sej, respectively. Both monetary value and emergy value could forecast the change in the value of marine ecosystem service, but they reflected different value structures and ecological energy, which could be used to more objectively evaluate the ecosystem service. Ecological civilization development, as an inherent driving force to impel the development of marine ecosystem service structure, was important for rational exploitation of marine resources and optimization of marine ecosystem service. PMID:26572041
Emergy Analysis of Biogas Systems Based on Different Raw Materials
Wang, Yang; Lin, Cong; Li, Jing; Duan, Na; Li, Xue; Fu, Yanyan
2013-01-01
Environmental pollution and energy crisis restrict the development of China, and the utilization of renewable technology is an effective strategy to alleviate the damage. Biogas engineering has rapidly developed attributes to solve environmental problems and create a renewable energy product biogas. In this paper, two different biogas plants' materials were analyzed by emergy method. One of them is a biogas project whose degraded material is feces (BPF system), and the other is the one whose degraded material is corn straw (BPC system). As a result, the ecological-economic values of BPF and BPC are $28,300/yr and $8,100/yr, respectively. Considering currency, environment, and human inputs, both of the biogas projects have the ability of disposing waste and potential for development. The proportion of biogas output is much more than fertilizer output; so, fertilizer utilization should be emphasized in the future. In comparison, BPF is better than BPC in the aspects of ecological-economic benefits, environmental benefits, and sustainability. The reason is the difficulty of corn straw seasonal collection and degradation. Thus it is proposed that BPC should be combined with the other raw materials. PMID:23476134
Emergy analysis of biogas systems based on different raw materials.
Wang, Yang; Lin, Cong; Li, Jing; Duan, Na; Li, Xue; Fu, Yanyan
2013-01-01
Environmental pollution and energy crisis restrict the development of China, and the utilization of renewable technology is an effective strategy to alleviate the damage. Biogas engineering has rapidly developed attributes to solve environmental problems and create a renewable energy product biogas. In this paper, two different biogas plants' materials were analyzed by emergy method. One of them is a biogas project whose degraded material is feces (BPF system), and the other is the one whose degraded material is corn straw (BPC system). As a result, the ecological-economic values of BPF and BPC are $28,300/yr and $8,100/yr, respectively. Considering currency, environment, and human inputs, both of the biogas projects have the ability of disposing waste and potential for development. The proportion of biogas output is much more than fertilizer output; so, fertilizer utilization should be emphasized in the future. In comparison, BPF is better than BPC in the aspects of ecological-economic benefits, environmental benefits, and sustainability. The reason is the difficulty of corn straw seasonal collection and degradation. Thus it is proposed that BPC should be combined with the other raw materials. PMID:23476134
Dean, Marleah; Gill, Rebecca; Barbour, Joshua B
2016-12-01
Communication is key to hospital emergency department (ED) caregiving. Interventions in ED processes (and health care organizing in general) have struggled when they have ignored the professional role expectations that enable and constrain providers with patients and each other. Informed by a communication as design (CAD) approach, this study explored the intersections of professional roles, physical space, and communication at EmergiCare-an academic medical center and level-1 trauma center hospital. Based on an ethnographic analysis of field notes from 70 hours of shadowing at the EmergiCare ED, this study identified two specific communication patterns, "case talk" and "comfort talk," that reflect different logics for communication in health care organizing. The findings indicate (a) that case and comfort talk have different status and therefore different influence in EmergiCare ED interprofessional communication and (b) that the arrangement of physical space at EmergiCare ED reflects the requirements of case talk more so than comfort talk. These findings have important implications for theory and practice, including the importance of considering the macro-discursive construction of professional roles reified in the arrangement of work space. PMID:27093130
The idea that the methods and models of accounting and bookkeeping might be useful in describing, understanding, and managing environmental systems is implicit in the title of H.T. Odum's book, Environmental Accounting: Emergy and Environmental Decision Making. In this paper, I ...
Relationships among the energy, emergy, and money flows of the United States from 1900 to 2011.
Energy Systems Language models of the resource base for the U.S. economy and of economic exchange were used, respectively, (1) to show how energy consumption and emergy use contribute to real and nominal gross domestic product (GDP) and (2) to propose a model of coupled flows tha...
Relationships Among the Energy, Emergy, and Money Flows of the United States From 1900 to 2011
In this paper, we examine the relationships among the energy, emergy, and money flows of the United States from 1900 to 2011. To establish a theoretical basis for understanding these relationships, Energy Systems Language models of the resource base for the World System and of e...
Integrated Emergy and Economic Evaluation of Tea Production Chains in Anxi, China
Emergy and economic methods were used to evaluate and compare tea production systems in Anxi, China. Tea production was classified into three phases, i.e., the nursery, the plantation and tea processing, and each phase was evaluated. The results showed that the nursery subsystems...
A Brief History of the Emergy Society and its Mission in the World
In 2002, H.T. Odum authorized the formation of a society dedicated to research, communication, and education focused on the new ideas of emergy and transformity and their basis in Energy Systems Theory. From this initial concept and after a 5 period of incubation, the Internation...
A reexamination of the emergy input to a system from the wind
With the establishment of a new, rigorously-determined, solar equivalence baseline for the geobiosphere, 12.0E+24 seJ y-1, it is now appropriate to reexamine the calculation of the emergy delivered by the major secondary products of the geobiosphere, e.g., wind and rainfall, whi...
This study evaluated the link between watershed activities and salt marsh structure, function, and condition using spatial emergy flow density (areal empower density) in the watershed and field data from 10 tidal salt marshes in Narragansett Bay, RI. The field-collected data wer...
Emergy and Evaluating Ecosystem Services in a Sumatran Peat Swamp, Indonesia. Chapter 13
The purpose of this article is to document preliminary investigations into valuing peat swamp ecosystem function and services in Indonesia and to compare these values with the current development alternative, Acacia pulp wood plantation, using the emergy methodology. The Zamrud N...
Emergy evaluation of management measures for derelict fishing gears in Korea
NASA Astrophysics Data System (ADS)
Hong, Sunwook; Lee, Jongmyoung; Kang, Daeseok
2015-09-01
Derelict fishing gears (DFGs) have been recognized as an important marine debris issue that requires urgent action in Korea. This study used the emergy methodology to evaluate the cost efficiency of three DFG management measures of Korea from a biophysical perspective. Selected measures were the cleanup-using-ships (CL) program, the buyback (BB) program, and the floating reception barge (FB) program that ranged from more preventive approaches to curative ones in the management spectrum of DFGs. Among three measures, the CL program was the costliest one to implement both in emergy and monetary terms. The FB program that is closest to the preventive side of the spectrum required the least emergy input and monetary cost. The emergy requirements per ton of DFGs collected for the CL and BB programs were 4.4 and 3.6 times that of the FB program, respectively. The CL and BB program also required more inputs in monetary terms - 8.6 and 6.8 times higher, respectively, than the FB program did. The closer a measure is to the preventive side of the management spectrum, the less costly its implementation. This suggests that in terms of cost to implement, the current DFG management policy needs to be reorganized so that preventive measures can play a larger role in dealing with DFG issues in Korea.
KEEPING THE BOOKS FOR ENVIRONMENTAL SYSTEMS: AN EMERGY ANALYSIS OF WEST VIRGINIA
Emergy provides a general accounting mechanism that allows us to view the economy and the environment on the same income statement and balance sheet. This allows an auditor to verify the economic picture by checking it against a more complete representation of the flows and stora...
An energy systems view of sustainability: emergy evaluation of the San Luis Basin, Colorado.
Campbell, Daniel E; Garmestani, Ahjond S
2012-03-01
Energy Systems Theory (EST) provides a framework for understanding and interpreting sustainability. EST implies that "what is sustainable" for a system at any given level of organization is determined by the cycles of change originating in the next larger system and within the system of concern. The pulsing paradigm explains the ubiquitous cycles of change that apparently govern ecosystems, rather than succession to a steady state that is then sustainable. Therefore, to make robust decisions among environmental policies and alternatives, decision-makers need to know where their system resides in the cycles of change that govern it. This theory was examined by performing an emergy evaluation of the sustainability of a regional system, the San Luis Basin (SLB), CO. By 1980, the SLB contained a climax stage agricultural system with well-developed crop and livestock production along with food and animal waste processing. The SLB is also a hinterland in that it exports raw materials and primary products (exploitation stage) to more developed areas. Emergy indices calculated for the SLB from 1995 to 2005 revealed changes in the relative sustainability of the system over this time. The sustainability of the region as indicated by the renewable emergy used as a percent of total use declined 4%, whereas, the renewable carrying capacity declined 6% over this time. The Emergy Sustainability Index (ESI) showed the largest decline (27%) in the sustainability of the region. The total emergy used by the SLB, a measure of system well-being, was fairly stable (CV = 0.05). In 1997, using renewable emergy alone, the SLB could support 50.7% of its population at the current standard of living, while under similar conditions the U.S. could support only 4.8% of its population. In contrast to other indices of sustainability, a new index, the Emergy Sustainable Use Index (ESUI), which considers the benefits gained by the larger system compared to the potential for local environmental
LCA and emergy accounting of aquaculture systems: towards ecological intensification.
Wilfart, Aurélie; Prudhomme, Jehane; Blancheton, Jean-Paul; Aubin, Joël
2013-05-30
An integrated approach is required to optimise fish farming systems by maximising output while minimising their negative environmental impacts. We developed a holistic approach to assess the environmental performances by combining two methods based on energetic and physical flow analysis. Life Cycle Assessment (LCA) is a normalised method that estimates resource use and potential impacts throughout a product's life cycle. Emergy Accounting (EA) refers the amount of energy directly or indirectly required by a product or a service. The combination of these two methods was used to evaluate the environmental impacts of three contrasting fish-farming systems: a farm producing salmon in a recirculating system (RSF), a semi-extensive polyculture pond (PF1) and an extensive polyculture pond (PF2). The RSF system, with a low feed-conversion ratio (FCR = 0.95), had lower environmental impacts per tonne of live fish produced than did the two pond farms, when the effects on climate change, acidification, total cumulative energy demand, land competition and water dependence were considered. However, RSF was clearly disconnected from the surrounding environment and depended highly on external resources (e.g. nutrients, energy). Ponds adequately incorporated renewable natural resources but had higher environmental impacts due to incomplete use of external inputs. This study highlighted key factors necessary for the successful ecological intensification of fish farming, i.e., minimise external inputs, lower the FCR, and increase the use of renewable resources from the surrounding environment. The combination of LCA and EA seems to be a practical approach to address the complexity of optimising biophysical efficiency in aquaculture systems. PMID:23531606
Twisted Quantum Toroidal Algebras
NASA Astrophysics Data System (ADS)
Jing, Naihuan; Liu, Rongjia
2014-09-01
We construct a principally graded quantum loop algebra for the Kac-Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations.
Algebraic vs physical N = 6 3-algebras
Cantarini, Nicoletta; Kac, Victor G.
2014-01-15
In our previous paper, we classified linearly compact algebraic simple N = 6 3-algebras. In the present paper, we classify their “physical” counterparts, which actually appear in the N = 6 supersymmetric 3-dimensional Chern-Simons theories.
ERIC Educational Resources Information Center
National Council of Teachers of Mathematics, Inc., Reston, VA.
This is a reprint of the historical capsules dealing with algebra from the 31st Yearbook of NCTM,"Historical Topics for the Mathematics Classroom." Included are such themes as the change from a geometric to an algebraic solution of problems, the development of algebraic symbolism, the algebraic contributions of different countries, the origin and…
Figueroa-O'Farrill, Jose Miguel
2009-11-15
We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on the case of n=3 and explore the deformations of 3-algebras of relevance to three-dimensional superconformal Chern-Simons theories with matter.
Quantum cluster algebras and quantum nilpotent algebras
Goodearl, Kenneth R.; Yakimov, Milen T.
2014-01-01
A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197
Emergy-based comparative analysis of energy intensity in different industrial systems.
Liu, Zhe; Geng, Yong; Wang, Hui; Sun, Lu; Ma, Zhixiao; Tian, Xu; Yu, Xiaoman
2015-12-01
With the rapid economic development, energy consumption of China has been the second place in the world next to the USA. Usually, measuring energy consumption intensity or efficiency applies heat unit which is joule per gross domestic production (GDP) or coal equivalent per GDP. However, this measuring approach is only oriented by the conversion coefficient of heat combustion which does not match the real value of the materials during their formation in the ecological system. This study applied emergy analysis to evaluate the energy consumption intensity to fill this gap. Emergy analysis is considered as a bridge between ecological system and economic system, which can evaluate the contribution of ecological products and services as well as the load placed on environmental systems. In this study, emergy indicator for performing energy consumption intensity of primary energy was proposed. Industrial production is assumed as the main contributor of energy consumption compared to primary and tertiary industries. Therefore, this study validated this method by investigating the two industrial case studies which were Dalian Economic Development Area (DEDA) and Fuzhou economic and technological area (FETA), to comparatively study on their energy consumption intensity between the different kinds of industrial systems and investigate the reasons behind the differences. The results show that primary energy consumption (PEC) of DEDA was much higher than that of FETA during 2006 to 2010 and its primary energy consumption ratio (PECR) to total emergy involvement had a dramatically decline from year 2006 to 2010. In the same time, nonrenewable energy of PEC in DEDA was also much higher than that in FETA. The reason was that industrial structure of DEDA was mainly formed by heavy industries like petro-chemistry industry, manufacturing industries, and high energy-intensive industries. However, FETA was formed by electronic business, food industry, and light industries. Although
Learning Algebra in a Computer Algebra Environment
ERIC Educational Resources Information Center
Drijvers, Paul
2004-01-01
This article summarises a doctoral thesis entitled "Learning algebra in a computer algebra environment, design research on the understanding of the concept of parameter" (Drijvers, 2003). It describes the research questions, the theoretical framework, the methodology and the results of the study. The focus of the study is on the understanding of…
Realizations of Galilei algebras
NASA Astrophysics Data System (ADS)
Nesterenko, Maryna; Pošta, Severin; Vaneeva, Olena
2016-03-01
All inequivalent realizations of the Galilei algebras of dimensions not greater than five are constructed using the algebraic approach proposed by Shirokov. The varieties of the deformed Galilei algebras are discussed and families of one-parametric deformations are presented in explicit form. It is also shown that a number of well-known and physically interesting equations and systems are invariant with respect to the considered Galilei algebras or their deformations.
Applied Algebra Curriculum Modules.
ERIC Educational Resources Information Center
Texas State Technical Coll., Marshall.
This collection of 11 applied algebra curriculum modules can be used independently as supplemental modules for an existing algebra curriculum. They represent diverse curriculum styles that should stimulate the teacher's creativity to adapt them to other algebra concepts. The selected topics have been determined to be those most needed by students…
NASA Technical Reports Server (NTRS)
Iachello, Franco
1995-01-01
An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.
Orientation in operator algebras
Alfsen, Erik M.; Shultz, Frederic W.
1998-01-01
A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics. PMID:9618457
Developing Thinking in Algebra
ERIC Educational Resources Information Center
Mason, John; Graham, Alan; Johnson-Wilder, Sue
2005-01-01
This book is for people with an interest in algebra whether as a learner, or as a teacher, or perhaps as both. It is concerned with the "big ideas" of algebra and what it is to understand the process of thinking algebraically. The book has been structured according to a number of pedagogic principles that are exposed and discussed along the way,…
Connecting Arithmetic to Algebra
ERIC Educational Resources Information Center
Darley, Joy W.; Leapard, Barbara B.
2010-01-01
Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…
Ternary Virasoro - Witt algebra.
Zachos, C.; Curtright, T.; Fairlie, D.; High Energy Physics; Univ. of Miami; Univ. of Durham
2008-01-01
A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations.
Profiles of Algebraic Competence
ERIC Educational Resources Information Center
Humberstone, J.; Reeve, R.A.
2008-01-01
The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…
Computer algebra and operators
NASA Technical Reports Server (NTRS)
Fateman, Richard; Grossman, Robert
1989-01-01
The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.
Fuzzy-algebra uncertainty assessment
Cooper, J.A.; Cooper, D.K.
1994-12-01
A significant number of analytical problems (for example, abnormal-environment safety analysis) depend on data that are partly or mostly subjective. Since fuzzy algebra depends on subjective operands, we have been investigating its applicability to these forms of assessment, particularly for portraying uncertainty in the results of PRA (probabilistic risk analysis) and in risk-analysis-aided decision-making. Since analysis results can be a major contributor to a safety-measure decision process, risk management depends on relating uncertainty to only known (not assumed) information. The uncertainties due to abnormal environments are even more challenging than those in normal-environment safety assessments; and therefore require an even more judicious approach. Fuzzy algebra matches these requirements well. One of the most useful aspects of this work is that we have shown the potential for significant differences (especially in perceived margin relative to a decision threshold) between fuzzy assessment and probabilistic assessment based on subtle factors inherent in the choice of probability distribution models. We have also shown the relation of fuzzy algebra assessment to ``bounds`` analysis, as well as a description of how analyses can migrate from bounds analysis to fuzzy-algebra analysis, and to probabilistic analysis as information about the process to be analyzed is obtained. Instructive examples are used to illustrate the points.
Emergy and economic methods were used to evaluate and compare a traditional tropical fruit cultivation system, for bananas, and three newly introduced fruit cultivation systems, for papaya, guava and wampee, on reclaimed wetlands of the Pearl River Estuary, China. The evaluations...
NASA Astrophysics Data System (ADS)
Chen, Dan; Luo, Zhaohui; Webber, Michael; Chen, Jing; Wang, Weiguang
2014-09-01
Emergy theory and method are used to evaluate the contribution of irrigation water, and the process of its utilization, in three agricultural systems. The agricultural systems evaluated in this study were rice, wheat, and oilseed rape productions in an irrigation pumping district of China. A corresponding framework for emergy evaluation and sensitivity analysis methods was proposed. Two new indices, the fraction of irrigation water ( FIW), and the irrigation intensity of agriculture ( IIA), were developed to depict the contribution of irrigation water. The calculated FIW indicated that irrigation water used for the rice production system (34.7%) contributed more than irrigation water used for wheat (5.3%) and oilseed rape (11.2%) production systems in a typical dry year. The wheat production with an IIA of 19.0 had the highest net benefit from irrigation compared to the rice (2.9) and oilseed rape (8.9) productions. The transformities of the systems' products represented different energy efficiencies for rice (2.50E + 05 sej·J-1), wheat (1.66E + 05 sej·J-1) and oilseed rape (2.14E + 05 sej·J-1) production systems. According to several emergy indices, of the three systems evaluated, the rice system had the greatest level of sustainability. However, all of them were less sustainable than the ecological agricultural systems. A sensitivity analysis showed that the emergy inputs of irrigation water and nitrogenous fertilizer were the highest sensitivity factors influencing the emergy ratios. Best Management Practices, and other agroecological strategies, could be implemented to make further improvements in the sustainability of the three systems.
Emergy analysis of the recycling options for construction and demolition waste.
Yuan, Fang; Shen, Li-yin; Li, Qi-ming
2011-12-01
Construction and demolition (C&D) waste is becoming a major contributor to environmental pollution. In Shanghai, China, the quantity of C&D waste is 2.11E+07 t/yr, which accounts for 45% of the total quantity of solid waste. There has been a growing promotion of recycling C&D waste as an effective way to solve this waste problem. However, the evaluation of the efficiency of recycling C&D waste as a potential source of resources is largely based on traditional economic analysis. The economic analysis emphasizes money instead of the harmony between economic benefit and environmental effects. There is a need for a new strategic approach to investigate the efficiency of recycling C&D waste to achieve the integration between economic, social and environmental effects. Emergy theory can be employed to analyze different recycling options for C&D waste. With reference to the Chinese construction industry, this paper demonstrates that the close-loop recycling option is better than the open-loop recycling option for C&D waste in terms of the integration of social, environmental and sustainable aspects. To evaluate different technology solutions for C&D waste recycling, the emergy theory and method is not limited to a cost-benefit balance but can include economic, social, environmental and sustainable effects. PMID:21820302
Ren, Jingzheng; Liang, Hanwei; Dong, Liang; Sun, Lu; Gao, Zhiqiu
2016-08-15
Industrial symbiosis provides novel and practical pathway to the design for the sustainability. Decision support tool for its verification is necessary for practitioners and policy makers, while to date, quantitative research is limited. The objective of this work is to present an innovative approach for supporting decision-making in the design for the sustainability with the implementation of industrial symbiosis in chemical complex. Through incorporating the emergy theory, the model is formulated as a multi-objective approach that can optimize both the economic benefit and sustainable performance of the integrated industrial system. A set of emergy based evaluation index are designed. Multi-objective Particle Swarm Algorithm is proposed to solve the model, and the decision-makers are allowed to choose the suitable solutions form the Pareto solutions. An illustrative case has been studied by the proposed method, a few of compromises between high profitability and high sustainability can be obtained for the decision-makers/stakeholders to make decision. PMID:27110990
Emergy-based urban ecosystem health assessment: A case study of Baotou, China
NASA Astrophysics Data System (ADS)
Liu, G. Y.; Yang, Z. F.; Chen, B.; Zhang, Y.; Zhang, L. X.; Zhao, Y. W.; Jiang, M. M.
2009-03-01
Ecosystem health has been a hot topic of ecosystem management research for years. Considering the urban area as a complex ecosystem consisted of natural, societal and economic entities, urban ecosystem health assessment is necessary to be conducted for the scientific management and proper ecological restoration. Combining with the ecosystem service function of the urban ecosystem, theoretical framework and methodology of the urban ecosystem health assessment based on emergy are proposed and the temporal variation of the health level of the city are also outlined in this paper. Following the principle of ecosystem health assessment, four major factors, including vigor (V), organizational structure (O), resilience (R) and function maintenance (F), are integrated to construct a novel emergy-based urban ecosystem health index (EUEHI). Based on the EUEHI and comparing with those of five other typical Chinese cities, the case study of Baotou city shows that its urban ecosystem health level is steadily arising despite the year 2001 as a turning point. Due to the emphasis on the resource structure adjustment and utilization efficiency, Baotou has obtained a better organizational structure and service function for the total urban ecosystem.
Tilley, David Rogers; Swank, Wayne T
2003-11-01
Emergy (with an 'm') synthesis was used to assess the balance between nature and humanity and the equity among forest outcomes of a US Forest Service ecosystem management demonstration project on the Wine Spring Creek watershed, a high-elevation (1600 m), temperate forest located in the southern Appalachian mountains of North Carolina, USA. EM embraces a holistic perspective, accounting for the multiple temporal and spatial scales of forest processes and public interactions, to balance the ecological, economic, and social demands placed on land resources. Emergy synthesis is a modeling tool that allows the structure and function of forest ecosystems to be quantified in common units (solar emergy-joules, sej) for easy and meaningful comparison, determining 'system-value' for forcing factors, components, and processes based on the amount of resources required to develop and sustain them, whether they are money, material, energy, or information. The Environmental Loading Ratio (ELR), the units of solar emergy imported into the watershed via human control per unit of indigenous, natural solar emergy, was determined to be 0.42, indicating that the load on the natural environment was not ecologically damaging and that excess ecological capacity existed for increasing non-ecological activities (e.g. timbering, recreation) to achieve an ELR of 1.0 (perfect ecological-economic balance). Three forest outcomes selected to represent the three categories of desired sustainability (ecological, economic, and social) were evaluated in terms of their solar emergy flow to measure outcome equity. Direct economic contribution was an order of magnitude less (224 x 10(12)solar emergy-joules (sej) ha(-1)) than the ecological and social contributions, which were provided at annual rates of 3083 and 2102 x 10(12)sejha(-1), respectively. Emergy synthesis was demonstrated to holistically integrate and quantify the interconnections of a coupled nature-human system allowing the goals of
A Richer Understanding of Algebra
ERIC Educational Resources Information Center
Foy, Michelle
2008-01-01
Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number, pre-algebra, and algebra…
EMERGY ANALYSIS AND ECONOMIC ANALYSIS A COMPARATIVE STUDY
Our mission at USEPA is to protect human health and safeguard the natural environment. We aim to base our environmental regulations and policies on sound scientific and, where appropriate, economic analyses. Although EPA has conducted analysis of the impact of regulations on ...
Connecting Algebra and Chemistry.
ERIC Educational Resources Information Center
O'Connor, Sean
2003-01-01
Correlates high school chemistry curriculum with high school algebra curriculum and makes the case for an integrated approach to mathematics and science instruction. Focuses on process integration. (DDR)
ERIC Educational Resources Information Center
Cavanagh, Sean
2008-01-01
A popular humorist and avowed mathphobe once declared that in real life, there's no such thing as algebra. Kathie Wilson knows better. Most of the students in her 8th grade class will be thrust into algebra, the definitive course that heralds the beginning of high school mathematics, next school year. The problem: Many of them are about three…
ERIC Educational Resources Information Center
Levy, Alissa Beth
2012-01-01
The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this…
NASA Technical Reports Server (NTRS)
Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.
1982-01-01
The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.
ERIC Educational Resources Information Center
Merlin, Ethan M.
2013-01-01
This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…
Ren, Jingzheng; Manzardo, Alessandro; Mazzi, Anna; Fedele, Andrea; Scipioni, Antonio
2013-01-01
Biodiesel as a promising alternative energy resource has been a hot spot in chemical engineering nowadays, but there is also an argument about the sustainability of biodiesel. In order to analyze the sustainability of biodiesel production systems and select the most sustainable scenario, various kinds of crop-based biodiesel including soybean-, rapeseed-, sunflower-, jatropha- and palm-based biodiesel production options are studied by emergy analysis; soybean-based scenario is recognized as the most sustainable scenario that should be chosen for further study in China. DEA method is used to evaluate the sustainability efficiencies of these options, and the biodiesel production systems based on soybean, sunflower, and palm are considered as DEA efficient, whereas rapeseed-based and jatropha-based scenarios are needed to be improved, and the improved methods have also been specified. PMID:23766723
Municipal wastes and their solar transformities: an emergy synthesis for Macao.
Lei, Kampeng; Wang, Zhishi
2008-12-01
The debate over waste management practices has become increasingly important as human activities have begun to overload the biosphere's assimilative capacity. An effective waste management policy should be based on the principles of sustainable development, with wastes regarded as a potential resource rather than solely as something to eliminate. This approach requires an integrated waste management plan that makes full use of all available technologies. Macao is a highly populated consumer society that lacks natural resources and must therefore import almost all of its life-supporting goods and raw materials from regions outside the city. During the past 20 years, Macao has experienced an economic boom, accompanied by rapid socioeconomic development. Its discharged wastes have increased steadily during this period. This paper employs emergy analysis to investigate Macao's waste treatment in 1995, 1999, 2003 and 2004. The emergy of gaseous emissions was estimated to be 4.76 x 10(21) sej in 2004. Since 1992, Macao's municipal solid waste (MSW) has been incinerated to reduce its volume. The transformity of the fly ash and slag produced by this treatment in 2004, and the electricity generated by the incinerator, equaled 5.11 x 10(11) sej/g, 6.01 x 10(10) sej/g, and 7.61 x 10(6) sej/J, respectively. A large investment of natural resources and technology is required for the treatment of wastes; the feedback ratio of wastes, which represents the scale of the treatment of inputs, equaled 0.02 for MSW, 0.11 for sewage, and 0.06 for gaseous emissions. PMID:18304794
Semigroups and computer algebra in algebraic structures
NASA Astrophysics Data System (ADS)
Bijev, G.
2012-11-01
Some concepts in semigroup theory can be interpreted in several algebraic structures. A generalization fA,B,fA,B(X) = A(X')B of the complement operator (') on Boolean matrices is made, where A and B denote any rectangular Boolean matrices. While (') is an isomorphism between Boolean semilattices, the generalized complement operator is homomorphism in the general case. The map fA,B and its general inverse (fA,B)+ have quite similar properties to those in the linear algebra and are useful for solving linear equations in Boolean matrix algebras. For binary relations on a finite set, necessary and sufficient conditions for the equation αξβ = γ to have a solution ξ are proved. A generalization of Green's equivalence relations in semigroups for rectangular matrices is proposed. Relationships between them and the Moore-Penrose inverses are investigated. It is shown how any generalized Green's H-class could be constructed by given its corresponding linear subspaces and converted into a group isomorphic to a linear group. Some information about using computer algebra methods concerning this paper is given.
Lie algebra extensions of current algebras on S3
NASA Astrophysics Data System (ADS)
Kori, Tosiaki; Imai, Yuto
2015-06-01
An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac-Moody algebras give it for two-dimensional conformal field theory.
Leibniz algebras associated with representations of filiform Lie algebras
NASA Astrophysics Data System (ADS)
Ayupov, Sh. A.; Camacho, L. M.; Khudoyberdiyev, A. Kh.; Omirov, B. A.
2015-12-01
In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L / I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I ×nn,1 → I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4.
Coreflections in Algebraic Quantum Logic
NASA Astrophysics Data System (ADS)
Jacobs, Bart; Mandemaker, Jorik
2012-07-01
Various generalizations of Boolean algebras are being studied in algebraic quantum logic, including orthomodular lattices, orthomodular po-sets, orthoalgebras and effect algebras. This paper contains a systematic study of the structure in and between categories of such algebras. It does so via a combination of totalization (of partially defined operations) and transfer of structure via coreflections.
Developing Algebraic Thinking.
ERIC Educational Resources Information Center
Alejandre, Suzanne
2002-01-01
Presents a teaching experience that resulted in students getting to a point of full understanding of the kinesthetic activity and the algebra behind it. Includes a lesson plan for a traffic jam activity. (KHR)
Algebraic integrability: a survey.
Vanhaecke, Pol
2008-03-28
We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems. PMID:17588863
Algebraic Semantics for Narrative
ERIC Educational Resources Information Center
Kahn, E.
1974-01-01
This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)
Aprepro - Algebraic Preprocessor
Energy Science and Technology Software Center (ESTSC)
2005-08-01
Aprepro is an algebraic preprocessor that reads a file containing both general text and algebraic, string, or conditional expressions. It interprets the expressions and outputs them to the output file along witht the general text. Aprepro contains several mathematical functions, string functions, and flow control constructs. In addition, functions are included that, with some additional files, implement a units conversion system and a material database lookup system.
Geometric Algebra for Physicists
NASA Astrophysics Data System (ADS)
Doran, Chris; Lasenby, Anthony
2007-11-01
Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.
Covariant deformed oscillator algebras
NASA Technical Reports Server (NTRS)
Quesne, Christiane
1995-01-01
The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.
NASA Astrophysics Data System (ADS)
Hiley, B. J.
In this chapter, we examine in detail the non-commutative symplectic algebra underlying quantum dynamics. By using this algebra, we show that it contains both the Weyl-von Neumann and the Moyal quantum algebras. The latter contains the Wigner distribution as the kernel of the density matrix. The underlying non-commutative geometry can be projected into either of two Abelian spaces, so-called `shadow phase spaces'. One of these is the phase space of Bohmian mechanics, showing that it is a fragment of the basic underlying algebra. The algebraic approach is much richer, giving rise to two fundamental dynamical time development equations which reduce to the Liouville equation and the Hamilton-Jacobi equation in the classical limit. They also include the Schrödinger equation and its wave-function, showing that these features are a partial aspect of the more general non-commutative structure. We discuss briefly the properties of this more general mathematical background from which the non-commutative symplectic algebra emerges.
DG Poisson algebra and its universal enveloping algebra
NASA Astrophysics Data System (ADS)
Lü, JiaFeng; Wang, XingTing; Zhuang, GuangBin
2016-05-01
In this paper, we introduce the notions of differential graded (DG) Poisson algebra and DG Poisson module. Let $A$ be any DG Poisson algebra. We construct the universal enveloping algebra of $A$ explicitly, which is denoted by $A^{ue}$. We show that $A^{ue}$ has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over $A$ is isomorphic to the category of DG modules over $A^{ue}$. Furthermore, we prove that the notion of universal enveloping algebra $A^{ue}$ is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.
NASA Astrophysics Data System (ADS)
Roitman, Michael
2008-08-01
In this paper we prove that for any commutative (but in general non-associative) algebra A with an invariant symmetric non-degenerate bilinear form there is a graded vertex algebra V = V0 Å V2 Å V3 Å ¼, such that dim V0 = 1 and V2 contains A. We can choose V so that if A has a unit e, then 2e is the Virasoro element of V, and if G is a finite group of automorphisms of A, then G acts on V as well. In addition, the algebra V can be chosen with a non-degenerate invariant bilinear form, in which case it is simple.
Adaptive Algebraic Multigrid Methods
Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J
2004-04-09
Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.
Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction
ERIC Educational Resources Information Center
Wasserman, Nicholas H.
2016-01-01
This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…
Missing Modules, the Gnome Lie Algebra, and E10
NASA Astrophysics Data System (ADS)
Bärwald, O.; Gebert, R. W.; Günaydin, M.; Nicolai, H.
We study the embedding of Kac-Moody algebras into Borcherds (or generalized Kac-Moody) algebras which can be explicitly realized as Lie algebras of physical states of some completely compactified bosonic string. The extra ``missing states'' can be decomposed into irreducible highest or lowest weight ``missing modules'' w.r.t. the relevant Kac-Moody subalgebra; the corresponding lowest weights are associated with imaginary simple roots whose multiplicities can be simply understood in terms of certain polarization states of the associated string. We analyse in detail two examples where the momentum lattice of the string is given by the unique even unimodular Lorentzian lattice or , respectively. The former leads to the Borcherds algebra , which we call ``gnome Lie algebra'', with maximal Kac--Moody subalgebra A1. By the use of the denominator formula a complete set of imaginary simple roots can be exhibited, while the DDF construction provides an explicit Lie algebra basis in terms of purely longitudinal states of the compactified string in two dimensions. The second example is the Borcherds algebra , whose maximal Kac-Moody subalgebra is the hyperbolic algebra E10. The imaginary simple roots at level 1, which give rise to irreducible lowest weight modules for E10, can be completely characterized; furthermore, our explicit analysis of two non-trivial level-2 root spaces leads us to conjecture that these are in fact the only imaginary simple roots for .
Computer Program For Linear Algebra
NASA Technical Reports Server (NTRS)
Krogh, F. T.; Hanson, R. J.
1987-01-01
Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.
NASA Astrophysics Data System (ADS)
Bouwknegt, Peter
1988-06-01
We investigate extensions of the Virasoro algebra by a single primary field of integer or halfinteger conformal dimension Δ. We argue that for vanishing structure constant CΔΔΔ, the extended conformal algebra can only be associative for a generic c-value if Δ=1/2, 1, 3/2, 2 or 3. For the other Δ<=5 we compute the finite set of allowed c-values and identify the rational solutions. The case CΔΔΔ≠0 is also briefly discussed. I would like to thank Kareljan Schoutens for discussions and Sander Bais for a careful reading of the manuscript.
NASA Technical Reports Server (NTRS)
Shahshahani, M.
1991-01-01
The performance characteristics are discussed of certain algebraic geometric codes. Algebraic geometric codes have good minimum distance properties. On many channels they outperform other comparable block codes; therefore, one would expect them eventually to replace some of the block codes used in communications systems. It is suggested that it is unlikely that they will become useful substitutes for the Reed-Solomon codes used by the Deep Space Network in the near future. However, they may be applicable to systems where the signal to noise ratio is sufficiently high so that block codes would be more suitable than convolutional or concatenated codes.
NASA Astrophysics Data System (ADS)
Siche, Raúl; Pereira, Lucas; Agostinho, Feni; Ortega, Enrique
2010-10-01
In the last decade, two scientific tools have been extensively used worldwide to measure the human impact on nature: ecological footprint (EF) and emergy analysis (EA). Papers trying to combine the strong points of EF and EA, and obtain more accurate results have appeared in scientific literature, in which Zhao's et al. (2005) [61] approach is an important one. Unfortunately, some weak points of the original methods still remain on the new approaches proposed. The aim of this present work is to discuss some weak points found in Zhao's approach, trying to overcome them through a new approach called emergetic ecological footprint (EEF). The main difference between Zhao's approach and EEF is that the last one accounted for the internal storage of capital natural in the biocapacity calculation. Besides that, soil loss and water for human consume were considered as additional categories in the footprint calculation. After discussing it through comparisons with other approaches, EEF was used to assess Peru as a case study, resulting in a biocapacity of 51.76 gha capita-1 and a footprint of 12.23 gha capita-1, with 2004 data; that resulted in an ecological surplus of 39.53 gha capita-1. The load capacity factor obtained was 4.23, meaning that Peru can support a population 4.23 times bigger considering the life style of 2004. The main limitations of the EEF are: (i) it is impossible to make comparisons between the biocapacity and footprint for each category; (ii) a need for a handbook with emergy intensity factors with good quality. On the other hand, the main positive points are: (i) its easiness of application in global and national scales; (ii) its final indicators account for all the previous energy (or emergy) used to make something; (iii) internal natural capital storage was accounted for in the biocapacity calculation, which can be a valid step towards the evaluation and assess of services provided by nature.
Assessing Elementary Algebra with STACK
ERIC Educational Resources Information Center
Sangwin, Christopher J.
2007-01-01
This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…
Teaching Arithmetic and Algebraic Expressions
ERIC Educational Resources Information Center
Subramaniam, K.; Banerjee, Rakhi
2004-01-01
A teaching intervention study was conducted with sixth grade students to explore the interconnections between students' growing understanding of arithmetic expressions and beginning algebra. Three groups of students were chosen, with two groups receiving instruction in arithmetic and algebra, and one group in algebra without arithmetic. Students…
Spinors in the hyperbolic algebra
NASA Astrophysics Data System (ADS)
Ulrych, S.
2006-01-01
The three-dimensional universal complex Clifford algebra Cbar3,0 is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the dependance on an explicit matrix representation of the algebra.
Thinking Visually about Algebra
ERIC Educational Resources Information Center
Baroudi, Ziad
2015-01-01
Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…
ERIC Educational Resources Information Center
Glick, David
1995-01-01
Presents a technique that helps students concentrate more on the science and less on the mechanics of algebra while dealing with introductory physics formulas. Allows the teacher to do complex problems at a lower level and not be too concerned about the mathematical abilities of the students. (JRH)
ERIC Educational Resources Information Center
Nwabueze, Kenneth K.
2004-01-01
The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…
Computer Algebra versus Manipulation
ERIC Educational Resources Information Center
Zand, Hossein; Crowe, David
2004-01-01
In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…
ERIC Educational Resources Information Center
Boiteau, Denise; Stansfield, David
This document describes mathematical programs on the basic concepts of algebra produced by Louisiana Public Broadcasting. Programs included are: (1) "Inverse Operations"; (2) "The Order of Operations"; (3) "Basic Properties" (addition and multiplication of numbers and variables); (4) "The Positive and Negative Numbers"; and (5) "Using Positive…
ERIC Educational Resources Information Center
Kennedy, John
This text provides information and exercises on arithmetic topics which should be mastered before a student enrolls in an Elementary Algebra course. Section I describes the fundamental properties and relationships of whole numbers, focusing on basic operations, divisibility tests, exponents, order of operations, prime numbers, greatest common…
ERIC Educational Resources Information Center
Ketterlin-Geller, Leanne R.; Jungjohann, Kathleen; Chard, David J.; Baker, Scott
2007-01-01
Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…
Algebraic parameters identification of DC motors: methodology and analysis
NASA Astrophysics Data System (ADS)
Becedas, J.; Mamani, G.; Feliu, V.
2010-10-01
A fast, non-asymptotic, algebraic parameter identification method is applied to an uncertain DC motor to estimate the uncertain parameters: viscous friction coefficient and inertia. In this work, the methodology is developed and analysed, its convergence, a comparative study between the traditional recursive least square method and the algebraic identification method is carried out, and an analysis of the estimator in a noisy system is presented. Computer simulations were carried out to validate the suitability of the identification algorithm.
NASA Astrophysics Data System (ADS)
Zhang, Ming; Yao, JingTao
2004-04-01
The XML is a new standard for data representation and exchange on the Internet. There are studies on XML query languages as well as XML algebras in literature. However, attention has not been paid to research on XML algebras for data mining due to partially the fact that there is no widely accepted definition of XML mining tasks. This paper tries to examine the XML mining tasks and provide guidelines to design XML algebras for data mining. Some summarization and comparison have been done to existing XML algebras. We argue that by adding additional operators for mining tasks, XML algebras may work well for data mining with XML documents.
Dang, Xiaohu; Liu, Guobin
2012-07-15
Evaluating the sustainability of a target region for an ecological restoration programme is challenging because it involves different aspects of human society and environment as well as multiple disciplines. Carrying capacity provides a useful measure of the sustainability of a given region where an ecological restoration programme is implemented. In this article, the Yangou catchment, a geomorphic unit, was used as a case study in the Loess Hilly Region of China, where emergy synthesis was used to measure the environmental resources base. The specific standard of living in terms of emergy was employed to calculate carrying capacity over the period 1998-2005 and to assess the sustainability of the Yangou catchment where an ecological restoration programme was carried out. The results of the evaluation indicated that after implementing the ecological restoration programme, there was some improvement in the environmental aspects of the Yangou catchment during the study period, suggesting that the ecological restoration programme alleviated ecological degradation. However, several emergy-based indices and the support areas also illustrated that the ecological restoration programme was not successful enough in terms of preservation and utilisation of environmental resources to enhance sustainability. This indicates that further actions are necessary on conserving environmental resources, improving the emergy input structure for agricultural production and in lifestyle changes for the local people in living in the Yangou catchment. PMID:22425879
On Dunkl angular momenta algebra
NASA Astrophysics Data System (ADS)
Feigin, Misha; Hakobyan, Tigran
2015-11-01
We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl( N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.
Algebraic connectivity and graph robustness.
Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.
2009-07-01
Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.
Eco-exergy and emergy based self-organization of three forest plantations in lower subtropical China
Lu, Hongfang; Fu, Fangyan; Li, Hao; Campbell, Daniel E.; Ren, Hai
2015-01-01
The bio-thermodynamic structures of a mixed native species plantation, a conifer plantation and an Acacia mangium plantation in Southern China were quantified over a period of 15 years based on eco-exergy methods. The efficiencies of structural development and maintenance were quantified through an integrated application of eco-exergy and emergy methods. The results showed that the storage of eco-exergy increased over 3 times in all three plantations, as predicted by the maximum eco-exergy principle. This trend was primarily seen due to the accumulation of biomass, instead of an increase in the specific eco-exergy (eco-exergy per unit biomass), although species richness did increase. The eco-exergy to emergy and eco-exergy to empower ratios of the three plantations generally increased during the study period, but the rate of increase slowed down after 20 years. The dominant trees are the largest contributors to the eco-exergy stored in the plantations, and thus, the introduction of suitable indigenous tree species should be considered after the existing trees pass through their period of most rapid growth or around 20 years after planting. The combined application of C-values and suggested weighting factors in the eco-exergy calculation can imply opposite results, but may also supply useful information for forest management. PMID:26486821
Lu, Hongfang; Fu, Fangyan; Li, Hao; Campbell, Daniel E; Ren, Hai
2015-01-01
The bio-thermodynamic structures of a mixed native species plantation, a conifer plantation and an Acacia mangium plantation in Southern China were quantified over a period of 15 years based on eco-exergy methods. The efficiencies of structural development and maintenance were quantified through an integrated application of eco-exergy and emergy methods. The results showed that the storage of eco-exergy increased over 3 times in all three plantations, as predicted by the maximum eco-exergy principle. This trend was primarily seen due to the accumulation of biomass, instead of an increase in the specific eco-exergy (eco-exergy per unit biomass), although species richness did increase. The eco-exergy to emergy and eco-exergy to empower ratios of the three plantations generally increased during the study period, but the rate of increase slowed down after 20 years. The dominant trees are the largest contributors to the eco-exergy stored in the plantations, and thus, the introduction of suitable indigenous tree species should be considered after the existing trees pass through their period of most rapid growth or around 20 years after planting. The combined application of C-values and suggested weighting factors in the eco-exergy calculation can imply opposite results, but may also supply useful information for forest management. PMID:26486821
NASA Astrophysics Data System (ADS)
Ingwersen, Wesley W.
Life cycle assessment (LCA) is an internationally standardized framework for assessing the environmental impacts of products that is rapidly evolving to improve understanding and quantification of how complex product systems depend upon and affect the environment. This dissertation contributes to that evolution through the development of new methods for measuring impacts, estimating the uncertainty of impacts, and measuring ranges of environmental performance, with a focus on product systems in non-OECD countries that have not been well characterized. The integration of a measure of total energy use, emergy, is demonstrated in an LCA of gold from the Yanacocha mine in Peru in the second chapter. A model for estimating the accuracy of emergy results is proposed in the following chapter. The fourth chapter presents a template for LCA-based quantification of the range of environmental performance for tropical agricultural products using the example of fresh pineapple production for export in Costa Rica that can be used to create product labels with environmental information. The final chapter synthesizes how each methodological contribution will together improve the science of measuring product environmental performance.
Marquette, Ian
2013-07-15
We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently.
NASA Astrophysics Data System (ADS)
Dankova, T. S.; Rosensteel, G.
1998-10-01
Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.
Richgels, M A; Biffle, J H
1980-09-01
ALGEBRA is a program that allows the user to process output data from finite-element analysis codes before they are sent to plotting routines. These data take the form of variable values (stress, strain, and velocity components, etc.) on a tape that is both the output tape from the analyses code and the input tape to ALGEBRA. The ALGEBRA code evaluates functions of these data and writes the function values on an output tape that can be used as input to plotting routines. Convenient input format and error detection capabilities aid the user in providing ALGEBRA with the functions to be evaluated. 1 figure.
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.
ERIC Educational Resources Information Center
Beigie, Darin
2014-01-01
Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…
Vertex Algebras, Kac-Moody Algebras, and the Monster
NASA Astrophysics Data System (ADS)
Borcherds, Richard E.
1986-05-01
It is known that the adjoint representation of any Kac-Moody algebra A can be identified with a subquotient of a certain Fock space representation constructed from the root lattice of A. I define a product on the whole of the Fock space that restricts to the Lie algebra product on this subquotient. This product (together with a infinite number of other products) is constructed using a generalization of vertex operators. I also construct an integral form for the universal enveloping algebra of any Kac-Moody algebra that can be used to define Kac-Moody groups over finite fields, some new irreducible integrable representations, and a sort of affinization of any Kac-Moody algebra. The ``Moonshine'' representation of the Monster constructed by Frenkel and others also has products like the ones constructed for Kac-Moody algebras, one of which extends the Griess product on the 196884-dimensional piece to the whole representation.
NASA Astrophysics Data System (ADS)
Palmkvist, Jakob
2014-01-01
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D - 2 - p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
Palmkvist, Jakob
2014-01-15
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
NASA Technical Reports Server (NTRS)
Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.
1999-01-01
This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.
Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras
NASA Astrophysics Data System (ADS)
Paseka, Jan; Riečanová, Zdenka
2010-12-01
We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L. Moreover, if L is complete then L is (o)-topological. Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated.
Locally finite dimensional Lie algebras
NASA Astrophysics Data System (ADS)
Hennig, Johanna
We prove that in a locally finite dimensional Lie algebra L, any maximal, locally solvable subalgebra is the stabilizer of a maximal, generalized flag in an integrable, faithful module over L. Then we prove two structure theorems for simple, locally finite dimensional Lie algebras over an algebraically closed field of characteristic p which give sufficient conditions for the algebras to be of the form [K(R, *), K( R, *)] / (Z(R) ∩ [ K(R, *), K(R, *)]) for a simple, locally finite dimensional associative algebra R with involution *. Lastly, we explore the noncommutative geometry of locally simple representations of the diagonal locally finite Lie algebras sl(ninfinity), o( ninfinity), and sp(n infinity).
Quantum computation using geometric algebra
NASA Astrophysics Data System (ADS)
Matzke, Douglas James
This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.
Verburgt, Lukas M
2016-01-01
This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s. PMID:26806075
On the cohomology of Leibniz conformal algebras
NASA Astrophysics Data System (ADS)
Zhang, Jiao
2015-04-01
We construct a new cohomology complex of Leibniz conformal algebras with coefficients in a representation instead of a module. The low-dimensional cohomology groups of this complex are computed. Meanwhile, we construct a Leibniz algebra from a Leibniz conformal algebra and prove that the category of Leibniz conformal algebras is equivalent to the category of equivalence classes of formal distribution Leibniz algebras.
Assessing Algebraic Solving Ability: A Theoretical Framework
ERIC Educational Resources Information Center
Lian, Lim Hooi; Yew, Wun Thiam
2012-01-01
Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…
ERIC Educational Resources Information Center
Novotna, Jarmila; Hoch, Maureen
2008-01-01
Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…
Higher level twisted Zhu algebras
Ekeren, Jethro van
2011-05-15
The study of twisted representations of graded vertex algebras is important for understanding orbifold models in conformal field theory. In this paper, we consider the general setup of a vertex algebra V, graded by {Gamma}/Z for some subgroup {Gamma} of R containing Z, and with a Hamiltonian operator H having real (but not necessarily integer) eigenvalues. We construct the directed system of twisted level p Zhu algebras Zhu{sub p,{Gamma}}(V), and we prove the following theorems: For each p, there is a bijection between the irreducible Zhu{sub p,{Gamma}}(V)-modules and the irreducible {Gamma}-twisted positive energy V-modules, and V is ({Gamma}, H)-rational if and only if all its Zhu algebras Zhu{sub p,{Gamma}}(V) are finite dimensional and semisimple. The main novelty is the removal of the assumption of integer eigenvalues for H. We provide an explicit description of the level p Zhu algebras of a universal enveloping vertex algebra, in particular of the Virasoro vertex algebra Vir{sup c} and the universal affine Kac-Moody vertex algebra V{sup k}(g) at non-critical level. We also compute the inverse limits of these directed systems of algebras.
Handheld Computer Algebra Systems in the Pre-Algebra Classroom
ERIC Educational Resources Information Center
Gantz, Linda Ann Galofaro
2010-01-01
This mixed method analysis sought to investigate several aspects of student learning in pre-algebra through the use of computer algebra systems (CAS) as opposed to non-CAS learning. This research was broken into two main parts, one which compared results from both the experimental group (instruction using CAS, N = 18) and the control group…
Algebra and Algebraic Thinking in School Math: 70th YB
ERIC Educational Resources Information Center
National Council of Teachers of Mathematics, 2008
2008-01-01
Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…
Abstract Algebra to Secondary School Algebra: Building Bridges
ERIC Educational Resources Information Center
Christy, Donna; Sparks, Rebecca
2015-01-01
The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…
Philip, Bobby; Chartier, Dr Timothy
2012-01-01
methods based on Local Sensitivity Analysis (LSA). The method can be used in the context of geometric and algebraic multigrid methods for constructing smoothers, and in the context of Krylov methods for constructing block preconditioners. It is suitable for both constant and variable coecient problems. Furthermore, the method can be applied to systems arising from both scalar and coupled system partial differential equations (PDEs), as well as linear systems that do not arise from PDEs. The simplicity of the method will allow it to be easily incorporated into existing multigrid and Krylov solvers while providing a powerful tool for adaptively constructing methods tuned to a problem.
Energy Science and Technology Software Center (ESTSC)
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumpsmore » and an anisotropy in one part.« less
Statecharts Via Process Algebra
NASA Technical Reports Server (NTRS)
Luttgen, Gerald; vonderBeeck, Michael; Cleaveland, Rance
1999-01-01
Statecharts is a visual language for specifying the behavior of reactive systems. The Language extends finite-state machines with concepts of hierarchy, concurrency, and priority. Despite its popularity as a design notation for embedded system, precisely defining its semantics has proved extremely challenging. In this paper, a simple process algebra, called Statecharts Process Language (SPL), is presented, which is expressive enough for encoding Statecharts in a structure-preserving and semantic preserving manner. It is establish that the behavioral relation bisimulation, when applied to SPL, preserves Statecharts semantics
An Example of Competence-Based Learning: Use of Maxima in Linear Algebra for Engineers
ERIC Educational Resources Information Center
Diaz, Ana; Garcia, Alfonsa; de la Villa, Agustin
2011-01-01
This paper analyses the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is…
Learning Algebra from Worked Examples
ERIC Educational Resources Information Center
Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.
2014-01-01
For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is…
ERIC Educational Resources Information Center
Instructional Objectives Exchange, Los Angeles, CA.
A complete set of behavioral objectives for first-year algebra taught in any of grades 8 through 12 is presented. Three to six sample test items and answers are provided for each objective. Objectives were determined by surveying the most used secondary school algebra textbooks. Fourteen major categories are included: (1) whole numbers--operations…
ERIC Educational Resources Information Center
Buerman, Margaret
2007-01-01
Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…
Online Algebraic Tools for Teaching
ERIC Educational Resources Information Center
Kurz, Terri L.
2011-01-01
Many free online tools exist to complement algebraic instruction at the middle school level. This article presents findings that analyzed the features of algebraic tools to support learning. The findings can help teachers select appropriate tools to facilitate specific topics. (Contains 1 table and 4 figures.)
The Algebra of Complex Numbers.
ERIC Educational Resources Information Center
LePage, Wilbur R.
This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…
Algebraic Squares: Complete and Incomplete.
ERIC Educational Resources Information Center
Gardella, Francis J.
2000-01-01
Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)
Linear Algebra and Image Processing
ERIC Educational Resources Information Center
Allali, Mohamed
2010-01-01
We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)
Exploring Algebraic Patterns through Literature.
ERIC Educational Resources Information Center
Austin, Richard A.; Thompson, Denisse R.
1997-01-01
Presents methods for using literature to develop algebraic thinking in an environment that connects algebra to various situations. Activities are based on the book "Anno's Magic Seeds" with additional resources listed. Students express a constant function, exponential function, and a recursive function in their own words as well as writing about…
Condensing Algebra for Technical Mathematics.
ERIC Educational Resources Information Center
Greenfield, Donald R.
Twenty Algebra-Packets (A-PAKS) were developed by the investigator for technical education students at the community college level. Each packet contained a statement of rationale, learning objectives, performance activities, performance test, and performance test answer key. The A-PAKS condensed the usual sixteen weeks of algebra into a six-week…
Algebraic Thinking in Adult Education
ERIC Educational Resources Information Center
Manly, Myrna; Ginsburg, Lynda
2010-01-01
In adult education, algebraic thinking can be a sense-making tool that introduces coherence among mathematical concepts for those who previously have had trouble learning math. Further, a modeling approach to algebra connects mathematics and the real world, demonstrating the usefulness of math to those who have seen it as just an academic…
Thermodynamics. [algebraic structure
NASA Technical Reports Server (NTRS)
Zeleznik, F. J.
1976-01-01
The fundamental structure of thermodynamics is purely algebraic, in the sense of atopological, and it is also independent of partitions, composite systems, the zeroth law, and entropy. The algebraic structure requires the notion of heat, but not the first law. It contains a precise definition of entropy and identifies it as a purely mathematical concept. It also permits the construction of an entropy function from heat measurements alone when appropriate conditions are satisfied. Topology is required only for a discussion of the continuity of thermodynamic properties, and then the weak topology is the relevant topology. The integrability of the differential form of the first law can be examined independently of Caratheodory's theorem and his inaccessibility axiom. Criteria are established by which one can determine when an integrating factor can be made intensive and the pseudopotential extensive and also an entropy. Finally, a realization of the first law is constructed which is suitable for all systems whether they are solids or fluids, whether they do or do not exhibit chemical reactions, and whether electromagnetic fields are or are not present.
Invariants of triangular Lie algebras
NASA Astrophysics Data System (ADS)
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman
2007-07-01
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated.
ERIC Educational Resources Information Center
Gonzalez-Vega, Laureano
1999-01-01
Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)
Chen, J.; Safro, I.
2011-01-01
Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.
Constraint algebra in bigravity
Soloviev, V. O.
2015-07-15
The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.
Quantum algebra of N superspace
Hatcher, Nicolas; Restuccia, A.; Stephany, J.
2007-08-15
We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the {kappa}-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra.
Using Homemade Algebra Tiles To Develop Algebra and Prealgebra Concepts.
ERIC Educational Resources Information Center
Leitze, Annette Ricks; Kitt, Nancy A.
2000-01-01
Describes how to use homemade tiles, sketches, and the box method to reach a broader group of students for successful algebra learning. Provides a list of concepts appropriate for such an approach. (KHR)
Effective Communication, Critical Aspects and Compositionality in Algebra
ERIC Educational Resources Information Center
Olteanu, Lucian
2014-01-01
This paper contains a discussion of how the concept of critical aspects and the principle of compositionality can provide a powerful tool to analyse and understand the communications that occur in the classroom. It is grounded in data collected in a longitudinal study. The content chosen is algebra. It is argued that the critical aspects and the…
Loop Virasoro Lie conformal algebra
Wu, Henan Chen, Qiufan; Yue, Xiaoqing
2014-01-15
The Lie conformal algebra of loop Virasoro algebra, denoted by CW, is introduced in this paper. Explicitly, CW is a Lie conformal algebra with C[∂]-basis (L{sub i} | i∈Z) and λ-brackets [L{sub i} {sub λ} L{sub j}] = (−∂−2λ)L{sub i+j}. Then conformal derivations of CW are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CW are classified.
Distance geometry and geometric algebra
NASA Astrophysics Data System (ADS)
Dress, Andreas W. M.; Havel, Timothy F.
1993-10-01
As part of his program to unify linear algebra and geometry using the language of Clifford algebra, David Hestenes has constructed a (well-known) isomorphism between the conformal group and the orthogonal group of a space two dimensions higher, thus obtaining homogeneous coordinates for conformal geometry.(1) In this paper we show that this construction is the Clifford algebra analogue of a hyperbolic model of Euclidean geometry that has actually been known since Bolyai, Lobachevsky, and Gauss, and we explore its wider invariant theoretic implications. In particular, we show that the Euclidean distance function has a very simple representation in this model, as demonstrated by J. J. Seidel.(18)
Hopf algebras and Dyson-Schwinger equations
NASA Astrophysics Data System (ADS)
Weinzierl, Stefan
2016-06-01
In this paper I discuss Hopf algebras and Dyson-Schwinger equations. This paper starts with an introduction to Hopf algebras, followed by a review of the contribution and application of Hopf algebras to particle physics. The final part of the paper is devoted to the relation between Hopf algebras and Dyson-Schwinger equations.
Curvature calculations with spacetime algebra
Hestenes, D.
1986-06-01
A new method for calculating the curvature tensor is developed and applied to the Scharzschild case. The method employs Clifford algebra and has definite advantages over conventional methods using differential forms or tensor analysis.
GCD, LCM, and Boolean Algebra?
ERIC Educational Resources Information Center
Cohen, Martin P.; Juraschek, William A.
1976-01-01
This article investigates the algebraic structure formed when the process of finding the greatest common divisor and the least common multiple are considered as binary operations on selected subsets of positive integers. (DT)
Sequential products on effect algebras
NASA Astrophysics Data System (ADS)
Gudder, Stan; Greechie, Richard
2002-02-01
A sequential effect algebra (SEA) is an effect algebra on which a sequential product with natural properties is defined. The properties of sequential products on Hilbert space effect algebras are discussed. For a general SEA, relationships between sequential independence, coexistence and compatibility are given. It is shown that the sharp elements of a SEA form an orthomodular poset. The sequential center of a SEA is discussed and a characterization of when the sequential center is isomorphic to a fuzzy set system is presented. It is shown that the existence, of a sequential product is a strong restriction that eliminates many effect algebras from being SEA's. For example, there are no finite nonboolean SEA's, A measure of sharpness called the sharpness index is studied. The existence of horizontal sums of SEA's is characterized and examples of horizontal sums and tensor products are presented.
Semiclassical states on Lie algebras
Tsobanjan, Artur
2015-03-15
The effective technique for analyzing representation-independent features of quantum systems based on the semiclassical approximation (developed elsewhere) has been successfully used in the context of the canonical (Weyl) algebra of the basic quantum observables. Here, we perform the important step of extending this effective technique to the quantization of a more general class of finite-dimensional Lie algebras. The case of a Lie algebra with a single central element (the Casimir element) is treated in detail by considering semiclassical states on the corresponding universal enveloping algebra. Restriction to an irreducible representation is performed by “effectively” fixing the Casimir condition, following the methods previously used for constrained quantum systems. We explicitly determine the conditions under which this restriction can be consistently performed alongside the semiclassical truncation.
Cartooning in Algebra and Calculus
ERIC Educational Resources Information Center
Moseley, L. Jeneva
2014-01-01
This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.
NASA Technical Reports Server (NTRS)
Klumpp, A. R.; Lawson, C. L.
1988-01-01
Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.
NASA Astrophysics Data System (ADS)
Lannes, A.; Teunissen, P. J. G.
2011-05-01
The first objective of this paper is to show that some basic concepts used in global navigation satellite systems (GNSS) are similar to those introduced in Fourier synthesis for handling some phase calibration problems. In experimental astronomy, the latter are at the heart of what is called `phase closure imaging.' In both cases, the analysis of the related structures appeals to the algebraic graph theory and the algebraic number theory. For example, the estimable functions of carrier-phase ambiguities, which were introduced in GNSS to correct some rank defects of the undifferenced equations, prove to be `closure-phase ambiguities:' the so-called `closure-delay' (CD) ambiguities. The notion of closure delay thus generalizes that of double difference (DD). The other estimable functional variables involved in the phase and code undifferenced equations are the receiver and satellite pseudo-clock biases. A related application, which corresponds to the second objective of this paper, concerns the definition of the clock information to be broadcasted to the network users for their precise point positioning (PPP). It is shown that this positioning can be achieved by simply having access to the satellite pseudo-clock biases. For simplicity, the study is restricted to relatively small networks. Concerning the phase for example, these biases then include five components: a frequency-dependent satellite-clock error, a tropospheric satellite delay, an ionospheric satellite delay, an initial satellite phase, and an integer satellite ambiguity. The form of the PPP equations to be solved by the network user is then similar to that of the traditional PPP equations. As soon as the CD ambiguities are fixed and validated, an operation which can be performed in real time via appropriate decorrelation techniques, estimates of these float biases can be immediately obtained. No other ambiguity is to be fixed. The satellite pseudo-clock biases can thus be obtained in real time. This is
Hopf algebras and topological recursion
NASA Astrophysics Data System (ADS)
Esteves, João N.
2015-11-01
We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293-309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347-452).
Energy Science and Technology Software Center (ESTSC)
2005-04-11
The ALGEBRA program allows the user to manipulate data from a finite element analysis before it is plotted. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database. The ALGEBRA program evaluates user-supplied functions of the data and writes the results to an output EXODUS II database that can be read by plot programs.
NASA Astrophysics Data System (ADS)
Kuzmin, Dmitri; Möller, Matthias; Gurris, Marcel
Flux limiting for hyperbolic systems requires a careful generalization of the design principles and algorithms introduced in the context of scalar conservation laws. In this chapter, we develop FCT-like algebraic flux correction schemes for the Euler equations of gas dynamics. In particular, we discuss the construction of artificial viscosity operators, the choice of variables to be limited, and the transformation of antidiffusive fluxes. An a posteriori control mechanism is implemented to make the limiter failsafe. The numerical treatment of initial and boundary conditions is discussed in some detail. The initialization is performed using an FCT-constrained L 2 projection. The characteristic boundary conditions are imposed in a weak sense, and an approximate Riemann solver is used to evaluate the fluxes on the boundary. We also present an unconditionally stable semi-implicit time-stepping scheme and an iterative solver for the fully discrete problem. The results of a numerical study indicate that the nonlinearity and non-differentiability of the flux limiter do not inhibit steady state convergence even in the case of strongly varying Mach numbers. Moreover, the convergence rates improve as the pseudo-time step is increased.
Nonnumeric Computer Applications to Algebra, Trigonometry and Calculus.
ERIC Educational Resources Information Center
Stoutemyer, David R.
1983-01-01
Described are computer program packages requiring little or no knowledge of computer programing for college algebra, calculus, and abstract algebra. Widely available computer algebra systems are listed. (MNS)
Virasoro algebra in the KN algebra; Bosonic string with fermionic ghosts on Riemann surfaces
Koibuchi, H. )
1991-10-10
In this paper the bosonic string model with fermionic ghosts is considered in the framework of the KN algebra. The authors' attentions are paid to representations of KN algebra and a Clifford algebra of the ghosts. The authors show that a Virasoro-like algebra is obtained from KN algebra when KN algebra has certain antilinear anti-involution, and that it is isomorphic to the usual Virasoro algebra. The authors show that there is an expected relation between a central charge of this Virasoro-like algebra and an anomaly of the combined system.
Invertible linear transformations and the Lie algebras
NASA Astrophysics Data System (ADS)
Zhang, Yufeng; Tam, Honwah; Guo, Fukui
2008-07-01
With the help of invertible linear transformations and the known Lie algebras, a way to generate new Lie algebras is given. These Lie algebras obtained have a common feature, i.e. integrable couplings of solitary hierarchies could be obtained by using them, specially, the Hamiltonian structures of them could be worked out. Some ways to construct the loop algebras of the Lie algebras are presented. It follows that some various loop algebras are given. In addition, a few new Lie algebras are explicitly constructed in terms of the classification of Lie algebras proposed by Ma Wen-Xiu, which are bases for obtaining new Lie algebras by using invertible linear transformations. Finally, some solutions of a (2 + 1)-dimensional partial-differential equation hierarchy are obtained, whose Hamiltonian form-expressions are manifested by using the quadratic-form identity.
Ternary generalization of Heisenberg's algebra
NASA Astrophysics Data System (ADS)
Kerner, Richard
2015-06-01
A concise study of ternary and cubic algebras with Z3 grading is presented. We discuss some underlying ideas leading to the conclusion that the discrete symmetry group of permutations of three objects, S3, and its abelian subgroup Z3 may play an important role in quantum physics. We show then how most of important algebras with Z2 grading can be generalized with ternary composition laws combined with a Z3 grading. We investigate in particular a ternary, Z3-graded generalization of the Heisenberg algebra. It turns out that introducing a non-trivial cubic root of unity, , one can define two types of creation operators instead of one, accompanying the usual annihilation operator. The two creation operators are non-hermitian, but they are mutually conjugate. Together, the three operators form a ternary algebra, and some of their cubic combinations generate the usual Heisenberg algebra. An analogue of Hamiltonian operator is constructed by analogy with the usual harmonic oscillator, and some properties of its eigenfunctions are briefly discussed.
Beyond Dirac - a Unified Algebra
NASA Astrophysics Data System (ADS)
Lundberg, Wayne R.
2001-10-01
A introductory insight will be shared regarding a 'separation of variables' approach to understanding the relationship between QCD and the origins of cosmological and particle mass. The discussion will then build upon work presented at DFP 2000, focussing on the formal basis for using 3x3x3 matrix algebra as it underlies and extends Dirac notation. A set of restrictions are established which break the multiple symmetries of the 3x3x3 matrix algebra, yielding Standard Model QCD objects and interactions. It will be shown that the 3x3x3 matrix representation unifies the algebra of strong and weak (and by extension, electromagnetic) interactions. A direct correspondence to string theoretic objects is established by considering the string to be partitioned in thirds. Rubik's cube is used as a graphical means of handling algebraic manipulation of 3x3x3 algebra. Further, its potential utility for advancing pedagogical methods through active engagement is discussed. A simulated classroom exercize will be conducted.
Bai, Xiaomei; Wen, Zhongming; An, Shaoshan; Li, Bicheng
2015-01-01
Evaluating the sustainability of cropland use is essential for guaranteeing a secure food supply and accomplishing agriculture sustainable development. This study was conducted in the ecologically vulnerable Loess Plateau region of China to evaluate the sustainability of cropland use based on an ecological footprint model that integrates emergy analysis. One modified method proposed in 2005 is known as the emergetic ecological footprint (EEF). We enhanced the method by accounting for both the surface soil energy in the carrying capacity calculation and the net topsoil loss for human consumption in the EF calculation. This paper evaluates whether the cropland of the study area was overloaded or sustainably managed during the period from 1981 to 2009. Toward this end, the final results obtained from EEF were compared to conventional EF and previous methods. The results showed that the cropland of Yuanzhou County has not been used sustainably since 1983, and the conventional EF analysis provided similar results. In contrast, a deficit did not appear during this time period when previous calculation methods of others were used. Additionally, the ecological sustainable index (ESI) from three models indicated that the recently used cropland system is unlikely to be unsustainable. PMID:25738289
Algebraic Lattices in QFT Renormalization
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2016-07-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
Algebraic Lattices in QFT Renormalization
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2016-04-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
Moving frames and prolongation algebras
NASA Technical Reports Server (NTRS)
Estabrook, F. B.
1982-01-01
Differential ideals generated by sets of 2-forms which can be written with constant coefficients in a canonical basis of 1-forms are considered. By setting up a Cartan-Ehresmann connection, in a fiber bundle over a base space in which the 2-forms live, one finds an incomplete Lie algebra of vector fields in the fields in the fibers. Conversely, given this algebra (a prolongation algebra), one can derive the differential ideal. The two constructs are thus dual, and analysis of either derives properties of both. Such systems arise in the classical differential geometry of moving frames. Examples of this are discussed, together with examples arising more recently: the Korteweg-de Vries and Harrison-Ernst systems.
Computer Algebra Systems in Undergraduate Instruction.
ERIC Educational Resources Information Center
Small, Don; And Others
1986-01-01
Computer algebra systems (such as MACSYMA and muMath) can carry out many of the operations of calculus, linear algebra, and differential equations. Use of them with sketching graphs of rational functions and with other topics is discussed. (MNS)
Generalized Galilean algebras and Newtonian gravity
NASA Astrophysics Data System (ADS)
González, N.; Rubio, G.; Salgado, P.; Salgado, S.
2016-04-01
The non-relativistic versions of the generalized Poincaré algebras and generalized AdS-Lorentz algebras are obtained. These non-relativistic algebras are called, generalized Galilean algebras of type I and type II and denoted by GBn and GLn respectively. Using a generalized Inönü-Wigner contraction procedure we find that the generalized Galilean algebras of type I can be obtained from the generalized Galilean algebras type II. The S-expansion procedure allows us to find the GB5 algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref. [1] allows us to show that the nonrelativistic limit of the five dimensional Einstein-Chern-Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.
Motivating Activities that Lead to Algebra
ERIC Educational Resources Information Center
Menon, Ramakrishnan
2004-01-01
Four activities consisting of puzzles are introduced, which help students to recognize the strength of algebraic generalizations. They also assist them to comprehend algebraic concepts, and enable them to develop their individual puzzles and games.
Scalable Parallel Algebraic Multigrid Solvers
Bank, R; Lu, S; Tong, C; Vassilevski, P
2005-03-23
The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.
Computational triadic algebras of signs
Zadrozny, W.
1996-12-31
We present a finite model of Peirce`s ten classes of signs. We briefly describe Peirce`s taxonomy of signs; we prove that any finite collection of signs can be extended to a finite algebra of signs in which all interpretants are themselves being interpreted; and we argue that Peirce`s ten classes of signs can be defined using constraints on algebras of signs. The paper opens the possibility of defining multimodal cognitive agents using Peirce`s classes of signs, and is a first step towards building a computational logic of signs based on Peirce`s taxonomies.
ERIC Educational Resources Information Center
Star, Jon R.; Rittle-Johnson, Bethany
2009-01-01
Competence in algebra is increasingly recognized as a critical milestone in students' middle and high school years. The transition from arithmetic to algebra is a notoriously difficult one, and improvements in algebra instruction are greatly needed (National Research Council, 2001). Algebra historically has represented students' first sustained…
Spatial-Operator Algebra For Robotic Manipulators
NASA Technical Reports Server (NTRS)
Rodriguez, Guillermo; Kreutz, Kenneth K.; Milman, Mark H.
1991-01-01
Report discusses spatial-operator algebra developed in recent studies of mathematical modeling, control, and design of trajectories of robotic manipulators. Provides succinct representation of mathematically complicated interactions among multiple joints and links of manipulator, thereby relieving analyst of most of tedium of detailed algebraic manipulations. Presents analytical formulation of spatial-operator algebra, describes some specific applications, summarizes current research, and discusses implementation of spatial-operator algebra in the Ada programming language.
The weak Hopf algebras related to generalized Kac-Moody algebra
Wu Zhixiang
2006-06-15
We define a kind of quantized enveloping algebra of a generalized Kac-Moody algebra G by adding a generator J satisfying J{sup m}=J{sup m-1} for some integer m. We denote this algebra by wU{sub q}{sup {tau}}(G). This algebra is a weak Hopf algebra if and only if m=2. In general, it is a bialgebra, and contains a Hopf subalgebra. This Hopf subalgebra is isomorphic to the usually quantum envelope algebra U{sub q}(G) of a generalized Kac-Moody algebra G.
Lessons for Algebraic Thinking. Grades K-2.
ERIC Educational Resources Information Center
von Rotz, Leyani; Burns, Marilyn
Algebra is one of the top priorities of mathematics instruction for the elementary and middle grades. This book is designed to help K-2 teachers meet the challenge of making algebra an integral part of their mathematics instruction and realize both what to teach and how to teach central algebraic concepts. Classroom-tested lessons help teachers…
Algebra? A Gate! A Barrier! A Mystery!
ERIC Educational Resources Information Center
Mathematics Educatio Dialogues, 2000
2000-01-01
This issue of Mathematics Education Dialogues focuses on the nature and the role of algebra in the K-14 curriculum. Articles on this theme include: (1) "Algebra For All? Why?" (Nel Noddings); (2) "Algebra For All: It's a Matter of Equity, Expectations, and Effectiveness" (Dorothy S. Strong and Nell B. Cobb); (3) "Don't Delay: Build and Talk about…
UCSMP Algebra. What Works Clearinghouse Intervention Report
ERIC Educational Resources Information Center
What Works Clearinghouse, 2007
2007-01-01
"University of Chicago School Mathematics Project (UCSMP) Algebra," designed to increase students' skills in algebra, is appropriate for students in grades 7-10, depending on the students' incoming knowledge. This one-year course highlights applications, uses statistics and geometry to develop the algebra of linear equations and inequalities, and…
New family of Maxwell like algebras
NASA Astrophysics Data System (ADS)
Concha, P. K.; Durka, R.; Merino, N.; Rodríguez, E. K.
2016-08-01
We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the S-expansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement.
Build an Early Foundation for Algebra Success
ERIC Educational Resources Information Center
Knuth, Eric; Stephens, Ana; Blanton, Maria; Gardiner, Angela
2016-01-01
Research tells us that success in algebra is a factor in many other important student outcomes. Emerging research also suggests that students who are started on an algebra curriculum in the earlier grades may have greater success in the subject in secondary school. What's needed is a consistent, algebra-infused mathematics curriculum all…
A Balancing Act: Making Sense of Algebra
ERIC Educational Resources Information Center
Gavin, M. Katherine; Sheffield, Linda Jensen
2015-01-01
For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…
Difficulties in Initial Algebra Learning in Indonesia
ERIC Educational Resources Information Center
Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja
2014-01-01
Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was…
Teaching Strategies to Improve Algebra Learning
ERIC Educational Resources Information Center
Zbiek, Rose Mary; Larson, Matthew R.
2015-01-01
Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…
Graphing Calculator Use in Algebra Teaching
ERIC Educational Resources Information Center
Dewey, Brenda L.; Singletary, Ted J.; Kinzel, Margaret T.
2009-01-01
This study examines graphing calculator technology availability, characteristics of teachers who use it, teacher attitudes, and how use reflects changes to algebra curriculum and instructional practices. Algebra I and Algebra II teachers in 75 high school and junior high/middle schools in a diverse region of a northwestern state were surveyed.…
Unifying the Algebra for All Movement
ERIC Educational Resources Information Center
Eddy, Colleen M.; Quebec Fuentes, Sarah; Ward, Elizabeth K.; Parker, Yolanda A.; Cooper, Sandi; Jasper, William A.; Mallam, Winifred A.; Sorto, M. Alejandra; Wilkerson, Trena L.
2015-01-01
There exists an increased focus on school mathematics, especially first-year algebra, due to recent efforts for all students to be college and career ready. In addition, there are calls, policies, and legislation advocating for all students to study algebra epitomized by four rationales of the "Algebra for All" movement. In light of this…
NASA Astrophysics Data System (ADS)
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2014-05-01
A complex key feature of turbulence is that the velocity is a vector field, whereas intermittency, another key feature, has been mostly understood, analysed and simulated in scalar frameworks. This gap has prevented many developments. Some years ago, the general framework of 'Lie cascades' was introduced (Schertzer and Lovejoy, 1993) to deal with both features by considering cascades generated by stochastic Lie algebra. However, the theoretical efforts were mostly concentrated on the decomposition of this algebra into its radical and a semi-simple algebra and faced too many degrees of freedom. In this communication, we show that the class of Clifford algebra is already wide enough, very convenient and physically meaningful to understand, analyse and simulate intermittent vector fields.
Entropy algebras and Birkhoff factorization
NASA Astrophysics Data System (ADS)
Marcolli, Matilde; Tedeschi, Nicolas
2015-11-01
We develop notions of Rota-Baxter structures and associated Birkhoff factorizations, in the context of min-plus semirings and their thermodynamic deformations, including deformations arising from quantum information measures such as the von Neumann entropy. We consider examples related to Manin's renormalization and computation program, to Markov random fields and to counting functions and zeta functions of algebraic varieties.
Algebra for All. Research Brief
ERIC Educational Resources Information Center
Bleyaert, Barbara
2009-01-01
The call for "algebra for all" is not a recent phenomenon. Concerns about the inadequacy of math (and science) preparation in America's high schools have been a steady drumbeat since the 1957 launch of Sputnik; a call for raising standards and the number of math (and science) courses required for graduation has been a part of countless national…
ERIC Educational Resources Information Center
Oishi, Lindsay
2011-01-01
"Solve for x." While many people first encountered this enigmatic instruction in high school, the last 20 years have seen a strong push to get students to take algebra in eighth grade or even before. Today, concerns about the economy highlight a familiar worry: American eighth-graders trailed their peers in five Asian countries on the 2007 TIMSS…
Exploring Algebraic Misconceptions with Technology
ERIC Educational Resources Information Center
Sakow, Matthew; Karaman, Ruveyda
2015-01-01
Many students struggle with algebra, from simplifying expressions to solving systems of equations. Students also have misconceptions about the meaning of variables. In response to the question "Can x + y + z ever equal x + p + z?" during a student interview, the student claimed, "Never . . . because p has to have a different value…
An Introduction to Algebraic Multigrid
Falgout, R D
2006-04-25
Algebraic multigrid (AMG) solves linear systems based on multigrid principles, but in a way that only depends on the coefficients in the underlying matrix. The author begins with a basic introduction to AMG methods, and then describes some more recent advances and theoretical developments
Elementary Algebra Connections to Precalculus
ERIC Educational Resources Information Center
Lopez-Boada, Roberto; Daire, Sandra Arguelles
2013-01-01
This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…
Adventures in Flipping College Algebra
ERIC Educational Resources Information Center
Van Sickle, Jenna
2015-01-01
This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses…
Kinds of Knowledge in Algebra.
ERIC Educational Resources Information Center
Lewis, Clayton
Solving equations in elementary algebra requires knowledge of the permitted operations, and knowledge of what operation to use at a given point in the solution process. While just these kinds of knowledge would be adequate for an ideal solver, human solvers appear to need and use other kinds of knowledge. First, many errors seem to indicate that…
Weaving Geometry and Algebra Together
ERIC Educational Resources Information Center
Cetner, Michelle
2015-01-01
When thinking about student reasoning and sense making, teachers must consider the nature of tasks given to students along with how to plan to use the tasks in the classroom. Students should be presented with tasks in a way that encourages them to draw connections between algebraic and geometric concepts. This article focuses on the idea that it…
Inequalities, Assessment and Computer Algebra
ERIC Educational Resources Information Center
Sangwin, Christopher J.
2015-01-01
The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in…
ERIC Educational Resources Information Center
Bosse, Michael J.; Ries, Heather; Chandler, Kayla
2012-01-01
Secondary school mathematics teachers often need to answer the "Why do we do that?" question in such a way that avoids confusion and evokes student interest. Understanding the properties of number systems can provide an avenue to better grasp algebraic structures, which in turn builds students' conceptual knowledge of secondary mathematics. This…
Implementing Change in College Algebra
ERIC Educational Resources Information Center
Haver, William E.
2007-01-01
In this paper, departments are urged to consider implementing the type of changes proposed in Beyond Crossroads in College Algebra. The author of this paper is chair of the Curriculum Renewal Across the First Two Years (CRAFTY) Committee of the Mathematical Association of America. The committee has members from two-year colleges, four-year…
Algebraic Activities Aid Discovery Lessons
ERIC Educational Resources Information Center
Wallace-Gomez, Patricia
2013-01-01
After a unit on the rules for positive and negative numbers and the order of operations for evaluating algebraic expressions, many students believe that they understand these principles well enough, but they really do not. They clearly need more practice, but not more of the same kind of drill. Wallace-Gomez provides three graphing activities that…
Algebra from Chips and Chopsticks
ERIC Educational Resources Information Center
Yun, Jeong Oak; Flores, Alfinio
2012-01-01
Students can use geometric representations of numbers as a way to explore algebraic ideas. With the help of these representations, students can think about the relations among the numbers, express them using their own words, and represent them with letters. The activities discussed here can stimulate students to try to find various ways of solving…
Celestial mechanics with geometric algebra
NASA Technical Reports Server (NTRS)
Hestenes, D.
1983-01-01
Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.
Algebraic methods in system theory
NASA Technical Reports Server (NTRS)
Brockett, R. W.; Willems, J. C.; Willsky, A. S.
1975-01-01
Investigations on problems of the type which arise in the control of switched electrical networks are reported. The main results concern the algebraic structure and stochastic aspects of these systems. Future reports will contain more detailed applications of these results to engineering studies.
Algebra, Home Mortgages, and Recessions
ERIC Educational Resources Information Center
Mariner, Jean A. Miller; Miller, Richard A.
2009-01-01
The current financial crisis and recession in the United States present an opportunity to discuss relevant applications of some topics in typical first-and second-year algebra and precalculus courses. Real-world applications of percent change, exponential functions, and sums of finite geometric sequences can help students understand the problems…
Principals + Algebra (- Fear) = Instructional Leadership
ERIC Educational Resources Information Center
Carver, Cynthia L.
2010-01-01
Recent state legislation in Michigan mandates that all graduating seniors successfully pass algebra I and II. Numerous initiatives have been enacted to help mathematics teachers meet this challenge, yet school principals have had little preparation for the necessary curricular and instructional changes. To address this unmet need, university-based…
Experts Question California's Algebra Edict
ERIC Educational Resources Information Center
Cavanagh, Sean
2008-01-01
Business leaders from important sectors of the American economy have been urging schools to set higher standards in math and science--and California officials, in mandating that 8th graders be tested in introductory algebra, have responded with one of the highest such standards in the land. Still, many California educators and school…
Very extended Kac Moody algebras and their interpretation at low levels
NASA Astrophysics Data System (ADS)
Kleinschmidt, Axel; Schnakenburg, Igor; West, Peter
2004-05-01
We analyse the very extended Kac Moody algebras as representations in terms of certain Ad-1 subalgebras and find the generators at low levels. Our results for low levels agree precisely with the bosonic field content of the theories containing gravity, forms and scalars which upon reduction to three dimensions can be described by a nonlinear realization. We explain how the Dynkin diagrams of the very extended algebras encode information about the field content and generalized T-duality transformations.
The Exocenter of a Generalized Effect Algebra
NASA Astrophysics Data System (ADS)
Foulis, David J.; Pulmannová, Sylvia
2011-12-01
Elements of the exocenter of a generalized effect algebra (GEA) correspond to decompositions of the GEA as a direct sum and thus the exocenter is a generalization to GEAs of the center of an effect algebra. The exocenter of a GEA is shown to be a boolean algebra, and the notion of a hull mapping for an effect algebra is generalized to a hull system for a GEA. We study Dedekind orthocompleteness of GEAs and extend to GEAs the notion of a centrally orthocomplete effect algebra.
Array algebra estimation in signal processing
NASA Astrophysics Data System (ADS)
Rauhala, U. A.
A general theory of linear estimators called array algebra estimation is interpreted in some terms of multidimensional digital signal processing, mathematical statistics, and numerical analysis. The theory has emerged during the past decade from the new field of a unified vector, matrix and tensor algebra called array algebra. The broad concepts of array algebra and its estimation theory cover several modern computerized sciences and technologies converting their established notations and terminology into one common language. Some concepts of digital signal processing are adopted into this language after a review of the principles of array algebra estimation and its predecessors in mathematical surveying sciences.