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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
The artificial water cycle: emergy analysis of waste water treatment.
Bastianoni, Simone; Fugaro, Laura; Principi, Ilaria; Rosini, Marco
2003-04-01
The artificial water cycle can be divided into the phases of water capture from the environment, potabilisation, distribution, waste water collection, waste water treatment and discharge back into the environment. The terminal phase of this cycle, from waste water collection to discharge into the environment, was assessed by emergy analysis. Emergy is the quantity of solar energy needed directly or indirectly to provide a product or energy flow in a given process. The emergy flow attributed to a process is therefore an index of the past and present environmental cost to support it. Six municipalities on the western side of the province of Bologna were analysed. Waste water collection is managed by the municipal councils and treatment is carried out in plants managed by a service company. Waste water collection was analysed by compiling a mass balance of the sewer system serving the six municipalities, including construction materials and sand for laying the pipelines. Emergy analysis of the water treatment plants was also carried out. The results show that the great quantity of emergy required to treat a gram of water is largely due to input of non renewable fossil fuels. As found in our previous analysis of the first part of the cycle, treatment is likewise characterised by high expenditure of non renewable resources, indicating a correlation with energy flows.
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...
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 ...
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. Copyright © 2010 Elsevier B.V. All rights reserved.
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...
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...
The geobiosphere emergy baseline: A synthesis.
The concept of emergy defined as the available energy (or exergy) of one form used up directly and indirectly to produce an item or action (Odum, Environmental Accounting Emergy and Environmental Decision Making, John Wiley & Sons, Inc., 1996) requires the specification of a unif...
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 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...
The geobiosphere emergy baseline: A synthesis.
The concept of emergy defined as the available energy (or exergy) of one form used up directly and indirectly to produce an item or action (Odum, Environmental Accounting Emergy and Environmental Decision Making, John Wiley & Sons, Inc., 1996) requires the specification of a unif...
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...
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...
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...
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...
Comparison of typical mega cities in China using emergy synthesis
NASA Astrophysics Data System (ADS)
Zhang, L. X.; Chen, B.; Yang, Z. F.; Chen, G. Q.; Jiang, M. M.; Liu, G. Y.
2009-06-01
An emergy-based comparison analysis is conducted for three typical mega cities in China, i.e., Beijing, Shanghai and Guangzhou, from 1990 to 2005 in four perspectives including emergy intensity, resource structure, environmental pressure and resource use efficiency. A new index of non-renewable emergy/money ratio is established to indicate the utilization efficiency of the non-renewable resources. The results show that for the three mega urban systems, Beijing, Shanghai and Guangzhou, the total emergy inputs were 3.76E+23, 3.54E+23, 2.52E+23 sej in 2005, of which 64.88%, 91.45% and 72.28% were imported from the outsides, respectively. As to the indicators of emergy intensity involving the total emergy use, emergy density and emergy use per cap, three cities exhibited similar overall increase trends with annual fluctuations from 1990 to 2005. Shanghai achieved the highest level of economic development and non-renewable resource use efficiency, and meanwhile, lower proportion of renewable resource use and higher environmental pressure compared to those of Beijing and Guangzhou. Guangzhou has long term sustainability considering an amount of local renewable resources used, per capita emergy used, energy consumption per unit GDP and the ratio of waste to renewable emergy. It can be concluded that different emergy-based evaluation results arise from different geographical locations, resources endowments, industrial structures and urban orientations of the concerned mega cities.
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 inconsistent set of…
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 inconsistent set of…
Using Toulmin analysis to analyse an instructor's proof presentation in abstract algebra
NASA Astrophysics Data System (ADS)
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 inconsistent set of written models for their work. Similarly, the analysis shows that the details the instructor says aloud differ from what she writes down. Although her verbal commentary provides additional detail and appears to have pedagogical value, for instance, by modelling thinking that supports proof writing, this value might be better realized if she were to change her teaching practices.
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…
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…
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 ...
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 ...
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...
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...
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 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...
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...
ERIC Educational Resources Information Center
Chiu, Ming Ming
2008-01-01
The micro-time context of group processes (such as argumentation) can affect a group's micro-creativity (new ideas). Eighty high school students worked in groups of four on an algebra problem. Groups with higher mathematics grades showed greater micro-creativity, and both were linked to better problem solving outcomes. Dynamic multilevel analyses…
New emergy indices for sustainable development.
Lu, Hong-fang; Lan, Sheng-fang; Li, Lei; Peng, Shao-lin
2003-07-01
The emergy indices for the evaluation of system's sustainable development ability were studied. Results indicated that the emergy indices are simplified and merged, and a new emergy index for sustainable development (EISD) is deduced. Employing EISD, two cases are conducted. The first one is to compare three different dike-pond agro-ecological engineering modes, which are: melon-melon-cabbage-four domestic fishes (mode I), melon-melon-cabbage-pig-four domestic fishes (mode II) and melon-melon-cabbage-pig-four domestic fishes combined with Siniperca chuatsi B. (mode III). The result is that the EISD of mode I is 0.53. Mode II's EISD is 5.26 times of mode I, and mode III's EISD is 6.83 times of mode I. The second one is to evaluate the development of Zhongshan City, Pearl Delta, during 1996 to 2000. The result indicated that the EISD of Zhongshan had appreciably declined from 1996 to 1998, and quickly improved from 1998 to 2000, partly because of its environment protection and product construction. Both of the two cases studies showed that EISD can assessment the sustainable development ability more roundly, with the consideration of environmental impact and social-economic effect at the same time.
[Emergy evaluation of power plant eco-industrial park].
Wang, Lingmei; Zhang, Jintun
2004-06-01
In this paper, new emergy indices for the material circulation utilization and energy cascade utilization were presented to evaluate the emergy of power plant eco-industrial park. The common contribution of the members in power plant eco-industrial park should be accounted for emergy yield ratio (PEYR) and emergy investment ratio (PEIR), namely, PEYR = sigma(i = 1)6 (Fi + Ri + Ni)/sigma(i = 1)6 Fi and PEIR = sigma(i = 1)6 Fi/sigma(i = 1)6 (Ni + Ri). Saved renewable and nonrenewable resources and purchased resources and decreased environmental load should be accounted for environmental loading ratio (PELR) and index of sustainability (PESI), namely, PELR = sigma(i = 1)6 Fi/F' and PESI = PEYR/PELR. Case analysis on the Shuozhou power plant eco-industrial park showed that new emergy indices were practical in evaluating the power plant eco-industrial park.
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…
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 ...
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 ...
[Emergy value evaluation on rice-duck organic farming mode].
Xi, Yunguan; Qin, Pei
2006-02-01
Employing emergy value evaluation method, this paper compared the ecological and economic benefits of rice-duck organic farming system (mode I) and conventional rice-wheat rotation system (mode II) in Shanghai suburb. The results showed that mode I had better emergy benefits, higher self-organizing ability and sustainability, and higher product safety. The net emergy yield ratio (EYR), feedback ratio of yield emergy (FYE), and emergy sustainable index (ESI) of mode I were respectively 1.57, 14.1, and 8.71 times as much as those of mode II, and the emergy index of product safety (EIPS) was 0 in mode I but -0.66 in mode II. The emergy investment ratio (EIR) and environmental loading ratio (ELR) of mode I were 40.1% and 18.3% of mode II, respectively, suggesting that mode I had less environmental pressure than mode II. Mode I had lower economic benefits than mode II. The economic output, gross income, and net income of mode I were 15.7%, 9.6%, and 29.6% less than those of mode II , respectively. As for Em dollars, the output, gross income, and net income of mode I were respectively 50%, 102.6%, and 136.4% higher than those of mode II. With the system optimization and the development of organic food market, mode I had the potential to improve its economic benefits.
NASA Astrophysics Data System (ADS)
Blumenhagen, Ralph; Fuchs, Michael; Traube, Matthias
2017-07-01
It is shown that the closure of the infinitesimal symmetry transformations underlying classical W algebras give rise to L∞ algebras with in general field dependent gauge parameters. Therefore, the class of well understood W algebras provides highly nontrivial examples of such strong homotopy Lie algebras. We develop the general formalism for this correspondence and apply it explicitly to the classical W_3 algebra.
[The Chinese urban metabolisms based on the emergy theory].
Song, Tao; Cai, Jian-Ming; Ni, Pan; Yang, Zhen-Shan
2014-04-01
By using emergy indices of urban metabolisms, this paper analyzed 31 Chinese urban metabolisms' systematic structures and characteristics in 2000 and 2010. The results showed that Chinese urban metabolisms were characterized as resource consumption and coastal external dependency. Non-renewable resource emergy accounted for a higher proportion of the total emergy in the inland cities' urban metabolisms. The emergy of imports and exports accounted for the vast majority of urban metabolic systems in metropolises and coastal cities such as Beijing and Shanghai, showing a significant externally-oriented metabolic characteristic. Based on that, the related policies were put forward: to develop the renewable resource and energy industry; to improve the non-renewable resource and energy utilization efficiencies; to optimize the import and export structure of services, cargo and fuel; and to establish the flexible management mechanism of urban metabolisms.
The Emergy Perspective of Sustainable Trends in Puerto Rico From 1960 to 2013
Emergy analysis quantifies the direct and indirect contributions of nature to human systems providing a sustainability assessment framework, which couples economic growth within biophysical constraints. In this study, Puerto Rico's sustainability was assessed with emergy flow dyn...
The Emergy Perspective of Sustainable Trends in Puerto Rico From 1960 to 2013
Emergy analysis quantifies the direct and indirect contributions of nature to human systems providing a sustainability assessment framework, which couples economic growth within biophysical constraints. In this study, Puerto Rico's sustainability was assessed with emergy flow dyn...
[Emergy analysis of ecological-economic system in Liaoning Province].
Liu, Hao; Wang, Qing; Li, Xiu-Juan; Song, Yang; Li, Guang-Jun
2008-03-01
By the methods of emergy analysis, this paper studied the emergy flow in the ecological-economic system in Liaoning Province in 1990-2005, and the relationships between the environmental stress caused by resources' input, output and consumption and the sustainable development of the Province. The results showed that in Liaoning Province, the non-renewable resources occupied over 74% of the total consumed emergy, and the realistic population in 2005 was 3.26 times higher than the supportable population. In 1990-2005, the emergy yield ratio decreased from 65.40 to 10.13, emergy loading ratio increased from 2.72 to 7.18, and emergy sustainable index decreased from 24.03 to 1.41. The rapid economic growth in Liaoning Province was chiefly supported by the consumption of vast non-renewable resources, which caused the pressure of economic development on ecosystem getting more and more intense, the economic development increasingly depending on exogenous resources, and the sustainable development of Liaoning ecological-economic system having a continuing decrease. To realize the sustainable development in Liaoning Province, the principles of reduction, reutilization and recycling should be taken as the guidelines for promoting the reuse of wastes and the closed fine circulation of resources to minimize the discharge of wastes.
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...
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.
The Emergy Perspective of Sustainable Trends in Puerto Rico ...
Emergy analysis quantifies the direct and indirect contributions of nature to human systems providing a sustainability assessment framework, which couples economic growth within biophysical constraints. In this study, Puerto Rico's sustainability was assessed with emergy flow dynamics from 1960 to 2013. During this period, the island shifted from an agriculture-based economy to an industrial base of manufacture and services (1960–1970). The emergy analysis indicated an exponential decline in sustainability during this period. From 1975 to 1992, the island became more industrialized and imported more goods and services. Since 1998, although more renewable production such as forest regeneration occurred, the rapid industrialization heavily relied on imported fossil fuels, goods, and services, resulting in a system that has not been self-sufficient, nor sustainable. The latest economic crisis and the most recently passed financial rescue bill represent an opportunity to redirect Puerto Rico towards a sustainable path with policies that decrease the ratio of imported y to exported emergy, and strategies that encourage efficient use of resources and local production based on the utilization of renewable sources within this U.S. territory. This study developed and explored a framework and indices using emergy analysis to holistically reflect the condition of a regional system like Puerto Rico and its sustainability over the past 50 years, determine if the island is
Integrated Emergy and Economic Evaluation of Lotus-Root ...
Lotus (Neumbo nucifera, Gaertn) is the most important aquatic vegetable in China, with a cultivation history of over 3000 years. The emergy, energy, material, and money flows of three lotus root cultivation modes in Wanqingsha, Nansha District, Guangzhou, China were examined using Energy Systems Language models and emergy evaluation to better understand their ecological and economic characteristics on multiple spatial and temporal scales. The natural resource foundations, economic characteristics and sustainability of these modes were evaluated and compared. The results showed that although all three modes were highly dependent on purchased emergy inputs, their potential impacts as measured by the local (ELRL) and global (ELRW) environmental loading ratios were less than 1.2 and 0.7, respectively. The lotus-fish mode was the most sustainable with its emergy index of sustainable development (EISD) 2.09 and 2.13 times that of the pure lotus and lotus-shrimp modes, respectively. All three lotus-root production modes had superior economic viability, since their Output/Input ratio ranged from 2.56 to 4.95. The results indicated that agricultural systems may have different environmental impacts and sustainability characteristics at different spatial and temporal scales, and that these impacts and characteristics can be simultaneously explored using integrated emergy and economic evaluations. This study provides some major new insights about agriculture and its potenti
1998-06-01
on courses being taught at NPS. LIST OF REFERENCES [1] Anton , Howard , Elementary Linear Algebra , John Wiley and Sons, New York, New York, 1994...and computational techniques for solving systems of linear equations. The goal is to enhance current matrix algebra textbooks and help the beginning... algebra is the study of algebraic operations on matrices and of their applications, primarily for solving systems of linear equations. Systems of
Zhang, L X; Ulgiati, S; Yang, Z F; Chen, B
2011-03-01
Emergy and economic methods were used to evaluate and compare three fish production models, i.e., cage fish farming system, pond intensive fish rearing system and semi-natural extensive pond fish rearing system, in Nansi Lake area in China in the year 2007. The goal of this study was to understand the benefits and driving forces of selected fish production models from ecological and economic points of view. The study considered input structure, production efficiency, environmental impacts, economic viability and sustainability. Results show that the main difference among the three production systems was the emergy cost for fish feed associated with their feeding system, i.e., feeding on natural biomass such as plankton and grass or on commercial feedstock. As indicated by EYR, ELR and ESI, it can be clearly shown that the intensive production model with commercial feed is not a sustainable pattern. However, the point is that more environmentally sound patterns do not seem able to provide a competitive net profit in the short run. The intensive pond fish farming system had a net profit of 2.57E+03 $/ha, much higher than 1.27E+03 $/ha for cage fish farming system and slightly higher than 2.37E+03 $/ha for semi-natural fish farming system. With regard to the drivers of local farmer's decisions, the accessibility of land for the required use and investment ability determine the farmer's choice of the production model and the scale of operation, while other factors seem to have little effect. Theoretically, the development of environmentally sustainable production patterns, namely water and land conservation measures, greener feed as well as low waste systems is urgently needed, to keep production activities within the carrying capacity of ecosystems. Coupled emergy and economic analyses can provide better insight into the environmental and economic benefits of fish production systems and help solve the problems encountered during policy making.
A Brief History of the Emergy Society and its Mission in the ...
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 International Society for the Advancement of Emergy Research (ISAER), a.k.a., the Emergy Society, was incorporated as a nonprofit corporation in the United States on July 28, 2007. In this talk, the history of the Emergy Society from its origin to the present time will be presented. The key ideas of emergy and transformity and their derivation and importance will be discussed. The structure of the Emergy Society and how it has carried out its mission over its history will be examined, including the formation of the China Chapter of ISAER. In many ways the history of ISAER is a story about its Presidents and the Executive Council members, who worked hard to promote the growth of the Emergy Society and to expand its services to its membership and the world. The development of the Emergy Society website as the major interface to communicate with its members and the general public will be recounted along with the story of the development of the Emergy Society logo and its esoteric meaning. Finally, the accomplishments of ISAER in the United States, China, Brazil and Europe to date will be considered and the future of the Emergy Society explored. This talk was delivered as a plenary address to the asse
A Brief History of the Emergy Society and its Mission in the ...
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 International Society for the Advancement of Emergy Research (ISAER), a.k.a., the Emergy Society, was incorporated as a nonprofit corporation in the United States on July 28, 2007. In this talk, the history of the Emergy Society from its origin to the present time will be presented. The key ideas of emergy and transformity and their derivation and importance will be discussed. The structure of the Emergy Society and how it has carried out its mission over its history will be examined, including the formation of the China Chapter of ISAER. In many ways the history of ISAER is a story about its Presidents and the Executive Council members, who worked hard to promote the growth of the Emergy Society and to expand its services to its membership and the world. The development of the Emergy Society website as the major interface to communicate with its members and the general public will be recounted along with the story of the development of the Emergy Society logo and its esoteric meaning. Finally, the accomplishments of ISAER in the United States, China, Brazil and Europe to date will be considered and the future of the Emergy Society explored. This talk was delivered as a plenary address to the asse
Emergy accounting for regional studies: case study of Canada and its provinces.
Hossaini, Navid; Hewage, Kasun
2013-03-30
Sustainable regional management (development) requires an understanding of interactions between the social, economic, and ecological systems within the boundaries of a region. In this paper, application of emergy (an environmental accounting method) for regional planning is discussed through a case study. Emergy (spelled with an "m") methodology is an environmental accounting technique that evaluates the energy system for the thermodynamics of an open system. Major renewable and non-renewable resource fluxes to a region, including energy, matter, human activities, and money can be converted to emergy by using corresponding transformity functions. As a case study, this paper discusses the emergy accounting of Canada and its provinces with various emergy-based indicators. Moreover, emergy maps were generated in a form of emergy geography. These maps are multi-dimensional illustrations that show resource consumption, emergy per person, and emergy density across Canada under two parameters: (1) the quantities of resources consumed and (2) the location of consumption. Emergy analysis also highlights concentrations of renewable and natural resources in Canada and distinguishes the provinces with the highest resource consumption. Analysis of emergy indicator for Canadian provinces shows that Alberta with the highest EYR (7.35) provides energy to the economy of Canada. However, ELR value of Alberta (8.5) indicates that the province's current economic approach is not sustainable as it relies mainly on non-renewable emergy inputs (mainly from fossil fuels). ELR of British Columbia and Manitoba indicates that these two provinces created a firm balance between emergy use of renewable and non-renewable resources. The characterizations of regions provided in this paper can be used for future land planning and management both in federal and provincial levels. Copyright © 2013 Elsevier Ltd. All rights reserved.
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...
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...
Emergy Analysis for the Sustainable Utilization of Biosolids ...
This contribution describes the application of an emergy-based methodology for comparing two management alternatives of biosolids produced in a wastewater treatment plant. The current management practice of using biosolids as soil fertilizers was evaluated and compared to another alternative, the recovery of energy from the biosolid gasification process. This emergy assessment and comparison approach identifies more sustainable processes which achieve economic and social benefits with a minimal environmental impact. In addition, emergy-based sustainability indicators and the GREENSCOPE methodology were used to compare the two biosolid management alternatives. According to the sustainability assessment results, the energy production from biosolid gasification is energetically profitable, economically viable, and environmentally suitable. Furthermore, it was found that the current use of biosolids as soil fertilizer does not generate any considerable environmental stress, has the potential to achieve more economic benefits, and a post-processing of biosolids prior to its use as soil fertilizer improves its sustainability performance. In conclusion, this emergy analysis provides a sustainability assessment of both alternatives of biosolid management and helps decision-makers to identify opportunities for improvement during the current process of biosolid management. This work aims to identify the best option for the use and management of biosolids generated in a wa
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...
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…
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 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...
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...
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...
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...
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…
A thermodynamic geography: night-time satellite imagery as a proxy measure of emergy.
Coscieme, Luca; Pulselli, Federico M; Bastianoni, Simone; Elvidge, Christopher D; Anderson, Sharolyn; Sutton, Paul C
2014-11-01
Night-time satellite imagery enables the measurement, visualization, and mapping of energy consumption in an area. In this paper, an index of the "sum of lights" as observed by night-time satellite imagery within national boundaries is compared with the emergy of the nations. Emergy is a measure of the solar energy equivalent used, directly or indirectly, to support the processes that characterize the economic activity in a country. Emergy has renewable and non-renewable components. Our results show that the non-renewable component of national emergy use is positively correlated with night-time satellite imagery. This relationship can be used to produce emergy density maps which enable the incorporation of spatially explicit representations of emergy in geographic information systems. The region of Abruzzo (Italy) is used to demonstrate this relationship as a spatially disaggregate case.
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.
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.…
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.…
ERIC Educational Resources Information Center
Amdahl, Kenn; Loats, Jim
This book discusses algebra in a non-threatening, fun way. It explains concepts, vocabulary, and strategies of algebra in understandable terms. Chapter titles include: "Numbers with Interesting Properties"; "Important Concepts"; "Fraction Refresher"; "Terms, Factors, and Polynomials"; "Rearranging Expressions"; "Handy Tricks and Magic Words";…
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...
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 baseline for the Earth: A historical review of the science and a new calculation
Quantifying the emergy baseline of the Earth is a practical necessity for emergy evaluations, because it serves as a unified basis for determining transformities of the available energy storages and flows of the geobiosphere. The current debate over the value and significance of ...
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...
Emergy baseline for the Earth: A historical review of the science and a new calculation
Quantifying the emergy baseline of the Earth is a practical necessity for emergy evaluations, because it serves as a unified basis for determining transformities of the available energy storages and flows of the geobiosphere. The current debate over the value and significance of ...
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...
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...
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...
A Reexamination of the Emergy Input to a System from the Wind.
The wind energy absorbed in the global boundary layer (GBL, 900 mb surface) is the basis for calculating the wind emergy input for any system on the Earth’s surface. Estimates of the wind emergy input to a system depend on the amount of wind energy dissipated, which can hav...
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...
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...
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...
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...
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.
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.
NASA Technical Reports Server (NTRS)
Mulligan, Jeffrey B.
2017-01-01
A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. We would like it to match the well-defined algebra of spectral functions describing lights and surface reflectances, but an exact correspondence is impossible after the spectra have been projected to a three-dimensional color space, because of metamerism physically different spectra can produce the same color sensation. Metameric spectra are interchangeable for the purposes of addition, but not multiplication, so any color algebra is necessarily an approximation to physical reality. Nevertheless, because the majority of naturally-occurring spectra are well-behaved (e.g., continuous and slowly-varying), color algebras can be formulated that are largely accurate and agree well with human intuition. Here we explore the family of algebras that result from associating each color with a member of a three-dimensional manifold of spectra. This association can be used to construct a color product, defined as the color of the spectrum of the wavelength-wise product of the spectra associated with the two input colors. The choice of the spectral manifold determines the behavior of the resulting system, and certain special subspaces allow computational efficiencies. The resulting systems can be used to improve computer graphic rendering techniques, and to model various perceptual phenomena such as color constancy.
ERIC Educational Resources Information Center
Hitt, Fernando; Saboya, Mireille; Cortés Zavala, Carlos
2016-01-01
This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the early algebraic thinking, which is considered a prelude to algebraic thinking. In the process of building this latter way of thinking, researchers analysed pupils' spontaneous production…
ERIC Educational Resources Information Center
Hitt, Fernando; Saboya, Mireille; Cortés Zavala, Carlos
2016-01-01
This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the early algebraic thinking, which is considered a prelude to algebraic thinking. In the process of building this latter way of thinking, researchers analysed pupils' spontaneous production…
NASA Astrophysics Data System (ADS)
Mikhalev, A. V.; Pinchuk, I. A.
2005-06-01
The structure of Steinberg conformal algebras is studied; these are analogues of Steinberg groups (algebras, superalgebras).A Steinberg conformal algebra is defined as an abstract algebra by a system of generators and relations between the generators. It is proved that a Steinberg conformal algebra is the universal central extension of the corresponding conformal Lie algebra; the kernel of this extension is calculated.
[Emergy of agro-ecosystem in Hunan Province: evolution and trend].
Zhu, Yu-Lin; Li, Ming-Jie
2012-02-01
By using emergy analysis method, a trend analysis was made on the total emergy, its input-output structure, and emergy indices of the agro-ecosystem in Hunan Province of South-central China from 1999 to 2008. In the study period, the available total emergy input of the ecosystem was basically maintained at a stable level, but the input structure changed with the input of non-renewable industrial auxiliary emergy increased from 4.00E+22 sej in 1999 to 5.53E+22 sej in 2008, while that of renewable organic emergy decreased from 1.32E+23 sej to 1.20E+23 sej. Both the total emergy output and the output efficiency of the ecosystem had a great increase, with the total output reached 1.69E+23 sej in 2008, which was 23.8% higher than that in 1999, and the net output ratio increased from 0.79 to 0.96. Owing to the ever-increasing trend of the environmental loading ratio which was from 1.12 to 1.79, the sustainable development index of the ecosystem presented a decreasing trend, from 0.71 to 0.54, indicating that the agriculture in Hunan Province was overall belonged to the type of ecosystem driven by high consumption, and had relatively apparent extensive development characteristics.
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 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.
ERIC Educational Resources Information Center
Capani, Antonio; De Dominicis, Gabriel
This paper proposes a model for a general interface between people and Computer Algebra Systems (CAS). The main features in the CAS interface are data navigation and the possibility of accessing powerful remote machines. This model is based on the idea of session management, in which the main engine of the tool enables interactions with the…
Chen, Chun-feng; Wang, Hong-yan; Xiao, Du-ning; Wang, Da-qing
2008-11-01
By using traditional ecological footprint method and its modification, emergy ecological footprint method, the sustainable development status of Heilongjiang Province in 2005 was analyzed. The results showed that the ecological deficits of Heilongjiang Province in 2005 based on emergy and conventional ecological footprint methods were 1.919 and 0.6256 hm2 x cap(-1), respectively. The ecological footprint value based on the two methods both exceeded its carrying capacity, which indicated that the social and economic development of the study area was not sustainable. Emergy ecological footprint method was used to discuss the relationships between human's material demand and ecosystem resources supply, and more stable parameters such as emergy transformity and emergy density were introduced into emergy ecological footprint method, which overcame some of the shortcomings of conventional ecological method.
NASA Astrophysics Data System (ADS)
Golenishcheva-Kutuzova, Maria I.; Kac, Victor G.
1998-04-01
Γ-conformal algebra is an axiomatic description of the operator product expansion of chiral fields with simple poles at finitely many points. We classify these algebras and their representations in terms of Lie algebras and their representations with an action of the group Γ. To every Γ-conformal algebra and a character of Γ we associate a Lie algebra generated by fields with the OPE with simple poles. Examples include twisted affine Kac-Moody algebras, the sin algebra (which is a "Γ-conformal" analogue of the general linear algebra) and its analogues, the algebra of pseudodifferential operators on the circle, etc.
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...
This contribution describes the application of an emergy-based methodology for comparing two management alternatives of biosolids produced in a wastewater treatment plant. The current management practice of using biosolids as soil fertilizers was evaluated and compared to another...
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...
Sustainable Biofuel Project: Emergy Analysis of South Florida Energy Crops
Amponsah, Nana Yaw; Izursa, Jose-Luis; Hanlon, Edward A.; Capece, John C.
2012-11-15
This study evaluates the sustainability of various farming systems, namely (1) sugarcane on organic and mineral soils and (2) energycane and sweet sorghum on mineral soils. The primary objective of the study is to compare the relative sustainability matrices of these energy crops and their respective farming systems. These matrices should guide decision and policy makers to determine the overall sustainability of an intended or proposed bioethanol project related to any of these studied crops. Several different methods of energy analysis have been proposed to assess the feasibility or sustainability of projects exploiting natural resources (such as (Life Cycle Analysis, Energy Analysis, Exergy Analysis, Cost Benefit Analysis, Ecological Footprint, etc.). This study primarily focused on the concept of Emergy Analysis, a quantitative analytical technique for determining the values of nonmonied and monied resources, services and commodities in common units of the solar energy it took to make them. With this Emergy Analysis study, the Hendry County Sustainable Biofuels Center intends to provide useful perspective for different stakeholder groups to (1) assess and compare the sustainability levels of above named crops cultivation on mineral soils and organic soils for ethanol production and (2) identify processes within the cultivation that could be targeted for improvements. The results provide as much insight into the assumptions inherent in the investigated approaches as they do into the farming systems in this study.
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.
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.
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
NASA Astrophysics Data System (ADS)
Vaninsky, Alexander
2011-04-01
This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos - satisfying an axiom sin2 + cos2 = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two different interpretations of the TF are discussed with many others potentially possible. The main objective of this article is to introduce a broader view of trigonometry that can serve as motivation for mathematics students and teachers to study and teach abstract algebraic structures.
Ternary algebraic approach to extended superconformal algebras
NASA Astrophysics Data System (ADS)
Günaydin, Murat; Hyun, Seungjoon
1992-04-01
The construction of extended ( N = 2 and N = 4) superconformal algebras (SCA) over very general classes of ternary algebras (triple systems) is given. For N = 2 this construction leads to superconformal algebras corresponding to certain Kählerian coset spaces of Lie groups with non-vanishing torsion. In general, a given Lie group admits more than one coset space of this type. The construction and a complete classification of N = 2 SCAs over Kantor triple system is given. In particular, the division algebras and their tensor products lead to N = 2 superconformal algebras associated with the coset spaces of the groups of the Magic Square. For a very special class of ternary algebras, namely the Freudenthal triple (FT) systems, the N = 2 superconformal algebras can be extended to N = 4 superconformal algebras with the gauge group SU(2)×SU(2)×U(1). The realization and a complete classification of N = 2 and N = 4
Derive Workshop Matrix Algebra and Linear Algebra.
ERIC Educational Resources Information Center
Townsley Kulich, Lisa; Victor, Barbara
This document presents the course content for a workshop that integrates the use of the computer algebra system Derive with topics in matrix and linear algebra. The first section is a guide to using Derive that provides information on how to write algebraic expressions, make graphs, save files, edit, define functions, differentiate expressions,…
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.
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.
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.
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.
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...
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...
ERIC Educational Resources Information Center
Edwards, Edgar L., Jr., Ed.
The fundamentals of algebra and algebraic thinking should be a part of the background of all citizens in society. The vast increase in the use of technology requires that school mathematics ensure the teaching of algebraic thinking as well as its use at both the elementary and secondary school levels. Algebra is a universal theme that runs through…
On Exceptional Superconformal Algebras
Poletaeva, Elena
2010-06-17
We obtain realizations of superconformal algebras K(2), K'(4) and the exceptional N = 6 superconformal algebra in matrices over a Weyl algebra of size 2x2, 4x4 and 8x8, respectively. A general construction of these realizations is based on the spin representations of the orthogonal Lie algebras. We give explicit descriptions of these matrix realizations.
NASA Astrophysics Data System (ADS)
Foulis, David J.; Jenčová, Anna; Pulmannová, Sylvia
2017-02-01
Different versions of the notion of a state have been formulated for various so-called quantum structures. In this paper, we investigate the interplay among states on synaptic algebras and on its sub-structures. A synaptic algebra is a generalization of the partially ordered Jordan algebra of all bounded self-adjoint operators on a Hilbert space. The paper culminates with a characterization of extremal states on a commutative generalized Hermitian algebra, a special kind of synaptic algebra.
Mao, De-Hua; Hu, Guang-Wei; Liu, Hui-Jie; Li, Zheng-Zui; Li, Zhi-Long; Tan, Zi-Fang
2014-02-01
The annual emergy and currency value of the main ecological service value of returning cropland to lake in Dongting Lake region from 1999 to 2010 was calculated based on emergy analysis. The calculation method of ecological compensation standard was established by calculating annual total emergy of ecological service function increment since the starting year of returning cropland to lake, and the annual ecological compensation standard and compensation area were analyzed from 1999 to 2010. The results indicated that ecological compensation standard from 1999 to 2010 was 40.31-86.48 yuan x m(-2) with the mean of 57.33 yuan x m(-2). The ecological compensation standard presented an increase trend year by year due to the effect of eco-recovery of returning cropland to lake. The ecological compensation standard in the research area presented a swift and steady growth trend after 2005 mainly due to the intensive economy development of Hunan Province, suggesting the value of natural ecological resources would increase along with the development of society and economy. Appling the emergy analysis to research the ecological compensation standard could reveal the dynamics of annual ecological compensation standard, solve the abutment problem of matter flow, energy flow and economic flow, and overcome the subjective and arbitrary of environment economic methods. The empirical research of ecological compensation standard in Dongting Lake region showed that the emergy analysis was feasible and advanced.
Quantum cluster algebras and quantum nilpotent algebras.
Goodearl, Kenneth R; Yakimov, Milen T
2014-07-08
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.
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
Deformed Virasoro Algebras from Elliptic Quantum Algebras
NASA Astrophysics Data System (ADS)
Avan, J.; Frappat, L.; Ragoucy, E.
2017-09-01
We revisit the construction of deformed Virasoro algebras from elliptic quantum algebras of vertex type, generalizing the bilinear trace procedure proposed in the 1990s. It allows us to make contact with the vertex operator techniques that were introduced separately at the same period. As a by-product, the method pinpoints two critical values of the central charge for which the center of the algebra is extended, as well as (in the gl(2) case) a Liouville formula.
[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.
Emergy Evaluation of the Natural Value of Water Resources in Chinese Rivers
NASA Astrophysics Data System (ADS)
Chen, Dan; Chen, Jing; Luo, Zhaohui; Lv, Zhuwu
2009-08-01
Emergy theory and method were used to evaluate the economy of China and the contributions of water resources in Chinese rivers to the real wealth of the Chinese economy. The water cycle and energy conversion were reviewed, and an emergy method for evaluating the natural value of water resources in a river watershed was developed. The indices for China calculated from the emergy evaluation were close to those of developing countries. Despite a small surplus in its balance of payments, China had a net emergy loss from its trade in 2002. The efficiency of Chinese natural resource use was still not high and did not match its economic growth rate. Furthermore, the Chinese economy placed a stress on its ecological environment and natural resources. Several indices of Chinese rivers from the emergy evaluation were close to those of average global river water. The main average indices of Chinese rivers were transformity (4.17 × 104 sej/J), emergy per volume (2.05 × 1011 sej/m3), and emdollar per volume (0.06 /m3). The total value of all the rivers’ water made up 13.0% of the GDP of China in 2002, and that of water consumption accounted for 2.1%. The value of the water resources in the Haihe-luanhe River (11.39 × 104 sej/J) was the highest, followed by the Yellow River (10.27 × 104 sej/J), while the rivers in Southwest China had the lowest values (2.92 × 104 sej/J).
Emergy evaluation of the natural value of water resources in Chinese rivers.
Chen, Dan; Chen, Jing; Luo, Zhaohui; Lv, Zhuwu
2009-08-01
Emergy theory and method were used to evaluate the economy of China and the contributions of water resources in Chinese rivers to the real wealth of the Chinese economy. The water cycle and energy conversion were reviewed, and an emergy method for evaluating the natural value of water resources in a river watershed was developed. The indices for China calculated from the emergy evaluation were close to those of developing countries. Despite a small surplus in its balance of payments, China had a net emergy loss from its trade in 2002. The efficiency of Chinese natural resource use was still not high and did not match its economic growth rate. Furthermore, the Chinese economy placed a stress on its ecological environment and natural resources. Several indices of Chinese rivers from the emergy evaluation were close to those of average global river water. The main average indices of Chinese rivers were transformity (4.17 x 10(4) sej/J), emergy per volume (2.05 x 10(11) sej/m(3)), and emdollar per volume (0.06 $/m(3)). The total value of all the rivers' water made up 13.0% of the GDP of China in 2002, and that of water consumption accounted for 2.1%. The value of the water resources in the Haiheluanhe River (11.39 x 10(4) sej/J) was the highest, followed by the Yellow River (10.27 x 10(4) sej/J), while the rivers in Southwest China had the lowest values (2.92 x 10(4) sej/J).
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…
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.
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…
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…
ERIC Educational Resources Information Center
Miller, L. Diane; England, David A.
1989-01-01
Describes a study in a large metropolitan high school to ascertain what influence the use of regular writing in algebra classes would have on students' attitudes towards algebra and their skills in algebra. Reports the simpler and more direct the writing topics the better. (MVL)
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…
Arithmetic: Prerequisite to Algebra?
ERIC Educational Resources Information Center
Rotman, Jack W.
Drawing from research and observations at Lansing Community College (Michigan) (LCC), this paper argues that typical arithmetic courses do little to prepare students to master algebra, and proposes an alternative set of arithmetic skills as actual prerequisites to algebra. The first section offers a description of the algebra sequence at LCC,…
ERIC Educational Resources Information Center
Mitchell, Sarah
2006-01-01
Many students find the leap from arithmetic to algebra a difficult one to make, and current literature suggests that a number of the common misconceptions held by students arise as a result of the methods which teachers use to present algebra. The abstract nature of algebra makes it difficult for students to grasp; students also struggle with the…
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,…
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.
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.
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.
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...
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...
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...
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 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...
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...
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...
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...
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...
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 ...
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.
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...
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...
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...
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...
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...
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...
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.
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 ...
Discrete Minimal Surface Algebras
NASA Astrophysics Data System (ADS)
Arnlind, Joakim; Hoppe, Jens
2010-05-01
We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.
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
The Algebra of the NODEN Analyser
1989-08-01
c, c, E, 0, 01 If the range of r is not 0 to upb, but lwb to upb, then the input value is derived by making a value for an input in the range 0 to upb... lwb as described above, and adding a literal value lwb to it (see section 6.3). So the value of an input with a range 1 to 6 (mapped onto three...outside the range of the constrained type. If F1 is a function defined to map between unconstrained numeric values and values of a type in the range lwb
On Derivations Of Genetic Algebras
NASA Astrophysics Data System (ADS)
Mukhamedov, Farrukh; Qaralleh, Izzat
2014-11-01
A genetic algebra is a (possibly non-associative) algebra used to model inheritance in genetics. In application of genetics this algebra often has a basis corresponding to genetically different gametes, and the structure constant of the algebra encode the probabilities of producing offspring of various types. In this paper, we find the connection between the genetic algebras and evolution algebras. Moreover, we prove the existence of nontrivial derivations of genetic algebras in dimension two.
A Reexamination of the Emergy Input to a System from the ...
The wind energy absorbed in the global boundary layer (GBL, 900 mb surface) is the basis for calculating the wind emergy input for any system on the Earth’s surface. Estimates of the wind emergy input to a system depend on the amount of wind energy dissipated, which can have a range of magnitudes for a given velocity depending on surface drag and atmospheric stability at the location and time period under study. In this study, we develop a method to consider this complexity in estimating the emergy input to a system from the wind. A new calculation of the transformity of the wind energy dissipated in the GBL (900 mb surface) based on general models of atmospheric circulation in the planetary boundary layer (PBL, 100 mb surface) is presented and expressed on the 12.0E+24 seJ y-1 geobiosphere baseline to complete the information needed to calculate the emergy input from the wind to the GBL of any system. The average transformity of wind energy dissipated in the GBL (below 900 mb) was 1241±650 sej J-1. The analysis showed that the transformity of the wind varies over the course of a year such that summer processes may require a different wind transformity than processes occurring with a winter or annual time boundary. This is a paper in the proceedings of Emergy Synthesis 9, thus it will be available online for those interested in this subject. The paper describes a new and more accurate way to estimate the wind energy input to any system. It also has a new cal
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. Copyright © 2013 Elsevier Ltd. All rights reserved.
Prediction of Algebraic Instabilities
NASA Astrophysics Data System (ADS)
Zaretzky, Paula; King, Kristina; Hill, Nicole; Keithley, Kimberlee; Barlow, Nathaniel; Weinstein, Steven; Cromer, Michael
2016-11-01
A widely unexplored type of hydrodynamic instability is examined - large-time algebraic growth. Such growth occurs on the threshold of (exponentially) neutral stability. A new methodology is provided for predicting the algebraic growth rate of an initial disturbance, when applied to the governing differential equation (or dispersion relation) describing wave propagation in dispersive media. Several types of algebraic instabilities are explored in the context of both linear and nonlinear waves.
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)
Infinite dimensional matrix algebras
NASA Astrophysics Data System (ADS)
Bordemann, M.; Hoppe, J.; Schaller, P.
1989-11-01
To each (finite dimensional) Lie algebra g we associate a class L λ(g) of infinite dimensional Lie algebras, induced by representations D λ(g). We show that in the case of sl(2, C) one obtains a series of pairwise non-isomorphic infinite dimensional Lie algebras depending continuously on a complex parameter λ. We connect this method with previous results on the relation between Diff AS 2 and su( N), and comment on a recent conjecture concerning higher spin algebras, and (2 + 1)-dimensional gravity.
The Virasoro vertex algebra and factorization algebras on Riemann surfaces
NASA Astrophysics Data System (ADS)
Williams, Brian
2017-08-01
This paper focuses on the connection of holomorphic two-dimensional factorization algebras and vertex algebras which has been made precise in the forthcoming book of Costello-Gwilliam. We provide a construction of the Virasoro vertex algebra starting from a local Lie algebra on the complex plane. Moreover, we discuss an extension of this factorization algebra to a factorization algebra on the category of Riemann surfaces. The factorization homology of this factorization algebra is computed as the correlation functions. We provide an example of how the Virasoro factorization algebra implements conformal symmetry of the beta-gamma system using the method of effective BV quantization.
Language Approaches to Beginning Algebra.
ERIC Educational Resources Information Center
Rotman, Jack W.
1990-01-01
Ideas which apply language concepts to the study of algebra are presented. Discussed are algebraic notation, vocabulary, vocalization, and written assignments. The careful use of algebraic language in mathematics classes is emphasized. (CW)
Bicovariant quantum algebras and quantum Lie algebras
NASA Astrophysics Data System (ADS)
Schupp, Peter; Watts, Paul; Zumino, Bruno
1993-10-01
A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(mathfrak{G}_q ) to U q g, given by elements of the pure braid group. These operators—the “reflection matrix” Y≡L + SL - being a special case—generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N).
Seo, Young Joo; Kim, Young Hee
2016-01-01
In this paper we construct some real algebras by using elementary functions, and discuss some relations between several axioms and its related conditions for such functions. We obtain some conditions for real-valued functions to be a (edge) d-algebra.
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…
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 dissertation,…
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…
Learning Activity Package, Algebra.
ERIC Educational Resources Information Center
Evans, Diane
A set of ten teacher-prepared Learning Activity Packages (LAPs) in beginning algebra and nine in intermediate algebra, these units cover sets, properties of operations, number systems, open expressions, solution sets of equations and inequalities in one and two variables, exponents, factoring and polynomials, relations and functions, radicals,…
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.
Algebraic Reasoning through Patterns
ERIC Educational Resources Information Center
Rivera, F. D.; Becker, Joanne Rossi
2009-01-01
This article presents the results of a three-year study that explores students' performance on patterning tasks involving prealgebra and algebra. The findings, insights, and issues drawn from the study are intended to help teach prealgebra and algebra. In the remainder of the article, the authors take a more global view of the three-year study on…
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 dissertation,…
Parastatistics Algebras and Combinatorics
NASA Astrophysics Data System (ADS)
Popov, T.
2005-03-01
We consider the algebras spanned by the creation parafermionic and parabosonic operators which give rise to generalized parastatistics Fock spaces. The basis of such a generalized Fock space can be labelled by Young tableaux which are combinatorial objects. By means of quantum deformations a nice combinatorial structure of the algebra of the plactic monoid that lies behind the parastatistics is revealed.
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…
Hu, Shi; Mo, Xingguo; Lin, Zhonghui; Qiu, Jianxiu
2010-10-01
Sustainable water use is seriously compromised in the North China Plain (NCP) due to the huge water requirements of agriculture, the largest use of water resources. An integrated approach which combines the ecosystem model with emergy analysis is presented to determine the optimum quantity of irrigation for sustainable development in irrigated cropping systems. Since the traditional emergy method pays little attention to the dynamic interaction among components of the ecological system and dynamic emergy accounting is in its infancy, it is hard to evaluate the cropping system in hypothetical situations or in response to specific changes. In order to solve this problem, an ecosystem model (Vegetation Interface Processes (VIP) model) is introduced for emergy analysis to describe the production processes. Some raw data, collected by investigating or observing in conventional emergy analysis, may be calculated by the VIP model in the new approach. To demonstrate the advantage of this new approach, we use it to assess the wheat-maize rotation cropping system at different irrigation levels and derive the optimum quantity of irrigation according to the index of ecosystem sustainable development in NCP. The results show, the optimum quantity of irrigation in this region should be 240-330 mm per year in the wheat system and no irrigation in the maize system, because with this quantity of irrigation the rotation crop system reveals: best efficiency in energy transformation (transformity = 6.05E + 4 sej/J); highest sustainability (renewability = 25%); lowest environmental impact (environmental loading ratio = 3.5) and the greatest sustainability index (Emergy Sustainability Index = 0.47) compared with the system in other irrigation amounts. This study demonstrates that application of the new approach is broader than the conventional emergy analysis and the new approach is helpful in optimizing resources allocation, resource-savings and maintaining agricultural sustainability.
NASA Astrophysics Data System (ADS)
Hu, Shi; Mo, Xingguo; Lin, Zhonghui; Qiu, Jianxiu
2010-10-01
Sustainable water use is seriously compromised in the North China Plain (NCP) due to the huge water requirements of agriculture, the largest use of water resources. An integrated approach which combines the ecosystem model with emergy analysis is presented to determine the optimum quantity of irrigation for sustainable development in irrigated cropping systems. Since the traditional emergy method pays little attention to the dynamic interaction among components of the ecological system and dynamic emergy accounting is in its infancy, it is hard to evaluate the cropping system in hypothetical situations or in response to specific changes. In order to solve this problem, an ecosystem model (Vegetation Interface Processes (VIP) model) is introduced for emergy analysis to describe the production processes. Some raw data, collected by investigating or observing in conventional emergy analysis, may be calculated by the VIP model in the new approach. To demonstrate the advantage of this new approach, we use it to assess the wheat-maize rotation cropping system at different irrigation levels and derive the optimum quantity of irrigation according to the index of ecosystem sustainable development in NCP. The results show, the optimum quantity of irrigation in this region should be 240-330 mm per year in the wheat system and no irrigation in the maize system, because with this quantity of irrigation the rotation crop system reveals: best efficiency in energy transformation (transformity = 6.05E + 4 sej/J); highest sustainability (renewability = 25%); lowest environmental impact (environmental loading ratio = 3.5) and the greatest sustainability index (Emergy Sustainability Index = 0.47) compared with the system in other irrigation amounts. This study demonstrates that application of the new approach is broader than the conventional emergy analysis and the new approach is helpful in optimizing resources allocation, resource-savings and maintaining agricultural sustainability.
NASA Astrophysics Data System (ADS)
Majewski, Władysław A.; Tylec, Tomasz I.
2010-12-01
Erik M. Alfsen and Frederic W. Shultz had recently developed the characterisation of state spaces of operator algebras. It established full equivalence (in the mathematical sense) between the Heisenberg and the Schrödinger picture, i.e. given a physical system we are able to construct its state space out of its observables as well as to construct algebra of observables from its state space. As an underlying mathematical structure they used the theory of duality of ordered linear spaces and obtained results are valid for various types of operator algebras (namely C *, von Neumann, JB and JBW algebras). Here, we show that the language they developed also admits a representation of an effect algebra.
[Integrative study of Guangdong ecological-economic system based on emergy analysis].
Sui, Chunhua; Lu, Hongfang; Zheng, Fengying
2006-11-01
Based on the theories and methodologies of emergy, a quantitative analysis on the development sustainability of Guangdong Province in 1990-2003 was made from the aspects of environment, society, and economy at system and subsystem levels. The results showed that Guangdong Province was of developed provinces in China, and highly depended on the input of feedback emergy. Though the pollution control was fruitful, the increasing environmental loading was still not relieved on the whole, and the development sustainability was relatively low. This Province was increasingly relied on international market, and actually, under the status to the bad in exporting primary products and importing high-tech products. To improve the development sustainability of this Province, more concerns should be paid on improving the added values of products, making full use of the natural and labor resources in its underdeveloped area, and further bringing the economic superiority of its developed area into play.
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.
The joint use of LCA and emergy evaluation for the analysis of two Italian wine farms.
Pizzigallo, A C I; Granai, C; Borsa, S
2008-01-01
The aim of this paper is to evaluate two agroindustrial productive processes in their entirety (one organic and one semi-industrial), focusing on the comparison of impacts derived from the inputs and outputs of the system (life cycle assessment, LCA), integrated with a physical evaluation of the resources and natural services, on a common basis (emergy). Methods based on the joint use of LCA and emergy evaluation are useful, as they measure the contribution of environmental services and products to the productive process thus focusing primarily on the environmental impact of emissions and non-renewable energy inputs. The complementarity of the methods used in this paper contributes important elements and information useful for the comprehension of the organization of agriculture within Siena's territory. The results show important elements and useful information: (1) for the comprehension of the two agroecosystems' organization; (2) for the use of the energy flows that determine their development. Moreover, the combined use of emergy and LCA gives a comparative thermodynamic performance evaluation between organic and semi-industrial farming.
Emergy-based ecological account for the Chinese economy in 2004
NASA Astrophysics Data System (ADS)
Jiang, M. M.; Zhou, J. B.; Chen, B.; Chen, G. Q.
2008-12-01
This paper provides an integrated study on the ecological account for the Chinese economy in 2004 based on emergy synthesis theory. The detailed flows of the Chinese economy is diagramed, accounted and analyzed in categories using the biophysically based ecological accounting. Through calculating environmental and economic inputs within and outside the Chinese economy, this paper discusses the Chinese international exchange, describes the resource structure, and assesses its sustainability as a whole. Also, the comparison of systematic indicators, such as emergy/dollar ratio, environmental load ratio, and emergy self-support ratio, with those of the other countries is tabled and explored to illustrate the general status of the Chinese economy in the world. Take, for example, the environmental load ratio, which was 9.29 in China 2004, it reveals that the Chinese economy put high pressure on the local environment compared with those of the environment-benign countries, such as Brazil (0.75), Australia (0.86) and New Zealand (0.81). In addition, in this paper, the accounting method of tourism is adjusted based on the previous researches.
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.
Algebraic Nonlinear Collective Motion
NASA Astrophysics Data System (ADS)
Troupe, J.; Rosensteel, G.
1998-11-01
Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real numberΛ. TheΛ=0 solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positiveΛ, the droplets have a neck that becomes more pronounced asΛincreases; for negativeΛ, the droplets contain a spherical bubble of radius |Λ|1/3. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm(3) which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm(3) Lie algebra. These representations model fissioning isotopes (Λ>0) and bubble and two-fluid nuclei (Λ<0).
Li, Chun-fa; Cao, Ying-ying; Yang, Jian-cho; Yang, Qi-qi
2015-08-01
Dynamic evaluation of sustainable development is one of the key fundamental parts of the success of Sino-Singapore Tianjin Eco-city, which is the first eco-city in China constructed by international cooperation. Based on the analysis of nature and economy, function and structure, planning control indices and so on, we constructed a sustainable development evaluation index system and a system dynamics model of Sino-Singapore Tianjin Eco-city to explore dynamic trends of its population, material and currency by comprehensive utilization of emergy analysis and system dynamics method. Five scenarios were set up and simulated, including inertial scenario, scientific and technological scenario, economic scenario, environmental scenario and harmonious development scenario. Then, the sustainability of the 5 scenarios was evaluated and compared. The results showed that in the economy and environment sustainable development scenario, there was a steady growth trend of GDP, accumulation of both emergy and currency, and relatively lower values in emergy waste ratio, emergy ratio of waste, and emergy loading ratio. Although both sustainable evaluation indices, such as ESI and UEI, were relatively low, the economy and environment sustainable development scenario was still the best development scenario which was more active than others.
NASA Astrophysics Data System (ADS)
Xi, L. M.; Liu, C. Q.; Liu, D. F.; Huang, W. L.; Sun, Y.
2017-08-01
According to the ecological restoration theory, this experiment establishes aquaculture systems controlled by biological chains in both Xiaoxidian area and Dujiadian area of Baiyangdian Lake separately in order to improve the environment and bring economic benefits. The appearance of Emergy Theory provides a new method for the quantitative analysis of ecological economic system. Based on the analysis of Emergy Theory, this thesis compares the eco-economic systems under different polyculture models between Xiaoxidian area and Dujiadian area. The result demonstrates that Xiaoxidian ecological system is of high Emergy Transformity with higher emergy output and economic income per unit area compared with Dujiadian area. While Dujiadian area has higher Emergy Yield Rate and lower Environment Load Rate. So Dujiadian area is more sustainable due to the overload non-renewable energy of Xiaoxidian area devoted by human. Therefore, it will be better if we adjust and optimize the management of aquaculture system in Xiaoxidian area in order to find a stable equilibrium point between environmental sustainability and economic benefits.
Algebraic invariants for homotopy types
NASA Astrophysics Data System (ADS)
Blanc, David
1999-11-01
We define a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the [Pi]-algebra [pi][low asterisk]X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology classes allows one to decide whether a given abstract [Pi]-algebra can be realized as the homotopy [Pi]-algebra of a space.
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,…
Adaptive algebraic reconstruction technique
Lu Wenkai; Yin Fangfang
2004-12-01
Algebraic reconstruction techniques (ART) are iterative procedures for reconstructing objects from their projections. It is proven that ART can be computationally efficient by carefully arranging the order in which the collected data are accessed during the reconstruction procedure and adaptively adjusting the relaxation parameters. In this paper, an adaptive algebraic reconstruction technique (AART), which adopts the same projection access scheme in multilevel scheme algebraic reconstruction technique (MLS-ART), is proposed. By introducing adaptive adjustment of the relaxation parameters during the reconstruction procedure, one-iteration AART can produce reconstructions with better quality, in comparison with one-iteration MLS-ART. Furthermore, AART outperforms MLS-ART with improved computational efficiency.
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
Pseudo-Riemannian Novikov algebras
NASA Astrophysics Data System (ADS)
Chen, Zhiqi; Zhu, Fuhai
2008-08-01
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. Pseudo-Riemannian Novikov algebras denote Novikov algebras with non-degenerate invariant symmetric bilinear forms. In this paper, we find that there is a remarkable geometry on pseudo-Riemannian Novikov algebras, and give a special class of pseudo-Riemannian Novikov algebras.
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.
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)
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)
Jordan Algebraic Quantum Categories
NASA Astrophysics Data System (ADS)
Graydon, Matthew; Barnum, Howard; Ududec, Cozmin; Wilce, Alexander
2015-03-01
State cones in orthodox quantum theory over finite dimensional complex Hilbert spaces enjoy two particularly essential features: homogeneity and self-duality. Orthodox quantum theory is not, however, unique in that regard. Indeed, all finite dimensional formally real Jordan algebras -- arenas for generalized quantum theories with close algebraic kinship to the orthodox theory -- admit homogeneous self-dual positive cones. We construct categories wherein these theories are unified. The structure of composite systems is cast from universal tensor products of the universal C*-algebras enveloping ambient spaces for the constituent state cones. We develop, in particular, a notion of composition that preserves the local distinction of constituent systems in quaternionic quantum theory. More generally, we explicitly derive the structure of hybrid quantum composites with subsystems of arbitrary Jordan algebraic type.
ERIC Educational Resources Information Center
Leron, Uri; Dubinsky, Ed
1995-01-01
Describes a constructivist, interactive approach for teaching undergraduate mathematics, abstract algebra in particular, using computer constructions programmed in ISETL to induce students' mental constructions and collaborative learning to help students reflect on these constructions. (18 references) (MKR)
Accounting Equals Applied Algebra.
ERIC Educational Resources Information Center
Roberts, Sondra
1997-01-01
Argues that students should be given mathematics credits for completing accounting classes. Demonstrates that, although the terminology is different, the mathematical concepts are the same as those used in an introductory algebra class. (JOW)
NASA Astrophysics Data System (ADS)
Markarian, Nikita
2017-03-01
We introduce Weyl n-algebras and show how their factorization complex may be used to define invariants of manifolds. In the appendix, we heuristically explain why these invariants must be perturbative Chern-Simons invariants.
Aprepro - Algebraic Preprocessor
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.
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.
Aprepro - Algebraic Preprocessor
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.
NASA Astrophysics Data System (ADS)
Fialowski, A.; Schlichenmaier, M.
2007-11-01
In two earlier articles we constructed algebraic-geometric families of genus one (i.e. elliptic) Lie algebras of Krichever Novikov type. The considered algebras are vector fields, current and affine Lie algebras. These families deform the Witt algebra, the Virasoro algebra, the classical current, and the affine Kac Moody Lie algebras respectively. The constructed families are not equivalent (not even locally) to the trivial families, despite the fact that the classical algebras are formally rigid. This effect is due to the fact that the algebras are infinite dimensional. In this article the results are reviewed and developed further. The constructions are induced by the geometric process of degenerating the elliptic curves to singular cubics. The algebras are of relevance in the global operator approach to the Wess Zumino Witten Novikov models appearing in the quantization of Conformal Field Theory.
Algebraic quantum gravity (AQG): II. Semiclassical analysis
NASA Astrophysics Data System (ADS)
Giesel, K.; Thiemann, T.
2007-05-01
In the previous paper (Giesel and Thiemann 2006 Conceptual setup Preprint gr-qc/0607099) a new combinatorial and thus purely algebraical approach to quantum gravity, called algebraic quantum gravity (AQG), was introduced. In the framework of AQG, existing semiclassical tools can be applied to operators that encode the dynamics of AQG such as the master constraint operator. In this paper, we will analyse the semiclassical limit of the (extended) algebraic master constraint operator and show that it reproduces the correct infinitesimal generators of general relativity. Therefore, the question of whether general relativity is included in the semiclassical sector of the theory, which is still an open problem in LQG, can be significantly improved in the framework of AQG. For the calculations, we will substitute SU(2) with U(1)3. That this substitution is justified will be demonstrated in the third paper (Giesel and Thiemann 2006 Semiclassical perturbation theory Preprint gr-qc/0607101) of this series.
Algebraic mesh quality metrics
KNUPP,PATRICK
2000-04-24
Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically meaningful parts. A nodally-invariant Jacobian matrix can be defined for simplicial elements using a weight matrix derived from the Jacobian matrix of an ideal reference element. Scale and orientation-invariant algebraic mesh quality metrics are defined. the singular value decomposition is used to study relationships between metrics. Equivalence of the element condition number and mean ratio metrics is proved. Condition number is shown to measure the distance of an element to the set of degenerate elements. Algebraic measures for skew, length ratio, shape, volume, and orientation are defined abstractly, with specific examples given. Combined metrics for shape and volume, shape-volume-orientation are algebraically defined and examples of such metrics are given. Algebraic mesh quality metrics are extended to non-simplical elements. A series of numerical tests verify the theoretical properties of the metrics defined.
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…
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…
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.
NASA Astrophysics Data System (ADS)
Durka, R.
2017-04-01
The S-expansion framework is analyzed in the context of a freedom in closing the multiplication tables for the abelian semigroups. Including the possibility of the zero element in the resonant decomposition, and associating the Lorentz generator with the semigroup identity element, leads to a wide class of the expanded Lie algebras introducing interesting modifications to the gauge gravity theories. Among the results, we find all the Maxwell algebras of type {{B}m} , {{C}m} , and the recently introduced {{D}m} . The additional new examples complete the resulting generalization of the bosonic enlargements for an arbitrary number of the Lorentz-like and translational-like generators. Some further prospects concerning enlarging the algebras are discussed, along with providing all the necessary constituents for constructing the gravity actions based on the obtained results.
Hatcher, N.; Restuccia, A.; Stephany, J.
2006-02-15
We present the complete set of N=1, D=4 quantum algebras associated to massive superparticles. We obtain the explicit solution of these algebras realized in terms of unconstrained operators acting on the Hilbert space of superfields. These solutions are expressed using the chiral, antichiral and tensorial projectors which define the three irreducible representations of the supersymmetry on the superfields. In each case the space-time variables are noncommuting and their commutators are proportional to the internal angular momentum of the representation. The quantum algebra associated to the chiral or the antichiral projector is the one obtained by the quantization of the Casalbuoni-Brink-Schwarz (superspin 0) massive superparticle. We present a new superparticle action for the (superspin 1/2) case and show that their wave functions are the ones associated to the irreducible tensor multiplet.
NASA Astrophysics Data System (ADS)
Roytenberg, Dmitry
2007-11-01
A Lie 2-algebra is a linear category equipped with a functorial bilinear operation satisfying skew-symmetry and Jacobi identity up to natural transformations which themselves obey coherence laws of their own. Functors and natural transformations between Lie 2-algebras can also be defined, yielding a 2-category. Passing to the normalized chain complex gives an equivalence of 2-categories between Lie 2-algebras and certain "up to homotopy" structures on the complex; for strictly skew-symmetric Lie 2-algebras these are L∞-algebras, by a result of Baez and Crans. Lie 2-algebras appear naturally as infinitesimal symmetries of solutions of the Maurer-Cartan equation in some differential graded Lie algebras and L∞-algebras. In particular, (quasi-) Poisson manifolds, (quasi-) Lie bialgebroids and Courant algebroids provide large classes of examples.
A Holistic Approach to Algebra.
ERIC Educational Resources Information Center
Barbeau, Edward J.
1991-01-01
Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)
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.
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.
Algebra for Gifted Third Graders.
ERIC Educational Resources Information Center
Borenson, Henry
1987-01-01
Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)
1985-03-13
AD-Ri55 296 ALGEBRA OF NEURON MATRICES(U) FOREIGN TECHNOLOGY DIV i/i WRIGHT-PATTERSON RF8 ON K~ G RGRBRBYRN 13 MAR 85 FTD-ID(RS)T-8@4i-85...ANCLASSIFIED F/G6/6 NL I. 1j.2 U .611111 ’’ K1*10 Vl( PIH OPY Pl (iLUTION TL T CHART I-" FTD-ID(RS )T-0041-85 FOREIGN TECHNOLOGY DIVISION In ALGEBRA OF NEURON ... NEURON MATRICES DTIC TAB Unannounced Q By: K.G. Agababyan JustLficatlon English pages: 10 By Distribution/ Source: Doklady Akademii Nauk SSSR, Vol. 199
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...
Liu, Zhe; Geng, Yong; Zhang, Pan; Dong, Huijuan; Liu, Zuoxi
2014-09-01
In China, local governments of many areas prefer to give priority to the development of heavy industrial clusters in pursuit of high value of gross domestic production (GDP) growth to get political achievements, which usually results in higher costs from ecological degradation and environmental pollution. Therefore, effective methods and reasonable evaluation system are urgently needed to evaluate the overall efficiency of industrial clusters. Emergy methods links economic and ecological systems together, which can evaluate the contribution of ecological products and services as well as the load placed on environmental systems. This method has been successfully applied in many case studies of ecosystem but seldom in industrial clusters. This study applied the methodology of emergy analysis to perform the efficiency of industrial clusters through a series of emergy-based indices as well as the proposed indicators. A case study of Shenyang Economic Technological Development Area (SETDA) was investigated to show the emergy method's practical potential to evaluate industrial clusters to inform environmental policy making. The results of our study showed that the industrial cluster of electric equipment and electronic manufacturing produced the most economic value and had the highest efficiency of energy utilization among the four industrial clusters. However, the sustainability index of the industrial cluster of food and beverage processing was better than the other industrial clusters.
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...
Emergy evaluations of three benthic ecosystem networks found in Mejillones, Antofagasta and Tongoy Bays, located on the coast of northern Chile, were carried out with the intent of documenting the contributions of these coastal ecosystems to the economy. The productivity of these...
Lotus (Neumbo nucifera, Gaertn) is the most important aquatic vegetable in China, with a cultivation history of over 3000 years. The emergy, energy, material, and money flows of three lotus root cultivation modes in Wanqingsha, Nansha District, Guangzhou, China were examined usin...
An algebra of reversible computation.
Wang, Yong
2016-01-01
We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules: basic reversible processes algebra, algebra of reversible communicating processes, recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.
Thomys, Janus; Zhang, Xiaohong
2013-01-01
We describe weak-BCC-algebras (also called BZ-algebras) in which the condition (x∗y)∗z = (x∗z)∗y is satisfied only in the case when elements x, y belong to the same branch. We also characterize ideals, nilradicals, and nilpotent elements of such algebras. PMID:24311983
Visual Salience of Algebraic Transformations
ERIC Educational Resources Information Center
Kirshner, David; Awtry, Thomas
2004-01-01
Information processing researchers have assumed that algebra symbol skills depend on mastery of the abstract rules presented in the curriculum (Matz, 1980; Sleeman, 1986). Thus, students' ubiquitous algebra errors have been taken as indicating the need to embed algebra in rich contextual settings (Kaput, 1995; National Council of Teachers of…
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 Thinking through Origami.
ERIC Educational Resources Information Center
Higginson, William; Colgan, Lynda
2001-01-01
Describes the use of paper folding to create a rich environment for discussing algebraic concepts. Explores the effect that changing the dimensions of two-dimensional objects has on the volume of related three-dimensional objects. (Contains 13 references.) (YDS)
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…
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,…
Algebraic Thinking through Origami.
ERIC Educational Resources Information Center
Higginson, William; Colgan, Lynda
2001-01-01
Describes the use of paper folding to create a rich environment for discussing algebraic concepts. Explores the effect that changing the dimensions of two-dimensional objects has on the volume of related three-dimensional objects. (Contains 13 references.) (YDS)
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…
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…
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…
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.
Chen, Han-Shen
2017-01-01
In this paper, the overall ecological and environmental sustainability in the Cing-Jing region in Taiwan is examined. As land use and cover change has been found to be an important analysis method, an emergy ecological footprint model was applied and the eco-security assessed to ensure authorities maintain a balance between ecological preservation and tourism development. While the ecological environment in the Cing-Jing region from 2008 to 2014 was found to be within safe levels, all related indices had increased considerably. A Grey model was used to predict the 2015–2024 ecological carrying capacities, from which it was found that there is expected to be a large increase in per capita ecological footprints (EFs), meaning that in the future there is going to be a larger ecological deficit and a higher ecological pressure index (EFI), with the eco-security predicted to reach a Grade 2 intermediate level in 2022. As the Cing-Jing region is predicted to become ecologically unsustainable, local, regional, and national governments need to implement regulations to strictly control the land use in the Cing-Jing region. This study demonstrated that emergy EF (EEF) theory application can give objective guidance to decision-makers to ensure that recreational non-urban eco-security can be maintained at a safe level. PMID:28146086
Chen, Han-Shen
2017-01-30
In this paper, the overall ecological and environmental sustainability in the Cing-Jing region in Taiwan is examined. As land use and cover change has been found to be an important analysis method, an emergy ecological footprint model was applied and the eco-security assessed to ensure authorities maintain a balance between ecological preservation and tourism development. While the ecological environment in the Cing-Jing region from 2008 to 2014 was found to be within safe levels, all related indices had increased considerably. A Grey model was used to predict the 2015-2024 ecological carrying capacities, from which it was found that there is expected to be a large increase in per capita ecological footprints (EFs), meaning that in the future there is going to be a larger ecological deficit and a higher ecological pressure index (EFI), with the eco-security predicted to reach a Grade 2 intermediate level in 2022. As the Cing-Jing region is predicted to become ecologically unsustainable, local, regional, and national governments need to implement regulations to strictly control the land use in the Cing-Jing region. This study demonstrated that emergy EF (EEF) theory application can give objective guidance to decision-makers to ensure that recreational non-urban eco-security can be maintained at a safe level.
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.
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.
Planar Para Algebras, Reflection Positivity
NASA Astrophysics Data System (ADS)
Jaffe, Arthur; Liu, Zhengwei
2017-05-01
We define a planar para algebra, which arises naturally from combining planar algebras with the idea of ZN para symmetry in physics. A subfactor planar para algebra is a Hilbert space representation of planar tangles with parafermionic defects that are invariant under para isotopy. For each ZN, we construct a family of subfactor planar para algebras that play the role of Temperley-Lieb-Jones planar algebras. The first example in this family is the parafermion planar para algebra (PAPPA). Based on this example, we introduce parafermion Pauli matrices, quaternion relations, and braided relations for parafermion algebras, which one can use in the study of quantum information. An important ingredient in planar para algebra theory is the string Fourier transform (SFT), which we use on the matrix algebra generated by the Pauli matrices. Two different reflections play an important role in the theory of planar para algebras. One is the adjoint operator; the other is the modular conjugation in Tomita-Takesaki theory. We use the latter one to define the double algebra and to introduce reflection positivity. We give a new and geometric proof of reflection positivity by relating the two reflections through the string Fourier transform.
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.
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.
On extensions of Leibniz algebras
NASA Astrophysics Data System (ADS)
Rakhimov, I. S.; Said Husain, Sh. K.; Mohammed, M. A.
2017-09-01
This paper is dedicated to the study extensions of Leibniz algebras using the annihilator approach. The extensions methods have been used earlier to classify certain classes of algebras. In the paper we first review and adjust theoretical background of the method for Leibniz algebras then apply it to classify four-dimensional Leibniz algebras over a field K. We obtain complete classification of four-dimensional nilpotent Leibniz algebras. The main idea of the method is to transfer the “base change” action to an action of automorphism group of the algebras of smaller dimension on cocycles constructed by the annihilator extensions. The method can be used to classify low-dimensional Leibniz algebras over other finite fields as well.
Toda theory and W-algebra from a gauged WZNW point of view
NASA Astrophysics Data System (ADS)
Balog, J.; Fehér, L.; O'Raifeartaigh, L.; Forgács, P.; Wipf, A.
1990-10-01
A new formulation of Toda theories is proposed by showing that they can be regarded as certain gauged Wess-Zumino-Novikov-Witten (WZNW) models. It is argued that the WZNW variables are the proper ones for Toda theory, since all the physically permitted Toda solutions are regular when expressed in these variables. A detailed study of classical Toda theories and their W-algebras is carried out from this unified WZNW point of view. We construct a primary field basis for the W-algebra for any group, we obtain a new method for calculating the W-algebra and its action on the Toda fields by constructing its Kac-Moody implementation, and we analyse the relationship between W-algebras and Casimir algebras. The W-algebra of G2 and the Casimir algebras for the classical groups are exhibited explicitly.
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.
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 ...
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 ...
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®,…
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®,…
Lee, Jaehoon; Wilczek, Frank
2013-11-27
Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.
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.
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.
Clifford Algebras and Their Decomposition into Conjugate Fermionic Heisenberg Algebras
NASA Astrophysics Data System (ADS)
Catto, Sultan; Gürcan, Yasemin; Khalfan, Amish; Kurt, Levent; Kato La, V.
2016-10-01
We discuss a construction scheme for Clifford numbers of arbitrary dimension. The scheme is based upon performing direct products of the Pauli spin and identity matrices. Conjugate fermionic algebras can then be formed by considering linear combinations of the Clifford numbers and the Hermitian conjugates of such combinations. Fermionic algebras are important in investigating systems that follow Fermi-Dirac statistics. We will further comment on the applications of Clifford algebras to Fueter analyticity, twistors, color algebras, M-theory and Leech lattice as well as unification of ancient and modern geometries through them.
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…
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.
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.
Lattice vertex algebras on general even, self-dual lattices
NASA Astrophysics Data System (ADS)
Kleinschmidt, Axel
2003-07-01
In this note we analyse the Lie algebras of physical states stemming from lattice constructions on general even, self-dual lattices Gammap,q with p geq q. It is known that if the lattice is at most lorentzian, the resulting Lie algebra is of generalized Kac-Moody type (or has a quotient that is). We show that this is not true as soon as q geq 1. By studying a certain sublattice in the case q > 1 we obtain results that lead to the conclusion that the resulting non-GKM Lie algebra cannot be described conveniently in terms of generators and relations and belongs to a new and qualitatively different class of Lie algebras.
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…
Applications of algebraic grid generation
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Smith, Robert E.
1990-01-01
Techniques and applications of algebraic grid generation are described. The techniques are univariate interpolations and transfinite assemblies of univariate interpolations. Because algebraic grid generation is computationally efficient, the use of interactive graphics in conjunction with the techniques is advocated. A flexible approach, which works extremely well in an interactive environment, called the control point form of algebraic grid generation is described. The applications discussed are three-dimensional grids constructed about airplane and submarine configurations.
Higher level twisted Zhu algebras
NASA Astrophysics Data System (ADS)
van Ekeren, Jethro
2011-05-01
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 Γ /{Z} for some subgroup Γ 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 operatorname{Zhu}_{p, Γ }(V), and we prove the following theorems: For each p, there is a bijection between the irreducible operatorname{Zhu}_{p, Γ }(V)-modules and the irreducible Γ-twisted positive energy V-modules, and V is (Γ, H)-rational if and only if all its Zhu algebras operatorname{Zhu}_{p, Γ }(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 operatorname{Vir}^c and the universal affine Kac-Moody vertex algebra V^k({g}) at non-critical level. We also compute the inverse limits of these directed systems of algebras.
Epetra Linear Algebra Services Package
2011-09-09
Epetra provides the fundamental construction routines and service functions that are required for serial and paraliellinear algebra libraries using double precision scalar values and int ordinal values.
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
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.
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…
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…
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…
The worth of land use: a GIS-emergy evaluation of natural and human-made capital.
Mellino, Salvatore; Buonocore, Elvira; Ulgiati, Sergio
2015-02-15
Natural systems make their natural capital and ecosystem services available to human economy. A careful analysis of the interplay between natural and human-made capital is needed to prevent natural capital being overexploited for present economic benefits, affecting lifestyles and wellbeing of future generations. In this study, the emergy synthesis is used to evaluate the natural and the human-made capital of Campania region (southern Italy) by accounting for the environmental support directly and indirectly provided by nature to resource generation. Furthermore, geographic information system (GIS) models are integrated with the emergy accounting procedure to generate maps of the spatial patterns of both natural and human-made capital distribution. Regional storages of natural and human-made capital are identified and evaluated in emergy units (seJ). The human-made capital of the Campania region (6.29E+24seJ) results to be about 11 times higher than the natural capital (5.69E+23seJ) due to the past and present exploitation of the natural resources needed to generate it over time. Moreover, by overlaying the total natural capital map and the total human-made capital map with a map of the protected areas within the region, only the 19% of the regional natural capital appears to be concentrated within protected areas, while most of it (81%) is concentrated outside. These findings suggest that the conservation of natural resources is also necessary outside protected areas by means of suitable policies, directives and investments. The human-made capital is mainly concentrated (88%) inside non-protected areas and interacts with the local natural capital. A management of the interactions between the two categories of wealth is crucial to prevent that the growth of human-made storages degrades the natural ecosystems and the environment. The proposed emergy-GIS framework reveals to be a useful tool for environmental planning and resource management aimed to conserve and
Zhang, Yiran; Liu, Jian; Zhang, Jian; Wang, Renqing
2013-07-01
Constructed wetland has been widely adopted to deal with degraded natural wetlands and water bodies; thus, more attention should be focused on ecological-economic sustainability and ecological efficiency of these projects for long-term success. Emergy accounting was conducted to investigate the energy and resource flows in constructed wetlands during the restoration process. Emergy-based indexes were adopted to evaluate the sustainability of a pilot large-scale constructed wetland in a large wetland restoration project in North China, carried out to enhance the river water quality and offset the degradation of natural wetland. Emergy and emdollar values for ecosystem services and natural capital were also calculated. The results showed that when outflow was considered as the product, the studied large-scale constructed wetland was more self-supporting and could be operated with lesser financial investment, although the waste treatment efficiency and the sustainability index were lower than conventional small-scale treatment constructed wetlands. Compared with natural wetlands, more visits from tourists and lesser financial investment coming in as feedback into the wetland would reduce system environment loading and promote system self-support ability, ultimately generating sustainability. In addition, the studied large-scale constructed wetland can effectively simulate energy and resource flows of natural wetland ecosystem and contribute a roughly equal value of ecosystem services in term of gross primary production. The studied large-scale constructed wetland can successfully achieve ecosystem functions as replacement for natural wetland and hasten the restoration process, although the restoration effectiveness of ecosystem structures in terms of living biomass and water using emergy-value accounting is still inconclusive.
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.
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
Patterns to Develop Algebraic Reasoning
ERIC Educational Resources Information Center
Stump, Sheryl L.
2011-01-01
What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…
Viterbi/algebraic hybrid decoder
NASA Technical Reports Server (NTRS)
Boyd, R. W.; Ingels, F. M.; Mo, C.
1980-01-01
Decoder computer program is hybrid between optimal Viterbi and optimal algebraic decoders. Tests have shown that hybrid decoder outperforms any strictly Viterbi or strictly algebraic decoder and effectively handles compound channels. Algorithm developed uses syndrome-detecting logic to direct two decoders to assume decoding load alternately, depending on real-time channel characteristics.
Teaching Algebra Conceptually: Student Achievement
ERIC Educational Resources Information Center
Linsell, Chris; Tozer, Lynn; Anakin, Megan; Cox, Anna; Jones, Rachel; McAuslan, Eric; Smith, Donna; Turner, Garry
2012-01-01
This paper reports findings from the second year of a two-year study designed to develop approaches to teaching algebra in years 9 and 10. The aim of the research was to explore and develop teaching approaches to assist students to acquire a conceptual understanding of algebra, and to document the impact of these approaches on student outcomes.…
SICs and Algebraic Number Theory
NASA Astrophysics Data System (ADS)
Appleby, Marcus; Flammia, Steven; McConnell, Gary; Yard, Jon
2017-08-01
We give an overview of some remarkable connections between symmetric informationally complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a connection with Hilbert's 12th problem. The paper is meant to be intelligible to a physicist who has no prior knowledge of either Galois theory or algebraic number theory.
Patterns to Develop Algebraic Reasoning
ERIC Educational Resources Information Center
Stump, Sheryl L.
2011-01-01
What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…
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 the…
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.)
Linear algebra and image processing
NASA Astrophysics Data System (ADS)
Allali, Mohamed
2010-09-01
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.
Multiplier operator algebras and applications.
Blecher, David P; Zarikian, Vrej
2004-01-20
The one-sided multipliers of an operator space X are a key to "latent operator algebraic structure" in X. We begin with a survey of these multipliers, together with several of the applications that they have had to operator algebras. We then describe several new results on one-sided multipliers, and new applications, mostly to one-sided M-ideals.
ERIC Educational Resources Information Center
1997
Astro Algebra is one of six titles in the Mighty Math Series from Edmark, a comprehensive line of math software for students from kindergarten through ninth grade. Many of the activities in Astro Algebra contain a unique technology that uses the computer to help students make the connection between concrete and abstract mathematics. This software…
Elementary maps on nest algebras
NASA Astrophysics Data System (ADS)
Li, Pengtong
2006-08-01
Let , be algebras and let , be maps. An elementary map of is an ordered pair (M,M*) such that for all , . In this paper, the general form of surjective elementary maps on standard subalgebras of nest algebras is described. In particular, such maps are automatically additive.
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…
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.)
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…
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…
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…
What ''Counts'' as Algebra in the Eyes of Preservice Elementary Teachers?
ERIC Educational Resources Information Center
Stephens, Ana C.
2008-01-01
This study examined conceptions of algebra held by 30 preservice elementary teachers. In addition to exploring participants' general ''definitions'' of algebra, this study examined, in particular, their analyses of tasks designed to engage students in relational thinking or a deep understanding of the equal sign as well as student work on these…
What ''Counts'' as Algebra in the Eyes of Preservice Elementary Teachers?
ERIC Educational Resources Information Center
Stephens, Ana C.
2008-01-01
This study examined conceptions of algebra held by 30 preservice elementary teachers. In addition to exploring participants' general ''definitions'' of algebra, this study examined, in particular, their analyses of tasks designed to engage students in relational thinking or a deep understanding of the equal sign as well as student work on these…
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.
Symplectic Clifford Algebraic Field Theory.
NASA Astrophysics Data System (ADS)
Dixon, Geoffrey Moore
We develop a mathematical framework on which is built a theory of fermion, scalar, and gauge vector fields. This field theory is shown to be equivalent to the original Weinberg-Salam model of weak and electromagnetic interactions, but since the new framework is more rigid than that on which the original Weinberg-Salam model was built, a concomitant reduction in the number of assumptions lying outside of the framework has resulted. In particular, parity violation is actually hiding within our framework, and with little difficulty we are able to manifest it. The mathematical framework upon which we build our field theory is arrived at along two separate paths. The first is by the marriage of a Clifford algebra and a Lie superalgebra, the result being called a super Clifford algebra. The second is by providing a new characterization for a Clifford algebra employing its generators and a symmetric array of metric coefficients. Subsequently we generalize this characterization to the case of an antisymmetric array of metric coefficients, and we call the algebra which results a symplectic Clifford algebra. It is upon one of these that we build our field theory, and it is shown that this symplectic Clifford algebra is a particular subalgebra of a super Clifford algebra. The final ingredient is the operation of bracketing which involves treating the elements of our algebra as endomorphisms of a particular inner product space, and employing this space and its inner product to provide us with maps from our algebra to the reals. It is this operation which enables us to manifest the parity violation hiding in our algebra.
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)
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)
Macdonald index and chiral algebra
NASA Astrophysics Data System (ADS)
Song, Jaewon
2017-08-01
For any 4d N = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. We conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type ( A 1 , A 2 n ) and ( A 1 , D 2 n+1) where the chiral algebras are given by Virasoro and \\widehat{su}(2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Grassi, P. A.; Hurth, T.; Steinhauser, M.
2001-09-01
Combining the effect of an intermediate renormalization prescription (zero momentum subtraction) and the background field method (BFM), we show that the algebraic renormalization procedure needed for the computation of radiative corrections within non-invariant regularization schemes is drastically simplified. The present technique is suitable for gauge models and, here, is applied to the Standard Model. The use of the BFM allows a powerful organization of the counterterms and avoids complicated Slavnov-Taylor identities. Furthermore, the Becchi-Rouet-Stora-Tyutin (BRST) variation of background fields plays a special role in disentangling Ward-Takahashi identities (WTI) and Slavnov-Taylor identities (STI). Finally, the strategy to be applied to physical processes is exemplified for the process b→ sγ.
Particle-like structure of Lie algebras
NASA Astrophysics Data System (ADS)
Vinogradov, A. M.
2017-07-01
If a Lie algebra structure 𝔤 on a vector space is the sum of a family of mutually compatible Lie algebra structures 𝔤i's, we say that 𝔤 is simply assembled from the 𝔤i's. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the 𝔤i's, one obtains a Lie algebra assembled in two steps from 𝔤i's, and so on. We describe the process of modular disassembling of a Lie algebra into a unimodular and a non-unimodular part. We then study two inverse questions: which Lie algebras can be assembled from a given family of Lie algebras, and from which Lie algebras can a given Lie algebra be assembled. We develop some basic assembling and disassembling techniques that constitute the elements of a new approach to the general theory of Lie algebras. The main result of our theory is that any finite-dimensional Lie algebra over an algebraically closed field of characteristic zero or over R can be assembled in a finite number of steps from two elementary constituents, which we call dyons and triadons. Up to an abelian summand, a dyon is a Lie algebra structure isomorphic to the non-abelian 2-dimensional Lie algebra, while a triadon is isomorphic to the 3-dimensional Heisenberg Lie algebra. As an example, we describe constructions of classical Lie algebras from triadons.
Investigating Teacher Noticing of Student Algebraic Thinking
ERIC Educational Resources Information Center
Walkoe, Janet Dawn Kim
2013-01-01
Learning algebra is critical for students in the U.S. today. Algebra concepts provide the foundation for much advanced mathematical content. In addition, algebra serves as a gatekeeper to opportunities such as admission to college. Yet many students in the U.S. struggle in algebra classes. Researchers claim that one reason for these difficulties…
Investigating Teacher Noticing of Student Algebraic Thinking
ERIC Educational Resources Information Center
Walkoe, Janet Dawn Kim
2013-01-01
Learning algebra is critical for students in the U.S. today. Algebra concepts provide the foundation for much advanced mathematical content. In addition, algebra serves as a gatekeeper to opportunities such as admission to college. Yet many students in the U.S. struggle in algebra classes. Researchers claim that one reason for these difficulties…
Generalized Lie algebras of type An
NASA Astrophysics Data System (ADS)
Lyubashenko, Volodymyr; Sudbery, Anthony
1998-06-01
It is shown that the quantized enveloping algebra of sl(n) contains a generalized Lie algebra, defined by means of axioms similar to Woronowicz's. This gives rise to Lie algebra-like generators and relations for the locally finite part of the quantized enveloping algebra, and suggests a canonical Poincaré-Birkhoff-Witt basis.
Readiness and Preparation for Beginning Algebra.
ERIC Educational Resources Information Center
Rotman, Jack W.
Drawing from experience at Lansing Community College (LCC), this paper discusses how to best prepare students for success in a beginning algebra course. First, an overview is presented of LCC's developmental math sequence, which includes Basic Arithmetic (MTH 008), Pre-Algebra (MTH 009), Beginning Algebra (MTH 012), and Intermediate Algebra (MTH…
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.
Central extensions of Lax operator algebras
NASA Astrophysics Data System (ADS)
Schlichenmaier, M.; Sheinman, O. K.
2008-08-01
Lax operator algebras were introduced by Krichever and Sheinman as a further development of Krichever's theory of Lax operators on algebraic curves. These are almost-graded Lie algebras of current type. In this paper local cocycles and associated almost-graded central extensions of Lax operator algebras are classified. It is shown that in the case when the corresponding finite-dimensional Lie algebra is simple the two-cohomology space is one-dimensional. An important role is played by the action of the Lie algebra of meromorphic vector fields on the Lax operator algebra via suitable covariant derivatives.
Chinese Whispers - Algebra Style: Grammatical, Notational, Mathematical and Activity Tensions
ERIC Educational Resources Information Center
Hewitt, Dave
2005-01-01
This paper analyses students' written work from an activity based on two well known games in the UK: Chinese Whispers and Consequences. Within this activity students were asked to translate formal algebraic equations into word statements and vice versa. Using the framework of affordances and constraints to offer an account for what the students'…
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…
Asymptotic aspect of derivations in Banach algebras.
Roh, Jaiok; Chang, Ick-Soon
2017-01-01
We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.
Computing Matrix Representations of Filiform Lie Algebras
NASA Astrophysics Data System (ADS)
Ceballos, Manuel; Núñez, Juan; Tenorio, Ángel F.
In this paper, we compute minimal faithful unitriangular matrix representations of filiform Lie algebras. To do it, we use the nilpotent Lie algebra, g_n, formed of n ×n strictly upper-triangular matrices. More concretely, we search the lowest natural number n such that the Lie algebra g_n contains a given filiform Lie algebra, also computing a representative of this algebra. All the computations in this paper have been done using MAPLE 9.5.
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.
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.
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.
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.
An "Arithmetic" Thinker Tackles Algebra
ERIC Educational Resources Information Center
Armstrong, Alayne C.
2006-01-01
Working from Carolyn Kieran's categorization of "arithmetic" and "algebraic" thinkers, the article describes one eighth-grade "arithmetic" thinker's progress as she attempts to solve one- and two-step equations.
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).
Quantum Process Algebra with Priorities
NASA Astrophysics Data System (ADS)
Ren, Xingtian; Wang, Yong; Dai, Guiping
2017-08-01
One of the most fascinating characteristics is the modularity of ACP (Algebra of Communicating Processes), that is, ACP can be extended easily. qACP also inherents the modularity characteristics of ACP. By introducing new operators or new constants, qACP can have more properties. In this paper, we extend the quantum process algebra qACP with priorities support in an elegant way. And we obtain the soundness and completeness of the extension.
Coherent States for Hopf Algebras
NASA Astrophysics Data System (ADS)
Škoda, Zoran
2007-07-01
Families of Perelomov coherent states are defined axiomatically in the context of unitary representations of Hopf algebras. A global geometric picture involving locally trivial noncommutative fibre bundles is involved in the construction. If, in addition, the Hopf algebra has a left Haar integral, then a formula for noncommutative resolution of identity in terms of the family of coherent states holds. Examples come from quantum groups.
Multiplier operator algebras and applications
Blecher, David P.; Zarikian, Vrej
2004-01-01
The one-sided multipliers of an operator space X are a key to “latent operator algebraic structure” in X. We begin with a survey of these multipliers, together with several of the applications that they have had to operator algebras. We then describe several new results on one-sided multipliers, and new applications, mostly to one-sided M-ideals. PMID:14711990
Algebraic Systems and Pushdown Automata
NASA Astrophysics Data System (ADS)
Petre, Ion; Salomaa, Arto
We concentrate in this chapter on the core aspects of algebraic series, pushdown automata, and their relation to formal languages. We choose to follow here a presentation of their theory based on the concept of properness. We introduce in Sect. 2 some auxiliary notions and results needed throughout the chapter, in particular the notions of discrete convergence in semirings and C-cycle free infinite matrices. In Sect. 3 we introduce the algebraic power series in terms of algebraic systems of equations. We focus on interconnections with context-free grammars and on normal forms. We then conclude the section with a presentation of the theorems of Shamir and Chomsky-Schützenberger. We discuss in Sect. 4 the algebraic and the regulated rational transductions, as well as some representation results related to them. Section 5 is dedicated to pushdown automata and focuses on the interconnections with classical (non-weighted) pushdown automata and on the interconnections with algebraic systems. We then conclude the chapter with a brief discussion of some of the other topics related to algebraic systems and pushdown automata.
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)
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, which are derived from the transformation of the solar equivalent joules supplied through the baseline. In this study, the methods for calculating the available energy of the wind dissipated in the planetary boundary layer are revisited and further elucidated. Particular consideration is given to the method used to estimate the geostrophic and gradient wind from measurements of surface wind and to the role of the drag coefficient in determining the available wind energy dissipated in the boundary layer (900 to 1000 mb or the lower 1000 m of the atmosphere) as it passes over various surfaces. In addition, we made a more rigorous estimate of the transformity of the available wind energy dissipated in the planetary boundary layer based on a synthesis of the results from three evaluations of a model of the general circulation of the atmosphere. The rounded estimate of the transformity of the wind from these combined studies was 1230 sej J-1. We consider the variability of the transformity of the wind dissipated in the boundary layer between summer and winter and between the Northern and Southern hemispheres. We conclude that the properties of the system and its spatial and temporal boundarie
An ecological compensation standard based on emergy theory for the Xiao Honghe River Basin.
Guan, Xinjian; Chen, Moyu; Hu, Caihong
2015-01-01
The calculation of an ecological compensation standard is an important, but also difficult aspect of current ecological compensation research. In this paper, the factors affecting the ecological-economic system in the Xiao Honghe River Basin, China, including the flow of energy, materials, and money, were calculated using the emergy analysis method. A consideration of the relationships between the ecological-economic value of water resources and ecological compensation allowed the ecological-economic value to be calculated. On this basis, the amount of water needed for dilution was used to develop a calculation model for the ecological compensation standard of the basin. Using the Xiao Honghe River Basin as an example, the value of water resources and the ecological compensation standard were calculated using this model according to the emission levels of the main pollutant in the basin, chemical oxygen demand. The compensation standards calculated for the research areas in Xipin, Shangcai, Pingyu, and Xincai were 34.91 yuan/m3, 32.97 yuan/m3, 35.99 yuan/m3, and 34.70 yuan/m3, respectively, and such research output would help to generate and support new approaches to the long-term ecological protection of the basin and improvement of the ecological compensation system.
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, which are derived from the transformation of the solar equivalent joules supplied through the baseline. In this study, the methods for calculating the available energy of the wind dissipated in the planetary boundary layer are revisited and further elucidated. Particular consideration is given to the method used to estimate the geostrophic and gradient wind from measurements of surface wind and to the role of the drag coefficient in determining the available wind energy dissipated in the boundary layer (900 to 1000 mb or the lower 1000 m of the atmosphere) as it passes over various surfaces. In addition, we made a more rigorous estimate of the transformity of the available wind energy dissipated in the planetary boundary layer based on a synthesis of the results from three evaluations of a model of the general circulation of the atmosphere. The rounded estimate of the transformity of the wind from these combined studies was 1230 sej J-1. We consider the variability of the transformity of the wind dissipated in the boundary layer between summer and winter and between the Northern and Southern hemispheres. We conclude that the properties of the system and its spatial and temporal boundarie
Algebraic approximations for transcendental equations with applications in nanophysics
NASA Astrophysics Data System (ADS)
Barsan, Victor
2015-09-01
Using algebraic approximations of trigonometric or hyperbolic functions, a class of transcendental equations can be transformed in tractable, algebraic equations. Studying transcendental equations this way gives the eigenvalues of Sturm-Liouville problems associated to wave equation, mainly to Schroedinger equation; these algebraic approximations provide approximate analytical expressions for the energy of electrons and phonons in quantum wells, quantum dots (QDs) and quantum wires, in the frame of one-particle models of such systems. The advantage of this approach, compared to the numerical calculations, is that the final result preserves the functional dependence on the physical parameters of the problem. The errors of this method, situated between some few percentages and ?, are carefully analysed. Several applications, for quantum wells, QDs and quantum wires, are presented.
Novikov algebras with associative bilinear forms
NASA Astrophysics Data System (ADS)
Zhu, Fuhai; Chen, Zhiqi
2007-11-01
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. The goal of this paper is to study Novikov algebras with non-degenerate associative symmetric bilinear forms, which we call quadratic Novikov algebras. Based on the classification of solvable quadratic Lie algebras of dimension not greater than 4 and Novikov algebras in dimension 3, we show that quadratic Novikov algebras up to dimension 4 are commutative. Furthermore, we obtain the classification of transitive quadratic Novikov algebras in dimension 4. But we find that not every quadratic Novikov algebra is commutative and give a non-commutative quadratic Novikov algebra in dimension 6.
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.
Quantum Q systems: from cluster algebras to quantum current algebras
NASA Astrophysics Data System (ADS)
Di Francesco, Philippe; Kedem, Rinat
2017-02-01
This paper gives a new algebraic interpretation for the algebra generated by the quantum cluster variables of the A_r quantum Q-system (Di Francesco and Kedem in Int Math Res Not IMRN 10:2593-2642, 2014). We show that the algebra can be described as a quotient of the localization of the quantum algebra U_{√{q}}({n}[u,u^{-1}])subset U_{√{q}}(widehat{{sl}}_2), in the Drinfeld presentation. The generating current is made up of a subset of the cluster variables which satisfy the Q-system, which we call fundamental. The other cluster variables are given by a quantum determinant-type formula, and are polynomials in the fundamental generators. The conserved quantities of the discrete evolution (Di Francesco and Kedem in Adv Math 228(1):97-152, 2011) described by quantum Q-system generate the Cartan currents at level 0, in a non-standard polarization. The rest of the quantum affine algebra is also described in terms of cluster variables.
(Fuzzy) Ideals of BN-Algebras.
Dymek, Grzegorz; Walendziak, Andrzej
2015-01-01
The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained.
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. Copyright © 2012 Elsevier Ltd. All rights reserved.
David Rogers Tilley; Wayne T. Swank
2003-01-01
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...
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.
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.
A Metric Conceptual Space Algebra
NASA Astrophysics Data System (ADS)
Adams, Benjamin; Raubal, Martin
The modeling of concepts from a cognitive perspective is important for designing spatial information systems that interoperate with human users. Concept representations that are built using geometric and topological conceptual space structures are well suited for semantic similarity and concept combination operations. In addition, concepts that are more closely grounded in the physical world, such as many spatial concepts, have a natural fit with the geometric structure of conceptual spaces. Despite these apparent advantages, conceptual spaces are underutilized because existing formalizations of conceptual space theory have focused on individual aspects of the theory rather than the creation of a comprehensive algebra. In this paper we present a metric conceptual space algebra that is designed to facilitate the creation of conceptual space knowledge bases and inferencing systems. Conceptual regions are represented as convex polytopes and context is built in as a fundamental element. We demonstrate the applicability of the algebra to spatial information systems with a proof-of-concept application.
Using Number Theory to Reinforce Elementary Algebra.
ERIC Educational Resources Information Center
Covillion, Jane D.
1995-01-01
Demonstrates that using the elementary number theory in algebra classes helps students to use acquired algebraic skills as well as helping them to more clearly understand concepts that are presented. Discusses factoring, divisibility rules, and number patterns. (AIM)
Colored Quantum Algebra and Its Bethe State
NASA Astrophysics Data System (ADS)
Wang, Jin-Zheng; Jia, Xiao-Yu; Wang, Shi-Kun
2014-12-01
We investigate the colored Yang—Baxter equation. Based on a trigonometric solution of colored Yang—Baxter equation, we construct a colored quantum algebra. Moreover we discuss its algebraic Bethe ansatz state and highest wight representation.
Comments on /N=4 superconformal algebras
NASA Astrophysics Data System (ADS)
Rasmussen, Jørgen
2001-01-01
We present a new and asymmetric N=4 superconformal algebra for arbitrary central charge, thus completing our recent work on its classical analogue with vanishing central charge. Besides the Virasoro generator and 4 supercurrents, the algebra consists of an internal SU(2)⊗U(1) Kac-Moody algebra in addition to two spin 1/2 fermions and a bosonic scalar. The algebra is shown to be invariant under a linear twist of the generators, except for a unique value of the continuous twist parameter. At this value, the invariance is broken and the algebra collapses to the small N=4 superconformal algebra. The asymmetric N=4 superconformal algebra may be seen as induced by an affine SL(2|2) current superalgebra. Replacing SL(2|2) with the coset SL(2|2)/U(1), results directly in the small N=4 superconformal algebra.
Tensor models and 3-ary algebras
NASA Astrophysics Data System (ADS)
Sasakura, Naoki
2011-10-01
Tensor models are the generalization of matrix models, and are studied as models of quantum gravity in general dimensions. In this paper, I discuss the algebraic structure in the fuzzy space interpretation of the tensor models which have a tensor with three indices as its only dynamical variable. The algebraic structure is studied mainly from the perspective of 3-ary algebras. It is shown that the tensor models have algebraic expressions, and that their symmetries are represented by 3-ary algebras. It is also shown that the 3-ary algebras of coordinates, which appear in the nonassociative fuzzy flat spacetimes corresponding to a certain class of configurations with Gaussian functions in the tensor models, form Lie triple systems, and the associated Lie algebras are shown to agree with those of the Snyder's noncommutative spacetimes. The Poincare transformations of the coordinates on the fuzzy flat spacetimes are shown to be generated by 3-ary algebras.
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.
Lu, Hongfang; Fu, Fangyan; Li, Hao; Campbell, Daniel E; Ren, Hai
2015-10-21
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.
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
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.
Algebraic orbifold conformal field theories
Xu, Feng
2000-01-01
The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown that the irreducible representations of orbifolds of rank one lattice vertex operator algebras give rise to unitary modular categories and determine the corresponding modular matrices, which has been conjectured for some time. PMID:11106383
Entropic Forms and Related Algebras
NASA Astrophysics Data System (ADS)
Scarfone, Antonio
2013-02-01
Starting from a very general trace-form entropy, we introduce a pair of algebraic structures endowed by a generalized sum and a generalized product. These algebras form, respectively, two Abelian fields in the realm of the complex numbers isomorphic each other. We specify our results to several entropic forms related to distributions recurrently observed in social, economical, biological and physical systems including the stretched exponential, the power-law and the interpolating Bosons-Fermions distributions. Some potential applications in the study of complex systems are advanced.
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.
Symmetry algebras of linear differential equations
NASA Astrophysics Data System (ADS)
Shapovalov, A. V.; Shirokov, I. V.
1992-07-01
The local symmetries of linear differential equations are investigated by means of proven theorems on the structure of the algebra of local symmetries of translationally and dilatationally invariant differential equations. For a nonparabolic second-order equation, the absence of nontrivial nonlinear local symmetries is proved. This means that the local symmetries reduce to the Lie algebra of linear differential symmetry operators. For the Laplace—Beltrami equation, all local symmetries reduce to the enveloping algebra of the algebra of the conformal group.
Discrimination in a General Algebraic Setting
Fine, Benjamin; Lipschutz, Seymour; Spellman, Dennis
2015-01-01
Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras. PMID:26171421
Post-Lie algebras and factorization theorems
NASA Astrophysics Data System (ADS)
Ebrahimi-Fard, Kurusch; Mencattini, Igor; Munthe-Kaas, Hans
2017-09-01
In this note we further explore the properties of universal enveloping algebras associated to a post-Lie algebra. Emphasizing the role of the Magnus expansion, we analyze the properties of group like-elements belonging to (suitable completions of) those Hopf algebras. Of particular interest is the case of post-Lie algebras defined in terms of solutions of modified classical Yang-Baxter equations. In this setting we will study factorization properties of the aforementioned group-like elements.
Twining characters and orbit Lie algebras
Fuchs, Jurgen; Ray, Urmie; Schellekens, Bert; Schweigert, Christoph
1996-12-05
We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary characters of some other generalized Kac-Moody algebra, the so-called orbit Lie algebra. Some applications to problems in conformal field theory, algebraic geometry and the theory of sporadic simple groups are sketched.
Discrimination in a General Algebraic Setting.
Fine, Benjamin; Gaglione, Anthony; Lipschutz, Seymour; Spellman, Dennis
2015-01-01
Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras.
Applications of Algebraic Logic and Universal Algebra to Computer Science
1989-06-21
conference, with roughly equal representation from Mathematics and Computer Science . The conference consisted of eight invited lectures (60 minutes...each) and 26 contributed talks (20-40 minutes each). There was also a round-table discussion on the role of algebra and logic in computer science . Keywords
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"…
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…
Teacher Actions to Facilitate Early Algebraic Reasoning
ERIC Educational Resources Information Center
Hunter, Jodie
2015-01-01
In recent years there has been an increased emphasis on integrating the teaching of arithmetic and algebra in primary school classrooms. This requires teachers to develop links between arithmetic and algebra and use pedagogical actions that facilitate algebraic reasoning. Drawing on findings from a classroom-based study, this paper provides an…
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…
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…
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…
Cyclic homology for Hom-associative algebras
NASA Astrophysics Data System (ADS)
Hassanzadeh, Mohammad; Shapiro, Ilya; Sütlü, Serkan
2015-12-01
In the present paper we investigate the noncommutative geometry of a class of algebras, called the Hom-associative algebras, whose associativity is twisted by a homomorphism. We define the Hochschild, cyclic, and periodic cyclic homology and cohomology for this class of algebras generalizing these theories from the associative to the Hom-associative setting.
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…
Embedding Algebraic Thinking throughout the Mathematics Curriculum
ERIC Educational Resources Information Center
Vennebush, G. Patrick; Marquez, Elizabeth; Larsen, Joseph
2005-01-01
This article explores the algebra that can be uncovered in many middle-grades mathematics tasks that, on first inspection, do not appear to be algebraic. It shows connections to the other four Standards that occur in traditional algebra problems, and it offers strategies for modifying activities so that they can be used to foster algebraic…
Constraint-Referenced Analytics of Algebra Learning
ERIC Educational Resources Information Center
Sutherland, Scot M.; White, Tobin F.
2016-01-01
The development of the constraint-referenced analytics tool for monitoring algebra learning activities presented here came from the desire to firstly, take a more quantitative look at student responses in collaborative algebra activities, and secondly, to situate those activities in a more traditional introductory algebra setting focusing on…
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"…
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…
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…
Quadratic Dynamical Systems and Algebras
NASA Astrophysics Data System (ADS)
Kinyon, M. K.; Sagle, A. A.
1995-03-01
Quadratic dynamical systems come from differential or discrete systems of the form Ẋ = Q(X) or X(k+1)=Q(X(k)), where Q:Rn→Rn is homogeneous of degree 2; i.e., Q(αX) = α2Q(X) for all α∈R, X∈Rn. Defining a bilinear mapping β:Rn × Rn→Rn by β(X, Y) ≔ {1}/{2}[Q(X+Y)-Q(X)-Q(Y)], we view XY≡β(X, Y) as a multiplication, and thus consider A=(Rn, β) to be a commutative, nonassociative algebra. The quadratic systems are then studied with the general theme that the structure of the algebras helps determine the behavior of the solutions. For example, semisimple algebras give a decoupling of the original system into systems occurring in simple algebras, and solvable algebras give solutions to differential systems via linear differential equations; the general three-dimensional example of the latter phenomenon is described. There are many classical examples and the scope of quadratic systems is large; every polynomial system can be embedded into a higher dimensional quadratic system such that solutions of the original system are obtained from the quadratic system. For differential systems, nilpotents of index 2 (N2=0) are equilibria and idempotents (E2=E) give ray solutions. The origin is never asymptotically stable, and the existence of nonzero idempotents implies that the origin is actually unstable. Nonzero equilibria are not hyperbolic, but can be studied by standard algebra techniques using nondegenerate bilinear forms as Lyapunov functions. Periodic orbits lie on "cones." They cannot occur in dimension 2 or in power-associative algebras. No periodic orbit can be an attractor but "limit cycles" (invariant cones) can exist. Automorphisms of the algebra A leave equilibria, periodic orbits, and domains of attraction invariant. Also, explicit solutions can be given by the action of automorphisms on an initial point; the general three-dimensional example of this is described. Thus if there are sufficient automorphisms, Hilbert‧s sixteenth problem in R3 has
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…
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…
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…
Dimension independence in exterior algebra.
Hawrylycz, M
1995-03-14
The identities between homogeneous expressions in rank 1 vectors and rank n - 1 covectors in a Grassmann-Cayley algebra of rank n, in which one set occurs multilinearly, are shown to represent a set of dimension-independent identities. The theorem yields an infinite set of nontrivial geometric identities from a given identity.
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 contemporary…
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…
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.
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…
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…
Kleene Algebra and Bytecode Verification
2016-04-27
Languages, ACM SIGPLAN/SIGACT, 1998, pp. 149–160. [2] Coglio, A., Simple verification technique for complex Java bytecode subroutines, Concurrency and...of Programming Languages (POPL’73), ACM , 1973, pp. 194–206. [6] Kot, L. and D. Kozen, Second-order abstract interpretation via Kleene algebra
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…
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…
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 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.
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 contemporary…
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.
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…
Easing Students' Transition to Algebra
ERIC Educational Resources Information Center
Baroudi, Ziad
2006-01-01
Traditionally, students learn arithmetic throughout their primary schooling, and this is seen as the ideal preparation for the learning of algebra in the junior secondary school. The four operations are taught and rehearsed in the early years and from this, it is assumed, "children will induce the fundamental structure of arithmetic" (Warren &…
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…
Generalized electromagnetism and Dirac algebra
Fryberger, D.
1989-02-01
Using a framework of Dirac algebra, the Clifford algebra appropriate for Minkowski space-time, the formulation of classical electromagnetism including both electric and magnetic charge is explored. Employing the two-potential approach of Cabibbo and Ferrari, a Lagrangian is obtained that is dyality invariant and from which it is possible to derive by Hamilton's principle both the symmetrized Maxwell's equations and the equations of motion for both electrically and magnetically charged particles. This latter result is achieved by defining the variation of the action associated with the cross terms of the interaction Lagrangian in terms of a surface integral. The surface integral has an equivalent path-integral form, showing that the contribution of the cross terms is local in nature. The form of these cross terms derives in a natural way from a Dirac algebraic formulation, and, in fact, the use of the geometric product of Dirac algebra is an essential aspect of this derivation. No kinematic restrictions are associated with the derivation, and no relationship between magnetic and electric charge evolves from the (classical) formulations. However, it is indicated that in bound states quantum mechanical considerations will lead to a version of Dirac's quantization condition. A discussion of parity violation of the generalized electromagnetic theory is given, and a new approach to the incorporation of this violation into the formalism is suggested. Possibilities for extensions are mentioned.
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…
Carry Groups: Abstract Algebra Projects
ERIC Educational Resources Information Center
Miller, Cheryl Chute; Madore, Blair F.
2004-01-01
Carry Groups are a wonderful collection of groups to introduce in an undergraduate Abstract Algebra course. These groups are straightforward to define but have interesting structures for students to discover. We describe these groups and give examples of in-class group projects that were developed and used by Miller.
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…
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…
Dimension independence in exterior algebra.
Hawrylycz, M
1995-01-01
The identities between homogeneous expressions in rank 1 vectors and rank n - 1 covectors in a Grassmann-Cayley algebra of rank n, in which one set occurs multilinearly, are shown to represent a set of dimension-independent identities. The theorem yields an infinite set of nontrivial geometric identities from a given identity. PMID:11607520
Carry Groups: Abstract Algebra Projects
ERIC Educational Resources Information Center
Miller, Cheryl Chute; Madore, Blair F.
2004-01-01
Carry Groups are a wonderful collection of groups to introduce in an undergraduate Abstract Algebra course. These groups are straightforward to define but have interesting structures for students to discover. We describe these groups and give examples of in-class group projects that were developed and used by Miller.
Monitoring Student Learning in Algebra
ERIC Educational Resources Information Center
Accardo, Amy L.; Kuder, S. Jay
2017-01-01
Mr. Perez and Mrs. Peterson co-teach a ninth-grade algebra class. Perez and Peterson's class includes four students with individualized education programs (IEPs). In response to legislation, such as the No Child Left Behind (NCLB) Act (2001) and the Individuals with Disabilities Education Improvement Act (2006), an increasing number of students…
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…
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…
Math Sense: Algebra and Geometry.
ERIC Educational Resources Information Center
Howett, Jerry
This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four strands: (1) skill lessons…
Teachers' Understanding of Algebraic Generalization
NASA Astrophysics Data System (ADS)
Hawthorne, Casey Wayne
Generalization has been identified as a cornerstone of algebraic thinking (e.g., Lee, 1996; Sfard, 1995) and is at the center of a rich conceptualization of K-8 algebra (Kaput, 2008; Smith, 2003). Moreover, mathematics teachers are being encouraged to use figural-pattern generalizing tasks as a basis of student-centered instruction, whereby teachers respond to and build upon the ideas that arise from students' explorations of these activities. Although more and more teachers are engaging their students in such generalizing tasks, little is known about teachers' understanding of generalization and their understanding of students' mathematical thinking in this domain. In this work, I addressed this gap, exploring the understanding of algebraic generalization of 4 exemplary 8th-grade teachers from multiple perspectives. A significant feature of this investigation is an examination of teachers' understanding of the generalization process, including the use of algebraic symbols. The research consisted of two phases. Phase I was an examination of the teachers' understandings of the underlying quantities and quantitative relationships represented by algebraic notation. In Phase II, I observed the instruction of 2 of these teachers. Using the lens of professional noticing of students' mathematical thinking, I explored the teachers' enacted knowledge of algebraic generalization, characterizing how it supported them to effectively respond to the needs and queries of their students. Results indicated that teachers predominantly see these figural patterns as enrichment activities, disconnected from course content. Furthermore, in my analysis, I identified conceptual difficulties teachers experienced when solving generalization tasks, in particular, connecting multiple symbolic representations with the quantities in the figures. Moreover, while the teachers strived to overcome the challenges of connecting different representations, they invoked both productive and unproductive
Algebra for All: California’s Eighth-Grade Algebra Initiative as Constrained Curricula
Domina, Thurston; Penner, Andrew M.; Penner, Emily K.; Conley, Annemarie
2015-01-01
prior achievement. Findings/Results We find that students’ odds of taking higher level mathematics courses increased as this district implemented the state’s Algebra mandate. However, even as the district implemented a constrained curriculum strategy, mathematics achievement growth between 6th sixth and 10th grade slowed and the achievement advantages associated with 8th eighth grade Algebra declined. Conclusions/Recommendations Our analyses suggest that curricular intensification increased the inclusiveness and decreased the selectivity of the mathematics tracking regime in Towering Pines middle schools. However, the findings suggest that this constrained curriculum strategy may have may have unintended negative consequences for student achievement. PMID:26120219
Algebra for All: California's Eighth-Grade Algebra Initiative as Constrained Curricula.
Domina, Thurston; Penner, Andrew M; Penner, Emily K; Conley, Annemarie
2014-08-01
district implemented the state's Algebra mandate. However, even as the district implemented a constrained curriculum strategy, mathematics achievement growth between 6th sixth and 10th grade slowed and the achievement advantages associated with 8th eighth grade Algebra declined. Our analyses suggest that curricular intensification increased the inclusiveness and decreased the selectivity of the mathematics tracking regime in Towering Pines middle schools. However, the findings suggest that this constrained curriculum strategy may have may have unintended negative consequences for student achievement.
Explicit field realizations of W algebras
NASA Astrophysics Data System (ADS)
Wei, Shao-Wen; Liu, Yu-Xiao; Zhang, Li-Jie; Ren, Ji-Rong
2009-06-01
The fact that certain nonlinear W2,s algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize W2,s algebras from linear W1,2,s algebras. In this paper, we first construct the explicit field realizations of linear W1,2,s algebras with double scalar and double spinor, respectively. Then, after a change of basis, the realizations of W2,s algebras are presented. The results show that all these realizations are Romans-type realizations.
Roughness in lattice ordered effect algebras.
Xin, Xiao Long; Hua, Xiu Juan; Zhu, Xi
2014-01-01
Many authors have studied roughness on various algebraic systems. In this paper, we consider a lattice ordered effect algebra and discuss its roughness in this context. Moreover, we introduce the notions of the interior and the closure of a subset and give some of their properties in effect algebras. Finally, we use a Riesz ideal induced congruence and define a function e(a, b) in a lattice ordered effect algebra E and build a relationship between it and congruence classes. Then we study some properties about approximation of lattice ordered effect algebras.
Roughness in Lattice Ordered Effect Algebras
Xin, Xiao Long; Hua, Xiu Juan; Zhu, Xi
2014-01-01
Many authors have studied roughness on various algebraic systems. In this paper, we consider a lattice ordered effect algebra and discuss its roughness in this context. Moreover, we introduce the notions of the interior and the closure of a subset and give some of their properties in effect algebras. Finally, we use a Riesz ideal induced congruence and define a function e(a, b) in a lattice ordered effect algebra E and build a relationship between it and congruence classes. Then we study some properties about approximation of lattice ordered effect algebras. PMID:25170523
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.
On special classes of n-algebras
NASA Astrophysics Data System (ADS)
Vainerman, L.; Kerner, R.
1996-05-01
We define n-algebras as linear spaces on which the internal composition law involves n elements: m:V⊗n■V. It is known that such algebraic structures are interesting for their applications to problems of modern mathematical physics. Using the notion of a commutant of two subalgebras of an n-algebra, we distinguish certain classes of n-algebras with reasonable properties: semisimple, Abelian, nilpotent, solvable. We also consider a few examples of n-algebras of different types, and show their properties.
Algebraically special Einstein-Maxwell fields
NASA Astrophysics Data System (ADS)
Van den Bergh, Norbert
2017-01-01
The Geroch-Held-Penrose formalism is used to re-analyse algebraically special non-null Einstein-Maxwell fields, aligned as well as non-aligned, in the presence of a possible non-vanishing cosmological constant. A new invariant characterization is given of the García-Plebański and Plebański-Hacyan metrics within the family of aligned solutions and of the Griffiths metrics within the family of the non-aligned solutions. As a corollary also the double alignment of the Debever-McLenaghan `class D' metrics with non-vanishing cosmological constant is shown to be equivalent with the shear-free and geodesic behavior of their Debever-Penrose vectors.
A graph algebra for scalable visual analytics.
Shaverdian, Anna A; Zhou, Hao; Michailidis, George; Jagadish, Hosagrahar V
2012-01-01
Visual analytics (VA), which combines analytical techniques with advanced visualization features, is fast becoming a standard tool for extracting information from graph data. Researchers have developed many tools for this purpose, suggesting a need for formal methods to guide these tools' creation. Increased data demands on computing requires redesigning VA tools to consider performance and reliability in the context of analysis of exascale datasets. Furthermore, visual analysts need a way to document their analyses for reuse and results justification. A VA graph framework encapsulated in a graph algebra helps address these needs. Its atomic operators include selection and aggregation. The framework employs a visual operator and supports dynamic attributes of data to enable scalable visual exploration of data.
Infinite order decompositions of C*-algebras.
Nematjonovich, Arzikulov Farhodjon
2016-01-01
The present paper is devoted to infinite order decompositions of C*-algebras. It is proved that an infinite order decomposition (IOD) of a C*-algebra forms the complexification of an order unit space, and, if the C*-algebra is monotone complete (not necessarily weakly closed) then its IOD is also monotone complete ordered vector space. Also it is established that an IOD of a C*-algebra is a C*-algebra if and only if this C*-algebra is a von Neumann algebra. As a summary we obtain that the norm of an infinite dimensional matrix is equal to the supremum of norms of all finite dimensional main diagonal submatrices of this matrix and an infinite dimensional matrix is positive if and only if all finite dimensional main diagonal submatrices of this matrix are positive.
Deformed Kac Moody and Virasoro algebras
NASA Astrophysics Data System (ADS)
Balachandran, A. P.; Queiroz, A. R.; Marques, A. M.; Teotonio-Sobrinho, P.
2007-07-01
Whenever the group {\\bb R}^n acts on an algebra {\\cal A} , there is a method to twist \\cal A to a new algebra {\\cal A}_\\theta which depends on an antisymmetric matrix θ (θμν = -θνμ = constant). The Groenewold-Moyal plane {\\cal A}_\\theta({\\bb R}^{d+1}) is an example of such a twisted algebra. We give a general construction to realize this twist in terms of {\\cal A} itself and certain 'charge' operators Qμ. For {\\cal A}_\\theta({\\bb R}^{d+1}), Q_\\mu are translation generators. This construction is then applied to twist the oscillators realizing the Kac-Moody (KM) algebra as well as the KM currents. They give different deformations of the KM algebra. From one of the deformations of the KM algebra, we construct, via the Sugawara construction, the Virasoro algebra. These deformations have an implication for statistics as well.
Filiform Lie algebras of order 3
Navarro, R. M.
2014-04-15
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases.
Recursion and feedback in image algebra
NASA Astrophysics Data System (ADS)
Ritter, Gerhard X.; Davidson, Jennifer L.
1991-04-01
Recursion and feedback are two important processes in image processing. Image algebra, a unified algebraic structure developed for use in image processing and image analysis, provides a common mathematical environment for expressing image processing transforms. It is only recently that image algebra has been extended to include recursive operations [1]. Recently image algebra was shown to incorporate neural nets [2], including a new type of neural net, the morphological neural net [3]. This paper presents the relationship of the recursive image algebra to the field of fractions of the ring of matrices, and gives the two dimensional moving average filter as an example. Also, the popular multilayer perceptron with back propagation and a morphology neural network with learning rule are presented in image algebra notation. These examples show that image algebra can express these important feedback concepts in a succinct way.
Powell, Sarah R; Fuchs, Lynn S
2014-08-01
According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 2(nd)- grade students, we administered (a) measures of calculations and word problems in the fall and (b) an assessment of pre-algebraic reasoning, with items that assessed solving equations and functions, in the spring. Based on the calculation and word-problem measures, we placed 148 students into 1 of 4 difficulty status categories: typically performing, calculation difficulty, word-problem difficulty, or difficulty with calculations and word problems. Analyses of variance were conducted on the 148 students; path analytic mediation analyses were conducted on the larger sample of 789 students. Across analyses, results corroborated the finding that word-problem difficulty is more strongly associated with difficulty with pre-algebraic reasoning. As an indicator of later algebra difficulty, word-problem difficulty may be a more useful predictor than calculation difficulty, and students with word-problem difficulty may require a different level of algebraic reasoning intervention than students with calculation difficulty.
Powell, Sarah R.; Fuchs, Lynn S.
2014-01-01
According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 2nd- grade students, we administered (a) measures of calculations and word problems in the fall and (b) an assessment of pre-algebraic reasoning, with items that assessed solving equations and functions, in the spring. Based on the calculation and word-problem measures, we placed 148 students into 1 of 4 difficulty status categories: typically performing, calculation difficulty, word-problem difficulty, or difficulty with calculations and word problems. Analyses of variance were conducted on the 148 students; path analytic mediation analyses were conducted on the larger sample of 789 students. Across analyses, results corroborated the finding that word-problem difficulty is more strongly associated with difficulty with pre-algebraic reasoning. As an indicator of later algebra difficulty, word-problem difficulty may be a more useful predictor than calculation difficulty, and students with word-problem difficulty may require a different level of algebraic reasoning intervention than students with calculation difficulty. PMID:25309044
Algebraic complexities and algebraic curves over finite fields
Chudnovsky, D. V.; Chudnovsky, G. V.
1987-01-01
We consider the problem of minimal (multiplicative) complexity of polynomial multiplication and multiplication in finite extensions of fields. For infinite fields minimal complexities are known [Winograd, S. (1977) Math. Syst. Theory 10, 169-180]. We prove lower and upper bounds on minimal complexities over finite fields, both linear in the number of inputs, using the relationship with linear coding theory and algebraic curves over finite fields. PMID:16593816
DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J
2015-05-01
To understand the development of mathematical cognition and to improve instructional practices, it is critical to identify early predictors of difficulty in learning complex mathematical topics such as algebra. Recent work has shown that performance with fractions on a number line estimation task predicts algebra performance, whereas performance with whole numbers on similar estimation tasks does not. We sought to distinguish more specific precursors to algebra by measuring multiple aspects of knowledge about rational numbers. Because fractions are the first numbers that are relational expressions to which students are exposed, we investigated how understanding the relational bipartite format (a/b) of fractions might connect to later algebra performance. We presented middle school students with a battery of tests designed to measure relational understanding of fractions, procedural knowledge of fractions, and placement of fractions, decimals, and whole numbers onto number lines as well as algebra performance. Multiple regression analyses revealed that the best predictors of algebra performance were measures of relational fraction knowledge and ability to place decimals (not fractions or whole numbers) onto number lines. These findings suggest that at least two specific components of knowledge about rational numbers--relational understanding (best captured by fractions) and grasp of unidimensional magnitude (best captured by decimals)--can be linked to early success with algebraic expressions.
Alternative algebraic approaches in quantum chemistry
Mezey, Paul G.
2015-01-22
Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies of molecular conformational and reaction processes. Two relevant theorems will be discussed.
Surface defects and chiral algebras
Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng
2017-05-26
Here, we investigate superconformal surface defects in four-dimensional N = 2 superconformal theories. Each such defect gives rise to a module of the associated chiral algebra and the surface defect Schur index is the character of this module. Various natural chiral algebra operations such as Drinfield-Sokolov reduction and spectral flow can be interpreted as constructions involving four-dimensional surface defects. We compute the index of these defects in the free hypermultiplet theory and Argyres-Douglas theories, using both infrared techniques involving BPS states, as well as renormalization group flows onto Higgs branches. We find perfect agreement with the predicted characters, in eachmore » case.« less
Algebraic Methods to Design Signals
2015-08-27
whose out-of-phase autocorrelation values are very small. We call the constructed sequences perfect sequences and they serve as perfect algebraic...matrices DISTRIBUTION A: Distribution approved for public release. 2. Gauss sum factorizations yield perfect sequences, (with John Dillon and...the p- ary case, the prefix " perfect " for the underlying sequence (i.e. 1-dimensional array) refers to the case when all the out-of-phase
Algebraic learning for language acquisition
NASA Astrophysics Data System (ADS)
Farrell, Kevin R.; Mammone, Richard J.; Gorin, Allen
1994-02-01
This paper explores the application of new algorithms to the adaptive language acquisition model formulated by Gorin. The new methods consists of incremental approaches for the algebraic learning of statistical associations proposed by Tishby. The incremental methods are evaluated on a text-based natural language experiment, namely the inward call manager task. Performance is evaluated with respect to the alternative methods, namely the smooth mutual information method and the pseudo-inverse solution.
Introduction to Image Algebra Ada
NASA Astrophysics Data System (ADS)
Wilson, Joseph N.
1991-07-01
Image Algebra Ada (IAA) is a superset of the Ada programming language designed to support use of the Air Force Armament Laboratory's image algebra in the development of computer vision application programs. The IAA language differs from other computer vision languages is several respects. It is machine independent, and an IAA translator has been implemented in the military standard Ada language. Its image operands and operations can be used to program a range of both low- and high-level vision algorithms. This paper provides an overview of the image algebra constructs supported in IAA and describes the embodiment of these constructs in the IAA extension of Ada. Examples showing the use of IAA for a range of computer vision tasks are given. The design of IAA as a superset of Ada and the implementation of the initial translator in Ada represent critical choices. The authors discuss the reasoning behind these choices as well as the benefits and drawbacks associated with them. Implementation strategies associated with the use of Ada as an implementation language for IAA are also discussed. While one can look on IAA as a program design language (PDL) for specifying Ada programs, it is useful to consider IAA as a separate language superset of Ada. This admits the possibility of directly translating IAA for implementation on special purpose architectures. This paper explores strategies for porting IAA to various architectures and notes the critical language and implementation features for porting to different architectures.
BLAS- BASIC LINEAR ALGEBRA SUBPROGRAMS
NASA Technical Reports Server (NTRS)
Krogh, F. T.
1994-01-01
The Basic Linear Algebra Subprogram (BLAS) library is a collection of FORTRAN callable routines for employing standard techniques in performing the basic operations of numerical linear algebra. The BLAS library was developed to provide a portable and efficient source of basic operations for designers of programs involving linear algebraic computations. The subprograms available in the library cover the operations of dot product, multiplication of a scalar and a vector, vector plus a scalar times a vector, Givens transformation, modified Givens transformation, copy, swap, Euclidean norm, sum of magnitudes, and location of the largest magnitude element. Since these subprograms are to be used in an ANSI FORTRAN context, the cases of single precision, double precision, and complex data are provided for. All of the subprograms have been thoroughly tested and produce consistent results even when transported from machine to machine. BLAS contains Assembler versions and FORTRAN test code for any of the following compilers: Lahey F77L, Microsoft FORTRAN, or IBM Professional FORTRAN. It requires the Microsoft Macro Assembler and a math co-processor. The PC implementation allows individual arrays of over 64K. The BLAS library was developed in 1979. The PC version was made available in 1986 and updated in 1988.
BLAS- BASIC LINEAR ALGEBRA SUBPROGRAMS
NASA Technical Reports Server (NTRS)
Krogh, F. T.
1994-01-01
The Basic Linear Algebra Subprogram (BLAS) library is a collection of FORTRAN callable routines for employing standard techniques in performing the basic operations of numerical linear algebra. The BLAS library was developed to provide a portable and efficient source of basic operations for designers of programs involving linear algebraic computations. The subprograms available in the library cover the operations of dot product, multiplication of a scalar and a vector, vector plus a scalar times a vector, Givens transformation, modified Givens transformation, copy, swap, Euclidean norm, sum of magnitudes, and location of the largest magnitude element. Since these subprograms are to be used in an ANSI FORTRAN context, the cases of single precision, double precision, and complex data are provided for. All of the subprograms have been thoroughly tested and produce consistent results even when transported from machine to machine. BLAS contains Assembler versions and FORTRAN test code for any of the following compilers: Lahey F77L, Microsoft FORTRAN, or IBM Professional FORTRAN. It requires the Microsoft Macro Assembler and a math co-processor. The PC implementation allows individual arrays of over 64K. The BLAS library was developed in 1979. The PC version was made available in 1986 and updated in 1988.
Computer algebra and transport theory.
Warsa, J. S.
2004-01-01
Modern symbolic algebra computer software augments and complements more traditional approaches to transport theory applications in several ways. The first area is in the development and enhancement of numerical solution methods for solving the Boltzmann transport equation. Typically, special purpose computer codes are designed and written to solve specific transport problems in particular ways. Different aspects of the code are often written from scratch and the pitfalls of developing complex computer codes are numerous and well known. Software such as MAPLE and MATLAB can be used to prototype, analyze, verify and determine the suitability of numerical solution methods before a full-scale transport application is written. Once it is written, the relevant pieces of the full-scale code can be verified using the same tools I that were developed for prototyping. Another area is in the analysis of numerical solution methods or the calculation of theoretical results that might otherwise be difficult or intractable. Algebraic manipulations are done easily and without error and the software also provides a framework for any additional numerical calculations that might be needed to complete the analysis. We will discuss several applications in which we have extensively used MAPLE and MATLAB in our work. All of them involve numerical solutions of the S{sub N} transport equation. These applications encompass both of the two main areas in which we have found computer algebra software essential.
Algebra: A Challenge at the Crossroads of Policy and Practice
ERIC Educational Resources Information Center
Stein, Mary Kay; Kaufman, Julia Heath; Sherman, Milan; Hillen, Amy F.
2011-01-01
The authors review what is known about early and universal algebra, including who is getting access to algebra and student outcomes associated with algebra course taking in general and specifically with universal algebra policies. The findings indicate that increasing numbers of students, some of whom are underprepared, are taking algebra earlier.…
Algebra: A Challenge at the Crossroads of Policy and Practice
ERIC Educational Resources Information Center
Stein, Mary Kay; Kaufman, Julia Heath; Sherman, Milan; Hillen, Amy F.
2011-01-01
The authors review what is known about early and universal algebra, including who is getting access to algebra and student outcomes associated with algebra course taking in general and specifically with universal algebra policies. The findings indicate that increasing numbers of students, some of whom are underprepared, are taking algebra earlier.…
Addendum to Effectiveness of Cognitive Tutor Algebra I at Scale. Working Paper WR-1050-DEIES
ERIC Educational Resources Information Center
Pane, John F.; Griffin, Beth Ann; McCaffrey, Daniel F.; Karam, Rita
2014-01-01
This addendum to previously published results presents alternative analyses of data from large-scale effectiveness studies of Cognitive Tutor Algebra I in middle schools and high schools. These alternative analyses produce results that are substantively the same as previously reported. We find a significant positive effect of 0.21 standard…
Walendziak, Andrzej
2015-01-01
The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained. PMID:26125050
Bilinear forms on fermionic Novikov algebras
NASA Astrophysics Data System (ADS)
Chen, Zhiqi; Zhu, Fuhai
2007-05-01
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in formal variational calculus. Fermionic Novikov algebras correspond to a certain Hamiltonian super-operator in a super-variable. In this paper, we show that there is a remarkable geometry on fermionic Novikov algebras with non-degenerate invariant symmetric bilinear forms, which we call pseudo-Riemannian fermionic Novikov algebras. They are related to pseudo-Riemannian Lie algebras. Furthermore, we obtain a procedure to classify pseudo-Riemannian fermionic Novikov algebras. As an application, we give the classification in dimension <=4. Motivated by the one in dimension 4, we construct some examples in high dimensions.
Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras
NASA Astrophysics Data System (ADS)
Zhang, Tianjie; Gao, Xing; Guo, Li
2016-10-01
The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum field theory. In particular, the Hopf algebra of rooted trees serves as the "baby model" of Feynman graphs in their approach and can be characterized by certain universal properties involving a Hochschild 1-cocycle. Decorated rooted trees have also been applied to study Feynman graphs. We will continue the study of universal properties of various spaces of decorated rooted trees with such a 1-cocycle, leading to the concept of a cocycle Hopf algebra. We further apply the universal properties to equip a free Rota-Baxter algebra with the structure of a cocycle Hopf algebra.
Lie algebras of classical and stochastic electrodynamics
NASA Astrophysics Data System (ADS)
Neto, J. J. Soares; Vianna, J. D. M.
1994-03-01
The Lie algebras associated with infinitesimal symmetry transformations of third-order differential equations of interest to classical electrodynamics and stochastic electrodynamics have been obtained. The structure constants for a general case are presented and the Lie algebra for each particular application is easily achieved. By the method used here it is not necessary to know the explicit expressions of the infinitesimal generators in order to determine the structure constants of the Lie algebra.
On classification of m-dimensional algebras
NASA Astrophysics Data System (ADS)
Bekbaev, U.
2017-03-01
A constructive approach to the classification and invariance problems, with respect to basis changes, of the finite dimensional algebras is offered. A construction of an invariant open, dense (in the Zariski topology) subset of the space of structure constants of algebras is given. A classification of all algebras with structure constants from this dense set is given by providing canonical representatives of their orbits. A finite system of generators for the corresponding field of invariant rational functions of structure constants is shown.
Symbolic Lie algebras manipulations using COMMON LISP
NASA Astrophysics Data System (ADS)
Cecchini, R.; Tarlini, M.
1989-01-01
We present a description and an implementation of a program in COMMON LISP to perform symbolic computations in a given Lie algebra. Using the general definitions of vector space Lie algebra and enveloping algebra, the program is able to compute commutators, to evaluate similarity transformations and the general Baker-Campbell-Hausdorff formula. All the computations are exact, including numerical coefficients. For the interactive user an optional menu facility and online help are available. LISP knowledge is unnecessary.
Numerical linear algebra algorithms and software
NASA Astrophysics Data System (ADS)
Dongarra, Jack J.; Eijkhout, Victor
2000-11-01
The increasing availability of advanced-architecture computers has a significant effect on all spheres of scientific computation, including algorithm research and software development in numerical linear algebra. Linear algebra - in particular, the solution of linear systems of equations - lies at the heart of most calculations in scientific computing. This paper discusses some of the recent developments in linear algebra designed to exploit these advanced-architecture computers. We discuss two broad classes of algorithms: those for dense, and those for sparse matrices.
NASA Astrophysics Data System (ADS)
Manerowska, Anna; Nieznański, Edward; Mulawka, Jan
2013-10-01
Our aim is to present the algebra of concepts in two formal languages. First, after introducing a primary relation between concepts, which is subsumption, we shall specify in a language that uses quantifiers, the Boolean algebra of general concepts. Next, we shall note down the same algebra in simplified non-quantifying language, in order to use it as basis for two specific implementations, i.e. to create the Boolean algebras of deontic concepts and axiological concepts.
Wang, Chengdong; Zhang, Shenyan; Yan, Wanglin; Wang, Renqing; Liu, Jian; Wang, Yutao
2016-01-01
Renewable natural resources, such as solar radiation, rainfall, wind, and geothermal heat, together with ecosystem services, provide the elementary supports for the sustainable development of human society. To improve regional sustainability, we studied the spatial distributions and quantities of renewable natural resources and net primary productivity (NPP) in Hokkaido, which is the second largest island of Japan. With the help of Geographic Information System (GIS) software, distribution maps for each type of renewable natural resource were generated by kriging interpolation based on statistical records. A composite map of the flow of all types of renewable natural resources was also generated by map layer overlapping. Additionally, we utilized emergy analysis to convert each renewable flow with different attributes into a unified unit (i.e., solar equivalent joules [sej]). As a result, the spatial distributions of the flow of renewable natural resources of the Hokkaido region are presented in the form of thematic emergy maps. Thus, the areas with higher renewable emergy can be easily visualized and identified. The dominant renewable flow in certain areas can also be directly distinguished. The results can provide useful information for regional sustainable development, environmental conservation and ecological management. PMID:27857230
NASA Astrophysics Data System (ADS)
Wang, Chengdong; Zhang, Shenyan; Yan, Wanglin; Wang, Renqing; Liu, Jian; Wang, Yutao
2016-11-01
Renewable natural resources, such as solar radiation, rainfall, wind, and geothermal heat, together with ecosystem services, provide the elementary supports for the sustainable development of human society. To improve regional sustainability, we studied the spatial distributions and quantities of renewable natural resources and net primary productivity (NPP) in Hokkaido, which is the second largest island of Japan. With the help of Geographic Information System (GIS) software, distribution maps for each type of renewable natural resource were generated by kriging interpolation based on statistical records. A composite map of the flow of all types of renewable natural resources was also generated by map layer overlapping. Additionally, we utilized emergy analysis to convert each renewable flow with different attributes into a unified unit (i.e., solar equivalent joules [sej]). As a result, the spatial distributions of the flow of renewable natural resources of the Hokkaido region are presented in the form of thematic emergy maps. Thus, the areas with higher renewable emergy can be easily visualized and identified. The dominant renewable flow in certain areas can also be directly distinguished. The results can provide useful information for regional sustainable development, environmental conservation and ecological management.
Wang, Chengdong; Zhang, Shenyan; Yan, Wanglin; Wang, Renqing; Liu, Jian; Wang, Yutao
2016-11-18
Renewable natural resources, such as solar radiation, rainfall, wind, and geothermal heat, together with ecosystem services, provide the elementary supports for the sustainable development of human society. To improve regional sustainability, we studied the spatial distributions and quantities of renewable natural resources and net primary productivity (NPP) in Hokkaido, which is the second largest island of Japan. With the help of Geographic Information System (GIS) software, distribution maps for each type of renewable natural resource were generated by kriging interpolation based on statistical records. A composite map of the flow of all types of renewable natural resources was also generated by map layer overlapping. Additionally, we utilized emergy analysis to convert each renewable flow with different attributes into a unified unit (i.e., solar equivalent joules [sej]). As a result, the spatial distributions of the flow of renewable natural resources of the Hokkaido region are presented in the form of thematic emergy maps. Thus, the areas with higher renewable emergy can be easily visualized and identified. The dominant renewable flow in certain areas can also be directly distinguished. The results can provide useful information for regional sustainable development, environmental conservation and ecological management.
Vertex representations of quantum affine algebras.
Frenkel, I B; Jing, N
1988-12-01
We construct vertex representations of quantum affine algebras of ADE type, which were first introduced in greater generality by Drinfeld and Jimbo. The limiting special case of our construction is the untwisted vertex representation of affine Lie algebras of Frenkel-Kac and Segal. Our representation is given by means of a new type of vertex operator corresponding to the simple roots and satisfying the defining relations. In the case of the quantum affine algebra of type A, we introduce vertex operators corresponding to all the roots and determine their commutation relations. This provides an analogue of a Chevalley basis of the affine Lie algebra [unk](n) in the basic representation.
Regular subalgebras of affine Kac Moody algebras
NASA Astrophysics Data System (ADS)
Felikson, Anna; Retakh, Alexander; Tumarkin, Pavel
2008-09-01
We classify regular subalgebras of Kac-Moody algebras in terms of their root systems. In the process, we establish that a root system of a subalgebra is always an intersection of the root system of the algebra with a sublattice of its root lattice. We also discuss applications to investigations of regular subalgebras of hyperbolic Kac-Moody algebras and conformally invariant subalgebras of affine Kac-Moody algebras. In particular, we provide explicit formulae for determining all Virasoro charges in coset constructions that involve regular subalgebras.
Dispersion Operators Algebra and Linear Canonical Transformations
NASA Astrophysics Data System (ADS)
Andriambololona, Raoelina; Ranaivoson, Ravo Tokiniaina; Hasimbola Damo Emile, Randriamisy; Rakotoson, Hanitriarivo
2017-02-01
This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.
Banach Algebras Associated to Lax Pairs
NASA Astrophysics Data System (ADS)
Glazebrook, James F.
2015-04-01
Lax pairs featuring in the theory of integrable systems are known to be constructed from a commutative algebra of formal pseudodifferential operators known as the Burchnall- Chaundy algebra. Such pairs induce the well known KP flows on a restricted infinite-dimensional Grassmannian. The latter can be exhibited as a Banach homogeneous space constructed from a Banach *-algebra. It is shown that this commutative algebra of operators generating Lax pairs can be associated with a commutative C*-subalgebra in the C*-norm completion of the *-algebra. In relationship to the Bose-Fermi correspondence and the theory of vertex operators, this C*-algebra has an association with the CAR algebra of operators as represented on Fermionic Fock space by the Gelfand-Naimark-Segal construction. Instrumental is the Plücker embedding of the restricted Grassmannian into the projective space of the associated Hilbert space. The related Baker and tau-functions provide a connection between these two C*-algebras, following which their respective state spaces and Jordan-Lie-Banach algebras structures can be compared.
Literal algebra for satellite dynamics. [perturbation analysis
NASA Technical Reports Server (NTRS)
Gaposchkin, E. M.
1975-01-01
A description of the rather general class of operations available is given and the operations are related to problems in satellite dynamics. The implementation of an algebra processor is discussed. The four main categories of symbol processors are related to list processing, string manipulation, symbol manipulation, and formula manipulation. Fundamental required operations for an algebra processor are considered. It is pointed out that algebra programs have been used for a number of problems in celestial mechanics with great success. The advantage of computer algebra is its accuracy and speed.
Dispersion Operators Algebra and Linear Canonical Transformations
NASA Astrophysics Data System (ADS)
Andriambololona, Raoelina; Ranaivoson, Ravo Tokiniaina; Hasimbola Damo Emile, Randriamisy; Rakotoson, Hanitriarivo
2017-04-01
This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.
Representations of Super Yang-Mills Algebras
NASA Astrophysics Data System (ADS)
Herscovich, Estanislao
2013-06-01
We study in this article the representation theory of a family of super algebras, called the super Yang-Mills algebras, by exploiting the Kirillov orbit method à la Dixmier for nilpotent super Lie algebras. These super algebras are an extension of the so-called Yang-Mills algebras, introduced by A. Connes and M. Dubois-Violette in (Lett Math Phys 61(2):149-158, 2002), and in fact they appear as a "background independent" formulation of supersymmetric gauge theory considered in physics, in a similar way as Yang-Mills algebras do the same for the usual gauge theory. Our main result states that, under certain hypotheses, all Clifford-Weyl super algebras {{Cliff}q(k) ⊗ Ap(k)}, for p ≥ 3, or p = 2 and q ≥ 2, appear as a quotient of all super Yang-Mills algebras, for n ≥ 3 and s ≥ 1. This provides thus a family of representations of the super Yang-Mills algebras.
Difficulties in initial algebra learning in Indonesia
NASA Astrophysics Data System (ADS)
Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja
2014-12-01
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 significantly below the average student performance in other Southeast Asian countries such as Thailand, Malaysia, and Singapore. This fact gave rise to this study which aims to investigate Indonesian students' difficulties in algebra. In order to do so, a literature study was carried out on students' difficulties in initial algebra. Next, an individual written test on algebra tasks was administered, followed by interviews. A sample of 51 grade VII Indonesian students worked the written test, and 37 of them were interviewed afterwards. Data analysis revealed that mathematization, i.e., the ability to translate back and forth between the world of the problem situation and the world of mathematics and to reorganize the mathematical system itself, constituted the most frequently observed difficulty in both the written test and the interview data. Other observed difficulties concerned understanding algebraic expressions, applying arithmetic operations in numerical and algebraic expressions, understanding the different meanings of the equal sign, and understanding variables. The consequences of these findings on both task design and further research in algebra education are discussed.
Multicloning and Multibroadcasting in Operator Algebras
NASA Astrophysics Data System (ADS)
Kaniowski, Krzysztof; Lubnauer, Katarzyna; Łuczak, Andrzej
2015-12-01
We investigate multicloning and multibroadcasting in the general operator algebra framework in arbitrary dimension, generalizing thus results obtained in this framework for simple cloning and broadcasting.
ERIC Educational Resources Information Center
Ozgun-Koca, S. Ash
2010-01-01
Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or handheld calculators create new possibilities for teaching and learning algebraic manipulation. This…
ERIC Educational Resources Information Center
Ozgun-Koca, S. Ash
2010-01-01
Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or handheld calculators create new possibilities for teaching and learning algebraic manipulation. This…
The Growing Importance of Linear Algebra in Undergraduate Mathematics.
ERIC Educational Resources Information Center
Tucker, Alan
1993-01-01
Discusses the theoretical and practical importance of linear algebra. Presents a brief history of linear algebra and matrix theory and describes the place of linear algebra in the undergraduate curriculum. (MDH)
Classification of filiform Lie algebras of order 3
NASA Astrophysics Data System (ADS)
Navarro, Rosa María
2016-12-01
Lie algebras of order 3 constitute a generalization of Lie algebras and superalgebras. Throughout this paper the classification problem of filiform Lie algebras of order 3 is considered and therefore this work is a continuation papers seen in the literature. We approach this classification by extending Vergne's result for filiform Lie algebras and by considering algebras of order 3 of high nilindex. We find the expression of the law to which any elementary filiform Lie algebra of order 3 is isomorphic.
Centroids and derivations of low-dimensional Leibniz algebra
NASA Astrophysics Data System (ADS)
Husain, Sh. K. Said; Rakhimov, I. S.; Basri, W.
2017-08-01
In this paper we introduce the concept of centroid and derivation of Leibniz algebras. By using the classification results of Leibniz algebras obtained earlier, we describe the centroids and derivations of low-dimensional Leibniz algebras. We also study some properties of centroids of Leibniz algebras and use these properties to categorize the algebras to have so-called small centroids. The description of the derivations enables us to specify an important subclass of Leibniz algebras called characteristically nilpotent.
The Algebra of Lexical Semantics
NASA Astrophysics Data System (ADS)
Kornai, András
The current generative theory of the lexicon relies primarily on tools from formal language theory and mathematical logic. Here we describe how a different formal apparatus, taken from algebra and automata theory, resolves many of the known problems with the generative lexicon. We develop a finite state theory of word meaning based on machines in the sense of Eilenberg [11], a formalism capable of describing discrepancies between syntactic type (lexical category) and semantic type (number of arguments). This mechanism is compared both to the standard linguistic approaches and to the formalisms developed in AI/KR.
Automated Angular Momentum Recoupling Algebra
NASA Astrophysics Data System (ADS)
Williams, H. T.; Silbar, Richard R.
1992-04-01
We present a set of heuristic rules for algebraic solution of angular momentum recoupling problems. The general problem reduces to that of finding an optimal path from one binary tree (representing the angular momentum coupling scheme for the reduced matrix element) to another (representing the sub-integrals and spin sums to be done). The method lends itself to implementation on a microcomputer, and we have developed such an implementation using a dialect of LISP. We describe both how our code, called RACAH, works and how it appears to the user. We illustrate the use of RACAH for several transition and scattering amplitude matrix elements occurring in atomic, nuclear, and particle physics.
Strengthening Effect Algebras in a Logical Perspective: Heyting-Wajsberg Algebras
NASA Astrophysics Data System (ADS)
Konig, Martinvaldo
2014-10-01
Heyting effect algebras are lattice-ordered pseudoboolean effect algebras endowed with a pseudocomplementation that maps on the center (i.e. Boolean elements). They are the algebraic counterpart of an extension of both Łukasiewicz many-valued logic and intuitionistic logic. We show that Heyting effect algebras are termwise equivalent to Heyting-Wajsberg algebras where the two different logical implications are defined as primitive operators. We prove this logic to be decidable, to be strongly complete and to have the deduction-detachment theorem.
Automorphisms and Derivations of the Insertion-Elimination Algebra and Related Graded Lie Algebras
NASA Astrophysics Data System (ADS)
Ondrus, Matthew; Wiesner, Emilie
2016-07-01
This paper addresses several structural aspects of the insertion-elimination algebra {mathfrak{g}}, a Lie algebra that can be realized in terms of tree-inserting and tree-eliminating operations on the set of rooted trees. In particular, we determine the finite-dimensional subalgebras of {mathfrak{g}}, the automorphism group of {mathfrak{g}}, the derivation Lie algebra of {mathfrak{g}}, and a generating set. Several results are stated in terms of Lie algebras admitting a triangular decomposition and can be used to reproduce results for the generalized Virasoro algebras.
Non-relativistic Bondi–Metzner–Sachs algebra
NASA Astrophysics Data System (ADS)
Batlle, Carles; Delmastro, Diego; Gomis, Joaquim
2017-09-01
We construct two possible candidates for non-relativistic bms4 algebra in four space-time dimensions by contracting the original relativistic bms4 algebra. bms4 algebra is infinite-dimensional and it contains the generators of the Poincaré algebra, together with the so-called super-translations. Similarly, the proposed nrbms4 algebras can be regarded as two infinite-dimensional extensions of the Bargmann algebra. We also study a canonical realization of one of these algebras in terms of the Fourier modes of a free Schrödinger field, mimicking the canonical realization of relativistic bms4 algebra using a free Klein–Gordon field.
Global Geometric Deformations of Current Algebras as Krichever-Novikov Type Algebras
NASA Astrophysics Data System (ADS)
Fialowski, Alice; Schlichenmaier, Martin
2005-12-01
We construct algebraic-geometric families of genus one (i.e. elliptic) current and affine Lie algebras of Krichever-Novikov type. These families deform the classical current, respectively affine Kac-Moody Lie algebras. The construction is induced by the geometric process of degenerating the elliptic curve to singular cubics. If the finite-dimensional Lie algebra defining the infinite dimensional current algebra is simple then, even if restricted to local families, the constructed families are non-equivalent to the trivial family. In particular, we show that the current algebra is geometrically not rigid, despite its formal rigidity. This shows that in the infinite dimensional Lie algebra case the relations between geometric deformations, formal deformations and Lie algebra two-cohomology are not that close as in the finite-dimensional case. The constructed families are e.g. of relevance in the global operator approach to the Wess-Zumino-Witten-Novikov models appearing in the quantization of Conformal Field Theory. The algebras are explicitly given by generators and structure equations and yield new examples of infinite dimensional algebras of current and affine Lie algebra type.
Deriving the Regression Line with Algebra
ERIC Educational Resources Information Center
Quintanilla, John A.
2017-01-01
Exploration with spreadsheets and reliance on previous skills can lead students to determine the line of best fit. To perform linear regression on a set of data, students in Algebra 2 (or, in principle, Algebra 1) do not have to settle for using the mysterious "black box" of their graphing calculators (or other classroom technologies).…
Algebraic Thinking: A Problem Solving Approach
ERIC Educational Resources Information Center
Windsor, Will
2010-01-01
Algebraic thinking is a crucial and fundamental element of mathematical thinking and reasoning. It initially involves recognising patterns and general mathematical relationships among numbers, objects and geometric shapes. This paper will highlight how the ability to think algebraically might support a deeper and more useful knowledge, not only of…
Learning from Student Approaches to Algebraic Proofs
ERIC Educational Resources Information Center
D'Ambrosio, Beatriz S.; Kastberg, Signe E.; Viola dos Santos, Joao Ricardo
2010-01-01
Many mathematics teachers struggle to support their students' developing understanding of proof as an essential element in investigations of mathematics. The area of mathematics where the development of an understanding of proof is most challenging is algebra. In the case of algebraic proof, analysis of student written work on tasks that demand…
Post-Lie Algebras and Isospectral Flows
NASA Astrophysics Data System (ADS)
Ebrahimi-Fard, Kurusch; Lundervold, Alexander; Mencattini, Igor; Munthe-Kaas, Hans Z.
2015-11-01
In this paper we explore the Lie enveloping algebra of a post-Lie algebra derived from a classical R-matrix. An explicit exponential solution of the corresponding Lie bracket flow is presented. It is based on the solution of a post-Lie Magnus-type differential equation.
Success in Algebra among Community College Students
ERIC Educational Resources Information Center
Reyes, Czarina
2010-01-01
College algebra is a required course for most majors, but is viewed by many as a gatekeeper course for degree completion by students. With almost half a million students taking college algebra each year, faculty are experimenting with new course lengths of time that might result in higher success, completion, and retention rates for college…
2-Supernilpotent Mal'cev algebras.
Mudrinski, Nebojša
In this note we prove that a Mal'cev algebra is 2-supernilpotent ([1, 1, 1] = 0) if and only if it is polynomially equivalent to a special expanded group. This generalizes Gumm's result that a Mal'cev algebra is abelian if and only if it is polynomially equivalent to a module over a ring.
Calif. Laws Shift Gears on Algebra, Textbooks
ERIC Educational Resources Information Center
Robelen, Erik W.
2012-01-01
New laws in California have set the state on a course for some potentially significant changes to the curriculum, including a measure that revisits the matter of teaching Algebra 1 in 8th grade and another that revamps the state's textbook-adoption process and hands districts greater leeway in choosing instructional materials. The algebra-related…
Algebraic Formulas for Areas between Curves.
ERIC Educational Resources Information Center
Gabai, Hyman
1982-01-01
Korean secondary school students preparing for college learn about a simple algebraic formula for area bounded by a parabola and line. The approach does not seem well-known among American students. It is noted that, while the formula derivations rely on integration, algebra students could use the formulas without proofs. (MP)
Some Applications of Algebraic System Solving
ERIC Educational Resources Information Center
Roanes-Lozano, Eugenio
2011-01-01
Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact…
Algebraic Thinking through Koch Snowflake Constructions
ERIC Educational Resources Information Center
Ghosh, Jonaki B.
2016-01-01
Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both…
Practicing Algebraic Skills: A Conceptual Approach
ERIC Educational Resources Information Center
Friedlander, Alex; Arcavi, Abraham
2012-01-01
Traditionally, a considerable part of teaching and learning algebra has focused on routine practice and the application of rules, procedures, and techniques. Although today's computerized environments may have decreased the need to master algebraic skills, procedural competence is still a central component in any mathematical activity. However,…
Some Applications of Algebraic System Solving
ERIC Educational Resources Information Center
Roanes-Lozano, Eugenio
2011-01-01
Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact…
Success in Algebra among Community College Students
ERIC Educational Resources Information Center
Reyes, Czarina
2010-01-01
College algebra is a required course for most majors, but is viewed by many as a gatekeeper course for degree completion by students. With almost half a million students taking college algebra each year, faculty are experimenting with new course lengths of time that might result in higher success, completion, and retention rates for college…
Deforming the Maxwell-Sim algebra
Gibbons, G. W.; Gomis, Joaquim; Pope, C. N.
2010-09-15
The Maxwell algebra is a noncentral extension of the Poincare algebra, in which the momentum generators no longer commute, but satisfy [P{sub {mu}},P{sub {nu}}]=Z{sub {mu}{nu}}. The charges Z{sub {mu}{nu}} commute with the momenta, and transform tensorially under the action of the angular momentum generators. If one constructs an action for a massive particle, invariant under these symmetries, one finds that it satisfies the equations of motion of a charged particle interacting with a constant electromagnetic field via the Lorentz force. In this paper, we explore the analogous constructions where one starts instead with the ISim subalgebra of Poincare, this being the symmetry algebra of very special relativity. It admits an analogous noncentral extension, and we find that a particle action invariant under this Maxwell-Sim algebra again describes a particle subject to the ordinary Lorentz force. One can also deform the ISim algebra to DISim{sub b}, where b is a nontrivial dimensionless parameter. We find that the motion described by an action invariant under the corresponding Maxwell-DISim algebra is that of a particle interacting via a Finslerian modification of the Lorentz force. In an appendix is it shown that the DISim{sub b} algebra is isomorphic to the extended Schroedinger algebra with its standard deformation parameter z, when b=(1/1-z).
Just Say Yes to Early Algebra!
ERIC Educational Resources Information Center
Stephens, Ana; Blanton, Maria; Knuth, Eric; Isler, Isil; Gardiner, Angela Murphy
2015-01-01
Mathematics educators have argued for some time that elementary school students are capable of engaging in algebraic thinking and should be provided with rich opportunities to do so. Recent initiatives like the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) have taken up this call by reiterating the place of early algebra in…
THE RADICAL OF A JORDAN ALGEBRA
McCrimmon, Kevin
1969-01-01
In this paper we define a Jacobson radical for Jordan algebras analogous to that for associative algebras and show that it enjoys many of the properties of the associative radical. We then relate the corresponding notion of “semisimplicity” to the previously defined notion of “nondegeneracy” (Jacobson, N., these Proceedings, 55, 243-251 (1966)). PMID:16591736
Cartan calculus on quantum Lie algebras
Schupp, P.; Watts, P.; Zumino, B.
1993-12-09
A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum spaces we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions au into one big algebra, the ``Cartan Calculus.``
An algebraic approach to the scattering equations
NASA Astrophysics Data System (ADS)
Huang, Rijun; Rao, Junjie; Feng, Bo; He, Yang-Hui
2015-12-01
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.
SAYD Modules over Lie-Hopf Algebras
NASA Astrophysics Data System (ADS)
Rangipour, Bahram; Sütlü, Serkan
2012-11-01
In this paper a general van Est type isomorphism is proved. The isomorphism is between the Lie algebra cohomology of a bicrossed sum Lie algebra and the Hopf cyclic cohomology of its Hopf algebra. We first prove a one to one correspondence between stable-anti-Yetter-Drinfeld (SAYD) modules over the total Lie algebra and those modules over the associated Hopf algebra. In contrast to the non-general case done in our previous work, here the van Est isomorphism is proved at the first level of a natural spectral sequence, rather than at the level of complexes. It is proved that the Connes-Moscovici Hopf algebras do not admit any finite dimensional SAYD modules except the unique one-dimensional one found by Connes-Moscovici in 1998. This is done by extending our techniques to work with the infinite dimensional Lie algebra of formal vector fields. At the end, the one to one correspondence is applied to construct a highly nontrivial four dimensional SAYD module over the Schwarzian Hopf algebra. We then illustrate the whole theory on this example. Finally explicit representative cocycles of the cohomology classes for this example are calculated.
Parabolas: Connection between Algebraic and Geometrical Representations
ERIC Educational Resources Information Center
Shriki, Atara
2011-01-01
A parabola is an interesting curve. What makes it interesting at the secondary school level is the fact that this curve is presented in both its contexts: algebraic and geometric. Being one of Apollonius' conic sections, the parabola is basically a geometric entity. It is, however, typically known for its algebraic characteristics, in particular…
Algebraic Formulas for Areas between Curves.
ERIC Educational Resources Information Center
Gabai, Hyman
1982-01-01
Korean secondary school students preparing for college learn about a simple algebraic formula for area bounded by a parabola and line. The approach does not seem well-known among American students. It is noted that, while the formula derivations rely on integration, algebra students could use the formulas without proofs. (MP)
From operator algebras to superconformal field theory
Kawahigashi, Yasuyuki
2010-01-15
We survey operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex operator algebras and Moonshine, connections to subfactor theory of Jones, and certain aspects of noncommutative geometry of Connes.
Focus on Fractions to Scaffold Algebra
ERIC Educational Resources Information Center
Ooten, Cheryl Thomas
2013-01-01
Beginning algebra is a gatekeeper course into the pipeline to higher mathematics courses required for respected professions in engineering, science, statistics, mathematics, education, and technology. Beginning algebra can also be a perfect storm if the necessary foundational skills are not within a student's grasp. What skills ensure beginning…