The Orion complex

International Nuclear Information System (INIS)

Goudis, C.

1982-01-01

This work deals with some of the most typical complexes of interstellar matter and presents a holistic view of the well studied complexes in Orion, built on information derived from various branches of modern astrophysics. A wealth of published data is presented in the form of photographs, contour maps, diagrams and numerous heavily annotated tables. Chapter 1, which is concerned with the large scale view of the Orion region, outlines the morphology of the area and examines in particular the nature of Barnard's Loop and the associated filamentary structure in addition to the origin of the I Orion OB association. Chapter 2 focuses on the Great Orion Nebula (M42 or NGC 1976) and the small H II region to the north (M43 or NGC 1982). Chapter 3 examines the Orion Complex as a whole, i.e. the H II regions M42 and M43, the associated molecular clouds OMC 1 and OMC 2 and their interrelations. Chapter 4 contains a discussion of the empirical models introduced to attempt to explain certain aspects of this very complex region, and chapter 5 investigates the second prominent H II region and molecular cloud complex, NGC 2024 (Orion B, W12). (Auth.)

Evolution of Orion Mission Design for Exploration Mission 1 and 2

Science.gov (United States)

Gutkowski, Jeffrey P.; Dawn, Timothy F.; Jedrey, Richard M.

2016-01-01

The evolving mission design and concepts of NASA’s next steps have shaped Orion into the spacecraft that it is today. Since the initial inception of Orion, through the Constellation Program, and now in the Exploration Mission frame-work with the Space Launch System (SLS), each mission design concept and pro-gram goal have left Orion with a set of capabilities that can be utilized in many different mission types. Exploration Missions 1 and 2 (EM-1 and EM-2) have now been at the forefront of the mission design focus for the last several years. During that time, different Design Reference Missions (DRMs) were built, analyzed, and modified to solve or mitigate enterprise level design trades to ensure a viable mission from launch to landing. The resulting DRMs for EM-1 and EM-2 were then expanded into multi-year trajectory scans to characterize vehicle performance as affected by variations in Earth-Moon geometry. This provides Orion’s subsystems with stressing reference trajectories to help design their system. Now that Orion has progressed through the Preliminary and Critical Design Reviews (PDR and CDR), there is a general shift in the focus of mission design from aiding the vehicle design to providing mission specific products needed for pre-flight and real time operations. Some of the mission specific products needed include, large quantities of nominal trajectories for multiple monthly launch periods and abort options at any point in the mission for each valid trajectory in the launch window.

Orion: Design of a system for assured low-cost human access to space

Science.gov (United States)

Elvander, Josh; Heifetz, Andy; Hunt, Teresa; Zhu, Martin

1994-01-01

In recent years, Congress and the American people have begun to seriously question the role and importance of future manned spaceflight. This is mainly due to two factors: a decline in technical competition caused by the collapse of communism, and the high costs associated with the Space Shuttle transportation system. With these factors in mind, the ORION system was designed to enable manned spaceflight at a low cost, while maintaining the ability to carry out diverse missions, each with a high degree of flexibility. It is capable of performing satellite servicing missions, supporting a space station via crew rotation and resupply, and delivering satellites into geosynchronous orbit. The components of the system are a primary launch module, an upper stage, and a manned spacecraft capable of dynamic reentry. For satellite servicing and space station resupply missions, the ORION system utilizes three primary modules, an upper stage, and the spacecraft, which is delivered to low earth orbit and used to rendezvous, transfer materials, and make repairs. For launching a geosynchronous satellite, one primary module and an upper stage are used to deliver the satellite, along with an apogee kick motor, into orbit. The system is designed with reusability and modularity in mind in an attempt to lower cost.

VISION - Vienna survey in Orion. I. VISTA Orion A Survey

Science.gov (United States)

Meingast, Stefan; Alves, João; Mardones, Diego; Teixeira, Paula Stella; Lombardi, Marco; Großschedl, Josefa; Ascenso, Joana; Bouy, Herve; Forbrich, Jan; Goodman, Alyssa; Hacar, Alvaro; Hasenberger, Birgit; Kainulainen, Jouni; Kubiak, Karolina; Lada, Charles; Lada, Elizabeth; Moitinho, André; Petr-Gotzens, Monika; Rodrigues, Lara; Román-Zúñiga, Carlos G.

2016-03-01

Context. Orion A hosts the nearest massive star factory, thus offering a unique opportunity to resolve the processes connected with the formation of both low- and high-mass stars. Here we present the most detailed and sensitive near-infrared (NIR) observations of the entire molecular cloud to date. Aims: With the unique combination of high image quality, survey coverage, and sensitivity, our NIR survey of Orion A aims at establishing a solid empirical foundation for further studies of this important cloud. In this first paper we present the observations, data reduction, and source catalog generation. To demonstrate the data quality, we present a first application of our catalog to estimate the number of stars currently forming inside Orion A and to verify the existence of a more evolved young foreground population. Methods: We used the European Southern Observatory's (ESO) Visible and Infrared Survey Telescope for Astronomy (VISTA) to survey the entire Orion A molecular cloud in the NIR J,H, and KS bands, covering a total of ~18.3 deg2. We implemented all data reduction recipes independently of the ESO pipeline. Estimates of the young populations toward Orion A are derived via the KS-band luminosity function. Results: Our catalog (799 995 sources) increases the source counts compared to the Two Micron All Sky Survey by about an order of magnitude. The 90% completeness limits are 20.4, 19.9, and 19.0 mag in J,H, and KS, respectively. The reduced images have 20% better resolution on average compared to pipeline products. We find between 2300 and 3000 embedded objects in Orion A and confirm that there is an extended foreground population above the Galactic field, in agreement with previous work. Conclusions: The Orion A VISTA catalog represents the most detailed NIR view of the nearest massive star-forming region and provides a fundamental basis for future studies of star formation processes toward Orion. Based on observations made with ESO Telescopes at the La Silla

Simple Sensitivity Analysis for Orion GNC

Science.gov (United States)

Pressburger, Tom; Hoelscher, Brian; Martin, Rodney; Sricharan, Kumar

2013-01-01

The performance of Orion flight software, especially its GNC software, is being analyzed by running Monte Carlo simulations of Orion spacecraft flights. The simulated performance is analyzed for conformance with flight requirements, expressed as performance constraints. Flight requirements include guidance (e.g. touchdown distance from target) and control (e.g., control saturation) as well as performance (e.g., heat load constraints). The Monte Carlo simulations disperse hundreds of simulation input variables, for everything from mass properties to date of launch.We describe in this paper a sensitivity analysis tool (Critical Factors Tool or CFT) developed to find the input variables or pairs of variables which by themselves significantly influence satisfaction of requirements or significantly affect key performance metrics (e.g., touchdown distance from target). Knowing these factors can inform robustness analysis, can inform where engineering resources are most needed, and could even affect operations. The contributions of this paper include the introduction of novel sensitivity measures, such as estimating success probability, and a technique for determining whether pairs of factors are interacting dependently or independently. The tool found that input variables such as moments, mass, thrust dispersions, and date of launch were found to be significant factors for success of various requirements. Examples are shown in this paper as well as a summary and physics discussion of EFT-1 driving factors that the tool found.

Spacecraft Charging Considerations and Design Efforts for the Orion Crew Module

Science.gov (United States)

Scully, Bob

2017-01-01

The Orion Crew Module (CM) is nearing completion for the next flight, designated as Exploration Mission 1 (EM-1). For the uncrewed mission, the flight path will take the CM through a Perigee Raise Maneuver (PRM) out to an altitude of approximately 1800 km, followed by a Trans-Lunar Injection burn, a pass through the Van Allen belts then out to the moon for a lunar flyby, a Distant Retrograde Insertion (DRI) burn, a Distant Retrograde Orbit (DRO), a Distant Retrograde Departure (DRD) burn, a second lunar flyby, an Earth Insertion (EI) burn, and finally entry and landing. All of this, with the exception of the DRO associated maneuvers, is similar to the previous Apollo 8 mission in late 1968. In recent discussions, it is now possible that EM-1 will be a crewed mission, and if this happens, the orbit may be quite different from that just described. In this case, the flight path may take the CM on an out and back pass through the Van Allen belts twice, then out to the moon, again passing through the Van Allen belts twice, then finally back home. Even if the current EM-1 mission doesn't end up as a crewed mission, EM-2 and subsequent missions will undoubtedly follow orbital trajectories that offer comparable exposures to heightened vehicle charging effects. Because of this, and regardless of flight path, the CM vehicle will likely experience a wide range of exposures to energetic ions and electrons, essentially covering the gamut between low earth orbit to geosynchronous orbit and beyond. National Aeronautical and Space Administration (NASA) and Lockheed Martin (LM) engineers and scientists have been working to fully understand and characterize the vehicle's immunity level with regard to surface and deep dielectric charging, and the ramifications of that immunity level pertaining to materials and impacts to operational avionics, communications, and navigational systems. This presentation attempts to chronicle these efforts in a summary fashion, and attempts to capture

NASA Alternative Orion Small Cell Battery Design Support

Science.gov (United States)

Haynes, Chuck

2016-01-01

The NASA Orion Crew Module Reference Design was produced to address large scale thermal runaway (TR) hazard with specific safety controls for the Orion Spacecraft. The design presented provides the description of a full scale battery design reference for implementation as a drop in replacement to meet all spacecraft energy requirements with compatible 120 Vdc electrical and mechanical interface using small cell technology (18650) packaging. The 32V SuperBrick incorporates unique support features and an electrical bus bar arrangement that allows cells negative can insertion into heat sink that is compressively coupled to the battery enclosure to promote good thermal management. The housing design also provides an internal flame suppression "filter tray" and positive venting path internal to the enclosure to allow hot effluent ejecta to escape in the event of single cell TR. Virtual cells (14P Banks) that are supported to provide cell spacing with interstitial materials to prevent side can failures that can produce cell to cell TR propagation. These features were successfully test in four separate TR run with the full scale DTA1 test article in February 2016. Successfully Completed Test Objectives - Four separate TR test runs with Full-Scale DTA1 housing with Two SuperBricks, Two SuperBrick Emulators All Tests resulted in "clean" gas with less than 6 C rise at Battery vent All Tests resulted in less than 2 C temperature rise on cold-plate outlet All Tests resulted in less than 6 psi pressure rise in the battery housing Test Run 1 -One neighbor cell TR, highest remaining neighbor 139 C. Ejecta shorted to bus caused prolonged additional heating, One shorted cell did experience TR after 12 minutes, remaining cells had adequate thermal margin Test Run 2 - No cell to cell propagation, highest neighbor cell 112 C; Test Run 3 - No cell to cell propagation, highest neighbor cell 96 C; Test Run 4 - No cell to cell propagation, highest neighbor cell 101 C; Primary TR testing

Automation Interfaces of the Orion GNC Executive Architecture

Science.gov (United States)

Hart, Jeremy

2009-01-01

This viewgraph presentation describes Orion mission's automation Guidance, Navigation and Control (GNC) architecture and interfaces. The contents include: 1) Orion Background; 2) Shuttle/Orion Automation Comparison; 3) Orion Mission Sequencing; 4) Orion Mission Sequencing Display Concept; and 5) Status and Forward Plans.

Archives: ORiON

African Journals Online (AJOL)

Items 1 - 27 of 27 ... Archives: ORiON. Journal Home > Archives: ORiON. Log in or Register to get access to full text downloads. Username, Password, Remember me, or Register · Journal Home · ABOUT THIS JOURNAL · Advanced Search · Current Issue · Archives. 1 - 27 of 27 Items. 2017. Vol 33, No 2 (2017) · Vol 33, No 1 ...

Orion Absolute Navigation System Progress and Challenges

Science.gov (United States)

Holt, Greg N.; D'Souza, Christopher

2011-01-01

The Orion spacecraft is being designed as NASA's next-generation exploration vehicle for crewed missions beyond Low-Earth Orbit. The navigation system for the Orion spacecraft is being designed in a Multi-Organizational Design Environment (MODE) team including contractor and NASA personnel. The system uses an Extended Kalman Filter to process measurements and determine the state. The design of the navigation system has undergone several iterations and modifications since its inception, and continues as a work-in-progress. This paper seeks to benchmark the current state of the design and some of the rationale and analysis behind it. There are specific challenges to address when preparing a timely and effective design for the Exploration Flight Test (EFT-1), while still looking ahead and providing software extensibility for future exploration missions. The primary measurements in a Near-Earth or Mid-Earth environment consist of GPS pseudorange and deltarange, but for future explorations missions the use of star-tracker and optical navigation sources need to be considered. Discussions are presented for state size and composition, processing techniques, and consider states. A presentation is given for the processing technique using the computationally stable and robust UDU formulation with an Agee-Turner Rank-One update. This allows for computational savings when dealing with many parameters which are modeled as slowly varying Gauss-Markov processes. Preliminary analysis shows up to a 50% reduction in computation versus a more traditional formulation. Several state elements are discussed and evaluated, including position, velocity, attitude, clock bias/drift, and GPS measurement biases in addition to bias, scale factor, misalignment, and non-orthogonalities of the accelerometers and gyroscopes. Another consideration is the initialization of the EKF in various scenarios. Scenarios such as single-event upset, ground command, pad alignment, cold start are discussed as are

75 FR 66728 - Action Affecting Export Privileges; Orion Air, S.L. and Syrian Pearl Airlines: Orion Air, S.L...

Science.gov (United States)

2010-10-29

... DEPARTMENT OF COMMERCE Bureau of Industry and Security Action Affecting Export Privileges; Orion Air, S.L. and Syrian Pearl Airlines: Orion Air, S.L., Canada Real de Merinas, 7 Edificio 5, 3'A... Denying the Export Privileges of Respondents Orion Air, S.L. (``Orion Air'') and Syrian Pearl Airlines...

ORION laser target diagnostics

International Nuclear Information System (INIS)

Bentley, C. D.; Edwards, R. D.; Andrew, J. E.; James, S. F.; Gardner, M. D.; Comley, A. J.; Vaughan, K.; Horsfield, C. J.; Rubery, M. S.; Rothman, S. D.; Daykin, S.; Masoero, S. J.; Palmer, J. B.; Meadowcroft, A. L.; Williams, B. M.; Gumbrell, E. T.; Fyrth, J. D.; Brown, C. R. D.; Hill, M. P.; Oades, K.

2012-01-01

The ORION laser facility is one of the UK's premier laser facilities which became operational at AWE in 2010. Its primary mission is one of stockpile stewardship, ORION will extend the UK's experimental plasma physics capability to the high temperature, high density regime relevant to Atomic Weapons Establishment's (AWE) program. The ORION laser combines ten laser beams operating in the ns regime with two sub ps short pulse chirped pulse amplification beams. This gives the UK a unique combined long pulse/short pulse laser capability which is not only available to AWE personnel but also gives access to our international partners and visiting UK academia. The ORION laser facility is equipped with a comprehensive suite of some 45 diagnostics covering optical, particle, and x-ray diagnostics all able to image the laser target interaction point. This paper focuses on a small selection of these diagnostics.

ORION laser target diagnostics.

Science.gov (United States)

Bentley, C D; Edwards, R D; Andrew, J E; James, S F; Gardner, M D; Comley, A J; Vaughan, K; Horsfield, C J; Rubery, M S; Rothman, S D; Daykin, S; Masoero, S J; Palmer, J B; Meadowcroft, A L; Williams, B M; Gumbrell, E T; Fyrth, J D; Brown, C R D; Hill, M P; Oades, K; Wright, M J; Hood, B A; Kemshall, P

2012-10-01

The ORION laser facility is one of the UK's premier laser facilities which became operational at AWE in 2010. Its primary mission is one of stockpile stewardship, ORION will extend the UK's experimental plasma physics capability to the high temperature, high density regime relevant to Atomic Weapons Establishment's (AWE) program. The ORION laser combines ten laser beams operating in the ns regime with two sub ps short pulse chirped pulse amplification beams. This gives the UK a unique combined long pulse/short pulse laser capability which is not only available to AWE personnel but also gives access to our international partners and visiting UK academia. The ORION laser facility is equipped with a comprehensive suite of some 45 diagnostics covering optical, particle, and x-ray diagnostics all able to image the laser target interaction point. This paper focuses on a small selection of these diagnostics.

Orion Optical Navigation Progress Toward Exploration Mission 1

Science.gov (United States)

Holt, Greg N.; D'Souza, Christopher N.; Saley, David

2018-01-01

Optical navigation of human spacecraft was proposed on Gemini and implemented successfully on Apollo as a means of autonomously operating the vehicle in the event of lost communication with controllers on Earth. The Orion emergency return system utilizing optical navigation has matured in design over the last several years, and is currently undergoing the final implementation and test phase in preparation for Exploration Mission 1 (EM-1) in 2019. The software development is past its Critical Design Review, and is progressing through test and certification for human rating. The filter architecture uses a square-root-free UDU covariance factorization. Linear Covariance Analysis (LinCov) was used to analyze the measurement models and the measurement error models on a representative EM-1 trajectory. The Orion EM-1 flight camera was calibrated at the Johnson Space Center (JSC) electro-optics lab. To permanently stake the focal length of the camera a 500 mm focal length refractive collimator was used. Two Engineering Design Unit (EDU) cameras and an EDU star tracker were used for a live-sky test in Denver. In-space imagery with high-fidelity truth metadata is rare so these live-sky tests provide one of the closest real-world analogs to operational use. A hardware-in-the-loop test rig was developed in the Johnson Space Center Electro-Optics Lab to exercise the OpNav system prior to integrated testing on the Orion vehicle. The software is verified with synthetic images. Several hundred off-nominal images are also used to analyze robustness and fault detection in the software. These include effects such as stray light, excess radiation damage, and specular reflections, and are used to help verify the tuning parameters chosen for the algorithms such as earth atmosphere bias, minimum pixel intensity, and star detection thresholds.

ORiON: Journal Sponsorship

African Journals Online (AJOL)

ORiON: Journal Sponsorship. Journal Home > About the Journal > ORiON: Journal Sponsorship. Log in or Register to get access to full text downloads. Username, Password, Remember me, or Register · Journal Home · ABOUT THIS JOURNAL · Advanced Search · Current Issue · Archives. Publisher. ORSSA. Sponsors.

Configuring the Orion Guidance, Navigation, and Control Flight Software for Automated Sequencing

Science.gov (United States)

Odegard, Ryan G.; Siliwinski, Tomasz K.; King, Ellis T.; Hart, Jeremy J.

2010-01-01

The Orion Crew Exploration Vehicle is being designed with greater automation capabilities than any other crewed spacecraft in NASA s history. The Guidance, Navigation, and Control (GN&C) flight software architecture is designed to provide a flexible and evolvable framework that accommodates increasing levels of automation over time. Within the GN&C flight software, a data-driven approach is used to configure software. This approach allows data reconfiguration and updates to automated sequences without requiring recompilation of the software. Because of the great dependency of the automation and the flight software on the configuration data, the data management is a vital component of the processes for software certification, mission design, and flight operations. To enable the automated sequencing and data configuration of the GN&C subsystem on Orion, a desktop database configuration tool has been developed. The database tool allows the specification of the GN&C activity sequences, the automated transitions in the software, and the corresponding parameter reconfigurations. These aspects of the GN&C automation on Orion are all coordinated via data management, and the database tool provides the ability to test the automation capabilities during the development of the GN&C software. In addition to providing the infrastructure to manage the GN&C automation, the database tool has been designed with capabilities to import and export artifacts for simulation analysis and documentation purposes. Furthermore, the database configuration tool, currently used to manage simulation data, is envisioned to evolve into a mission planning tool for generating and testing GN&C software sequences and configurations. A key enabler of the GN&C automation design, the database tool allows both the creation and maintenance of the data artifacts, as well as serving the critical role of helping to manage, visualize, and understand the data-driven parameters both during software development

Innovative Approach for Developing Spacecraft Interior Acoustic Requirement Allocation

Science.gov (United States)

Chu, S. Reynold; Dandaroy, Indranil; Allen, Christopher S.

2016-01-01

The Orion Multi-Purpose Crew Vehicle (MPCV) is an American spacecraft for carrying four astronauts during deep space missions. This paper describes an innovative application of Power Injection Method (PIM) for allocating Orion cabin continuous noise Sound Pressure Level (SPL) limits to the sound power level (PWL) limits of major noise sources in the Environmental Control and Life Support System (ECLSS) during all mission phases. PIM is simulated using both Statistical Energy Analysis (SEA) and Hybrid Statistical Energy Analysis-Finite Element (SEA-FE) models of the Orion MPCV to obtain the transfer matrix from the PWL of the noise sources to the acoustic energies of the receivers, i.e., the cavities associated with the cabin habitable volume. The goal of the allocation strategy is to control the total energy of cabin habitable volume for maintaining the required SPL limits. Simulations are used to demonstrate that applying the allocated PWLs to the noise sources in the models indeed reproduces the SPL limits in the habitable volume. The effects of Noise Control Treatment (NCT) on allocated noise source PWLs are investigated. The measurement of source PWLs of involved fan and pump development units are also discussed as it is related to some case-specific details of the allocation strategy discussed here.

Assessment of the Use of Nanofluids in Spacecraft Active Thermal Control Systems

Science.gov (United States)

Ungar, Eugene K.; Erickson, Lisa R.

2011-01-01

The addition of metallic nanoparticles to a base heat transfer fluid can dramatically increase its thermal conductivity. These nanofluids have been shown to have advantages in some heat transport systems. Their enhanced properties can allow lower system volumetric flow rates and can reduce the required pumping power. Nanofluids have been suggested for use as working fluids for spacecraft Active Thermal Control Systems (ATCSs). However, there are no studies showing the end-to-end effect of nanofluids on the design and performance of spacecraft ATCSs. In the present work, a parametric study is performed to assess the use of nanofluids in a spacecraft ATCSs. The design parameters of the current Orion capsule and the tabulated thermophysical properties of nanofluids are used to assess the possible benefits of nanofluids and how their incorporation affects the overall design of a spacecraft ATCS. The study shows that the unique system and component-level design parameters of spacecraft ATCSs render them best suited for pure working fluids. The addition of nanoparticles to typical spacecraft thermal control working fluids actually results in an increase in the system mass and required pumping power.

Simple Sensitivity Analysis for Orion Guidance Navigation and Control

Science.gov (United States)

Pressburger, Tom; Hoelscher, Brian; Martin, Rodney; Sricharan, Kumar

2013-01-01

The performance of Orion flight software, especially its GNC software, is being analyzed by running Monte Carlo simulations of Orion spacecraft flights. The simulated performance is analyzed for conformance with flight requirements, expressed as performance constraints. Flight requirements include guidance (e.g. touchdown distance from target) and control (e.g., control saturation) as well as performance (e.g., heat load constraints). The Monte Carlo simulations disperse hundreds of simulation input variables, for everything from mass properties to date of launch. We describe in this paper a sensitivity analysis tool ("Critical Factors Tool" or CFT) developed to find the input variables or pairs of variables which by themselves significantly influence satisfaction of requirements or significantly affect key performance metrics (e.g., touchdown distance from target). Knowing these factors can inform robustness analysis, can inform where engineering resources are most needed, and could even affect operations. The contributions of this paper include the introduction of novel sensitivity measures, such as estimating success probability, and a technique for determining whether pairs of factors are interacting dependently or independently. The tool found that input variables such as moments, mass, thrust dispersions, and date of launch were found to be significant factors for success of various requirements. Examples are shown in this paper as well as a summary and physics discussion of EFT-1 driving factors that the tool found.

Vertex algebras and algebraic curves

CERN Document Server

Frenkel, Edward

2004-01-01

Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book co...

Algebraic partial Boolean algebras

International Nuclear Information System (INIS)

Smith, Derek

2003-01-01

Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial Boolean algebras. First, we describe a restriction on the determinants of the elements of B(T) that are generated by a given set T. We then show that when the generating set T consists of the rays spanning the minimal vectors in a real irreducible root lattice, B(T) is infinite just if that root lattice has an A 5 sublattice. Finally, we characterize the rays of B(T) when T consists of the rays spanning the minimal vectors of the root lattice E 8

System Level Analysis of a Water PCM HX Integrated Into Orion's Thermal Control System Abstract

Science.gov (United States)

Navarro, Moses; Hansen, Scott; Ungar, Eugene; Sheth, Rubik

2015-01-01

In a cyclical heat load environment such as low Lunar orbit, a spacecraft's radiators are not sized to reject the full heat load requirement. Traditionally, a supplemental heat rejection device (SHReD) such as an evaporator or sublimator is used to act as a "topper" to meet the additional heat rejection demands. Utilizing a Phase Change Material (PCM) heat exchanger (HX) as a SHReD provides an attractive alternative to evaporators and sublimators as PCM HXs do not use a consumable, thereby leading to reduced launch mass and volume requirements. In continued pursuit of water PCM HX development an Orion system level analysis was performed using Thermal Desktop for a water PCM HX integrated into Orion's thermal control system and in a 100km Lunar orbit. The study analyzed 1) placing the PCM on the Internal Thermal Control System (ITCS) versus the External Thermal Control System (ETCS) 2) use of 30/70 PGW verses 50/50 PGW and 3) increasing the radiator area in order to reduce PCM freeze times. The analysis showed that for the assumed operating and boundary conditions utilizing a water PCM HX on Orion is not a viable option. Additionally, it was found that the radiator area would have to be increased over 20% in order to have a viable water-based PCM HX.

Chandra Finds X-ray Star Bonanza in the Orion Nebula

Science.gov (United States)

2000-01-01

Penn State; Steven Pravdo at the Jet Propulsion Laboratory; and Lynne Hillenbrand at the California Institute of Technology. NASA's Marshall Space Flight Center in Huntsville, Ala., manages the Chandra program. TRW, Inc., Redondo Beach, CA, is the prime contractor for the spacecraft. The Smithsonian's Chandra X-ray Center controls science and flight operations from Cambridge, MA. Other Press Room:Orion Nebula Press Release (PSU Sep 01) To follow Chandra's progress or download images visit the Chandra sites at http://chandra.harvard.edu/photo/2000/0054/index.html AND http://chandra.nasa.gov

Linear Algebra and Smarandache Linear Algebra

OpenAIRE

Vasantha, Kandasamy

2003-01-01

The present book, on Smarandache linear algebra, not only studies the Smarandache analogues of linear algebra and its applications, it also aims to bridge the need for new research topics pertaining to linear algebra, purely in the algebraic sense. We have introduced Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra and their fuzzy equivalents. Moreover, in this book, we have brought out the study of linear algebra and vector spaces over finite p...

Introduction to vertex algebras, Borcherds algebras and the Monster Lie algebras

International Nuclear Information System (INIS)

Gebert, R.W.

1993-09-01

The theory of vertex algebras constitutes a mathematically rigorous axiomatic formulation of the algebraic origins of conformal field theory. In this context Borcherds algebras arise as certain ''physical'' subspaces of vertex algebras. The aim of this review is to give a pedagogical introduction into this rapidly-developing area of mathematics. Based on the machinery of formal calculus we present the axiomatic definition of vertex algebras. We discuss the connection with conformal field theory by deriving important implications of these axioms. In particular, many explicit calculations are presented to stress the eminent role of the Jacobi identity axiom for vertex algebras. As a class of concrete examples the vertex algebras associated with even lattices are constructed and it is shown in detail how affine Lie algebras and the fake Monster Lie algebra naturally appear. This leads us to the abstract definition of Borcherds algebras as generalized Kac-Moody algebras and their basic properties. Finally, the results about the simplest generic Borcherds algebras are analysed from the point of view of symmetry in quantum theory and the construction of the Monster Lie algebra is sketched. (orig.)

System Level Analysis of a Water PCM HX Integrated into Orion's Thermal Control System

Science.gov (United States)

Navarro, Moses; Hansen, Scott; Seth, Rubik; Ungar, Eugene

2015-01-01

In a cyclical heat load environment such as low Lunar orbit, a spacecraft's radiators are not sized to reject the full heat load requirement. Traditionally, a supplemental heat rejection device (SHReD) such as an evaporator or sublimator is used to act as a "topper" to meet the additional heat rejection demands. Utilizing a Phase Change Material (PCM) heat exchanger (HX) as a SHReD provides an attractive alternative to evaporators and sublimators as PCM HXs do not use a consumable, thereby leading to reduced launch mass and volume requirements. In continued pursuit of water PCM HX development an Orion system level analysis was performed using Thermal Desktop for a water PCM HX integrated into Orion's thermal control system in a 100km Lunar orbit. The study verified of the thermal model by using a wax PCM and analyzed 1) placing the PCM on the Internal Thermal Control System (ITCS) versus the External Thermal Control System (ETCS) 2) use of 30/70 PGW verses 50/50 PGW and 3) increasing the radiator area in order to reduce PCM freeze times. The analysis showed that for the assumed operating and boundary conditions utilizing a water PCM HX on Orion is not a viable option for any case. Additionally, it was found that the radiator area would have to be increased by at least 40% in order to support a viable water-based PCM HX.

Orion Optical Navigation Progress Toward Exploration: Mission 1

Science.gov (United States)

Holt, Greg N.; D'Souza, Christopher N.; Saley, David

2018-01-01

Optical navigation of human spacecraft was proposed on Gemini and implemented successfully on Apollo as a means of autonomously operating the vehicle in the event of lost communication with controllers on Earth. It shares a history with the "method of lunar distances" that was used in the 18th century and gained some notoriety after its use by Captain James Cook during his 1768 Pacific voyage of the HMS Endeavor. The Orion emergency return system utilizing optical navigation has matured in design over the last several years, and is currently undergoing the final implementation and test phase in preparation for Exploration Mission 1 (EM-1) in 2019. The software development is being worked as a Government Furnished Equipment (GFE) project delivered as an application within the Core Flight Software of the Orion camera controller module. The mathematical formulation behind the initial ellipse fit in the image processing is detailed in Christian. The non-linear least squares refinement then follows the technique of Mortari as an estimation process of the planetary limb using the sigmoid function. The Orion optical navigation system uses a body fixed camera, a decision that was driven by mass and mechanism constraints. The general concept of operations involves a 2-hour pass once every 24 hours, with passes specifically placed before all maneuvers to supply accurate navigation information to guidance and targeting. The pass lengths are limited by thermal constraints on the vehicle since the OpNav attitude generally deviates from the thermally stable tail-to-sun attitude maintained during the rest of the orbit coast phase. Calibration is scheduled prior to every pass due to the unknown nature of thermal effects on the lens distortion and the mounting platform deformations between the camera and star trackers. The calibration technique is described in detail by Christian, et al. and simultaneously estimates the Brown-Conrady coefficients and the Star Tracker

ORiON

African Journals Online (AJOL)

ORSSA) and is published biannually. Papers in the following categories are typically published in ORiON: • Development of New Theory, which may be useful to Operations Research practitioners, or which may lead to the introduction of new ...

Quantum W-algebras and elliptic algebras

International Nuclear Information System (INIS)

Feigin, B.; Kyoto Univ.; Frenkel, E.

1996-01-01

We define a quantum W-algebra associated to sl N as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary W-algebra of sl N , or the q-deformed classical W-algebra of sl N . We construct free field realizations of the quantum W-algebras and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in U q (n). (orig.)

Orion A helium abundance

International Nuclear Information System (INIS)

Tsivilev, A.P.; Ershov, A.A.; Smirnov, G.T.; Sorochenko, R.L.

1986-01-01

The 22.4-GHz (H,He)66-alpha and 36.5-GHz (H,He)56-alpha radio recombination lines have been observed at several Jaffe-Pankonin positions in the central part of the Orion A source. The measured relative abundance of ionized helium increases with distance, averaging 11.6 percent at peripheral points. The observed behavior is interpreted by a blister-type model nebula, which implies that Orion A has a true He abundance of 12 percent, is moving with a radial velocity of 5 km/sec, and is expanding. 18 references

Recoupling Lie algebra and universal ω-algebra

International Nuclear Information System (INIS)

Joyce, William P.

2004-01-01

We formulate the algebraic version of recoupling theory suitable for commutation quantization over any gradation. This gives a generalization of graded Lie algebra. Underlying this is the new notion of an ω-algebra defined in this paper. ω-algebra is a generalization of algebra that goes beyond nonassociativity. We construct the universal enveloping ω-algebra of recoupling Lie algebras and prove a generalized Poincare-Birkhoff-Witt theorem. As an example we consider the algebras over an arbitrary recoupling of Z n graded Heisenberg Lie algebra. Finally we uncover the usual coalgebra structure of a universal envelope and substantiate its Hopf structure

Differential Hopf algebra structures on the universal enveloping algebra ofa Lie algebra

NARCIS (Netherlands)

N.W. van den Hijligenberg; R. Martini

1995-01-01

textabstractWe discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-Birkhoff-Witt-type on the universal enveloping algebra of a Lie algebra $g$. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra

The ORION Facility

International Nuclear Information System (INIS)

Noble, Robert

2003-01-01

ORION will be a user-oriented research facility for understanding the physics and developing the technology for future high-energy particle accelerators, as well as for research in related fields. The facility has as its centerpiece the Next Linear Collider Test Accelerator (NLCTA) at the Stanford Linear Accelerator Center (SLAC). The NLCTA will be modified with the addition of a new, high-brightness photoinjector, its drive laser, an S-band rf power system, a user laser room, a low-energy experimental hall supplied with electron beams up to 60 MeV in energy, and a high-energy hall supplied with beams up to 350 MeV. The facility design and parameters are described here along with highlights from the 2nd ORION Workshop held in February 2003

The Yoneda algebra of a K2 algebra need not be another K2 algebra

OpenAIRE

Cassidy, T.; Phan, C.; Shelton, B.

2010-01-01

The Yoneda algebra of a Koszul algebra or a D-Koszul algebra is Koszul. K2 algebras are a natural generalization of Koszul algebras, and one would hope that the Yoneda algebra of a K2 algebra would be another K2 algebra. We show that this is not necessarily the case by constructing a monomial K2 algebra for which the corresponding Yoneda algebra is not K2.

The CARMA-NRO Orion Survey

Science.gov (United States)

Kong, Shuo; Arce, Héctor G.; Feddersen, Jesse R.; Carpenter, John M.; Nakamura, Fumitaka; Shimajiri, Yoshito; Isella, Andrea; Ossenkopf-Okada, Volker; Sargent, Anneila I.; Sánchez-Monge, Álvaro; Suri, Sümeyye T.; Kauffmann, Jens; Pillai, Thushara; Pineda, Jaime E.; Koda, Jin; Bally, John; Lis, Dariusz C.; Padoan, Paolo; Klessen, Ralf; Mairs, Steve; Goodman, Alyssa; Goldsmith, Paul; McGehee, Peregrine; Schilke, Peter; Teuben, Peter J.; José Maureira, María; Hara, Chihomi; Ginsburg, Adam; Burkhart, Blakesley; Smith, Rowan J.; Schmiedeke, Anika; Pineda, Jorge L.; Ishii, Shun; Sasaki, Kazushige; Kawabe, Ryohei; Urasawa, Yumiko; Oyamada, Shuri; Tanabe, Yoshihiro

2018-06-01

We present the first results from a new, high-resolution 12CO(1–0), 13CO(1–0), and C18O(1–0) molecular-line survey of the Orion A cloud, hereafter referred to as the CARMA-NRO Orion Survey. CARMA observations have been combined with single-dish data from the Nobeyama 45 m telescope to provide extended images at about 0.01 pc resolution, with a dynamic range of approximately 1200 in spatial scale. Here we describe the practical details of the data combination in uv space, including flux scale matching, the conversion of single-dish data to visibilities, and joint deconvolution of single-dish and interferometric data. A Δ-variance analysis indicates that no artifacts are caused by combining data from the two instruments. Initial analysis of the data cubes, including moment maps, average spectra, channel maps, position–velocity diagrams, excitation temperature, column density, and line ratio maps, provides evidence of complex and interesting structures such as filaments, bipolar outflows, shells, bubbles, and photo-eroded pillars. The implications for star formation processes are profound, and follow-up scientific studies by the CARMA-NRO Orion team are now underway. We plan to make all the data products described here generally accessible; some are already available at https://dataverse.harvard.edu/dataverse/CARMA-NRO-Orion.

Cylindric-like algebras and algebraic logic

CERN Document Server

Ferenczi, Miklós; Németi, István

2013-01-01

Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski’s quest for finding structure in logic leads to cylindric-like algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways:  as an algebraic form of definability theory, as a study of higher-dimensional relations, as an enrichment of Boolean Algebra theory, or, as logic in geometric form (“cylindric” in the name refers to geometric aspects). Cylindric-like algebras have a wide range of applications, in, e.g., natural language theory, data-base theory, stochastics, and even in relativity theory. The present volume, consisting of 18 survey papers, intends to give an overview of the main achievements and new research directions in the past 30 years, since the publication of the Henkin-Monk-Tarski monographs. It is dedicated to the memory of Leon Henkin.

Methande detected in orion A

International Nuclear Information System (INIS)

Fox, K.; Jennings, D.E.; and Infrared and Radio Astronomy Branch, Laboratory for Extraterrestrial Physics, NASA Goddard Space Flight Center)

1978-01-01

Six distinct pure-rotational ΔJ=0 transitions in 1 2CH 4 have been detected in microwave emission from the Orion Molecular Cloud. The spectral frequencies range from 4.6004 to 82.874 GHz, corresponding to J values from 11 to 20, respectively. These spectral lines include all possible tetrahedral symmetry types A, E, and F. The methane transitions observed in Orion A show definite maser characteristics. This is the first observational evidence for methane outside the solar system

Distances, Kinematics, And Structure Of The Orion Complex

Science.gov (United States)

Kounkel, Marina; Hartmann, Lee

2018-01-01

I present an analysis of the structure and kinematics of the Orion Molecular Cloud Complex in an effort to better characterize the dynamical state of the closest region of ongoing massive star formation. I measured stellar parallax and proper motions with Orion Complex. This includes the first direct distance measurements for sources that are located outside of the Orion Nebula. I identified a number of binary systems in the VLBI dataset and fitted their orbital motion, which allows for the direct measurement of the masses of the individual components. Additionally, I have identified several stars that have been ejected from the Orion Nebula due to strong gravitational interactions with the most massive members. I complemented the parallax and proper motion measurements with the observations of optical radial velocities of the stars toward the Orion Complex, probing the histories of both dynamic evolution and star formation in the region, providing a 6-dimensional model of the Complex. These observations can serve as a baseline for comparison of the upcoming results from the Gaia space telescope

Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra

NARCIS (Netherlands)

van den Hijligenberg, N.W.; van den Hijligenberg, N.W.; Martini, Ruud

1995-01-01

We discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-Birkhoff-Witt-type on the universal enveloping algebra of a Lie algebra $g$. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra structure of

Layers in the Central Orion Nebula

Science.gov (United States)

O'Dell, C. R.

2018-04-01

The existence of multiple layers in the inner Orion Nebula has been revealed using data from an Atlas of spectra at 2″ and 12 km s-1 resolution. These data were sometimes grouped over Samples of 10″×10″ to produce high Signal to Noise spectra and sometimes grouped into sequences of pseudo-slit Spectra of 12{^''.}8 - 39″width for high spatial resolution studies. Multiple velocity systems were found: V_{MIF} traces the Main Ionization Front (MIF), V_{scat} arises from back-scattering of V_{MIF} emission by particles in the background Photon Dissociation Region (PDR), V_{low} is an ionized layer in front of the MIF and if it is the source of the stellar absorption lines seen in the Trapezium stars, it must lie between the foreground Veil and those stars, V_{new,[O III]} may represent ionized gas evaporating from the Veil away from the observer. There are features such as the Bright Bar where variations of velocities are due to changing tilts of the MIF, but velocity changes above about 25″ arise from variations in velocity of the background PDR. In a region 25″ ENE of the Orion-S Cloud one finds dramatic changes in the [O III] components, including the signals from the V_{low,[O III]} and V_{MIF,[O III]} becoming equal, indicating shadowing of gas from stellar photons of >24.6 eV. This feature is also seen in areas to the west and south of the Orion-S Cloud.

Chaos at the Heart of Orion

Science.gov (United States)

2006-01-01

NASA's Spitzer and Hubble Space Telescopes have teamed up to expose the chaos that baby stars are creating 1,500 light-years away in a cosmic cloud called the Orion nebula. This striking infrared and visible-light composite indicates that four monstrously massive stars at the center of the cloud may be the main culprits in the familiar Orion constellation. The stars are collectively called the 'Trapezium.' Their community can be identified as the yellow smudge near the center of the image. Swirls of green in Hubble's ultraviolet and visible-light view reveal hydrogen and sulfur gas that have been heated and ionized by intense ultraviolet radiation from the Trapezium's stars. Meanwhile, Spitzer's infrared view exposes carbon-rich molecules called polycyclic aromatic hydrocarbons in the cloud. These organic molecules have been illuminated by the Trapezium's stars, and are shown in the composite as wisps of red and orange. On Earth, polycyclic aromatic hydrocarbons are found on burnt toast and in automobile exhaust. Together, the telescopes expose the stars in Orion as a rainbow of dots sprinkled throughout the image. Orange-yellow dots revealed by Spitzer are actually infant stars deeply embedded in a cocoon of dust and gas. Hubble showed less embedded stars as specks of green, and foreground stars as blue spots. Stellar winds from clusters of newborn stars scattered throughout the cloud etched all of the well-defined ridges and cavities in Orion. The large cavity near the right of the image was most likely carved by winds from the Trapezium's stars. Located 1,500 light-years away from Earth, the Orion nebula is the brightest spot in the sword of the Orion, or the 'Hunter' constellation. The cosmic cloud is also our closest massive star-formation factory, and astronomers believe it contains more than 1,000 young stars. The Orion constellation is a familiar sight in the fall and winter night sky in the northern hemisphere. The nebula is invisible to the unaided eye

Kennedy Space Center Orion Processing Team Planning for Ground Operations

Science.gov (United States)

Letchworth, Gary; Schlierf, Roland

2011-01-01

Topics in this presentation are: Constellation Ares I/Orion/Ground Ops Elements Orion Ground Operations Flow Orion Operations Planning Process and Toolset Overview, including: 1 Orion Concept of Operations by Phase 2 Ops Analysis Capabilities Overview 3 Operations Planning Evolution 4 Functional Flow Block Diagrams 5 Operations Timeline Development 6 Discrete Event Simulation (DES) Modeling 7 Ground Operations Planning Document Database (GOPDb) Using Operations Planning Tools for Operability Improvements includes: 1 Kaizen/Lean Events 2 Mockups 3 Human Factors Analysis

Introduction to relation algebras relation algebras

CERN Document Server

Givant, Steven

2017-01-01

The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic. Upon completing this introduction, mathematics students may delve into areas of active research by progressing to the second volume, Advanced Topics in Relation Algebras; computer scientists, philosophers, and beyond will be equipped to apply these tools in their own field. The careful presentation establishes first the arithmetic of relation algebras, providing ample motivation and examples, then proceeds primarily on the basis of algebraic constructions: subalgebras, homomorphisms, quotient algebras, and direct products. Each chapter ends with a historical section and a substantial number of exercises. The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naïve set theory. The measured pace and outstanding clarity are particularly ...

From Rota-Baxter algebras to pre-Lie algebras

International Nuclear Information System (INIS)

An Huihui; Ba, Chengming

2008-01-01

Rota-Baxter algebras were introduced to solve some analytic and combinatorial problems and have appeared in many fields in mathematics and mathematical physics. Rota-Baxter algebras provide a construction of pre-Lie algebras from associative algebras. In this paper, we give all Rota-Baxter operators of weight 1 on complex associative algebras in dimension ≤3 and their corresponding pre-Lie algebras

Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras

International Nuclear Information System (INIS)

Marquette, Ian

2013-01-01

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

Algebraic approach to time-delay data analysis for LISA

International Nuclear Information System (INIS)

Dhurandhar, S.V.; Nayak, K. Rajesh; Vinet, J.-Y.

2002-01-01

Cancellation of laser frequency noise in interferometers is crucial for attaining the requisite sensitivity of the triangular three-spacecraft LISA configuration. Raw laser noise is several orders of magnitude above the other noises and thus it is essential to bring it down to the level of other noises such as shot, acceleration, etc. Since it is impossible to maintain equal distances between spacecrafts, laser noise cancellation must be achieved by appropriately combining the six beams with appropriate time delays. It has been shown in several recent papers that such combinations are possible. In this paper, we present a rigorous and systematic formalism based on algebraic geometrical methods involving computational commutative algebra, which generates in principle all the data combinations canceling the laser frequency noise. The relevant data combinations form the first module of syzygies, as it is called in the literature of algebraic geometry. The module is over a polynomial ring in three variables, the three variables corresponding to the three time delays around the LISA triangle. Specifically, we list several sets of generators for the module whose linear combinations with polynomial coefficients generate the entire module. We find that this formalism can also be extended in a straightforward way to cancel Doppler shifts due to optical bench motions. The two modules are in fact isomorphic. We use our formalism to obtain the transfer functions for the six beams and for the generators. We specifically investigate monochromatic gravitational wave sources in the LISA band and carry out the maximization over linear combinations of the generators of the signal-to-noise ratios with the frequency and source direction angles as parameters

A Reliability Comparison of Classical and Stochastic Thickness Margin Approaches to Address Material Property Uncertainties for the Orion Heat Shield

Science.gov (United States)

Sepka, Steve; Vander Kam, Jeremy; McGuire, Kathy

2018-01-01

The Orion Thermal Protection System (TPS) margin process uses a root-sum-square approach with branches addressing trajectory, aerothermodynamics, and material response uncertainties in ablator thickness design. The material response branch applies a bond line temperature reduction between the Avcoat ablator and EA9394 adhesive by 60 C (108 F) from its peak allowed value of 260 C (500 F). This process is known as the Bond Line Temperature Material Margin (BTMM) and is intended to cover material property and performance uncertainties. The value of 60 C (108 F) is a constant, applied at any spacecraft body location and for any trajectory. By varying only material properties in a random (monte carlo) manner, the perl-based script mcCHAR is used to investigate the confidence interval provided by the BTMM. In particular, this study will look at various locations on the Orion heat shield forebody for a guided and an abort (ballistic) trajectory.

Yoneda algebras of almost Koszul algebras

Indian Academy of Sciences (India)

Abstract. Let k be an algebraically closed field, A a finite dimensional connected. (p,q)-Koszul self-injective algebra with p, q ≥ 2. In this paper, we prove that the. Yoneda algebra of A is isomorphic to a twisted polynomial algebra A![t; β] in one inde- terminate t of degree q +1 in which A! is the quadratic dual of A, β is an ...

Quantum cluster algebras and quantum nilpotent algebras

Science.gov (United States)

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

An introduction to algebraic geometry and algebraic groups

CERN Document Server

Geck, Meinolf

2003-01-01

An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles.Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type.The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups

THE ORION H ii REGION AND THE ORION BAR IN THE MID-INFRARED

International Nuclear Information System (INIS)

Salgado, F.; Tielens, A. G. G. M.; Berné, O.; Adams, J. D.; Herter, T. L.; Keller, L. D.

2016-01-01

We present mid-infrared photometry of the Orion bar obtained with the Faint Object infraRed Camera for the SOFIA Telescope (FORCAST) on board SOFIA at 6.4, 6.6, 7.7, 19.7, 31.5, and 37.1 μ m. By complementing this observation with archival FORCAST and Herschel /PACS images, we are able to construct a complete infrared spectral energy distribution of the Huygens region in the Orion nebula. Comparing the infrared images with gas tracers, we find that PACS maps trace the molecular cloud, while the FORCAST data trace the photodissociation region (PDR) and the H ii region. Analysis of the energetics of the region reveal that the PDR extends for 0.28 pc along the line of sight and that the bar is inclined at an angle of 4°. The infrared and submillimeter images reveal that the Orion bar represents a swept-up shell with a thickness of 0.1 pc. The mass of the shell implies a shock velocity of ≃3 km s −1 and an age of ≃10 5 years for the H ii region. Our analysis shows that the UV and infrared dust opacities in the H ii region and the PDR are a factor 5 to 10 lower than in the diffuse interstellar medium. In the ionized gas, Ly α photons are a major source of dust heating at distances larger than ≃0.06 pc from θ 1 Ori C. Dust temperatures can be explained if the size of the grains is between 0.1 and 1 μ m. We derive the photoelectric heating efficiency of the atomic gas in the Orion bar. The results are in good qualitative agreement with models and the quantitative differences indicate a decreased polycyclic aromatic hydrocarbon abundance in this region.

THE ORION H ii REGION AND THE ORION BAR IN THE MID-INFRARED

Energy Technology Data Exchange (ETDEWEB)

Salgado, F.; Tielens, A. G. G. M. [Leiden Observatory, University of Leiden, P.O. Box 9513, 2300 RA Leiden (Netherlands); Berné, O. [Université de Toulouse, UPS-OMP, IRAP, Toulouse (France); Adams, J. D.; Herter, T. L. [Astronomy Department, 202 Space Sciences Building, Cornell University, Ithaca, NY 14853-6801 (United States); Keller, L. D. [Department of Physics and Astronomy, Ithaca College, Ithaca, NY 14850 (United States)

2016-10-20

We present mid-infrared photometry of the Orion bar obtained with the Faint Object infraRed Camera for the SOFIA Telescope (FORCAST) on board SOFIA at 6.4, 6.6, 7.7, 19.7, 31.5, and 37.1 μ m. By complementing this observation with archival FORCAST and Herschel /PACS images, we are able to construct a complete infrared spectral energy distribution of the Huygens region in the Orion nebula. Comparing the infrared images with gas tracers, we find that PACS maps trace the molecular cloud, while the FORCAST data trace the photodissociation region (PDR) and the H ii region. Analysis of the energetics of the region reveal that the PDR extends for 0.28 pc along the line of sight and that the bar is inclined at an angle of 4°. The infrared and submillimeter images reveal that the Orion bar represents a swept-up shell with a thickness of 0.1 pc. The mass of the shell implies a shock velocity of ≃3 km s{sup −1} and an age of ≃10{sup 5} years for the H ii region. Our analysis shows that the UV and infrared dust opacities in the H ii region and the PDR are a factor 5 to 10 lower than in the diffuse interstellar medium. In the ionized gas, Ly α photons are a major source of dust heating at distances larger than ≃0.06 pc from θ {sup 1} Ori C. Dust temperatures can be explained if the size of the grains is between 0.1 and 1 μ m. We derive the photoelectric heating efficiency of the atomic gas in the Orion bar. The results are in good qualitative agreement with models and the quantitative differences indicate a decreased polycyclic aromatic hydrocarbon abundance in this region.

Differential Hopf algebra structures on the Universal Enveloping Algebra of a Lie Algebra

NARCIS (Netherlands)

van den Hijligenberg, N.W.; van den Hijligenberg, N.; Martini, Ruud

1995-01-01

We discuss a method to construct a De Rham complex (differential algebra) of Poincaré–Birkhoff–Witt type on the universal enveloping algebra of a Lie algebra g. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebrastructure of U(g).

Orion FSW V and V and Kedalion Engineering Lab Insight

Science.gov (United States)

Mangieri, Mark L.

2010-01-01

NASA, along with its prime Orion contractor and its subcontractor s are adapting an avionics system paradigm borrowed from the manned commercial aircraft industry for use in manned space flight systems. Integrated Modular Avionics (IMA) techniques have been proven as a robust avionics solution for manned commercial aircraft (B737/777/787, MD 10/90). This presentation will outline current approaches to adapt IMA, along with its heritage FSW V&V paradigms, into NASA's manned space flight program for Orion. NASA's Kedalion engineering analysis lab is on the forefront of validating many of these contemporary IMA based techniques. Kedalion has already validated many of the proposed Orion FSW V&V paradigms using Orion's precursory Flight Test Article (FTA) Pad Abort 1 (PA-1) program. The Kedalion lab will evolve its architectures, tools, and techniques in parallel with the evolving Orion program.

The relation between quantum W algebras and Lie algebras

International Nuclear Information System (INIS)

Boer, J. de; Tjin, T.

1994-01-01

By quantizing the generalized Drinfeld-Sokolov reduction scheme for arbitrary sl 2 embeddings we show that a large set W of quantum W algebras can be viewed as (BRST) cohomologies of affine Lie algebras. The set W contains many known W algebras such as W N and W 3 (2) . Our formalism yields a completely algorithmic method for calculating the W algebra generators and their operator product expansions, replacing the cumbersome construction of W algebras as commutants of screening operators. By generalizing and quantizing the Miura transformation we show that any W algebra in W can be embedded into the universal enveloping algebra of a semisimple affine Lie algebra which is, up to shifts in level, isomorphic to a subalgebra of the original affine algebra. Therefore any realization of this semisimple affine Lie algebra leads to a realization of the W algebra. In particular, one obtains in this way a general and explicit method for constructing the free field realizations and Fock resolutions for all algebras in W. Some examples are explicitly worked out. (orig.)

2-Local derivations on matrix algebras over semi-prime Banach algebras and on AW*-algebras

International Nuclear Information System (INIS)

Ayupov, Shavkat; Kudaybergenov, Karimbergen

2016-01-01

The paper is devoted to 2-local derivations on matrix algebras over unital semi-prime Banach algebras. For a unital semi-prime Banach algebra A with the inner derivation property we prove that any 2-local derivation on the algebra M 2 n (A), n ≥ 2, is a derivation. We apply this result to AW*-algebras and show that any 2-local derivation on an arbitrary AW*-algebra is a derivation. (paper)

The first capsule implosion experiments on Orion

International Nuclear Information System (INIS)

Garbett, W J; Horsfield, C J; Gales, S G; Leatherland, A E; Rubery, M S; Coltman, J E; Meadowcroft, A E; Rice, S J; Simons, A J; Woolhead, V E

2016-01-01

Direct drive capsule implosions are being developed on the Orion laser at AWE as a platform for ICF and HED physics experiments. The Orion facility combines both long pulse and short-pulse beams, making it well suited for studying the physics of alternative ignition approaches. Orion implosions also provide the opportunity to study aspects of polar direct drive. Limitations on drive symmetry from the relatively small number of laser beams makes predictive modelling of the implosions challenging, resulting in some uncertainty in the expected capsule performance. Initial experiments have been fielded to evaluate baseline capsule performance and inform future design optimization. Highly promising DD fusion neutron yields in excess of 10 9 have been recorded. Results from the experiments are presented alongside radiation-hydrocode modelling. (paper)

Biodiversity Loss in the Orion Radio Zoo?

Science.gov (United States)

Henney, W. J.; García-Díaz, Ma. T.; Kurtz, S. E.

2001-03-01

We re-examine radio observations of compact sources in the core of the Orion nebula and find that 70% of the sources correspond to known proplyds. For all of these sources, including many that have been previously classified as variable and non-thermal, the radio flux between 1.5 and 86 Ghz is fully accounted for by thermal free-free emission from the photoevaporation flow. We therefore suggest that many of the proposed Orion FOXES are in fact EIDERS, and that their apparent variability reflects observational difficulties in detecting the lower surface-brightness portions of the proplyds. The PIGs turn out to be extinct in Orion, and the hybrid creatures that we dub PANTHERS (Proplyds Associated with Non-THErmal Radio Sources) remain elusive.

Quantum cluster algebra structures on quantum nilpotent algebras

CERN Document Server

Goodearl, K R

2017-01-01

All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always equal the corresponding upper quantum cluster algebras. Previous approaches to these problems for the construction of (quantum) cluster algebra structures on (quantized) coordinate rings arising in Lie theory were done on a case by case basis relying on the combinatorics of each concrete family. The results of the paper have a broad range of applications to these problems, including the construction of quantum cluster algebra structures on quantum unipotent groups and quantum double Bruhat cells (the Berenstein-Zelevinsky conjecture), and treat these problems from a unified perspective. All such applications also establish equality between the constructed quantum cluster algebras and their upper counterparts.

Quadratic algebras

CERN Document Server

Polishchuk, Alexander

2005-01-01

Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.

Regularity of C*-algebras and central sequence algebras

DEFF Research Database (Denmark)

Christensen, Martin S.

The main topic of this thesis is regularity properties of C*-algebras and how these regularity properties are re ected in their associated central sequence algebras. The thesis consists of an introduction followed by four papers [A], [B], [C], [D]. In [A], we show that for the class of simple...... Villadsen algebra of either the rst type with seed space a nite dimensional CW complex, or the second type, tensorial absorption of the Jiang-Su algebra is characterized by the absence of characters on the central sequence algebra. Additionally, in a joint appendix with Joan Bosa, we show that the Villadsen...... algebra of the second type with innite stable rank fails the corona factorization property. In [B], we consider the class of separable C*-algebras which do not admit characters on their central sequence algebra, and show that it has nice permanence properties. We also introduce a new divisibility property...

Real division algebras and other algebras motivated by physics

International Nuclear Information System (INIS)

Benkart, G.; Osborn, J.M.

1981-01-01

In this survey we discuss several general techniques which have been productive in the study of real division algebras, flexible Lie-admissible algebras, and other nonassociative algebras, and we summarize results obtained using these methods. The principal method involved in this work is to view an algebra A as a module for a semisimple Lie algebra of derivations of A and to use representation theory to study products in A. In the case of real division algebras, we also discuss the use of isotopy and the use of a generalized Peirce decomposition. Most of the work summarized here has appeared in more detail in various other papers. The exceptions are results on a class of algebras of dimension 15, motivated by physics, which admit the Lie algebra sl(3) as an algebra of derivations

Atomic hydrogen in the Orion star-forming region

International Nuclear Information System (INIS)

Chromey, F.R.; Elmegreen, B.G.; Elmegreen, D.M.

1989-01-01

A large-scale survey of atomic hydrogen in Orion reveals low-density material with a total mass comparable to that in dense molecular clouds. The atomic gas is sufficiently dense that it can shield the molecular material from photodissociative radiation and provide a pressure link to the low-density intercloud medium. An excess of H I emission comes from photodissociation fronts near the bright stars and from a giant shell in the Orion Belt region. This shell may have caused the apparent bifurcation between the Orion A and B clouds, and the associated pressures may have induced peculiar motions and star formation in NGC 2023 and 2024. 49 refs

Hom-Novikov algebras

International Nuclear Information System (INIS)

Yau, Donald

2011-01-01

We study a twisted generalization of Novikov algebras, called Hom-Novikov algebras, in which the two defining identities are twisted by a linear map. It is shown that Hom-Novikov algebras can be obtained from Novikov algebras by twisting along any algebra endomorphism. All algebra endomorphisms on complex Novikov algebras of dimensions 2 or 3 are computed, and their associated Hom-Novikov algebras are described explicitly. Another class of Hom-Novikov algebras is constructed from Hom-commutative algebras together with a derivation, generalizing a construction due to Dorfman and Gel'fand. Two other classes of Hom-Novikov algebras are constructed from Hom-Lie algebras together with a suitable linear endomorphism, generalizing a construction due to Bai and Meng.

SULFUR ABUNDANCES IN THE ORION ASSOCIATION B STARS

International Nuclear Information System (INIS)

Daflon, Simone; Cunha, Katia; De la Reza, Ramiro; Holtzman, Jon; Chiappini, Cristina

2009-01-01

Sulfur abundances are derived for a sample of 10 B main-sequence star members of the Orion association. The analysis is based on LTE plane-parallel model atmospheres and non-LTE line formation theory by means of a self-consistent spectrum synthesis analysis of lines from two ionization states of sulfur, S II and S III. The observations are high-resolution spectra obtained with the ARCES spectrograph at the Apache Point Observatory. The abundance distribution obtained for the Orion targets is homogeneous within the expected errors in the analysis: A(S) = 7.15 ± 0.05. This average abundance result is in agreement with the recommended solar value (both from modeling of the photospheres in one-dimensional and three-dimensional, and meteorites) and indicates that little, if any, chemical evolution of sulfur has taken place in the last ∼4.5 billion years. The sulfur abundances of the young stars in Orion are found to agree well with results for the Orion Nebulae, and place strong constraints on the amount of sulfur depletion onto grains as being very modest or nonexistent. The sulfur abundances for Orion are consistent with other measurements at a similar galactocentric radius: combined with previous results for other OB-type stars produce a relatively shallow sulfur abundance gradient with a slope of -0.037 ± 0.012 dex kpc -1 .

Linear algebra meets Lie algebra: the Kostant-Wallach theory

OpenAIRE

Shomron, Noam; Parlett, Beresford N.

2008-01-01

In two languages, Linear Algebra and Lie Algebra, we describe the results of Kostant and Wallach on the fibre of matrices with prescribed eigenvalues of all leading principal submatrices. In addition, we present a brief introduction to basic notions in Algebraic Geometry, Integrable Systems, and Lie Algebra aimed at specialists in Linear Algebra.

Molecular clouds in Orion and Monoceros

International Nuclear Information System (INIS)

Maddalena, R.J.

1986-01-01

About one-eighth of a well-sampled 850 deg 2 region of Orion and Monoceros, extending from the Taurus dark cloud complex to the CMa OB 1 association, shows emission at the frequency of the J = 1 → 0 transition of CO coming from either local clouds (d 8 from the galactic plane or from more distant objects located within a few degrees of the plane and well outside the solar circle. Local giant molecular clouds associated with Orion A and B have enhanced temperatures and densities near their western edges possibly due to compression of molecular gas by a high pressure region created by the cumulative effects of ∼10 supernovae that occurred in the Orion OB association. Another giant molecular cloud found to be associated with Mon R2 may be related to the Orion clouds. Two filamentary clouds (one possible 200 pc long but only 3-10 pc wide) were found that may represent a new class of object; magnetic fields probably play a role in confining these filaments. An expanding ring of clouds concentric with the H II region S 264 and its ionizing 08 star λ Ori was also investigated, and a possible evolutionary sequence for the ring is given in detail: the clouds probably constitute fragments of the original cloud from which λ Ori formed, the gas pressure of the H II region and the rocket effect having disrupted the cloud and accelerated the fragments to their present velocities

Orion Exploration Flight Test 1 (EFT-1) Best Estimated Trajectory Development

Science.gov (United States)

Holt, Greg N.; Brown, Aaron

2016-01-01

The Orion Exploration Flight Test 1 (EFT-1) mission successfully flew on Dec 5, 2014 atop a Delta IV Heavy launch vehicle. The goal of Orions maiden flight was to stress the system by placing an uncrewed vehicle on a high-energy trajectory replicating conditions similar to those that would be experienced when returning from an asteroid or a lunar mission. The Orion navigation team combined all trajectory data from the mission into a Best Estimated Trajectory (BET) product. There were significant challenges in data reconstruction and many lessons were learned for future missions. The team used an estimation filter incorporating radar tracking, onboard sensors (Global Positioning System and Inertial Measurement Unit), and day-of-flight weather balloons to evaluate the true trajectory flown by Orion. Data was published for the entire Orion EFT-1 flight, plus objects jettisoned during entry such as the Forward Bay Cover. The BET customers include approximately 20 disciplines within Orion who will use the information for evaluating vehicle performance and influencing future design decisions.

In the Shadow of Pennhurst: The Orion Community.

Science.gov (United States)

Lutfiyya, Zana Marie

This case study is based on a 1988 site visit to the Orion Community, in which a group of nondisabled and disabled people have chosen to live and work with each other in Chester County, Pennsylvania. Orion's founding is described, beginning with an informal support group of professionals, parents, advocates, and members of Camphill (agricultural…

On-Board Rendezvous Targeting for Orion

Science.gov (United States)

Weeks, Michael W.; DSouza, Christopher N.

2010-01-01

The Orion On-board GNC system is among the most complex ever developed for a space mission. It is designed to operate autonomously (independent of the ground). The rendezvous system in particular was designed to operate on the far side of the moon, and in the case of loss-of-communications with the ground. The vehicle GNC system is designed to retarget the rendezvous maneuvers, given a mission plan. As such, all the maneuvers which will be performed by Orion, have been designed and are being incorporated into the flight code.

Extended Virasoro algebra and algebra of area preserving diffeomorphisms

International Nuclear Information System (INIS)

Arakelyan, T.A.

1990-01-01

The algebra of area preserving diffeomorphism plays an important role in the theory of relativistic membranes. It is pointed out that the relation between this algebra and the extended Virasoro algebra associated with the generalized Kac-Moody algebras G(T 2 ). The highest weight representation of these infinite-dimensional algebras as well as of their subalgebras is studied. 5 refs

An application of the division algebras, Jordan algebras and split composition algebras

International Nuclear Information System (INIS)

Foot, R.; Joshi, G.C.

1992-01-01

It has been established that the covering group of the Lorentz group in D = 3, 4, 6, 10 can be expressed in a unified way, based on the four composition division algebras R, C, Q and O. In this paper, the authors discuss, in this framework, the role of the complex numbers of quantum mechanics. A unified treatment of quantum-mechanical spinors is given. The authors provide an explicit demonstration that the vector and spinor transformations recently constructed from a subgroup of the reduced structure group of the Jordan algebras M n 3 are indeed the Lorentz transformations. The authors also show that if the division algebras in the construction of the covering groups of the Lorentz groups in D = 3, 4, 6, 10 are replaced by the split composition algebras, then the sequence of groups SO(2, 2), SO(3, 3) and SO(5, 5) result. The analysis is presumed to be self-contained as the relevant aspects of the division algebras and Jordan algebras are reviewed. Some applications to physical theory are indicated

Interactions Between Representation Ttheory, Algebraic Topology and Commutative Algebra

CERN Document Server

Pitsch, Wolfgang; Zarzuela, Santiago

2016-01-01

This book includes 33 expanded abstracts of selected talks given at the two workshops "Homological Bonds Between Commutative Algebra and Representation Theory" and "Brave New Algebra: Opening Perspectives," and the conference "Opening Perspectives in Algebra, Representations, and Topology," held at the Centre de Recerca Matemàtica (CRM) in Barcelona between January and June 2015. These activities were part of the one-semester intensive research program "Interactions Between Representation Theory, Algebraic Topology and Commutative Algebra (IRTATCA)." Most of the abstracts present preliminary versions of not-yet published results and cover a large number of topics (including commutative and non commutative algebra, algebraic topology, singularity theory, triangulated categories, representation theory) overlapping with homological methods. This comprehensive book is a valuable resource for the community of researchers interested in homological algebra in a broad sense, and those curious to learn the latest dev...

Duncan F. Gregory, William Walton and the development of British algebra: 'algebraical geometry', 'geometrical algebra', abstraction.

Science.gov (United States)

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.

Monomial algebras

CERN Document Server

Villarreal, Rafael

2015-01-01

The book stresses the interplay between several areas of pure and applied mathematics, emphasizing the central role of monomial algebras. It unifies the classical results of commutative algebra with central results and notions from graph theory, combinatorics, linear algebra, integer programming, and combinatorial optimization. The book introduces various methods to study monomial algebras and their presentation ideals, including Stanley-Reisner rings, subrings and blowup algebra-emphasizing square free quadratics, hypergraph clutters, and effective computational methods.

Algebra

CERN Document Server

Tabak, John

2004-01-01

Looking closely at algebra, its historical development, and its many useful applications, Algebra examines in detail the question of why this type of math is so important that it arose in different cultures at different times. The book also discusses the relationship between algebra and geometry, shows the progress of thought throughout the centuries, and offers biographical data on the key figures. Concise and comprehensive text accompanied by many illustrations presents the ideas and historical development of algebra, showcasing the relevance and evolution of this branch of mathematics.

Iwahori-Hecke algebras and Schur algebras of the symmetric group

CERN Document Server

Mathas, Andrew

1999-01-01

This volume presents a fully self-contained introduction to the modular representation theory of the Iwahori-Hecke algebras of the symmetric groups and of the q-Schur algebras. The study of these algebras was pioneered by Dipper and James in a series of landmark papers. The primary goal of the book is to classify the blocks and the simple modules of both algebras. The final chapter contains a survey of recent advances and open problems. The main results are proved by showing that the Iwahori-Hecke algebras and q-Schur algebras are cellular algebras (in the sense of Graham and Lehrer). This is proved by exhibiting natural bases of both algebras which are indexed by pairs of standard and semistandard tableaux respectively. Using the machinery of cellular algebras, which is developed in Chapter 2, this results in a clean and elegant classification of the irreducible representations of both algebras. The block theory is approached by first proving an analogue of the Jantzen sum formula for the q-Schur algebras. T...

Algebra of pseudo-differential operators over C*-algebra

International Nuclear Information System (INIS)

Mohammad, N.

1982-08-01

Algebras of pseudo-differential operators over C*-algebras are studied for the special case when in Hormander class Ssub(rho,delta)sup(m)(Ω) Ω = Rsup(n); rho = 1, delta = 0, m any real number, and the C*-algebra is infinite dimensional non-commutative. The space B, i.e. the set of A-valued C*-functions in Rsup(n) (or Rsup(n) x Rsup(n)) whose derivatives are all bounded, plays an important role. A denotes C*-algebra. First the operator class Ssub(phi,0)sup(m) is defined, and through it, the class Lsub(1,0)sup(m) of pseudo-differential operators. Then the basic asymptotic expansion theorems concerning adjoint and product of operators of class Ssub(1,0)sup(m) are stated. Finally, proofs are given of L 2 -continuity theorem and the main theorem, which states that algebra of all pseudo-differential operators over C*-algebras is itself C*-algebra

Commutative algebra with a view toward algebraic geometry

CERN Document Server

Eisenbud, David

1995-01-01

Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algeb...

Mapping young stellar populations towards Orion with Gaia DR1

Science.gov (United States)

Zari, Eleonora; Brown, Anthony G. A.

2018-04-01

OB associations are prime sites for the study of star formation processes and of the interaction between young massive stars with the interstellar medium. Furthermore, the kinematics and structure of the nearest OB associations provide detailed insight into the properties and origin of the Gould Belt. In this context, the Orion complex has been extensively studied. However, the spatial distribution of the stellar population is still uncertain: in particular, the distances and ages of the various sub-groups composing the Orion OB association, and their connection to the surrounding interstellar medium, are not well determined. We used the first Gaia data release to characterize the stellar population in Orion, with the goal to obtain new distance and age estimates of the numerous stellar groups composing the Orion OB association. We found evidence of the existence of a young and rich population spread over the entire region, loosely clustered around some known groups. This newly discovered population of young stars provides a fresh view of the star formation history of the Orion region.

Space Launch System Spacecraft and Payload Elements: Progress Toward Crewed Launch and Beyond

Science.gov (United States)

Schorr, Andrew A.; Smith, David Alan; Holcomb, Shawn; Hitt, David

2017-01-01

While significant and substantial progress continues to be accomplished toward readying the Space Launch System (SLS) rocket for its first test flight, work is already underway on preparations for the second flight - using an upgraded version of the vehicle - and beyond. Designed to support human missions into deep space, SLS is the most powerful human-rated launch vehicle the United States has ever undertaken, and is one of three programs being managed by the National Aeronautics and Space Administration's (NASA's) Exploration Systems Development division. The Orion spacecraft program is developing a new crew vehicle that will support human missions beyond low Earth orbit (LEO), and the Ground Systems Development and Operations (GSDO) program is transforming Kennedy Space Center (KSC) into a next-generation spaceport capable of supporting not only SLS but also multiple commercial users. Together, these systems will support human exploration missions into the proving ground of cislunar space and ultimately to Mars. For its first flight, SLS will deliver a near-term heavy-lift capability for the nation with its 70-metric-ton (t) Block 1 configuration. Each element of the vehicle now has flight hardware in production in support of the initial flight of the SLS, which will propel Orion around the moon and back. Encompassing hardware qualification, structural testing to validate hardware compliance and analytical modeling, progress is on track to meet the initial targeted launch date. In Utah and Mississippi, booster and engine testing are verifying upgrades made to proven shuttle hardware. At Michoud Assembly Facility (MAF) in Louisiana, the world's largest spacecraft welding tool is producing tanks for the SLS core stage. Providing the Orion crew capsule/launch vehicle interface and in-space propulsion via a cryogenic upper stage, the Spacecraft/Payload Integration and Evolution (SPIE) element serves a key role in achieving SLS goals and objectives. The SPIE element

Jordan algebras versus C*- algebras

International Nuclear Information System (INIS)

Stormer, E.

1976-01-01

The axiomatic formulation of quantum mechanics and the problem of whether the observables form self-adjoint operators on a Hilbert space, are discussed. The relation between C*- algebras and Jordan algebras is studied using spectral theory. (P.D.)

Is gas in the Orion nebula depleted

International Nuclear Information System (INIS)

Aiello, S.; Guidi, I.

1978-01-01

Depletion of heavy elements has been recognized to be important in the understanding of the chemical composition of the interstellar medium. This problem is also relevant to the study of H II regions. In this paper the gaseous depletion in the physical conditions of the Orion nebula is investigated. The authors reach the conclusion that very probably no depletion of heavy elements, due to sticking on dust grains, took place during the lifetime of the Orion nebula. (Auth.)

Star distribution in the Orion spiral arm

International Nuclear Information System (INIS)

Basharina, T.S.; Pavlovskaya, E.D.; Filippova, A.A.

1985-01-01

The structure of the Orion spiral arm is studied by numerical experiments, assuming that in each direction considered the star distribution along the line of sight is a combination of two Gaussian laws. The corresponding parameters are evaluated for four Milky Way fields; the bimodal laws now fit the observations by the chi 2 criterion. In the Orion arm the line-of-sight star densities follow asymmetric curves, steeper at the outer edge of the arm

Methodology for Developing a Probabilistic Risk Assessment Model of Spacecraft Rendezvous and Dockings

Science.gov (United States)

Farnham, Steven J., II; Garza, Joel, Jr.; Castillo, Theresa M.; Lutomski, Michael

2011-01-01

In 2007 NASA was preparing to send two new visiting vehicles carrying logistics and propellant to the International Space Station (ISS). These new vehicles were the European Space Agency s (ESA) Automated Transfer Vehicle (ATV), the Jules Verne, and the Japanese Aerospace and Explorations Agency s (JAXA) H-II Transfer Vehicle (HTV). The ISS Program wanted to quantify the increased risk to the ISS from these visiting vehicles. At the time, only the Shuttle, the Soyuz, and the Progress vehicles rendezvoused and docked to the ISS. The increased risk to the ISS was from an increase in vehicle traffic, thereby, increasing the potential catastrophic collision during the rendezvous and the docking or berthing of the spacecraft to the ISS. A universal method of evaluating the risk of rendezvous and docking or berthing was created by the ISS s Risk Team to accommodate the increasing number of rendezvous and docking or berthing operations due to the increasing number of different spacecraft, as well as the future arrival of commercial spacecraft. Before the first docking attempt of ESA's ATV and JAXA's HTV to the ISS, a probabilistic risk model was developed to quantitatively calculate the risk of collision of each spacecraft with the ISS. The 5 rendezvous and docking risk models (Soyuz, Progress, Shuttle, ATV, and HTV) have been used to build and refine the modeling methodology for rendezvous and docking of spacecrafts. This risk modeling methodology will be NASA s basis for evaluating the addition of future ISS visiting spacecrafts hazards, including SpaceX s Dragon, Orbital Science s Cygnus, and NASA s own Orion spacecraft. This paper will describe the methodology used for developing a visiting vehicle risk model.

Implicative Algebras

African Journals Online (AJOL)

Tadesse

In this paper we introduce the concept of implicative algebras which is an equivalent definition of lattice implication algebra of Xu (1993) and further we prove that it is a regular Autometrized. Algebra. Further we remark that the binary operation → on lattice implicative algebra can never be associative. Key words: Implicative ...

Open algebraic surfaces

CERN Document Server

Miyanishi, Masayoshi

2000-01-01

Open algebraic surfaces are a synonym for algebraic surfaces that are not necessarily complete. An open algebraic surface is understood as a Zariski open set of a projective algebraic surface. There is a long history of research on projective algebraic surfaces, and there exists a beautiful Enriques-Kodaira classification of such surfaces. The research accumulated by Ramanujan, Abhyankar, Moh, and Nagata and others has established a classification theory of open algebraic surfaces comparable to the Enriques-Kodaira theory. This research provides powerful methods to study the geometry and topology of open algebraic surfaces. The theory of open algebraic surfaces is applicable not only to algebraic geometry, but also to other fields, such as commutative algebra, invariant theory, and singularities. This book contains a comprehensive account of the theory of open algebraic surfaces, as well as several applications, in particular to the study of affine surfaces. Prerequisite to understanding the text is a basic b...

Adaptation and Re-Use of Spacecraft Power System Models for the Constellation Program

Science.gov (United States)

Hojnicki, Jeffrey S.; Kerslake, Thomas W.; Ayres, Mark; Han, Augustina H.; Adamson, Adrian M.

2008-01-01

NASA's Constellation Program is embarking on a new era of space exploration, returning to the Moon and beyond. The Constellation architecture will consist of a number of new spacecraft elements, including the Orion crew exploration vehicle, the Altair lunar lander, and the Ares family of launch vehicles. Each of these new spacecraft elements will need an electric power system, and those power systems will need to be designed to fulfill unique mission objectives and to survive the unique environments encountered on a lunar exploration mission. As with any new spacecraft power system development, preliminary design work will rely heavily on analysis to select the proper power technologies, size the power system components, and predict the system performance throughout the required mission profile. Constellation projects have the advantage of leveraging power system modeling developments from other recent programs such as the International Space Station (ISS) and the Mars Exploration Program. These programs have developed mature power system modeling tools, which can be quickly modified to meet the unique needs of Constellation, and thus provide a rapid capability for detailed power system modeling that otherwise would not exist.

Separable algebras

CERN Document Server

Ford, Timothy J

2017-01-01

This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of étale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups. The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.

Generalized EMV-Effect Algebras

Science.gov (United States)

Borzooei, R. A.; Dvurečenskij, A.; Sharafi, A. H.

2018-04-01

Recently in Dvurečenskij and Zahiri (2017), new algebraic structures, called EMV-algebras which generalize both MV-algebras and generalized Boolean algebras, were introduced. We present equivalent conditions for EMV-algebras. In addition, we define a partial algebraic structure, called a generalized EMV-effect algebra, which is close to generalized MV-effect algebras. Finally, we show that every generalized EMV-effect algebra is either an MV-effect algebra or can be embedded into an MV-effect algebra as a maximal ideal.

Special set linear algebra and special set fuzzy linear algebra

OpenAIRE

Kandasamy, W. B. Vasantha; Smarandache, Florentin; Ilanthenral, K.

2009-01-01

The authors in this book introduce the notion of special set linear algebra and special set fuzzy Linear algebra, which is an extension of the notion set linear algebra and set fuzzy linear algebra. These concepts are best suited in the application of multi expert models and cryptology. This book has five chapters. In chapter one the basic concepts about set linear algebra is given in order to make this book a self contained one. The notion of special set linear algebra and their fuzzy analog...

75 FR 54388 - General Motors Company Formerly Known as General Motors Corporation, Orion Assembly Plant...

Science.gov (United States)

2010-09-07

... Formerly Known as General Motors Corporation, Orion Assembly Plant Including On-Site Leased Workers From Aerotek Automotive Lake Orion, MI; Amended Certification Regarding Eligibility To Apply for Worker... Motors Corporation, Orion Assembly Plant, Lake Orion, Michigan. The notice was published in the Federal...

Banach Synaptic Algebras

Science.gov (United States)

Foulis, David J.; Pulmannov, Sylvia

2018-04-01

Using a representation theorem of Erik Alfsen, Frederic Schultz, and Erling Størmer for special JB-algebras, we prove that a synaptic algebra is norm complete (i.e., Banach) if and only if it is isomorphic to the self-adjoint part of a Rickart C∗-algebra. Also, we give conditions on a Banach synaptic algebra that are equivalent to the condition that it is isomorphic to the self-adjoint part of an AW∗-algebra. Moreover, we study some relationships between synaptic algebras and so-called generalized Hermitian algebras.

Grassmann algebras

International Nuclear Information System (INIS)

Garcia, R.L.

1983-11-01

The Grassmann algebra is presented briefly. Exponential and logarithm of matrices functions, whose elements belong to this algebra, are studied with the help of the SCHOONSCHIP and REDUCE 2 algebraic manipulators. (Author) [pt

Algebraic geometry

CERN Document Server

Lefschetz, Solomon

2005-01-01

An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

Converting nested algebra expressions into flat algebra expressions

NARCIS (Netherlands)

Paredaens, J.; Van Gucht, D.

1992-01-01

Nested relations generalize ordinary flat relations by allowing tuple values to be either atomic or set valued. The nested algebra is a generalization of the flat relational algebra to manipulate nested relations. In this paper we study the expressive power of the nested algebra relative to its

Millimeter emission lines in Orion A

International Nuclear Information System (INIS)

Lovas, F.J.; Johnson, D.R.; Buhl, D.; Snyder, L.E.

1976-01-01

During the course of a search of Orion A for signals from three large, organic molecules, several millimeter wave lines from known interstellar molecules were observed. Results of observations on methanol (CH 3 OH), methyl cyanide (CH 3 CN), methyl acetylene (CH 3 CCH), acetaldehyde (CH 3 CHO) and 29 SiO are reported here. Emission signals from two hydrogen recombination lines (H41α and H42α) detected from the H II region of Orion A are also reported. Negative results were obtained for several millimeter wave transitions of ethylene oxide (CH 2 OCH 2 ), acetone [(CH 3 ) 2 CO], and cyclopropenone (HCCOCH)

'Orion-2': first scientific results

International Nuclear Information System (INIS)

Gurzadyan, G.A.

1975-01-01

The first results of proceeding some data collected by the 'Orion-2' observatory set up in the 'Soyuz-13' are presented. The goal of the experiment is to get the photographs of ultraviolet (UV) spectra of weak stars in the range of 2000-5000 A. Spectrograms are obtained for stars with brightness of 9-9.5 stellar magnitude at 1.5 min exposure. It has been possible to take spectrograms of many stars weaker than the 12-th magnitude at the 18 min exposure and at the short-wave boundary of a spectrum of 2500 A. A group of stars of an unknown type has been observed not far from Capella. The group contains approximately twenty stars weaker than the 10-th photographic magnitude. The average position of the group is α=0.5sup(m)10sup(m), delta=+44deg30'. Spectrograms of more than twenty hot stars in the Sails constellation in the South Sky are obtained. According to the 'Orion-2' data the light absorption in the interstellar space in the range of 2000-3000 A is caused by graphite particles of an almost spheric shape, that is in accordance with present assumptions. In spectra of over 100 stars the doublet of ionized magnesium, 2800 Mg 2, has been distinguished and measured. Spectral photographs made by the 'Orion-2' allow one to reveal chromosphere of cool stars. A strange star is discovered (12sup(m),6 brigthness in photographic rays) not far from Capella, its spectrum displaying many emission lines. A unique spectrogram of the NGC 2 2149 planetary nebula and its nucleus has been obtained. The question is whether it is possible to classify stars not only by their lines but also by the continuous UV spectrum up to 2000 A. This method may turn out to be very effective for weak stars. The 'Orion-2' has demonstrated ample possibilities of carrying out astrophysical researches outside the atmosphere

Fibered F-Algebra

OpenAIRE

Kleyn, Aleks

2007-01-01

The concept of F-algebra and its representation can be extended to an arbitrary bundle. We define operations of fibered F-algebra in fiber. The paper presents the representation theory of of fibered F-algebra as well as a comparison of representation of F-algebra and of representation of fibered F-algebra.

The bubble algebra: structure of a two-colour Temperley-Lieb Algebra

International Nuclear Information System (INIS)

Grimm, Uwe; Martin, Paul P

2003-01-01

We define new diagram algebras providing a sequence of multiparameter generalizations of the Temperley-Lieb algebra, suitable for the modelling of dilute lattice systems of two-dimensional statistical mechanics. These algebras give a rigorous foundation to the various 'multi-colour algebras' of Grimm, Pearce and others. We determine the generic representation theory of the simplest of these algebras, and locate the nongeneric cases (at roots of unity of the corresponding parameters). We show by this example how the method used (Martin's general procedure for diagram algebras) may be applied to a wide variety of such algebras occurring in statistical mechanics. We demonstrate how these algebras may be used to solve the Yang-Baxter equations

SPECTROSCOPIC CHARACTERIZATION AND DETECTION OF ETHYL MERCAPTAN IN ORION

International Nuclear Information System (INIS)

Kolesniková, L.; Alonso, J. L.; Daly, A. M.; Tercero, B.; Cernicharo, J.; Gordon, B. P.; Shipman, S. T.

2014-01-01

New laboratory data of ethyl mercaptan, CH 3 CH 2 SH, in the millimeter- and submillimeter-wave domains (up to 880 GHz) provided very precise values of the spectroscopic constants that allowed the detection of gauche-CH 3 CH 2 SH toward Orion KL. This identification is supported by 77 unblended or slightly blended lines plus no missing transitions in the range 80-280 GHz. A detection of methyl mercaptan, CH 3 SH, in the spectral survey of Orion KL is reported as well. Our column density results indicate that methyl mercaptan is ≅ 5 times more abundant than ethyl mercaptan in the hot core of Orion KL

Orion: a glimpse of hope in life span extension?

Science.gov (United States)

Muradian, K; Bondar, V; Bezrukov, V; Zhukovsky, O; Polyakov, V; Utko, N

2010-01-01

Orion is a multicomponent drug based on derivatives of taurocholic acid and several other compounds. Application of Orion into the feeding medium of Drosophila melanogaster resulted in increased life span and survival at stressful conditions. Two paradoxical features of the drug should be stressed: The "age-threshold" (life span extension was observed only when the drug was applied starting from the second half of life) and induction of "centenarian" flies (older 100 days). Orion enhanced survival at heat shock (38 degrees C) and acidic (pH = 1.6) or alkaline (pH = 11.8) feeding mediums, but not at oxidative stresses modeled by 100% oxygen or application of hydrogen peroxide (H(2)O(2)).

SPECTROSCOPIC CHARACTERIZATION AND DETECTION OF ETHYL MERCAPTAN IN ORION

Energy Technology Data Exchange (ETDEWEB)

Kolesniková, L.; Alonso, J. L.; Daly, A. M. [Grupo de Espectroscopía Molecular (GEM), Edificio Quifima, Laboratorios de Espectroscopía y Bioespectroscopía, Parque Científico UVa, Unidad Asociada CSIC, Universidad de Valladolid, E-47011 Valladolid (Spain); Tercero, B.; Cernicharo, J. [Departamento de Astrofísica, Centro de Astrobiología CAB, CSIC-INTA, Ctra. de Torrejón a Ajalvir km 4, E-28850 Madrid (Spain); Gordon, B. P.; Shipman, S. T., E-mail: lucie.kolesnikova@uva.es, E-mail: jlalonso@qf.uva.es, E-mail: adammichael.daly@uva.es, E-mail: terceromb@cab.inta-csic.es, E-mail: jcernicharo@cab.inta-csic.es, E-mail: brittany.gordon@ncf.edu, E-mail: shipman@ncf.edu [Division of Natural Sciences, New College of Florida, Sarasota, FL 34243 (United States)

2014-03-20

New laboratory data of ethyl mercaptan, CH{sub 3}CH{sub 2}SH, in the millimeter- and submillimeter-wave domains (up to 880 GHz) provided very precise values of the spectroscopic constants that allowed the detection of gauche-CH{sub 3}CH{sub 2}SH toward Orion KL. This identification is supported by 77 unblended or slightly blended lines plus no missing transitions in the range 80-280 GHz. A detection of methyl mercaptan, CH{sub 3}SH, in the spectral survey of Orion KL is reported as well. Our column density results indicate that methyl mercaptan is ≅ 5 times more abundant than ethyl mercaptan in the hot core of Orion KL.

76 FR 22865 - Action Affecting Export Privileges; Orion Air, S.L. and Syrian Pearl Airlines

Science.gov (United States)

2011-04-25

... DEPARTMENT OF COMMERCE Bureau of Industry and Security Action Affecting Export Privileges; Orion Air, S.L. and Syrian Pearl Airlines In the Matter of: Orion Air, S.L., Canada Real de Merinas, 7... days the Order Temporarily Denying the Export Privileges of Respondents Orion Air, S.L. (``Orion Air...

Algebraic monoids, group embeddings, and algebraic combinatorics

CERN Document Server

Li, Zhenheng; Steinberg, Benjamin; Wang, Qiang

2014-01-01

This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids.   Topics presented include:   v  structure and representation theory of reductive algebraic monoids v  monoid schemes and applications of monoids v  monoids related to Lie theory v  equivariant embeddings of algebraic groups v  constructions and properties of monoids from algebraic combinatorics v  endomorphism monoids induced from vector bundles v  Hodge–Newton decompositions of reductive monoids   A portion of these articles are designed to serve as a self-contained introduction to these topics, while the remaining contributions are research articles containing previously unpublished results, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and Lex Renner showing that the algebraic semigroups are strongly π-regular.   Graduate students as well a...

Leavitt path algebras

CERN Document Server

Abrams, Gene; Siles Molina, Mercedes

2017-01-01

This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume. Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry. Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and...

Approximation of complex algebraic numbers by algebraic numbers of bounded degree

OpenAIRE

Bugeaud, Yann; Evertse, Jan-Hendrik

2007-01-01

We investigate how well complex algebraic numbers can be approximated by algebraic numbers of degree at most n. We also investigate how well complex algebraic numbers can be approximated by algebraic integers of degree at most n+1. It follows from our investigations that for every positive integer n there are complex algebraic numbers of degree larger than n that are better approximable by algebraic numbers of degree at most n than almost all complex numbers. As it turns out, these numbers ar...

Operadic formulation of topological vertex algebras and gerstenhaber or Batalin-Vilkovisky algebras

International Nuclear Information System (INIS)

Huang Yizhi

1994-01-01

We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we obtain a conceptual and geometric construction of the Batalin-Vilkovisky algebraic structure (or the Gerstenhaber algebra structure) on the cohomology of a topological vertex algebra (or of a weak topological vertex algebra) by combining this operadic formulation with a theorem of Getzler (or of Cohen) which formulates Batalin-Vilkovisky algebras (or Gerstenhaber algebras) in terms of the homology of the framed little disk operad (or of the little disk operad). (orig.)

Detection of the OH Zeeman effect toward Orion A

International Nuclear Information System (INIS)

Troland, T.H.; Crutcher, R.M.; Kazes, I.; Paris Observatoire, Meudon, France; Kentucky Univ., Lexington)

1986-01-01

The Zeeman effect in the 18 cm OH absorption spectrum of Orion A is detected. From this effect, a line-of-sight magnetic field strength of - 125 + or - 20 is derived. At the same position, an H I Zeeman effect equivalent to a magnetic field of - 49 + or - 4 micro-G is found. Thus, the magnetic field in the molecular gas toward Orion A is significantly stronger than that in the atomic gas, contrary to the recent determination for the Cas A line of sight. Densities in the atomic and molecular regions toward Orion A are estimated and it is found that for this region the data are consistent with B proportional to n exp kappa, kappa = 0.3. 23 references

Wn(2) algebras

International Nuclear Information System (INIS)

Feigin, B.L.; Semikhatov, A.M.

2004-01-01

We construct W-algebra generalizations of the sl-circumflex(2) algebra-W algebras W n (2) generated by two currents E and F with the highest pole of order n in their OPE. The n=3 term in this series is the Bershadsky-Polyakov W 3 (2) algebra. We define these algebras as a centralizer (commutant) of the Uqs-bar (n vertical bar 1) quantum supergroup and explicitly find the generators in a factored, 'Miura-like' form. Another construction of the W n (2) algebras is in terms of the coset sl-circumflex(n vertical bar 1)/sl-circumflex(n). The relation between the two constructions involves the 'duality' (k+n-1)(k'+n-1)=1 between levels k and k' of two sl-circumflex(n) algebras

76 FR 14101 - Bruss North America; Russell Springs, KY; Bruss North America; Orion, MI; Amended Revised...

Science.gov (United States)

2011-03-15

... America; Russell Springs, KY; Bruss North America; Orion, MI; Amended Revised Determination on... relevant time period at the Orion, Michigan location of Bruss North America, Inc. The Orion, Michigan..., Kentucky facility also led to worker separations at the Orion, Michigan location during the relevant time...

The vacuum preserving Lie algebra of a classical W-algebra

International Nuclear Information System (INIS)

Feher, L.; Tsutsui, I.

1993-07-01

We simplify and generalize an argument due to Bowcock and Watts showing that one can associate a finite Lie algebra (the 'classical vacuum preserving algebra') containing the Moebius sl(2) subalgebra to any classical W-algebra. Our construction is based on a kinematical analysis of the Poisson brackets of quasi-fields. In the case of the W S G -subalgebra S of a simple Lie algebra G, we exhibit a natural isomorphism between this finite Lie algebra and G whereby the Moebius sl(2) is identified with S. (orig.)

Nonflexible Lie-admissible algebras

International Nuclear Information System (INIS)

Myung, H.C.

1978-01-01

We discuss the structure of Lie-admissible algebras which are defined by nonflexible identities. These algebras largely arise from the antiflexible algebras, 2-varieties and associator dependent algebras. The nonflexible Lie-admissible algebras in our discussion are in essence byproducts of the study of nonassociative algebras defined by identities of degree 3. The main purpose is to discuss the classification of simple Lie-admissible algebras of nonflexible type

On 2-Banach algebras

International Nuclear Information System (INIS)

Mohammad, N.; Siddiqui, A.H.

1987-11-01

The notion of a 2-Banach algebra is introduced and its structure is studied. After a short discussion of some fundamental properties of bivectors and tensor product, several classical results of Banach algebras are extended to the 2-Banach algebra case. A condition under which a 2-Banach algebra becomes a Banach algebra is obtained and the relation between algebra of bivectors and 2-normed algebra is discussed. 11 refs

A non-equilibrium ortho-to-para ratio of water in the Orion PDR

NARCIS (Netherlands)

Choi, Y.; van der Tak, F. F. S.; Bergin, E. A.; Plume, R.

2014-01-01

Context. The ortho-to-para ratio (OPR) of H2O is thought to be sensitive to the temperature of water formation. The OPR of H2O is thus useful for studying the formation mechanism of water. Aims: We investigate the OPR of water in the Orion PDR (photon-dominated region), at the Orion Bar and Orion S

Algebra

CERN Document Server

Flanders, Harley

1975-01-01

Algebra presents the essentials of algebra with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered, together with exponentials and logarithms.Comprised of eight chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of a

Starlight excitation of permitted lines in the Orion Nebula

International Nuclear Information System (INIS)

Grandi, S.A.

1975-01-01

From an idealized model of the Orion Nebula and from an analysis of line ratios it is shown that direct starlight excitation of the permitted O I line dominates over recombination and Lyman line fluorescence. The line strengths predicted by this mechanism agree reasonably well with those observed in the Orion Nebula. The application of direct starlight excitation to other ions is also discussed

Lukasiewicz-Moisil algebras

CERN Document Server

Boicescu, V; Georgescu, G; Rudeanu, S

1991-01-01

The Lukasiewicz-Moisil algebras were created by Moisil as an algebraic counterpart for the many-valued logics of Lukasiewicz. The theory of LM-algebras has developed to a considerable extent both as an algebraic theory of intrinsic interest and in view of its applications to logic and switching theory.This book gives an overview of the theory, comprising both classical results and recent contributions, including those of the authors. N-valued and &THgr;-valued algebras are presented, as well as &THgr;-algebras with negation.Mathematicians interested in lattice theory or symbolic logic, and computer scientists, will find in this monograph stimulating material for further research.

Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

Science.gov (United States)

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…

The Boolean algebra and central Galois algebras

Directory of Open Access Journals (Sweden)

George Szeto

2001-01-01

Full Text Available Let B be a Galois algebra with Galois group G, Jg={b∈B∣bx=g(xb   for all   x∈B} for g∈G, and BJg=Beg for a central idempotent eg. Then a relation is given between the set of elements in the Boolean algebra (Ba,≤ generated by {0,eg∣g∈G} and a set of subgroups of G, and a central Galois algebra Be with a Galois subgroup of G is characterized for an e∈Ba.

Lunar Entry Downmode Options for Orion

Science.gov (United States)

Smith, Kelly M.; Rea, Jeremy

2016-01-01

For Exploration Missions 1 and 2, the Orion capsules will be entering the Earth's atmosphere with speeds in excess of 11 km/s. In the event of a degraded Guidance, Navigation, and Control system, attempting the nominal guided entry may be inadvisable due to the potential for failures that result in a loss of vehicle (or crew, when crew are aboard). In such a case, a method of assuring Earth capture, water landing, and observence of trajectory constraints (heating, loads) is desired. Such a method should also be robust to large state uncertainty and variations in entry interface states. This document will explore four approaches evaluated and their performance in ensuring a safe return of the Orion capsule in the event of onboard system degradation.

Wavelets and quantum algebras

International Nuclear Information System (INIS)

Ludu, A.; Greiner, M.

1995-09-01

A non-linear associative algebra is realized in terms of translation and dilation operators, and a wavelet structure generating algebra is obtained. We show that this algebra is a q-deformation of the Fourier series generating algebra, and reduces to this for certain value of the deformation parameter. This algebra is also homeomorphic with the q-deformed su q (2) algebra and some of its extensions. Through this algebraic approach new methods for obtaining the wavelets are introduced. (author). 20 refs

Novikov-Jordan algebras

OpenAIRE

Dzhumadil'daev, A. S.

2002-01-01

Algebras with identity $(a\\star b)\\star (c\\star d) -(a\\star d)\\star(c\\star b)$ $=(a,b,c)\\star d-(a,d,c)\\star b$ are studied. Novikov algebras under Jordan multiplication and Leibniz dual algebras satisfy this identity. If algebra with such identity has unit, then it is associative and commutative.

Using Linear Algebra to Introduce Computer Algebra, Numerical Analysis, Data Structures and Algorithms (and To Teach Linear Algebra, Too).

Science.gov (United States)

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)

SOFIA/EXES High Spectral Resolution Observations of the Orion Hot Core

Science.gov (United States)

Rangwala, Naseem; Colgan, Sean; Le Gal, Romane; Acharya, Kinsuk; Huang, Xinchuan; Herbst, Eric; Lee, Timothy J.; Richter, Matthew J.; Boogert, Adwin

2018-01-01

The Orion hot core has one of the richest molecular chemistries observed in the ISM. In the MIR, the Orion hot core composition is best probed by the closest, compact, bright background continuum source in this region, IRc2. We present high-spectral resolution observations from 12.96 - 13.33 μm towards Orion IRc2 using the mid-infrared spectrograph, EXES, on SOFIA, to probe the physical and chemical conditions of the Orion hot core. All ten of the rovibrational C2H2 transitions expected in our spectral coverage, are detected with high S/N, yielding continuous coverage of the R-branch lines from J=9-8 to J=18-17, including both ortho and para species. Eight of these rovibrational transitions are newly reported detections. These data show distinct ortho and para ladders towards the Orion hot core for the first time, with an ortho to para ratio (OPR) of only 0.6 - much lower than the high temperature equilibrium value of 3. A non-equilibrium OPR is a further indication of the Orion hot core being heated externally by shocks likely resulting from a well-known explosive event which occurred 500 yrs ago. The OPR conversion timescales are much longer than the 500 yr shock timescale and thus a low OPR might be a remnant from an earlier colder pre-stellar phase before the density enhancement (now the hot core) was impacted by shocks.We will also present preliminary results from an on-going SOFIA Cycle-5 impact program to use EXES to conduct an unbiased, high-S/N, continuous, molecular line survey of the Orion hot core from 12.5 - 28.3 microns. This survey is expected to be 50 times better than ISO in detecting isolated, narrow lines to (a) resolve the ro-vibrational structure of the gas phase molecules and their kinematics, (b) detect new gas phase molecules missed by ISO, and (c) provide useful constraints on the hot core chemistry and the source of Orion hot core excitation. This survey will greatly enhance the inventory of resolved line features in the MIR for hot cores

(Quasi-)Poisson enveloping algebras

OpenAIRE

Yang, Yan-Hong; Yao, Yuan; Ye, Yu

2010-01-01

We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category of left modules over its quasi-Poisson enveloping algebra, and the category of Poisson modules is equivalent to the category of left modules over its Poisson enveloping algebra.

Iterated Leavitt Path Algebras

International Nuclear Information System (INIS)

Hazrat, R.

2009-11-01

Leavitt path algebras associate to directed graphs a Z-graded algebra and in their simplest form recover the Leavitt algebras L(1,k). In this note, we introduce iterated Leavitt path algebras associated to directed weighted graphs which have natural ± Z grading and in their simplest form recover the Leavitt algebras L(n,k). We also characterize Leavitt path algebras which are strongly graded. (author)

Algebraic topological entropy

International Nuclear Information System (INIS)

Hudetz, T.

1989-01-01

As a 'by-product' of the Connes-Narnhofer-Thirring theory of dynamical entropy for (originally non-Abelian) nuclear C * -algebras, the well-known variational principle for topological entropy is eqivalently reformulated in purly algebraically defined terms for (separable) Abelian C * -algebras. This 'algebraic variational principle' should not only nicely illustrate the 'feed-back' of methods developed for quantum dynamical systems to the classical theory, but it could also be proved directly by 'algebraic' methods and could thus further simplify the original proof of the variational principle (at least 'in principle'). 23 refs. (Author)

Linearizing W-algebras

International Nuclear Information System (INIS)

Krivonos, S.O.; Sorin, A.S.

1994-06-01

We show that the Zamolodchikov's and Polyakov-Bershadsky nonlinear algebras W 3 and W (2) 3 can be embedded as subalgebras into some linear algebras with finite set of currents. Using these linear algebras we find new field realizations of W (2) 3 and W 3 which could be a starting point for constructing new versions of W-string theories. We also reveal a number of hidden relationships between W 3 and W (2) 3 . We conjecture that similar linear algebras can exist for other W-algebra as well. (author). 10 refs

Quantum deformed su(mvertical stroke n) algebra and superconformal algebra on quantum superspace

International Nuclear Information System (INIS)

Kobayashi, Tatsuo

1993-01-01

We study a deformed su(mvertical stroke n) algebra on a quantum superspace. Some interesting aspects of the deformed algebra are shown. As an application of the deformed algebra we construct a deformed superconformal algebra. From the deformed su(1vertical stroke 4) algebra, we derive deformed Lorentz, translation of Minkowski space, iso(2,2) and its supersymmetric algebras as closed subalgebras with consistent automorphisms. (orig.)

75 FR 25202 - Action Affecting Export Privileges; Orion Air, S.L. and Syrian Pearl Airlines; Order Renewing...

Science.gov (United States)

2010-05-07

... DEPARTMENT OF COMMERCE Bureau of Industry and Security Action Affecting Export Privileges; Orion Air, S.L. and Syrian Pearl Airlines; Order Renewing Order Temporarily Denying Export Privileges Orion... Denying the Export Privileges of Respondents Orion Air, S.L. (``Orion Air'') and Syrian Pearl Airlines...

75 FR 67770 - General Motors Company, Formerly Known as General Motors Corporation, Orion Assembly Plant...

Science.gov (United States)

2010-11-03

..., Formerly Known as General Motors Corporation, Orion Assembly Plant, Including On-Site Leased Workers From Aerotek Automotive, Ryder and Premier Manufacturing Support Services, Lake Orion, MI; Amended... of General Motors Company, formerly known as General Motors Corporation, Orion Assembly Plant, Lake...

Linear algebraic groups

CERN Document Server

Springer, T A

1998-01-01

"[The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author [has a] student-friendly style… [The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literature…appear for the first time in a text." –Mathematical Reviews (Review of the Second Edition) "This book is a completely new version of the first edition. The aim of the old book was to present the theory of linear algebraic groups over an algebraically closed field. Reading that book, many people entered the research field of linear algebraic groups. The present book has a wider scope. Its aim is to treat the theory of linear algebraic groups over arbitrary fields. Again, the author keeps the treatment of prerequisites self-contained. The material of t...

Extended conformal algebras

International Nuclear Information System (INIS)

Goddard, Peter

1990-01-01

The algebra of the group of conformal transformations in two dimensions consists of two commuting copies of the Virasoro algebra. In many mathematical and physical contexts, the representations of ν which are relevant satisfy two conditions: they are unitary and they have the ''positive energy'' property that L o is bounded below. In an irreducible unitary representation the central element c takes a fixed real value. In physical contexts, the value of c is a characteristic of a theory. If c < 1, it turns out that the conformal algebra is sufficient to ''solve'' the theory, in the sense of relating the calculation of the infinite set of physically interesting quantities to a finite subset which can be handled in principle. For c ≥ 1, this is no longer the case for the algebra alone and one needs some sort of extended conformal algebra, such as the superconformal algebra. It is these algebras that this paper aims at addressing. (author)

Generalized symmetry algebras

International Nuclear Information System (INIS)

Dragon, N.

1979-01-01

The possible use of trilinear algebras as symmetry algebras for para-Fermi fields is investigated. The shortcomings of the examples are argued to be a general feature of such generalized algebras. (author)

Rota-Baxter algebras and the Hopf algebra of renormalization

Energy Technology Data Exchange (ETDEWEB)

Ebrahimi-Fard, K.

2006-06-15

Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

Rota-Baxter algebras and the Hopf algebra of renormalization

International Nuclear Information System (INIS)

Ebrahimi-Fard, K.

2006-06-01

Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

Galilean contractions of W-algebras

Directory of Open Access Journals (Sweden)

Jørgen Rasmussen

2017-09-01

Full Text Available Infinite-dimensional Galilean conformal algebras can be constructed by contracting pairs of symmetry algebras in conformal field theory, such as W-algebras. Known examples include contractions of pairs of the Virasoro algebra, its N=1 superconformal extension, or the W3 algebra. Here, we introduce a contraction prescription of the corresponding operator-product algebras, or equivalently, a prescription for contracting tensor products of vertex algebras. With this, we work out the Galilean conformal algebras arising from contractions of N=2 and N=4 superconformal algebras as well as of the W-algebras W(2,4, W(2,6, W4, and W5. The latter results provide evidence for the existence of a whole new class of W-algebras which we call Galilean W-algebras. We also apply the contraction prescription to affine Lie algebras and find that the ensuing Galilean affine algebras admit a Sugawara construction. The corresponding central charge is level-independent and given by twice the dimension of the underlying finite-dimensional Lie algebra. Finally, applications of our results to the characterisation of structure constants in W-algebras are proposed.

Quantum affine algebras and deformations of the virasoro and W-algebras

International Nuclear Information System (INIS)

Frenkel, E.; Reshetikhin, N.

1996-01-01

Using the Wakimoto realization of quantum affine algebras we define new Poisson algebras, which are q-deformations of the classical W-algebras. We also define their free field realizations, i.e. homomorphisms into some Heisenberg-Poisson algebras. The formulas for these homomorphisms coincide with formulas for spectra of transfer-matrices in the corresponding quantum integrable models derived by the Bethe-Ansatz method. (orig.)

Algebraic entropy for algebraic maps

International Nuclear Information System (INIS)

Hone, A N W; Ragnisco, Orlando; Zullo, Federico

2016-01-01

We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Bäcklund transformations. (letter)

On hyper BCC-algebras

OpenAIRE

Borzooei, R. A.; Dudek, W. A.; Koohestani, N.

2006-01-01

We study hyper BCC-algebras which are a common generalization of BCC-algebras and hyper BCK-algebras. In particular, we investigate different types of hyper BCC-ideals and describe the relationship among them. Next, we calculate all nonisomorphic 22 hyper BCC-algebras of order 3 of which only three are not hyper BCK-algebras.

On hyper BCC-algebras

Directory of Open Access Journals (Sweden)

R. A. Borzooei

2006-01-01

Full Text Available We study hyper BCC-algebras which are a common generalization of BCC-algebras and hyper BCK-algebras. In particular, we investigate different types of hyper BCC-ideals and describe the relationship among them. Next, we calculate all nonisomorphic 22 hyper BCC-algebras of order 3 of which only three are not hyper BCK-algebras.

Algebraic theory of numbers

CERN Document Server

Samuel, Pierre

2008-01-01

Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics - algebraic geometry, in particular.This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Gal

The BRS algebra of a free differential algebra

International Nuclear Information System (INIS)

Boukraa, S.

1987-04-01

We construct in this work, the Weil and the universal BRS algebras of theories that can have as a gauge symmetry a free differential (Sullivan) algebra, the natural extension of Lie algebras allowing the definition of p-form gauge potentials (p>1). The finite gauge transformations of these potentials are deduced from the infinitesimal ones and the group structure is shown. The geometrical meaning of these p-form gauge potentials is given by the notion of a Quillen superconnection. (author). 19 refs

Orion Emergency Mask Approach

Science.gov (United States)

Tuan, George C.; Graf, John C.

2009-01-01

Emergency mask approach on Orion poses a challenge to the traditional Shuttle or Station approaches. Currently, in the case of a fire or toxic spill event, the crew utilizes open loop oxygen masks that provide the crew with oxygen to breath, but also dumps the exhaled oxygen into the cabin. For Orion, with a small cabin volume, the extra oxygen will exceed the flammability limit within a short period of time, unless a nitrogen purge is also provided. Another approach to a fire or toxic spill event is the use of a filtering emergency masks. These masks utilize some form of chemical beds to scrub the air clean of toxic providing the crew safe breathing air for a period without elevating the oxygen level in the cabin. Using the masks and a form of smoke-eater filter, it may be possible to clean the cabin completely or to a level for safe transition to a space suit to perform a cabin purge. Issues with filters in the past have been the reaction time, breakthroughs, and high breathing resistance. Development in a new form of chemical filters has shown promise to make the filtering approach feasible.

Pseudo-Riemannian Novikov algebras

Energy Technology Data Exchange (ETDEWEB)

Chen Zhiqi; Zhu Fuhai [School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071 (China)], E-mail: chenzhiqi@nankai.edu.cn, E-mail: zhufuhai@nankai.edu.cn

2008-08-08

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.

On the PR-algebras

International Nuclear Information System (INIS)

Lebedenko, V.M.

1978-01-01

The PR-algebras, i.e. the Lie algebras with commutation relations of [Hsub(i),Hsub(j)]=rsub(ij)Hsub(i)(i< j) type are investigated. On the basis of former results a criterion for the membership of 2-solvable Lie algebras to the PR-algebra class is given. The conditions imposed by the criterion are formulated in the linear algebra language

Introduction to W-algebras

International Nuclear Information System (INIS)

Takao, Masaru

1989-01-01

We review W-algebras which are generated by stress tensor and primary fields. Associativity plays an important role in determining the extended algebra and further implies the algebras to exist for special values of central charges. Explicitly constructing the algebras including primary fields of spin less than 4, we investigate the closure structure of the Jacobi identity of the extended algebras. (author)

Design and Flight Performance of the Orion Pre-Launch Navigation System

Science.gov (United States)

Zanetti, Renato

2016-01-01

Launched in December 2014 atop a Delta IV Heavy from the Kennedy Space Center, the Orion vehicle's Exploration Flight Test-1 (EFT-1) successfully completed the objective to test the prelaunch and entry components of the system. Orion's pre-launch absolute navigation design is presented, together with its EFT-1 performance.

(Modular Effect Algebras are Equivalent to (Frobenius Antispecial Algebras

Directory of Open Access Journals (Sweden)

Dusko Pavlovic

2017-01-01

Full Text Available Effect algebras are one of the generalizations of Boolean algebras proposed in the quest for a quantum logic. Frobenius algebras are a tool of categorical quantum mechanics, used to present various families of observables in abstract, often nonstandard frameworks. Both effect algebras and Frobenius algebras capture their respective fragments of quantum mechanics by elegant and succinct axioms; and both come with their conceptual mysteries. A particularly elegant and mysterious constraint, imposed on Frobenius algebras to characterize a class of tripartite entangled states, is the antispecial law. A particularly contentious issue on the quantum logic side is the modularity law, proposed by von Neumann to mitigate the failure of distributivity of quantum logical connectives. We show that, if quantum logic and categorical quantum mechanics are formalized in the same framework, then the antispecial law of categorical quantum mechanics corresponds to the natural requirement of effect algebras that the units are each other's unique complements; and that the modularity law corresponds to the Frobenius condition. These correspondences lead to the equivalence announced in the title. Aligning the two formalisms, at the very least, sheds new light on the concepts that are more clearly displayed on one side than on the other (such as e.g. the orthogonality. Beyond that, it may also open up new approaches to deep and important problems of quantum mechanics (such as the classification of complementary observables.

An algorithm to construct the basic algebra of a skew group algebra

NARCIS (Netherlands)

Horobeţ, E.

2016-01-01

We give an algorithm for the computation of the basic algebra Morita equivalent to a skew group algebra of a path algebra by obtaining formulas for the number of vertices and arrows of the new quiver Qb. We apply this algorithm to compute the basic algebra corresponding to all simple quaternion

Compact quantum group C*-algebras as Hopf algebras with approximate unit

International Nuclear Information System (INIS)

Do Ngoc Diep; Phung Ho Hai; Kuku, A.O.

1999-04-01

In this paper, we construct and study the representation theory of a Hopf C*-algebra with approximate unit, which constitutes quantum analogue of a compact group C*-algebra. The construction is done by first introducing a convolution-product on an arbitrary Hopf algebra H with integral, and then constructing the L 2 and C*-envelopes of H (with the new convolution-product) when H is a compact Hopf *-algebra. (author)

Intervals in Generalized Effect Algebras and their Sub-generalized Effect Algebras

Directory of Open Access Journals (Sweden)

Zdenka Riečanová

2013-01-01

Full Text Available We consider subsets G of a generalized effect algebra E with 0∈G and such that every interval [0, q]G = [0, q]E ∩ G of G (q ∈ G , q ≠ 0 is a sub-effect algebra of the effect algebra [0, q]E. We give a condition on E and G under which every such G is a sub-generalized effect algebra of E.

Application of Terrestrial Environments in Orion Assessments

Science.gov (United States)

Barbre, Robert E.

2016-01-01

This presentation summarizes the Marshall Space Flight Center Natural Environments Terrestrial and Planetary Environments (TPE) Team support to the NASA Orion space vehicle. The TPE utilizes meteorological data to assess the sensitivities of the vehicle due to the terrestrial environment. The Orion vehicle, part of the Multi-Purpose Crew Vehicle Program, is designed to carry astronauts beyond low-earth orbit and is currently undergoing a series of tests including Exploration Test Flight (EFT) - 1. The presentation describes examples of TPE support for vehicle design and several tests, as well as support for EFT-1 and planning for upcoming Exploration Missions while emphasizing the importance of accounting for the natural environment's impact to the vehicle early in the vehicle's program.

Variants of bosonization in parabosonic algebra: the Hopf and super-Hopf structures in parabosonic algebra

International Nuclear Information System (INIS)

Kanakoglou, K; Daskaloyannis, C

2008-01-01

Parabosonic algebra in finite or infinite degrees of freedom is considered as a Z 2 -graded associative algebra, and is shown to be a Z 2 -graded (or super) Hopf algebra. The super-Hopf algebraic structure of the parabosonic algebra is established directly without appealing to its relation to the osp(1/2n) Lie superalgebraic structure. The notion of super-Hopf algebra is equivalently described as a Hopf algebra in the braided monoidal category CZ 2 M. The bosonization technique for switching a Hopf algebra in the braided monoidal category H M (where H is a quasitriangular Hopf algebra) into an ordinary Hopf algebra is reviewed. In this paper, we prove that for the parabosonic algebra P B , beyond the application of the bosonization technique to the original super-Hopf algebra, a bosonization-like construction is also achieved using two operators, related to the parabosonic total number operator. Both techniques switch the same super-Hopf algebra P B to an ordinary Hopf algebra, thus producing two different variants of P B , with an ordinary Hopf structure

ORiON: Site Map

African Journals Online (AJOL)

Journal Home · Journals · ORiON · About · Log In · Register · Advanced Search · By Author · By Title. Issues. Current Issue · Archives · Open Journal Systems · Help. ISSN: 0529-191-X. AJOL African Journals Online. HOW TO USE AJOL... for Researchers · for Librarians · for Authors · FAQ's · More about AJOL · AJOL's ...

The C*-algebra of a vector bundle and fields of Cuntz algebras

OpenAIRE

Vasselli, Ezio

2004-01-01

We study the Pimsner algebra associated with the module of continuous sections of a Hilbert bundle, and prove that it is a continuous bundle of Cuntz algebras. We discuss the role of such Pimsner algebras w.r.t. the notion of inner endomorphism. Furthermore, we study bundles of Cuntz algebras carrying a global circle action, and assign to them a class in the representable KK-group of the zero-grade bundle. We compute such class for the Pimsner algebra of a vector bundle.

Bicovariant quantum algebras and quantum Lie algebras

International Nuclear Information System (INIS)

Schupp, P.; Watts, P.; Zumino, B.

1993-01-01

A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(G q ) to U q g, given by elements of the pure braid group. These operators - the 'reflection matrix' Y= triple bond 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). (orig.)

Environmental impact study of Orion Nebula dust

International Nuclear Information System (INIS)

Cardelli, J.A.; Clayton, G.C.

1988-01-01

In this paper, new high-quality extinction curves are presented for Theta-1 Ori A, C, and D, and Theta-2 Ori A and B, over the wavelength range 3300-6000 A. These are coupled with near-infrared and ultraviolet data to produce extinction curves from 0.12 to 3.5 microns. The Orion Nebula region is interesting in that most of the known processes of dust-grain growth, processing, and destruction may be operating nearly simultaneously in close proximity to one another. Each of these processes is considered with respect to the observed extinction curves and environmental conditions in the Orion Nebula and its associated molecular cloud. Plausible grain populations are fit to the observed extinction curves. A good fit to the average Theta Ori extinction curve can be obtained with: (1) a combination of larger than normal silicate grains produced through coagulation and accretion; (2) evaporation of volatile mantles; and (3) a reduction in the column density of small (smaller than 0.01 micron) grains responsible for the bump and far-ultraviolet extinction through differential acceleration due to radiation pressure and possible evaporation. It seems plausible to explain the observed peculiar extinction in the Orion Nebula simply by environmental effects on otherwise normal grains. 59 references

Simple relation algebras

CERN Document Server

Givant, Steven

2017-01-01

This monograph details several different methods for constructing simple relation algebras, many of which are new with this book. By drawing these seemingly different methods together, all are shown to be aspects of one general approach, for which several applications are given. These tools for constructing and analyzing relation algebras are of particular interest to mathematicians working in logic, algebraic logic, or universal algebra, but will also appeal to philosophers and theoretical computer scientists working in fields that use mathematics. The book is written with a broad audience in mind and features a careful, pedagogical approach; an appendix contains the requisite background material in relation algebras. Over 400 exercises provide ample opportunities to engage with the material, making this a monograph equally appropriate for use in a special topics course or for independent study. Readers interested in pursuing an extended background study of relation algebras will find a comprehensive treatme...

Ultraviolet spectrophotometry of some stars in the Orion OBI association

International Nuclear Information System (INIS)

Oganesyan, R.Kh.; Gasparyan, K.G.

1980-01-01

The results of measurements of 56 short wavelength spectra of 22 stars in the Orion OBI association obtained by means of the space observatory Orion-2 are presented. The absolute energy distribution in their continuum is obtained. The measured energy distributions in the spectra of B-type stars in the region 2150-3700 A are in good agreement with the theoretical blocking model developed by Van Citters and Morton, and those of two A-type stars with Kurucz model. It has been found that for several B-type Orion stars there exists some discrepancy between the spectral type and their effective temperature, the last one being higher than for MK spectral types. The depression in the continuous spectra of A-type stars can be explained by the blocking effect

Boolean algebra

CERN Document Server

Goodstein, R L

2007-01-01

This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions.

Combinatorial commutative algebra

CERN Document Server

Miller, Ezra

2005-01-01

Offers an introduction to combinatorial commutative algebra, focusing on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determined rings. The chapters in this work cover topics ranging from homological invariants of monomial ideals and their polyhedral resolutions, to tools for studying algebraic varieties.

Topological أ-algebras with Cأ-enveloping algebras II

Indian Academy of Sciences (India)

necessarily complete) pro-Cأ-topology which coincides with the relative uniform .... problems in Cأ-algebras, Phillips introduced more general weakly Cأ- .... Banach أ-algebra obtained by completing A=Np in the norm jjxpjjp ¼ pًxق where.

C*-algebras by example

CERN Document Server

Davidson, Kenneth R

1996-01-01

The subject of C*-algebras received a dramatic revitalization in the 1970s by the introduction of topological methods through the work of Brown, Douglas, and Fillmore on extensions of C*-algebras and Elliott's use of K-theory to provide a useful classification of AF algebras. These results were the beginning of a marvelous new set of tools for analyzing concrete C*-algebras. This book is an introductory graduate level text which presents the basics of the subject through a detailed analysis of several important classes of C*-algebras. The development of operator algebras in the last twenty yea

Observations of far-infrared line profiles in the Orion-KL region

International Nuclear Information System (INIS)

Crawford, M.K.; Lugten, J.B.; Fitelson, W.; Genzel, R.; Melnick, G.; Harvard-Smithsonian Center for Astrophysics, Cambridge, MA)

1986-01-01

Measurements of several far-infrared emission line profiles in the Orion-KL region are reported. The emission from the CO, OH, and forbidden O I emission lines toward the BN-KL and H2 peak 1 positions probably comes from dense, hot molecular gas in the Orion-KL shock. The CO and forbidden O I lines have similar profiles, suggesting that the high-velocity forbidden O I emission also arises in magnetohydrodynamic cloud shocks. The velocity centroids of the lines are somewhat blueshifted. The far-infrared data thus support the interpretation that the blue asymmetry of the H2 2 micron lines is not mainly due to differential dust extinction, but rather to the kinematics and geometry of the shocked gas in the Orion-KL outflow. The forbidden O I and CO lines, however, have significantly less extreme blueshifted emission than the H2 lines. Both the forbidden O I 63 micron and forbidden C II 158 micron lines have features strongly supporting a common origin near the surface of the Orion molecular cloud. 28 references

Non-freely generated W-algebras and construction of N=2 super W-algebras

International Nuclear Information System (INIS)

Blumenhagen, R.

1994-07-01

Firstly, we investigate the origin of the bosonic W-algebras W(2, 3, 4, 5), W(2, 4, 6) and W(2, 4, 6) found earlier by direct construction. We present a coset construction for all three examples leading to a new type of finitely, non-freely generated quantum W-algebras, which we call unifying W-algebras. Secondly, we develop a manifest covariant formalism to construct N = 2 super W-algebras explicitly on a computer. Applying this algorithm enables us to construct the first four examples of N = 2 super W-algebras with two generators and the N = 2 super W 4 algebra involving three generators. The representation theory of the former ones shows that all examples could be divided into four classes, the largest one containing the N = 2 special type of spectral flow algebras. Besides the W-algebra of the CP(3) Kazama-Suzuki coset model, the latter example with three generators discloses a second solution which could also be explained as a unifying W-algebra for the CP(n) models. (orig.)

On fuorlike variations of brightness of the Orion association stars

International Nuclear Information System (INIS)

Paesamyan, Eh.S.; Gasparyan, K.G.

1987-01-01

The results of observations of fourlike Sugano and Chanal objects in Orion association are given. The light curve, amplitude to flare and colour index are determined. It has been shown that the Sugano object is both Orion variable and a flare star. An assumption about the intensification of outflow of matter with same velocities in those objects as made. The luminosity of P Cyg before the flare is determined

Algebraic conformal field theory

International Nuclear Information System (INIS)

Fuchs, J.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica

1991-11-01

Many conformal field theory features are special versions of structures which are present in arbitrary 2-dimensional quantum field theories. So it makes sense to describe 2-dimensional conformal field theories in context of algebraic theory of superselection sectors. While most of the results of the algebraic theory are rather abstract, conformal field theories offer the possibility to work out many formulae explicitly. In particular, one can construct the full algebra A-bar of global observables and the endomorphisms of A-bar which represent the superselection sectors. Some explicit results are presented for the level 1 so(N) WZW theories; the algebra A-bar is found to be the enveloping algebra of a Lie algebra L-bar which is an extension of the chiral symmetry algebra of the WZW theory. (author). 21 refs., 6 figs

Internal Acoustics of the ISS and Other Spacecraft

Science.gov (United States)

Allen, Christopher S.

2017-01-01

It is important to control the acoustic environment inside spacecraft and space habitats to protect for astronaut communications, alarm audibility, and habitability, and to reduce astronauts' risk for sleep disturbance, and hear-ing loss. But this is not an easy task, given the various design trade-offs, and it has been difficult, historically, to achieve. Over time it has been found that successful control of spacecraft acoustic levels is achieved by levying firm requirements at the system-level, using a systems engineering approach for design and development, and then validating these requirements with acoustic testing. In the systems engineering method, the system-level requirements must be flowed down to sub-systems and component noise sources, using acoustic analysis and acoustic modelling to develop allocated requirements for the sub-systems and components. Noise controls must also be developed, tested, and implemented so the sub-systems and components can achieve their allocated limits. It is also important to have management support for acoustics efforts to maintain their priority against the various trade-offs, including mass, volume, power, cost, and schedule. In this extended abstract and companion presentation, the requirements, approach, and results for controlling acoustic levels in most US spacecraft since Apollo will be briefly discussed. The approach for controlling acoustic levels in the future US space vehicle, Orion Multipurpose Crew Vehicle (MPCV), will also be briefly discussed. These discussions will be limited to the control of continuous noise inside the space vehicles. Other types of noise, such as launch, landing, and abort noise, intermittent noise, Extra-Vehicular Activity (EVA) noise, emergency operations/off-nominal noise, noise exposure, and impulse noise are important, but will not be discussed because of time limitations.

The Large-Scale Distribution and Motions of Older Stars in Orion

NARCIS (Netherlands)

Brown, A. G. A.; Walter, F. M.; Blaauw, Adriaan

1998-01-01

Abstract: We review the current knowledge of the population of `older' stars in the Orion OB1 association, specifically those in subgroups 1a and 1b. We briefly outline the history of the subject and then continue with a summary of the present state of knowledge of the early-type stars in Orion OB1.

Boolean algebra essentials

CERN Document Server

Solomon, Alan D

2012-01-01

REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Boolean Algebra includes set theory, sentential calculus, fundamental ideas of Boolean algebras, lattices, rings and Boolean algebras, the structure of a Boolean algebra, and Boolean

q-deformed Poincare algebra

International Nuclear Information System (INIS)

Ogievetsky, O.; Schmidke, W.B.; Wess, J.; Muenchen Univ.; Zumino, B.; Lawrence Berkeley Lab., CA

1992-01-01

The q-differential calculus for the q-Minkowski space is developed. The algebra of the q-derivatives with the q-Lorentz generators is found giving the q-deformation of the Poincare algebra. The reality structure of the q-Poincare algebra is given. The reality structure of the q-differentials is also found. The real Laplaacian is constructed. Finally the comultiplication, counit and antipode for the q-Poincare algebra are obtained making it a Hopf algebra. (orig.)

Generalizing the bms3 and 2D-conformal algebras by expanding the Virasoro algebra

Science.gov (United States)

Caroca, Ricardo; Concha, Patrick; Rodríguez, Evelyn; Salgado-Rebolledo, Patricio

2018-03-01

By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the bms3 algebra are obtained from the Virasoro algebra. We extend this result to construct new families of expanded Virasoro algebras that turn out to be infinite-dimensional lifts of the so-called Bk, Ck and Dk algebras recently introduced in the literature in the context of (super)gravity. We also show how some of these new infinite-dimensional symmetries can be obtained from expanded Kač-Moody algebras using modified Sugawara constructions. Applications in the context of three-dimensional gravity are briefly discussed.

Aperture synthesis observations of NH3 in OMC-1 - Filamentary structures around Orion-KL

International Nuclear Information System (INIS)

Murata, Yasuhiro; Kawabe, Ryohei; Ishiguro, Masato; Morita, Kohichiro; Kasuga, Takashi

1990-01-01

Aperture synthesis observations of the Orion molecular cloud 1 (OMC-1) have been made in NH 3 (1, 1) and (2, 2) emission at 23.7 GHz, using the Nobeyama Millimeter Array (NMA), and obtained 16 arcsec resolution maps for OMC-1 and 8 arcsec resolution maps for the Orion-KL region. Filamentary structures extending over 0.5 pc from the Orion-KL region to the north and northwest directions were found. These structures are associated with the H2 finger structures and Herbig-Haro objects which are located at the blue-shifted side of the bipolar molecular outflow. The results suggest that these filaments are ambient molecular cloudlets with shocked surfaces caused by the strong stellar wind from the Orion-KL region. The 8 arcsec resolution NH 3 (2, 2) maps show the extended features around the hot core of Orion-KL. These extended features correspond to the rotating disk and shocked shell associated with the bipolar molecular outflow. 37 refs

Introduction to quantum algebras

International Nuclear Information System (INIS)

Kibler, M.R.

1992-09-01

The concept of a quantum algebra is made easy through the investigation of the prototype algebras u qp (2), su q (2) and u qp (1,1). The latter quantum algebras are introduced as deformations of the corresponding Lie algebras; this is achieved in a simple way by means of qp-bosons. The Hopf algebraic structure of u qp (2) is also discussed. The basic ingredients for the representation theory of u qp (2) are given. Finally, in connection with the quantum algebra u qp (2), the qp-analogues of the harmonic oscillator are discussed and of the (spherical and hyperbolical) angular momenta. (author) 50 refs

Continuum analogues of contragredient Lie algebras

International Nuclear Information System (INIS)

Saveliev, M.V.; Vershik, A.M.

1989-03-01

We present an axiomatic formulation of a new class of infinite-dimensional Lie algebras - the generalizations of Z-graded Lie algebras with, generally speaking, an infinite-dimensional Cartan subalgebra and a contiguous set of roots. We call such algebras ''continuum Lie algebras''. The simple Lie algebras of constant growth are encapsulated in our formulation. We pay particular attention to the case when the local algebra is parametrized by a commutative algebra while the Cartan operator (the generalization of the Cartan matrix) is a linear operator. Special examples of these algebras are the Kac-Moody algebras, algebras of Poisson brackets, algebras of vector fields on a manifold, current algebras, and algebras with differential or integro-differential Cartan operator. The nonlinear dynamical systems associated with the continuum contragredient Lie algebras are also considered. (author). 9 refs

Lectures on algebraic statistics

CERN Document Server

Drton, Mathias; Sullivant, Seth

2009-01-01

How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models.

Quiver W-algebras

Science.gov (United States)

Kimura, Taro; Pestun, Vasily

2018-06-01

For a quiver with weighted arrows, we define gauge-theory K-theoretic W-algebra generalizing the definition of Shiraishi et al. and Frenkel and Reshetikhin. In particular, we show that the qq-character construction of gauge theory presented by Nekrasov is isomorphic to the definition of the W-algebra in the operator formalism as a commutant of screening charges in the free field representation. Besides, we allow arbitrary quiver and expect interesting applications to representation theory of generalized Borcherds-Kac-Moody Lie algebras, their quantum affinizations and associated W-algebras.

Abstract algebra

CERN Document Server

Garrett, Paul B

2007-01-01

Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal

College algebra

CERN Document Server

Kolman, Bernard

1985-01-01

College Algebra, Second Edition is a comprehensive presentation of the fundamental concepts and techniques of algebra. The book incorporates some improvements from the previous edition to provide a better learning experience. It provides sufficient materials for use in the study of college algebra. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, exponential and logarithmic functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter c

Orion European Service Module (ESM) Development, Integration and Qualification Status

Science.gov (United States)

Berthe, Philippe; Over, Ann P.; Picardo, Michelle; Byers, Anthony W.

2017-01-01

ESA and the European Industry are supplying the European Service Module for Orion. An overview of the system and subsystem configuration of the Orion European Service Module (ESM) as designed and built for the EM-1 mission is provided as well as an outline of its development, assembly, integration and verification process performed by ESA and NASA in coordination with their respective Industrial prime contractors, Airbus Defence and Space and Lockheed Martin.

Twisted classical Poincare algebras

International Nuclear Information System (INIS)

Lukierski, J.; Ruegg, H.; Tolstoy, V.N.; Nowicki, A.

1993-11-01

We consider the twisting of Hopf structure for classical enveloping algebra U(g), where g is the inhomogeneous rotations algebra, with explicite formulae given for D=4 Poincare algebra (g=P 4 ). The comultiplications of twisted U F (P 4 ) are obtained by conjugating primitive classical coproducts by F element of U(c)xU(c), where c denotes any Abelian subalgebra of P 4 , and the universal R-matrices for U F (P 4 ) are triangular. As an example we show that the quantum deformation of Poincare algebra recently proposed by Chaichian and Demiczev is a twisted classical Poincare algebra. The interpretation of twisted Poincare algebra as describing relativistic symmetries with clustered 2-particle states is proposed. (orig.)

Pre-Algebra Essentials For Dummies

CERN Document Server

Zegarelli, Mark

2010-01-01

Many students worry about starting algebra. Pre-Algebra Essentials For Dummies provides an overview of critical pre-algebra concepts to help new algebra students (and their parents) take the next step without fear. Free of ramp-up material, Pre-Algebra Essentials For Dummies contains content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical pre-algebra course, from fractions, decimals, and percents to scientific notation and simple variable equations. This guide is also a perfect reference for parents who need to review critical pre-algebra

The MagOrion - A propulsion system for human exploration of the outer planets

International Nuclear Information System (INIS)

Andrews, Jason; Andrews, Dana

2000-01-01

Manned exploration beyond Mars requires very high specific energy. The only potential solution under discussion is fusion propulsion. However, fusion has been ten years away for forty years. We have an available solution that combines new technology with an old concept-'Project Orion'. The proposed 'MagOrion' Propulsion System combines a magnetic sail (MagSail) with conventional small yield (0.5 to 1.0 kiloton) shaped nuclear fission devices. At denonation, roughly eighty percent of the yield appears as a highly-ionized plasma, and when detonated two kilometers behind a robust MagSail, approximately half of this plasma can be stopped and turned into thrust. A MagOrion can provide a system acceleration of one or more gravities with effective specific impulses ranging from 15,000 to 45,000 seconds. Dana Andrews and Robert Zubrin published a paper in 1997 that described the operating principles of the MagOrion. We have taken that concept through conceptual design to identify the major operational features and risks. The risks are considerable, but the potential payoff is staggering. Our proposed MagOrion will enable affordable exploration of the solar system

Representations of quantum bicrossproduct algebras

International Nuclear Information System (INIS)

Arratia, Oscar; Olmo, Mariano A del

2002-01-01

We present a method to construct induced representations of quantum algebras which have a bicrossproduct structure. We apply this procedure to some quantum kinematical algebras in (1+1) dimensions with this kind of structure: null-plane quantum Poincare algebra, non-standard quantum Galilei algebra and quantum κ-Galilei algebra

Algorithms in Algebraic Geometry

CERN Document Server

Dickenstein, Alicia; Sommese, Andrew J

2008-01-01

In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its

Computer algebra and operators

Science.gov (United States)

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.

Abstract Algebra to Secondary School Algebra: Building Bridges

Science.gov (United States)

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…

Infinite dimension algebra and conformal symmetry

International Nuclear Information System (INIS)

Ragoucy-Aubezon, E.

1991-04-01

A generalisation of Kac-Moody algebras (current algebras defined on a circle) to algebras defined on a compact supermanifold of any dimension and with any number of supersymmetries is presented. For such a purpose, we compute all the central extensions of loop algebras defined on this supermanifold, i.e. all the cohomology classes of these loop algebras. Then, we try to extend the relation (i.e. semi-direct sum) that exists between the two dimensional conformal algebras (called Virasoro algebra) and the usual Kac-Moody algebras, by considering the derivation algebra of our extended Kac-Moody algebras. The case of superconformal algebras (used in superstrings theories) is treated, as well as the cases of area-preserving diffeomorphisms (used in membranes theories), and Krichever-Novikov algebras (used for interacting strings). Finally, we present some generalizations of the Sugawara construction to the cases of extended Kac-Moody algebras, and Kac-Moody of superalgebras. These constructions allow us to get new realizations of the Virasoro, and Ramond, Neveu-Schwarz algebras

Equivalency of two-dimensional algebras

International Nuclear Information System (INIS)

Santos, Gildemar Carneiro dos; Pomponet Filho, Balbino Jose S.

2011-01-01

Full text: Let us consider a vector z = xi + yj over the field of real numbers, whose basis (i,j) satisfy a given algebra. Any property of this algebra will be reflected in any function of z, so we can state that the knowledge of the properties of an algebra leads to more general conclusions than the knowledge of the properties of a function. However structural properties of an algebra do not change when this algebra suffers a linear transformation, though the structural constants defining this algebra do change. We say that two algebras are equivalent to each other whenever they are related by a linear transformation. In this case, we have found that some relations between the structural constants are sufficient to recognize whether or not an algebra is equivalent to another. In spite that the basis transform linearly, the structural constants change like a third order tensor, but some combinations of these tensors result in a linear transformation, allowing to write the entries of the transformation matrix as function of the structural constants. Eventually, a systematic way to find the transformation matrix between these equivalent algebras is obtained. In this sense, we have performed the thorough classification of associative commutative two-dimensional algebras, and find that even non-division algebra may be helpful in solving non-linear dynamic systems. The Mandelbrot set was used to have a pictorial view of each algebra, since equivalent algebras result in the same pattern. Presently we have succeeded in classifying some non-associative two-dimensional algebras, a task more difficult than for associative one. (author)

Chemical homogeneity in the Orion Association: Oxygen abundances of B stars

Directory of Open Access Journals (Sweden)

Lanz T.

2012-02-01

Full Text Available We present non-LTE oxygen abundances for a sample of B stars in the Orion association. The abundance calculations included non-LTE line formation and used fully blanketed non-LTE model atmospheres. The stellar parameters were the same as adopted in the previous study by Cunha & Lambert (1994. We find that the young Orion stars in this sample of 10 stars are described by a single oxygen abundance with an average value of A(O = 8.78 and a small dispersion of ±0.05, dex which is of the order of the uncertainties in the analysis. This average oxygen abundance compares well with the average oxygen abundance obtained previously in Cunha & Lambert (1994: A(O = 8.72 ± 0.13 although this earlier study, based upon non-blanketed model atmospheres in LTE, displayed larger scatter. Small scatter of chemical abundances in Orion B stars had also been found in our previous studies for neon and argon; all based on the same effective temperature scale. The derived oxygen abundance distribution for the Orion association compares well with other results for the oxygen abundance in the solar neighborhood.

Dynamical explanation for the high water abundance detected in Orion

International Nuclear Information System (INIS)

Elitzur, M.

1979-01-01

Shock wave chemistry is suggested as the likely explanation for the high water abundance which has been recently detected in Orion by Phyllips et al. The existence of such a shock and its inferred properties are in agreement with other observations of Orion such as the broad velocity feature and H 2 vibration emission. Shock waves are proposed as the likely explanation for high water abundances observed in other sources such as the strong H 2 O masers

THREE-DIMENSIONAL DUST MAPPING REVEALS THAT ORION FORMS PART OF A LARGE RING OF DUST

International Nuclear Information System (INIS)

Schlafly, E. F.; Rix, H.-W.; Martin, N. F.; Green, G.; Finkbeiner, D. P.; Burgett, W. S.; Chambers, K. C.; Kaiser, N.; Morgan, J. S.; Tonry, J. L.; Wainscoat, R. J.; Waters, C.; Draper, P. W.; Metcalfe, N.; Price, P. A.

2015-01-01

The Orion Molecular Complex is the nearest site of ongoing high-mass star formation, making it one of the most extensively studied molecular complexes in the Galaxy. We have developed a new technique for mapping the three-dimensional distribution of dust in the Galaxy using Pan-STARRS1 photometry. We isolate the dust at the distance to Orion using this technique, revealing a large (100 pc, 14° diameter), previously unrecognized ring of dust, which we term the ''Orion dust ring''. The ring includes Orion A and B, and is not coincident with current Hα features. The circular morphology suggests formation as an ancient bubble in the interstellar medium, though we have not been able to conclusively identify the source of the bubble. This hint at the history of Orion may have important consequences for models of high-mass star formation and triggered star formation

Axis Problem of Rough 3-Valued Algebras

Institute of Scientific and Technical Information of China (English)

Jianhua Dai; Weidong Chen; Yunhe Pan

2006-01-01

The collection of all the rough sets of an approximation space has been given several algebraic interpretations, including Stone algebras, regular double Stone algebras, semi-simple Nelson algebras, pre-rough algebras and 3-valued Lukasiewicz algebras. A 3-valued Lukasiewicz algebra is a Stone algebra, a regular double Stone algebra, a semi-simple Nelson algebra, a pre-rough algebra. Thus, we call the algebra constructed by the collection of rough sets of an approximation space a rough 3-valued Lukasiewicz algebra. In this paper,the rough 3-valued Lukasiewicz algebras, which are a special kind of 3-valued Lukasiewicz algebras, are studied. Whether the rough 3-valued Lukasiewicz algebra is a axled 3-valued Lukasiewicz algebra is examined.

Enveloping σ-C C C-algebra of a smooth Frechet algebra crossed ...

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences; Volume 116; Issue 2. Enveloping -*-Algebra of a Smooth Frechet Algebra Crossed Product by R R , K -Theory and Differential Structure in *-Algebras. Subhash J Bhatt. Regular Articles Volume 116 Issue 2 May 2006 pp 161-173 ...

Hecke algebras with unequal parameters

CERN Document Server

Lusztig, G

2003-01-01

Hecke algebras arise in representation theory as endomorphism algebras of induced representations. One of the most important classes of Hecke algebras is related to representations of reductive algebraic groups over p-adic or finite fields. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KL-basis) in a Hecke algebra, which is very important in studying relations between representation theory and geometry of the corresponding flag varieties. It turned out that the elements of the KL-basis also possess very interesting combinatorial properties. In the present book, the author extends the theory of the KL-basis to a more general class of Hecke algebras, the so-called algebras with unequal parameters. In particular, he formulates conjectures describing the properties of Hecke algebras with unequal parameters and presents examples verifying these conjectures in particular cases. Written in the author's precise style, the book gives rese...

The Space Operations Simulation Center (SOSC) and Closed-Loop Hardware Testing for Orion Rendezvous System Design

Science.gov (United States)

Milenkovic, Zoran; DSouza, Christopher; Huish, David; Bendle, John; Kibler, Angela

2012-01-01

The exploration goals of Orion / MPCV Project will require a mature Rendezvous, Proximity Operations and Docking (RPOD) capability. Ground testing autonomous docking with a next-generation sensor such as the Vision Navigation Sensor (VNS) is a critical step along the path of ensuring successful execution of autonomous RPOD for Orion. This paper will discuss the testing rationale, the test configuration, the test limitations and the results obtained from tests that have been performed at the Lockheed Martin Space Operations Simulation Center (SOSC) to evaluate and mature the Orion RPOD system. We will show that these tests have greatly increased the confidence in the maturity of the Orion RPOD design, reduced some of the latent risks and in doing so validated the design philosophy of the Orion RPOD system. This paper is organized as follows: first, the objectives of the test are given. Descriptions of the SOSC facility, and the Orion RPOD system and associated components follow. The details of the test configuration of the components in question are presented prior to discussing preliminary results of the tests. The paper concludes with closing comments.

Categories and Commutative Algebra

CERN Document Server

Salmon, P

2011-01-01

L. Badescu: Sur certaines singularites des varietes algebriques.- D.A. Buchsbaum: Homological and commutative algebra.- S. Greco: Anelli Henseliani.- C. Lair: Morphismes et structures algebriques.- B.A. Mitchell: Introduction to category theory and homological algebra.- R. Rivet: Anneaux de series formelles et anneaux henseliens.- P. Salmon: Applicazioni della K-teoria all'algebra commutativa.- M. Tierney: Axiomatic sheaf theory: some constructions and applications.- C.B. Winters: An elementary lecture on algebraic spaces.

Particle-like structure of Lie algebras

Science.gov (United States)

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.

Project Orion, Environmental Control and Life Support System Integrated Studies

Science.gov (United States)

Russell, James F.; Lewis, John F.

2008-01-01

Orion is the next vehicle for human space travel. Humans will be sustained in space by the Orion subystem, environmental control and life support (ECLS). The ECLS concept at the subsystem level is outlined by function and technology. In the past two years, the interface definition with other subsystems has increased through different integrated studies. The paper presents the key requirements and discusses three recent studies (e.g., unpressurized cargo) along with the respective impacts on the ECLS design moving forward.

Dynamical entropy of C* algebras and Von Neumann algebras

International Nuclear Information System (INIS)

Connes, A.; Narnhofer, H.; Thirring, W.

1986-01-01

The definition of the dynamical entropy is extended for automorphism groups of C * algebras. As example the dynamical entropy of the shift of a lattice algebra is studied and it is shown that in some cases it coincides with the entropy density. (Author)

Gradings on simple Lie algebras

CERN Document Server

Elduque, Alberto

2013-01-01

Gradings are ubiquitous in the theory of Lie algebras, from the root space decomposition of a complex semisimple Lie algebra relative to a Cartan subalgebra to the beautiful Dempwolff decomposition of E_8 as a direct sum of thirty-one Cartan subalgebras. This monograph is a self-contained exposition of the classification of gradings by arbitrary groups on classical simple Lie algebras over algebraically closed fields of characteristic not equal to 2 as well as on some nonclassical simple Lie algebras in positive characteristic. Other important algebras also enter the stage: matrix algebras, the octonions, and the Albert algebra. Most of the presented results are recent and have not yet appeared in book form. This work can be used as a textbook for graduate students or as a reference for researchers in Lie theory and neighboring areas.

Orion EFT-1 Catalytic Tile Experiment Overview and Flight Measurements

Science.gov (United States)

Salazar, Giovanni; Amar, Adam; Hyatt, Andrew; Rezin, Marc D.

2016-01-01

This paper describes the design and results of a surface catalysis flight experiment flown on the Orion Multipurpose Crew Vehicle during Exploration Flight Test 1 (EFT1). Similar to previous Space Shuttle catalytic tile experiments, the present test consisted of a highly catalytic coating applied to an instrumented TPS tile. However, the present catalytic tile experiment contained significantly more instrumentation in order to better resolve the heating overshoot caused by the change in surface catalytic efficiency at the interface between two distinct materials. In addition to collecting data with unprecedented spatial resolution of the "overshoot" phenomenon, the experiment was also designed to prove if such a catalytic overshoot would be seen in turbulent flow in high enthalpy regimes. A detailed discussion of the results obtained during EFT1 is presented, as well as the challenges associated with data interpretation of this experiment. Results of material testing carried out in support of this flight experiment are also shown. Finally, an inverse heat conduction technique is employed to reconstruct the flight environments at locations upstream and along the catalytic coating. The data and analysis presented in this work will greatly contribute to our understanding of the catalytic "overshoot" phenomenon, and have a significant impact on the design of future spacecraft.

The Integral Field View of the Orion Nebula

Directory of Open Access Journals (Sweden)

Adal Mesa-Delgado

2014-01-01

Full Text Available This paper reviews the major advances achieved in the Orion Nebula through the use of integral field spectroscopy (IFS. Since the early work of Vasconcelos and collaborators in 2005, this technique has facilitated the investigation of global properties of the nebula and its morphology, providing new clues to better constrain its 3D structure. IFS has led to the discovery of shock-heated zones at the leading working surfaces of prominent Herbig-Haro objects as well as the first attempt to determine the chemical composition of Orion protoplanetary disks, also known as proplyds. The analysis of these morphologies using IFS has given us new insights into the abundance discrepancy problem, a long-standing and unresolved issue that casts doubt on the reliability of current methods used for the determination of metallicities in the universe from the analysis of H II regions. Results imply that high-density clumps and high-velocity flows may play an active role in the production of such discrepancies. Future investigations based on the large-scale IFS mosaic of Orion will be very valuable for exploring how the integrated effect of small-scale structures may have impact at larger scales in the framework of star-forming regions.

ORION - Crew Module Side Hatch: Proof Pressure Test Anomaly Investigation

Science.gov (United States)

Evernden, Brent A.; Guzman, Oscar J.

2018-01-01

The Orion Multi-Purpose Crew Vehicle program was performing a proof pressure test on an engineering development unit (EDU) of the Orion Crew Module Side Hatch (CMSH) assembly. The purpose of the proof test was to demonstrate structural capability, with margin, at 1.5 times the maximum design pressure, before integrating the CMSH to the Orion Crew Module structural test article for subsequent pressure testing. The pressure test was performed at lower pressures of 3 psig, 10 psig and 15.75 psig with no apparent abnormal behavior or leaking. During pressurization to proof pressure of 23.32 psig, a loud 'pop' was heard at 21.3 psig. Upon review into the test cell, it was noted that the hatch had prematurely separated from the proof test fixture, thus immediately ending the test. The proof pressure test was expected be a simple verification but has since evolved into a significant joint failure investigation from both Lockheed Martin and NASA.

Topological conformal algebra and BRST algebra in non-critical string theories

International Nuclear Information System (INIS)

Fujikawa, Kazuo; Suzuki, Hiroshi.

1991-03-01

The operator algebra in non-critical string theories is studied by treating the cosmological term as a perturbation. The algebra of covariantly regularized BRST and related currents contains a twisted N = 2 superconformal algebra only at d = -2 in bosonic strings, and a twisted N = 3 superconformal algebra only at d = ±∞ in spinning strings. The bosonic string at d = -2 is examined by replacing the string coordinate by a fermionic matter with c = -2. The resulting bc-βγ system accommodates various forms of BRST cohomology, and the ghost number assignment and BRST cohomology are different in the c = -2 string theory and two-dimensional topological gravity. (author)

Fossil DCN in Orion-KL

International Nuclear Information System (INIS)

Mangum, J.G.; Plambeck, R.L.; Wootten, A.

1991-01-01

The J = 1 - 0 transition of DCN was mapped toward Orion-KL with the BIMA array. With a synthesized beam width of 7.6 arcsec, emission from the hot core, compact ridge, and northern cloud regions was identified. Over half of the integrated DCN emission detected originates from the hot core component, with progressively smaller contributions from the compact ridge and northern cloud. The DCN fractional abundance is 10 to the -9th in the hot core, 4 x 10 to the -10th in the compact ridge, and 2 x 10 to the -10th in the northern cloud; it is estimated that the corresponding DCN/HCN ratios are about 0.005, 0.02, and 0.02. Chemical models suggest that such high DCN/HCN abundance ratios are produced only in clouds colder than about 20 K. Since the present temperatures near Orion-KL are 50-275 K, it is evident that most of the DCN formed before this region was heated by massive star formation. Much of the fossil DCN which is now observed may have sublimated from icy grain mantles. 32 refs

Algebraic K-theory

CERN Document Server

Srinivas, V

1996-01-01

Algebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and graduate students in mathematics. The book is based on lectures given at the author's home institution, the Tata Institute in Bombay, and elsewhere. A detailed appendix on topology was provided in the first edition to make the treatment accessible to readers with a limited background in topology. The second edition also includes an appendix on algebraic geometry that contains the required definitions and results needed to understand the core of the book; this makes the book accessible to a wider audience. A central part of the book is a detailed exposition of the ideas of Quillen as contained in his classic papers "Higher Algebraic K-Theory, I, II." A more elementary proof of the theorem of Merkujev--Suslin is given in this edition; this makes the treatment of this topic self-contained. An application ...

Head First Algebra A Learner's Guide to Algebra I

CERN Document Server

Pilone, Tracey

2008-01-01

Having trouble understanding algebra? Do algebraic concepts, equations, and logic just make your head spin? We have great news: Head First Algebra is designed for you. Full of engaging stories and practical, real-world explanations, this book will help you learn everything from natural numbers and exponents to solving systems of equations and graphing polynomials. Along the way, you'll go beyond solving hundreds of repetitive problems, and actually use what you learn to make real-life decisions. Does it make sense to buy two years of insurance on a car that depreciates as soon as you drive i

Novikov algebras with associative bilinear forms

Energy Technology Data Exchange (ETDEWEB)

Zhu Fuhai; Chen Zhiqi [School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071 (China)

2007-11-23

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.

Lie algebra in quantum physics by means of computer algebra

OpenAIRE

Kikuchi, Ichio; Kikuchi, Akihito

2017-01-01

This article explains how to apply the computer algebra package GAP (www.gap-system.org) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary computations which readers would follow in the desktop PC: such as, the brief review of elementary ideas of Lie algebra, the angular momentum in quantum mechanics, the quark eight-fold way model, and the usage of Weyl character formula (in order to construct w...

Tensor spaces and exterior algebra

CERN Document Server

Yokonuma, Takeo

1992-01-01

This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. To facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. In particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.

Profinite algebras and affine boundedness

OpenAIRE

Schneider, Friedrich Martin; Zumbrägel, Jens

2015-01-01

We prove a characterization of profinite algebras, i.e., topological algebras that are isomorphic to a projective limit of finite discrete algebras. In general profiniteness concerns both the topological and algebraic characteristics of a topological algebra, whereas for topological groups, rings, semigroups, and distributive lattices, profiniteness turns out to be a purely topological property as it is is equivalent to the underlying topological space being a Stone space. Condensing the core...

Double-partition Quantum Cluster Algebras

DEFF Research Database (Denmark)

Jakobsen, Hans Plesner; Zhang, Hechun

2012-01-01

A family of quantum cluster algebras is introduced and studied. In general, these algebras are new, but sub-classes have been studied previously by other authors. The algebras are indexed by double parti- tions or double flag varieties. Equivalently, they are indexed by broken lines L. By grouping...... together neighboring mutations into quantum line mutations we can mutate from the cluster algebra of one broken line to another. Compatible pairs can be written down. The algebras are equal to their upper cluster algebras. The variables of the quantum seeds are given by elements of the dual canonical basis....

Algebra II workbook for dummies

CERN Document Server

Sterling, Mary Jane

2014-01-01

To succeed in Algebra II, start practicing now Algebra II builds on your Algebra I skills to prepare you for trigonometry, calculus, and a of myriad STEM topics. Working through practice problems helps students better ingest and retain lesson content, creating a solid foundation to build on for future success. Algebra II Workbook For Dummies, 2nd Edition helps you learn Algebra II by doing Algebra II. Author and math professor Mary Jane Sterling walks you through the entire course, showing you how to approach and solve the problems you encounter in class. You'll begin by refreshing your Algebr

Very true operators on MTL-algebras

Directory of Open Access Journals (Sweden)

Wang Jun Tao

2016-01-01

Full Text Available The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras.

Hopf algebras in noncommutative geometry

International Nuclear Information System (INIS)

Varilly, Joseph C.

2001-10-01

We give an introductory survey to the use of Hopf algebras in several problems of non- commutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of non- commutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups. (author)

W-realization of Lie algebras. Application to so(4,2) and Poincare algebras

International Nuclear Information System (INIS)

Barbarin, F.; Ragoucy, E.; Sorba, P.

1996-05-01

The property of some finite W-algebras to appear as the commutant of a particular subalgebra in a simple Lie algebra G is exploited for the obtention of new G-realizations from a 'canonical' differential one. The method is applied to the conformal algebra so(4,2) and therefore yields also results for its Poincare subalgebra. Unitary irreducible representations of these algebras are recognized in this approach, which is naturally compared -or associated to - the induced representation technique. (author)

Extended Kac-Moody algebras and applications

International Nuclear Information System (INIS)

Ragoucy, E.; Sorba, P.

1991-04-01

The notion of a Kac-Moody algebra defined on the S 1 circle is extended to super Kac-Moody algebras defined on MxG N , M being a smooth closed compact manifold of dimension greater than one, and G N the Grassman algebra with N generators. All the central extensions of these algebras are computed. Then, for each such algebra the derivation algebra constructed from the MxG N diffeomorphism is determined. The twists of such super Kac-Moody algebras as well as the generalization to non-compact surfaces are partially studied. Finally, the general construction is applied to the study of conformal and superconformal algebras, as well as area-preserving diffeomorphisms algebra and its supersymmetric extension. (author) 65 refs

Million-degree plasma pervading the extended Orion Nebula.

Science.gov (United States)

Güdel, Manuel; Briggs, Kevin R; Montmerle, Thierry; Audard, Marc; Rebull, Luisa; Skinner, Stephen L

2008-01-18

Most stars form as members of large associations within dense, very cold (10 to 100 kelvin) molecular clouds. The nearby giant molecular cloud in Orion hosts several thousand stars of ages less than a few million years, many of which are located in or around the famous Orion Nebula, a prominent gas structure illuminated and ionized by a small group of massive stars (the Trapezium). We present x-ray observations obtained with the X-ray Multi-Mirror satellite XMM-Newton, revealing that a hot plasma with a temperature of 1.7 to 2.1 million kelvin pervades the southwest extension of the nebula. The plasma flows into the adjacent interstellar medium. This x-ray outflow phenomenon must be widespread throughout our Galaxy.

Lie algebras and applications

CERN Document Server

Iachello, Francesco

2015-01-01

This course-based primer provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, it concisely presents the basic concepts of Lie algebras, their representations and their invariants. The second part includes a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book highlights a number of examples that help to illustrate the abstract algebraic definitions and includes a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators...

MASSIVE PROTOPLANETARY DISKS IN ORION BEYOND THE TRAPEZIUM CLUSTER

International Nuclear Information System (INIS)

Mann, Rita K.; Williams, Jonathan P.

2009-01-01

We present Submillimeter Array 1 The Submillimeter Array is a joint project between the Submillimeter Astrophysical Observatory and the Academica Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academica Sinica. observations of the 880 μm continuum emission from three circumstellar disks around young stars in Orion that lie several arcminutes (∼> 1 pc) north of the Trapezium cluster. Two of the three disks are in the binary system 253-1536. Silhouette disks 216-0939 and 253-1536a are found to be more massive than any previously observed Orion disks, with dust masses derived from their submillimeter emission of 0.045 M sun and 0.066 M sun , respectively. The existence of these massive disks reveals that the disk mass distribution in Orion does extend to high masses, and that the truncation observed in the central Trapezium cluster is a result of photoevaporation due to the proximity of O-stars. 253-1536b has a disk mass of 0.018 M sun , making the 253-1536 system the first optical binary in which each protoplanetary disk is massive enough to potentially form solar systems.

(Fuzzy) Ideals of BN-Algebras

Science.gov (United States)

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

Marketingová strategie miničokolád značky Orion na českém trhu

OpenAIRE

Růžičková, Anna

2017-01-01

The aim of this master thesis is to evaluate Orion product portfolio and recent launch of a new product, Orion minichocolates, after that to propose customized adaptation of product marketing strategy. The thesis consists of three parts, where the first part is mainly theoretical and describes the basic terminology of marketing strategy. The second part is dedicated to Nestlé and its product portfolio, Orion chocolate tablets included. The last part describes launch development of Orion minic...

Non-relativistic Bondi-Metzner-Sachs algebra

Science.gov (United States)

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.

KINETIC TEMPERATURES OF THE DENSE GAS CLUMPS IN THE ORION KL MOLECULAR CORE

International Nuclear Information System (INIS)

Wang, K.-S.; Kuan, Y.-J.; Liu, S.-Y.; Charnley, Steven B.

2010-01-01

High angular-resolution images of the J = 18 K -17 K emission of CH 3 CN in the Orion KL molecular core were observed with the Submillimeter Array (SMA). Our high-resolution observations clearly reveal that CH 3 CN emission originates mainly from the Orion Hot Core and the Compact Ridge, both within ∼15'' of the warm and dense part of Orion KL. The clumpy nature of the molecular gas in Orion KL can also be readily seen from our high-resolution SMA images. In addition, a semi-open cavity-like kinematic structure is evident at the location between the Hot Core and the Compact Ridge. We performed excitation analysis with the 'population diagram' method toward the Hot Core, IRc7, and the northern part of the Compact Ridge. Our results disclose a non-uniform temperature structure on small scales in Orion KL, with a range of temperatures from 190-620 K in the Hot Core. Near the Compact Ridge, the temperatures are found to be 170-280 K. Comparable CH 3 CN fractional abundances of 10 -8 to 10 -7 are found around both in the Hot Core and the Compact Ridge. Such high abundances require that a hot gas phase chemistry, probably involving ammonia released from grain mantles, plays an important role in forming these CH 3 CN molecules.

The Unitality of Quantum B-algebras

Science.gov (United States)

Han, Shengwei; Xu, Xiaoting; Qin, Feng

2018-02-01

Quantum B-algebras as a generalization of quantales were introduced by Rump and Yang, which cover the majority of implicational algebras and provide a unified semantic for a wide class of substructural logics. Unital quantum B-algebras play an important role in the classification of implicational algebras. The main purpose of this paper is to construct unital quantum B-algebras from non-unital quantum B-algebras.

On Weak-BCC-Algebras

Science.gov (United States)

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

G-identities of non-associative algebras

International Nuclear Information System (INIS)

Bakhturin, Yu A; Zaitsev, M V; Sehgal, S K

1999-01-01

The main class of algebras considered in this paper is the class of algebras of Lie type. This class includes, in particular, associative algebras, Lie algebras and superalgebras, Leibniz algebras, quantum Lie algebras, and many others. We prove that if a finite group G acts on such an algebra A by automorphisms and anti-automorphisms and A satisfies an essential G-identity, then A satisfies an ordinary identity of degree bounded by a function that depends on the degree of the original identity and the order of G. We show in the case of ordinary Lie algebras that if L is a Lie algebra, a finite group G acts on L by automorphisms and anti-automorphisms, and the order of G is coprime to the characteristic of the field, then the existence of an identity on skew-symmetric elements implies the existence of an identity on the whole of L, with the same kind of dependence between the degrees of the identities. Finally, we generalize Amitsur's theorem on polynomial identities in associative algebras with involution to the case of alternative algebras with involution

W-realization of Lie algebras. Application to so(4,2) and Poincare algebras

Energy Technology Data Exchange (ETDEWEB)

Barbarin, F.; Ragoucy, E.; Sorba, P.

1996-05-01

The property of some finite W-algebras to appear as the commutant of a particular subalgebra in a simple Lie algebra G is exploited for the obtention of new G-realizations from a `canonical` differential one. The method is applied to the conformal algebra so(4,2) and therefore yields also results for its Poincare subalgebra. Unitary irreducible representations of these algebras are recognized in this approach, which is naturally compared -or associated to - the induced representation technique. (author). 12 refs.

On Dunkl angular momenta algebra

Energy Technology Data Exchange (ETDEWEB)

Feigin, Misha [School of Mathematics and Statistics, University of Glasgow,15 University Gardens, Glasgow G12 8QW (United Kingdom); Hakobyan, Tigran [Yerevan State University,1 Alex Manoogian, 0025 Yerevan (Armenia); Tomsk Polytechnic University,Lenin Ave. 30, 634050 Tomsk (Russian Federation)

2015-11-17

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 subalgebra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.

Algebraic computing

International Nuclear Information System (INIS)

MacCallum, M.A.H.

1990-01-01

The implementation of a new computer algebra system is time consuming: designers of general purpose algebra systems usually say it takes about 50 man-years to create a mature and fully functional system. Hence the range of available systems and their capabilities changes little between one general relativity meeting and the next, despite which there have been significant changes in the period since the last report. The introductory remarks aim to give a brief survey of capabilities of the principal available systems and highlight one or two trends. The reference to the most recent full survey of computer algebra in relativity and brief descriptions of the Maple, REDUCE and SHEEP and other applications are given. (author)

Large proper motions in the Orion nebula

International Nuclear Information System (INIS)

Cudworth, K.M.; Stone, R.C.

1977-01-01

Several nebular features, as well as one faint star, with large proper motions were identified within the Orion nebula. The measured proper motions correspond to tangential velocities of up to approximately 70 km sec -1 . One new probable variable star was also found

Optical Property Requirements for Glasses, Ceramics and Plastics in Spacecraft Window Systems

Science.gov (United States)

Estes, Lynda

2011-01-01

This is a preliminary draft of a standard published by the National Aeronautics and Space Administration (NASA) Johnson Space Center (JSC) that is intended to provide uniform window optical design requirements in support of the development of human-rated spaceflight hardware. The material covered in this standard is based on data from extensive testing by the Advanced Sensing and Optical Measurement Branch at NASA Langley Research Center, and compiled into requirements format by the NASA JSC Structural Engineering Division. At the time of this initial document release, a broader technical community has not reviewed this standard. The technical content of this standard is primarily based on the Constellation Program Orion Crew Exploration Vehicle Window Optical Properties Requirements, CxP 72407, Baseline. Unlike other optical requirements documents available for human rated spacecraft, this document includes requirements that ensure functionality for windows that contain glass/ceramic and/or plastic window substrate materials. These requirements were derived by measuring the optical properties of fused silica and aluminosilicate glass window assemblies and ensuring that the performance of any window assembly that includes a plastic pane or panes will meet the performance level of the all-glass assemblies. The resulting requirements are based upon the performance and parameter metrology testing of a variety of materials, including glass, transparent ceramics, acrylics, and polycarbonates. In general, these requirements are minimum specifications for each optical parameter in order to achieve the function specified for each functional category, A through D. Because acrylic materials perform at a higher level than polycarbonates in the optics regime, and CxP/Orion is planning to use acrylic in the Orion spacecraft, these requirements are based heavily on metrology from that material. As a result, two of the current Category D requirements for plastics are cited in

Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra

CERN Document Server

Cox, David A; O'Shea, Donal

2015-01-01

This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry—the elimination theorem, the extension theorem, the closure theorem, and the Nullstellensatz—this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D). The book may serve as a first or second course in undergraduate abstract algebra and, with some supplementation perhaps, for beginning graduate level courses in algebraic geom...

Connections between algebra, combinatorics, and geometry

CERN Document Server

Sather-Wagstaff, Sean

2014-01-01

Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics, and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University, February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resou...

Abstract algebra for physicists

International Nuclear Information System (INIS)

Zeman, J.

1975-06-01

Certain recent models of composite hadrons involve concepts and theorems from abstract algebra which are unfamiliar to most theoretical physicists. The algebraic apparatus needed for an understanding of these models is summarized here. Particular emphasis is given to algebraic structures which are not assumed to be associative. (2 figures) (auth)

Photographic colorimetry of stellar flares in the Pleiades and Orion. II

International Nuclear Information System (INIS)

Mirzoian, L.V.; Chavushian, O.S.; Melikian, N.D.; Natsvlishvili, R.Sh.; Ambarian, V.V.; Brutian, G.A.

1984-01-01

Synchronous three-telescope UBV photographic colorimetry of Pleiades and Orion stellar flares obtained at Biurakan Astrophysical Observatory and Abastumani Astrophysical Observatory during 86 observing hours in 1980 and 1981 is presented. The data are compiled in tables and discussed in terms of color differences appearing at different stages of a flare. A total of 32 flares are observed (25 in the Pleiades and 7 in Orion), and four new flare stars are identified in each region. 12 references

Basic notions of algebra

CERN Document Server

Shafarevich, Igor Rostislavovich

2005-01-01

This book is wholeheartedly recommended to every student or user of mathematics. Although the author modestly describes his book as 'merely an attempt to talk about' algebra, he succeeds in writing an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields, commutative rings and groups studied in every university math course, through Lie groups and algebras to cohomology and category theory, the author shows how the origins of each algebraic concept can be related to attempts to model phenomena in physics or in other branches

Characterizations of locally C*-algebras

International Nuclear Information System (INIS)

Mohammad, N.; Somasundaram, S.

1991-08-01

We seek the generalization of the Gelfand-Naimark theorems for locally C*-algebras. Precisely, if A is a unital commutative locally C*-algebra, then it is shown that A is *-isomorphic (topologically and algebraically) to C(Δ). Further, if A is any locally C*-algebra, then it is realized as a closed *-subalgebra of some L(H) up to a topological algebraic *-isomorphism. Also, a brief exposition of the Gelfand-Naimark-Segal construction is given and some of its consequences are discussed. (author). 16 refs

Galois Theory of Differential Equations, Algebraic Groups and Lie Algebras

NARCIS (Netherlands)

Put, Marius van der

1999-01-01

The Galois theory of linear differential equations is presented, including full proofs. The connection with algebraic groups and their Lie algebras is given. As an application the inverse problem of differential Galois theory is discussed. There are many exercises in the text.

Brauer algebras of type B

NARCIS (Netherlands)

Cohen, A.M.; Liu, S.

2011-01-01

For each n>0, we define an algebra having many properties that one might expect to hold for a Brauer algebra of type Bn. It is defined by means of a presentation by generators and relations. We show that this algebra is a subalgebra of the Brauer algebra of type Dn+1 and point out a cellular

The Orion Exploration Flight Test Post Flight Solid Particle Flight Environment Inspection and Analysis

Science.gov (United States)

Miller, Joshua E.

2016-01-01

Orbital debris in the millimeter size range can pose a hazard to current and planned spacecraft due to the high relative impact speeds in Earth orbit. Fortunately, orbital debris has a relatively short life at lower altitudes due to atmospheric effects; however, at higher altitudes orbital debris can survive much longer and has resulted in a band of high flux around 700 to 1,500 km above the surface of the Earth. While large orbital debris objects are tracked via ground based observation, little information can be gathered about small particles except by returned surfaces, which until the Orion Exploration Flight Test number one (EFT-1), has only been possible for lower altitudes (400 to 500 km). The EFT-1 crew module backshell, which used a porous, ceramic tile system with surface coatings, has been inspected post-flight for potential micrometeoroid and orbital debris (MMOD) damage. This paper describes the pre- and post-flight activities of inspection, identification and analysis of six candidate MMOD impact craters from the EFT-1 mission.

A course in BE-algebras

CERN Document Server

Mukkamala, Sambasiva Rao

2018-01-01

This book presents a unified course in BE-algebras with a comprehensive introduction, general theoretical basis and several examples. It introduces the general theoretical basis of BE-algebras, adopting a credible style to offer students a conceptual understanding of the subject. BE-algebras are important tools for certain investigations in algebraic logic, because they can be considered as fragments of any propositional logic containing a logical connective implication and the constant "1", which is considered as the logical value “true”.  Primarily aimed at graduate and postgraduate students of mathematics, it also helps researchers and mathematicians to build a strong foundation in applied abstract algebra. Presenting insights into some of the abstract thinking that constitutes modern abstract algebra, it provides a transition from elementary topics to advanced topics in BE-algebras. With abundant examples and exercises arranged after each section, it offers readers a comprehensive, easy-to-follow int...

The Sword of Orion

Science.gov (United States)

2006-01-01

[figure removed for brevity, see original site] [figure removed for brevity, see original site] AnimationFigure 1 This infrared image from NASA's Spitzer Space Telescope shows the Orion nebula, our closest massive star-making factory, 1,450 light-years from Earth. The nebula is close enough to appear to the naked eye as a fuzzy star in the sword of the popular hunter constellation. The nebula itself is located on the lower half of the image, surrounded by a ring of dust. It formed in a cold cloud of gas and dust and contains about 1,000 young stars. These stars illuminate the cloud, creating the beautiful nebulosity, or swirls of material, seen here in infrared. In the center of the nebula (bottom inset of figure 1) are four monstrously massive stars, up to 100,000 times as luminous as our sun, called the Trapezium (tiny yellow smudge to the lower left of green splotches. Radiation and winds from these stars are blasting gas and dust away, excavating a cavity walled in by the large ring of dust. Behind the Trapezium, still buried deeply in the cloud, a second generation of massive stars is forming (in the area with green splotches). The speckled green fuzz in this bright region is created when bullets of gas shoot out from the juvenile stars and ram into the surrounding cloud. Above this region of intense activity are networks of cold material that appear as dark veins against the pinkish nebulosity (upper inset pf figure 1). These dark veins contain embryonic stars. Some of the natal stars illuminate the cloud, creating small, aqua-colored wisps. In addition, jets of gas from the stars ram into the cloud, resulting in the green horseshoe-shaped globs. Spitzer surveyed a significant swath of the Orion constellation, beyond what is highlighted in this image. Within that region, called the Orion cloud complex, the telescope found 2,300 stars circled by disks of planet-forming dust and 200 stellar embryos too young to have developed disks. This image shows infrared

Multi-Terrain Earth Landing Systems Applicable for Manned Space Capsules

Science.gov (United States)

Fasanella, Edwin L.

2008-01-01

A key element of the President's Vision for Space Exploration is the development of a new space transportation system to replace the Shuttle that will enable manned exploration of the moon, Mars, and beyond. NASA has tasked the Constellation Program with the development of this architecture, which includes the Ares launch vehicle and Orion manned spacecraft. The Orion spacecraft must carry six astronauts and its primary structure should be reusable, if practical. These requirements led the Constellation Program to consider a baseline land landing on return to earth. To assess the landing system options for Orion, a review of current operational parachute landing systems such as those used for the F-111 escape module and the Soyuz is performed. In particular, landing systems with airbags and retrorockets that would enable reusability of the Orion capsule are investigated. In addition, Apollo tests and analyses conducted in the 1960's for both water and land landings are reviewed. Finally, tests and dynamic finite element simulations to understand land landings for the Orion spacecraft are also presented.

On Associative Conformal Algebras of Linear Growth

OpenAIRE

Retakh, Alexander

2000-01-01

Lie conformal algebras appear in the theory of vertex algebras. Their relation is similar to that of Lie algebras and their universal enveloping algebras. Associative conformal algebras play a role in conformal representation theory. We introduce the notions of conformal identity and unital associative conformal algebras and classify finitely generated simple unital associative conformal algebras of linear growth. These are precisely the complete algebras of conformal endomorphisms of finite ...

The Linear Span of Projections in AH Algebras and for Inclusions of C*-Algebras

Directory of Open Access Journals (Sweden)

Dinh Trung Hoa

2013-01-01

Full Text Available In the first part of this paper, we show that an AH algebra A=lim→(Ai,ϕi has the LP property if and only if every element of the centre of Ai belongs to the closure of the linear span of projections in A. As a consequence, a diagonal AH-algebra has the LP property if it has small eigenvalue variation in the sense of Bratteli and Elliott. The second contribution of this paper is that for an inclusion of unital C*-algebras P⊂A with a finite Watatani index, if a faithful conditional expectation E:A→P has the Rokhlin property in the sense of Kodaka et al., then P has the LP property under the condition thatA has the LP property. As an application, let A be a simple unital C*-algebra with the LP property, α an action of a finite group G onto Aut(A. If α has the Rokhlin property in the sense of Izumi, then the fixed point algebra AG and the crossed product algebra A ⋊α G have the LP property. We also point out that there is a symmetry on the CAR algebra such that its fixed point algebra does not have the LP property.

Non-commutative multiple-valued logic algebras

CERN Document Server

Ciungu, Lavinia Corina

2014-01-01

This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects.   A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing.   Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.

Automorphic Lie algebras with dihedral symmetry

International Nuclear Information System (INIS)

Knibbeler, V; Lombardo, S; A Sanders, J

2014-01-01

The concept of automorphic Lie algebras arises in the context of reduction groups introduced in the early 1980s in the field of integrable systems. automorphic Lie algebras are obtained by imposing a discrete group symmetry on a current algebra of Krichever–Novikov type. Past work shows remarkable uniformity between algebras associated to different reduction groups. For example, if the base Lie algebra is sl 2 (C) and the poles of the automorphic Lie algebra are restricted to an exceptional orbit of the symmetry group, changing the reduction group does not affect the Lie algebra structure. In this research we fix the reduction group to be the dihedral group and vary the orbit of poles as well as the group action on the base Lie algebra. We find a uniform description of automorphic Lie algebras with dihedral symmetry, valid for poles at exceptional and generic orbits. (paper)

Certain number-theoretic episodes in algebra

CERN Document Server

Sivaramakrishnan, R

2006-01-01

Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutative algebra arising from number theory. Self-contained, the book examines situations where explicit algebraic analogues of theorems of number theory are available. Coverage is divided into four parts, beginning with elements of number theory and algebra such as theorems of Euler, Fermat, and Lagrange, Euclidean domains, and finite groups. In the second part, the book details ordered fields, fields with valuation, and other algebraic structures. This is followed by a review of fundamentals of algebraic number theory in the third part. The final part explores links with ring theory, finite dimensional algebras, and the Goldbach problem.

NGC 1980 Is Not a Foreground Population of Orion: Spectroscopic Survey of Young Stars with Low Extinction in Orion A

International Nuclear Information System (INIS)

Fang, Min; Kim, Jinyoung Serena; Apai, Dániel; Pascucci, Ilaria; Zhang, Lan; Sicilia-Aguilar, Aurora; Alonso-Martínez, Miguel; Eiroa, Carlos; Wang, Hongchi

2017-01-01

We perform a spectroscopic survey of the foreground population in Orion A with MMT/Hectospec. We use these data, along with archival spectroscopic data and photometric data, to derive spectral types, extinction values, and masses for 691 stars. Using the Spitzer Space Telescope data, we characterize the disk properties of these sources. We identify 37 new transition disk (TD) objects, 1 globally depleted disk candidate, and 7 probable young debris disks. We discover an object with a mass of less than 0.018–0.030 M ⊙ , which harbors a flaring disk. Using the H α emission line, we characterize the accretion activity of the sources with disks, and confirm that the fraction of accreting TDs is lower than that of optically thick disks (46% ± 7% versus 73% ± 9%, respectively). Using kinematic data from the Sloan Digital Sky Survey and APOGEE INfrared Spectroscopy of the Young Nebulous Clusters program (IN-SYNC), we confirm that the foreground population shows similar kinematics to their local molecular clouds and other young stars in the same regions. Using the isochronal ages, we find that the foreground population has a median age of around 1–2 Myr, which is similar to that of other young stars in Orion A. Therefore, our results argue against the presence of a large and old foreground cluster in front of Orion A.

NGC 1980 Is Not a Foreground Population of Orion: Spectroscopic Survey of Young Stars with Low Extinction in Orion A

Energy Technology Data Exchange (ETDEWEB)

Fang, Min; Kim, Jinyoung Serena; Apai, Dániel [Department of Astronomy, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721 (United States); Pascucci, Ilaria [Department of Planetary Sciences, University of Arizona, 1629 East University Boulevard, Tucson, AZ 85721 (United States); Zhang, Lan [Key Lab of Optical Astronomy, National Astronomical Observatories, CAS, 20A Datun Road, Chaoyang District, 100012 Beijing (China); Sicilia-Aguilar, Aurora [SUPA, School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews KY16 9SS (United Kingdom); Alonso-Martínez, Miguel; Eiroa, Carlos [Departamento de Fisica Teorica, Facultad de Ciencias, Universidad Autonoma de Madrid, E-28049 Cantoblanco, Madrid (Spain); Wang, Hongchi [Purple Mountain Observatory and Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, 2 West Beijing Road, 210008 Nanjing (China)

2017-04-01

We perform a spectroscopic survey of the foreground population in Orion A with MMT/Hectospec. We use these data, along with archival spectroscopic data and photometric data, to derive spectral types, extinction values, and masses for 691 stars. Using the Spitzer Space Telescope data, we characterize the disk properties of these sources. We identify 37 new transition disk (TD) objects, 1 globally depleted disk candidate, and 7 probable young debris disks. We discover an object with a mass of less than 0.018–0.030 M {sub ⊙}, which harbors a flaring disk. Using the H α emission line, we characterize the accretion activity of the sources with disks, and confirm that the fraction of accreting TDs is lower than that of optically thick disks (46% ± 7% versus 73% ± 9%, respectively). Using kinematic data from the Sloan Digital Sky Survey and APOGEE INfrared Spectroscopy of the Young Nebulous Clusters program (IN-SYNC), we confirm that the foreground population shows similar kinematics to their local molecular clouds and other young stars in the same regions. Using the isochronal ages, we find that the foreground population has a median age of around 1–2 Myr, which is similar to that of other young stars in Orion A. Therefore, our results argue against the presence of a large and old foreground cluster in front of Orion A.

Fusion rules of chiral algebras

International Nuclear Information System (INIS)

Gaberdiel, M.

1994-01-01

Recently we showed that for the case of the WZW and the minimal models fusion can be understood as a certain ring-like tensor product of the symmetry algebra. In this paper we generalize this analysis to arbitrary chiral algebras. We define the tensor product of conformal field theory in the general case and prove that it is associative and symmetric up to equivalence. We also determine explicitly the action of the chiral algebra on this tensor product. In the second part of the paper we demonstrate that this framework provides a powerful tool for calculating restrictions for the fusion rules of chiral algebras. We exhibit this for the case of the W 3 algebra and the N=1 and N=2 NS superconformal algebras. (orig.)

Computations in finite-dimensional Lie algebras

Directory of Open Access Journals (Sweden)

A. M. Cohen

1997-12-01

Full Text Available This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System, within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. Since then, in a collaborative effort with G. Ivanyos, the authors have continued to develop algorithms which were implemented in ELIAS by the second author. These activities are part of a bigger project, called ACELA and financed by STW, the Dutch Technology Foundation, which aims at an interactive book on Lie algebras (cf. Cohen and Meertens [2]. This paper gives a global description of the main ways in which to present Lie algebras on a computer. We focus on the transition from a Lie algebra abstractly given by an array of structure constants to a Lie algebra presented as a subalgebra of the Lie algebra of n×n matrices. We describe an algorithm typical of the structure analysis of a finite-dimensional Lie algebra: finding a Levi subalgebra of a Lie algebra.

Coset realization of unifying W-algebras

International Nuclear Information System (INIS)

Blumenhagen, R.; Huebel, R.

1994-06-01

We construct several quantum coset W-algebras, e.g. sl(2,R)/U(1) and sl(2,R)+sl(2,R)/sl(2,R), and argue that they are finitely nonfreely generated. Furthermore, we discuss in detail their role as unifying W-algebras of Casimir W-algebras. We show that it is possible to give coset realizations of various types of unifying W-algebras, e.g. the diagonal cosets based on the symplectic Lie algebras sp(2n) realize the unifying W-algebras which have previously been introduced as 'WD -n '. In addition, minimal models of WD -n are studied. The coset realizations provide a generalization of level-rank-duality of dual coset pairs. As further examples of finitely nonfreely generated quantum W-algebras we discuss orbifolding of W-algebras which on the quantum level has different properties than in the classical case. We demonstrate in some examples that the classical limit according to Bowcock and Watts of these nonfreely finitely generated quantum W-algebras probably yields infinitely nonfreely generated classical W-algebras. (orig.)

Orion Burn Management, Nominal and Response to Failures

Science.gov (United States)

Odegard, Ryan; Goodman, John L.; Barrett, Charles P.; Pohlkamp, Kara; Robinson, Shane

2016-01-01

An approach for managing Orion on-orbit burn execution is described for nominal and failure response scenarios. The burn management strategy for Orion takes into account per-burn variations in targeting, timing, and execution; crew and ground operator intervention and overrides; defined burn failure triggers and responses; and corresponding on-board software sequencing functionality. Burn-to- burn variations are managed through the identification of specific parameters that may be updated for each progressive burn. Failure triggers and automatic responses during the burn timeframe are defined to provide safety for the crew in the case of vehicle failures, along with override capabilities to ensure operational control of the vehicle. On-board sequencing software provides the timeline coordination for performing the required activities related to targeting, burn execution, and responding to burn failures.

Algebra

CERN Document Server

Sepanski, Mark R

2010-01-01

Mark Sepanski's Algebra is a readable introduction to the delightful world of modern algebra. Beginning with concrete examples from the study of integers and modular arithmetic, the text steadily familiarizes the reader with greater levels of abstraction as it moves through the study of groups, rings, and fields. The book is equipped with over 750 exercises suitable for many levels of student ability. There are standard problems, as well as challenging exercises, that introduce students to topics not normally covered in a first course. Difficult problems are broken into manageable subproblems

IDENTIFICATION OF BURSTING WATER MASER FEATURES IN ORION KL

International Nuclear Information System (INIS)

Hirota, Tomoya; Honma, Mareki; Kim, Mi Kyoung; Kobayashi, Hideyuki; Shibata, Katsunori M.; Tsuboi, Masato; Fujisawa, Kenta; Kawaguchi, Noriyuki; Imai, Hiroshi; Omodaka, Toshihiro; Shimoikura, Tomomi; Yonekura, Yoshinori

2011-01-01

In 2011 February, a burst event of the H 2 O maser in Orion KL (Kleinmann-Low object) has started after a 13 year silence. This is the third time such phenomena has been detected in Orion KL, followed by the events in 1979-1985 and 1998. We have carried out astrometric observations of the bursting H 2 O maser features in Orion KL with the VLBI Exploration of Radio Astrometry (VERA), a Japanese very long baseline interferometry network dedicated for astrometry. The total flux of the bursting feature at the local standard of rest (LSR) velocity of 7.58 km s -1 reaches 4.4 x 10 4 Jy in 2011 March. The intensity of the bursting feature is three orders of magnitude larger than that of the same velocity feature in the quiescent phase in 2006. Two months later, another new feature appears at the LSR velocity of 6.95 km s -1 in 2011 May, separated by 12 mas north of the 7.58 km s -1 feature. Thus, the current burst occurs at two spatially different features. The bursting masers are elongated along the northwest-southeast direction as reported in the previous burst in 1998. We determine the absolute positions of the bursting features for the first time ever with a submilliarcsecond (mas) accuracy. Their positions are coincident with the shocked molecular gas called the Orion Compact Ridge. We tentatively detect the absolute proper motions of the bursting features toward the southwest direction. It is most likely that the outflow from the radio source I or another young stellar object interacting with the Compact Ridge is a possible origin of the H 2 O maser burst.

Identities and derivations for Jacobian algebras

International Nuclear Information System (INIS)

Dzhumadil'daev, A.S.

2001-09-01

Constructions of n-Lie algebras by strong n-Lie-Poisson algebras are given. First cohomology groups of adjoint module of Jacobian algebras are calculated. Minimal identities of 3-Jacobian algebra are found. (author)

Situating the Debate on "Geometrical Algebra" within the Framework of Premodern Algebra.

Science.gov (United States)

Sialaros, Michalis; Christianidis, Jean

2016-06-01

Argument The aim of this paper is to employ the newly contextualized historiographical category of "premodern algebra" in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on "geometrical algebra." Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related to Elem. II.5 as a case study, we discuss Euclid's geometrical proofs, the so-called "semi-algebraic" alternative demonstrations attributed to Heron of Alexandria, as well as the solutions given by Diophantus, al-Sulamī, and al-Khwārizmī to the corresponding numerical problem. This comparative analysis offers a new reading of Heron's practice, highlights the significance of contextualizing "premodern algebra," and indicates that the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition.

Cohomology of Effect Algebras

Directory of Open Access Journals (Sweden)

Frank Roumen

2017-01-01

Full Text Available We will define two ways to assign cohomology groups to effect algebras, which occur in the algebraic study of quantum logic. The first way is based on Connes' cyclic cohomology. The resulting cohomology groups are related to the state space of the effect algebra, and can be computed using variations on the Kunneth and Mayer-Vietoris sequences. The second way involves a chain complex of ordered abelian groups, and gives rise to a cohomological characterization of state extensions on effect algebras. This has applications to no-go theorems in quantum foundations, such as Bell's theorem.

On the spatial distributions of dense cores in Orion B

Science.gov (United States)

Parker, Richard J.

2018-05-01

We quantify the spatial distributions of dense cores in three spatially distinct areas of the Orion B star-forming region. For L1622, NGC 2068/NGC 2071, and NGC 2023/NGC 2024, we measure the amount of spatial substructure using the Q-parameter and find all three regions to be spatially substructured (Q Orion B, the mass segregation cannot be dynamical. Our results are also inconsistent with simulations in which the most massive stars form via competitive accretion, and instead hint that magnetic fields may be important in influencing the primordial spatial distributions of gas and stars in star-forming regions.

Topology general & algebraic

CERN Document Server

Chatterjee, D

2007-01-01

About the Book: This book provides exposition of the subject both in its general and algebraic aspects. It deals with the notions of topological spaces, compactness, connectedness, completeness including metrizability and compactification, algebraic aspects of topological spaces through homotopy groups and homology groups. It begins with the basic notions of topological spaces but soon going beyond them reaches the domain of algebra through the notions of homotopy, homology and cohomology. How these approaches work in harmony is the subject matter of this book. The book finally arrives at the

Graded associative conformal algebras of finite type

OpenAIRE

Kolesnikov, Pavel

2011-01-01

In this paper, we consider graded associative conformal algebras. The class of these objects includes pseudo-algebras over non-cocommutative Hopf algebras of regular functions on some linear algebraic groups. In particular, an associative conformal algebra which is graded by a finite group $\\Gamma $ is a pseudo-algebra over the coordinate Hopf algebra of a linear algebraic group $G$ such that the identity component $G^0$ is the affine line and $G/G^0\\simeq \\Gamma $. A classification of simple...

Principles of linear algebra with Mathematica

CERN Document Server

Shiskowski, Kenneth M

2013-01-01

A hands-on introduction to the theoretical and computational aspects of linear algebra using Mathematica® Many topics in linear algebra are simple, yet computationally intensive, and computer algebra systems such as Mathematica® are essential not only for learning to apply the concepts to computationally challenging problems, but also for visualizing many of the geometric aspects within this field of study. Principles of Linear Algebra with Mathematica uniquely bridges the gap between beginning linear algebra and computational linear algebra that is often encountered in applied settings,

Einstein algebras and general relativity

International Nuclear Information System (INIS)

Heller, M.

1992-01-01

A purely algebraic structure called an Einstein algebra is defined in such a way that every spacetime satisfying Einstein's equations is an Einstein algebra but not vice versa. The Gelfand representation of Einstein algebras is defined, and two of its subrepresentations are discussed. One of them is equivalent to the global formulation of the standard theory of general relativity; the other one leads to a more general theory of gravitation which, in particular, includes so-called regular singularities. In order to include other types of singularities one must change to sheaves of Einstein algebras. They are defined and briefly discussed. As a test of the proposed method, the sheaf of Einstein algebras corresponding to the space-time of a straight cosmic string with quasiregular singularity is constructed. 22 refs

TEARING THE VEIL: INTERACTION OF THE ORION NEBULA WITH ITS NEUTRAL ENVIRONMENT

International Nuclear Information System (INIS)

Van der Werf, Paul P.; Goss, W. M.; O'Dell, C. R.

2013-01-01

We present H I 21 cm observations of the Orion Nebula, obtained with the Karl G. Jansky Very Large Array, at an angular resolution of 7.''2 × 5.''7 and a velocity resolution of 0.77 km s –1 . Our data reveal H I absorption in the Veil toward the radio continuum of the H II region, and H I emission arising from the Orion Bar photon-dominated region (PDR) and from the Orion-KL outflow. In the Orion Bar PDR, the H I signal peaks in the same layer as the H 2 near-infrared vibrational line emission, in agreement with models of the photodissociation of H 2 . The gas temperature in this region is approximately 540 K, and the H I abundance in the interclump gas in the PDR is 5%-10% of the available hydrogen nuclei. Most of the gas in this region therefore remains molecular. Mechanical feedback on the Veil manifests itself through the interaction of ionized flow systems in the Orion Nebula, in particular the Herbig-Haro object HH 202, with the Veil. These interactions give rise to prominent blueward velocity shifts of the gas in the Veil. The unambiguous evidence for interaction of this flow system with the Veil shows that the distance between the Veil and the Trapezium stars needs to be revised downward to about 0.4 pc. The depth of the ionized cavity is about 0.7 pc, which is much smaller than the depth and the lateral extent of the Veil. Our results reaffirm the blister model for the M42 H II region, while also revealing its relation to the neutral environment on a larger scale.

Analytic real algebras.

Science.gov (United States)

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.

THE SPITZER INFRARED SPECTROGRAPH SURVEY OF PROTOPLANETARY DISKS IN ORION A. I. DISK PROPERTIES

Energy Technology Data Exchange (ETDEWEB)

Kim, K. H. [Korea Astronomy and Space Science Institute (KASI), 776, Daedeokdae-ro, Yuseong-gu, Daejeon 305-348 (Korea, Republic of); Watson, Dan M.; Manoj, P.; Forrest, W. J. [Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627 (United States); Furlan, Elise [Infrared Processing and Analysis Center, Caltech, 770 S. Wilson Avenue, Pasadena, CA 91125 (United States); Najita, Joan [National Optical Astronomy Observatory, 950 North Cherry Avenue, Tucson, AZ 85719 (United States); Sargent, Benjamin [Center for Imaging Science and Laboratory for Multiwavelength Astrophysics, Rochester Institute of Technology, 54 Lomb Memorial Dr., Rochester, NY 14623 (United States); Hernández, Jesús [Centro de Investigaciones de Astronomía, Apdo. Postal 264, Mérida 5101-A (Venezuela, Bolivarian Republic of); Calvet, Nuria [Department of Astronomy, University of Michigan, 830 Dennison Building, 500 Church Street, Ann Arbor, MI 48109 (United States); Adame, Lucía [Facultad de Ciencias Físico-Matemáticas, Universidad Autónoma de Nuevo León, Av. Universidad S/N, San Nicolás de los Garza, Nuevo León, C.P. 66451, México (Mexico); Espaillat, Catherine [Department of Astronomy, Boston University, 725 Commonwealth Avenue, Boston, MA 02215 (United States); Megeath, S. T. [Ritter Astrophysical Research Center, Department of Physics and Astronomy, University of Toledo, 2801 W. Bancroft St., Toledo, OH 43606 (United States); Muzerolle, James, E-mail: quarkosmos@kasi.re.kr [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States); and others

2016-09-01

We present our investigation of 319 Class II objects in Orion A observed by Spitzer /IRS. We also present the follow-up observations of 120 of these Class II objects in Orion A from the Infrared Telescope Facility/SpeX. We measure continuum spectral indices, equivalent widths, and integrated fluxes that pertain to disk structure and dust composition from IRS spectra of Class II objects in Orion A. We estimate mass accretion rates using hydrogen recombination lines in the SpeX spectra of our targets. Utilizing these properties, we compare the distributions of the disk and dust properties of Orion A disks with those of Taurus disks with respect to position within Orion A (Orion Nebular Cluster [ONC] and L1641) and with the subgroups by the inferred radial structures, such as transitional disks (TDs) versus radially continuous full disks (FDs). Our main findings are as follows. (1) Inner disks evolve faster than the outer disks. (2) The mass accretion rates of TDs and those of radially continuous FDs are statistically significantly displaced from each other. The median mass accretion rate of radially continuous disks in the ONC and L1641 is not very different from that in Taurus. (3) Less grain processing has occurred in the disks in the ONC compared to those in Taurus, based on analysis of the shape index of the 10 μ m silicate feature ( F {sub 11.3}/ F {sub 9.8}). (4) The 20–31 μ m continuum spectral index tracks the projected distance from the most luminous Trapezium star, θ {sup 1} Ori C. A possible explanation is UV ablation of the outer parts of disks.

An Airborne Parachute Compartment Test Bed for the Orion Parachute Test Program

Science.gov (United States)

Moore, James W.; Romero, Leah M.

2013-01-01

The test program developing parachutes for the Orion/MPCV includes drop tests with parachutes deployed from an Orion-like parachute compartment at a wide range of dynamic pressures. Aircraft and altitude constraints precluded the use of an Orion boilerplate capsule for several test points. Therefore, a dart-shaped test vehicle with a hi-fidelity mock-up of the Orion parachute compartment has been developed. The available aircraft options imposed constraints on the test vehicle development and concept of operations. Delivery of this test vehicle to the desired velocity, altitude, and orientation required for the test is a di cult problem involving multiple engineering disciplines. This paper describes the development of the test technique. The engineering challenges include extraction from an aircraft, reposition of the extraction parachute, and mid-air separation of two vehicles, neither of which has an active attitude control system. The desired separation behavior is achieved by precisely controlling the release point using on-board monitoring of the motion. The design of the test vehicle is also described. The trajectory simulations and other analyses used to develop this technique and predict the behavior of the test vehicle are reviewed in detail. The application of the technique on several successful drop tests is summarized.

Biderivations of W-algebra $W(2,2)$ and Virasoro algebra without skewsymmetric condition and their applications

OpenAIRE

Tang, Xiaomin

2016-01-01

In this paper, we characterize the biderivations of W-algebra $W(2,2)$ and Virasoro algebra $Vir$ without skewsymmetric condition. We get two classes of non-inner biderivations. As applications, we also get the forms of linear commuting maps on W-algebra $W(2,2)$ and Virasoro algebra $Vir$.

Evolution algebras generated by Gibbs measures

International Nuclear Information System (INIS)

Rozikov, Utkir A.; Tian, Jianjun Paul

2009-03-01

In this article we study algebraic structures of function spaces defined by graphs and state spaces equipped with Gibbs measures by associating evolution algebras. We give a constructive description of associating evolution algebras to the function spaces (cell spaces) defined by graphs and state spaces and Gibbs measure μ. For finite graphs we find some evolution subalgebras and other useful properties of the algebras. We obtain a structure theorem for evolution algebras when graphs are finite and connected. We prove that for a fixed finite graph, the function spaces have a unique algebraic structure since all evolution algebras are isomorphic to each other for whichever Gibbs measures are assigned. When graphs are infinite graphs then our construction allows a natural introduction of thermodynamics in studying of several systems of biology, physics and mathematics by theory of evolution algebras. (author)

Classical algebraic chromodynamics

International Nuclear Information System (INIS)

Adler, S.L.

1978-01-01

I develop an extension of the usual equations of SU(n) chromodynamics which permits the consistent introduction of classical, noncommuting quark source charges. The extension involves adding a singlet gluon, giving a U(n) -based theory with outer product P/sup a/(u,v) = (1/2)(d/sup a/bc + if/sup a/bc)(u/sup b/v/sup c/ - v/sup b/u/sup c/) which obeys the Jacobi identity, inner product S (u,v) = (1/2)(u/sup a/v/sup a/ + v/sup a/u/sup a/), and with the n 2 gluon fields elevated to algebraic fields over the quark color charge C* algebra. I show that provided the color charge algebra satisfies the condition S (P (u,v),w) = S (u,P (v,w)) for all elements u,v,w of the algebra, all the standard derivations of Lagrangian chromodynamics continue to hold in the algebraic chromodynamics case. I analyze in detail the color charge algebra in the two-particle (qq, qq-bar, q-barq-bar) case and show that the above consistency condition is satisfied for the following unique (and, interestingly, asymmetric) choice of quark and antiquark charges: Q/sup a//sub q/ = xi/sup a/, Q/sup a//sub q/ = xi-bar/sup a/ + delta/sup a/0(n/2)/sup 3/2/1, with xi/sup a/xi/sup b/ = (1/2)(d/sup a/bc + if/sup a/bc) xi/sup c/, xi-bar/sup a/xi-bar/sup b/ = -(1/2)(d/sup a/bc - if/sup a/bc) xi-bar/sup c/. The algebraic structure of the two-particle U(n) force problem, when expressed on an appropriately diagonalized basis, leads for all n to a classical dynamics problem involving an ordinary SU(2) Yang-Mills field with uniquely specified classical source charges which are nonparallel in the color-singlet state. An explicit calculation shows that local algebraic U(n) gauge transformations lead only to a rigid global rotation of axes in the overlying classical SU(2) problem, which implies that the relative orientations of the classical source charges have physical significance

Polarimetry at 1.3 mm using MILLIPOL - methods and preliminary results for Orion

International Nuclear Information System (INIS)

Barvainis, R.; Clemens, D.P.; Leach, R.

1988-01-01

This paper describes a polarimeter for use at wavelengths near 1 mm, designed to be self-contained and portable. Only minor modifications should be required to adapt this instrument for use on any of several millimeter and submillimeter telescopes. The polarimeter system and data-taking techniques are described, and a preliminary measurement is reported of the polarized dust emission from the Orion KL region at 1.3 mm using the NRAO 12 m telescope. The results are similar to previous polarization measurements of Orion at far-infrared and submillimeter wavelengths. The magnetic field direction implied by the polarization position angle is parallel to that found in the surrounding Orion region using optical and near- to midinfrared polarimetric techniques. 17 references

On the classification of quantum W-algebras

International Nuclear Information System (INIS)

Bowcock, P.; Watts, G.T.M.

1992-01-01

In this paper we consider the structure of general quantum W-algebras. We introduce the notions of deformability, positive-definiteness, and reductivity of a W-algebra. We show that one can associate a reductive finite Lie algebra to each reductive W-algebra. The finite Lie algebra is also endowed with a preferred sl(2) subalgebra, which gives the conformal weights of the W-algebra. We extend this to cover W-algebras containing both bosonic and fermionic fields, and illustrate our ideas with the Poisson bracket algebras of generalised Drinfeld-Sokolov hamiltonian systems. We then discuss the possibilities of classifying deformable W-algebras which fall outside this class in the context of automorphisms of Lie algebras. In conclusion we list the cases in which the W-algebra has no weight-one fields, and further, those in which it has only one weight-two field. (orig.)

Lie-Algebras. Pt. 1

International Nuclear Information System (INIS)

Baeuerle, G.G.A.; Kerf, E.A. de

1990-01-01

The structure of the laws in physics is largely based on symmetries. This book is on Lie algebras, the mathematics of symmetry. It gives a thorough mathematical treatment of finite dimensional Lie algebras and Kac-Moody algebras. Concepts such as Cartan matrix, root system, Serre's construction are carefully introduced. Although the book can be read by an undergraduate with only an elementary knowledge of linear algebra, the book will also be of use to the experienced researcher. Experience has shown that students who followed the lectures are well-prepared to take on research in the realms of string-theory, conformal field-theory and integrable systems. 48 refs.; 66 figs.; 3 tabs

Semiprojectivity of universal -algebras generated by algebraic elements

DEFF Research Database (Denmark)

Shulman, Tatiana

2012-01-01

Let be a polynomial in one variable whose roots all have multiplicity more than 1. It is shown that the universal -algebra of a relation , , is semiprojective and residually finite-dimensional. Applications to polynomially compact operators are given.......Let be a polynomial in one variable whose roots all have multiplicity more than 1. It is shown that the universal -algebra of a relation , , is semiprojective and residually finite-dimensional. Applications to polynomially compact operators are given....

Hyperloops, Nuclear Spacecraft, and the New York City Subway

Science.gov (United States)

Granade, Stephen

2014-03-01

Frustrated by the speed and high cost-per-mile of the California High-Speed Rail project linking Los Angeles with San Francisco, Elon Musk proposed the Hyperloop: a high-speed train running in a sealed, partially-evacuated tube. Musk released a white paper that described the technology and concluded that the Hyperloop could be built for less than a tenth of a cost of the California High-Speed Rail. Musk's white paper focused heavily on the scientific and technical questions that must be answered, but public transportation is a domain at the intersection of science and society. Public transportation infrastructure is shaped as much by the pressures of government and citizens as by the technology behind the transportation. Tube-based transport like the Hyperloop has been proposed before, but has never gone further than words on a page. Why? Historical examples like the development of the New York City subway and the proposed nuclear-powered Orion spacecraft shed light on the societal barriers that new transportation must overcome, and help illuminate why technology-based answers are not a full response to transportation questions.

The formal theory of Hopf algebras part II: the case of Hopf algebras ...

African Journals Online (AJOL)

The category HopfR of Hopf algebras over a commutative unital ring R is analyzed with respect to its categorical properties. The main results are: (1) For every ring R the category HopfR is locally presentable, it is coreflective in the category of bialgebras over R, over every R-algebra there exists a cofree Hopf algebra. (2) If ...

Macdonald index and chiral algebra

Science.gov (United States)

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.

Vertex algebras and mirror symmetry

International Nuclear Information System (INIS)

Borisov, L.A.

2001-01-01

Mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties is by now well established. However, previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror. We are able to calculate explicitly vertex algebras that correspond to holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in toric varieties. We establish the relation between these vertex algebras for mirror Calabi-Yau manifolds. This should eventually allow us to rewrite the whole story of toric mirror symmetry in the language of sheaves of vertex algebras. Our approach is purely algebraic and involves simple techniques from toric geometry and homological algebra, as well as some basic results of the theory of vertex algebras. Ideas of this paper may also be useful in other problems related to maps from curves to algebraic varieties.This paper could also be of interest to physicists, because it contains explicit description of holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in terms of free bosons and fermions. (orig.)

Search for HOOH in Orion

Science.gov (United States)

Liseau, R.; Larsson, B.

2015-11-01

Context. The abundance of key molecules determines the level of cooling that is necessary for the formation of stars and planetary systems. In this context, one needs to understand the details of the time dependent oxygen chemistry, leading to the formation of O2 and H2O. Aims: We aim to determine the degree of correlation between the occurrence of O2 and HOOH (hydrogen peroxide) in star-forming molecular clouds. We first detected O2 and HOOH in ρ Oph A, we now search for HOOH in Orion OMC A, where O2 has also been detected. Methods: We mapped a 3'×3' region around Orion H2-Peak 1 with the Atacama Pathfinder Experiment (APEX). In addition to several maps in two transitions of HOOH, viz. 219.17 GHz and 251.91 GHz, we obtained single-point spectra for another three transitions towards the position of maximum emission. Results: Line emission at the appropriate LSR-velocity (Local Standard of Rest) and at the level of ≥4σ was found for two transitions, with lower signal-to-noise ratio (2.8-3.5σ) for another two transitions, whereas for the remaining transition, only an upper limit was obtained. The emitting region, offset 18'' south of H2-Peak 1, appeared point-like in our observations with APEX. Conclusions: The extremely high spectral line density in Orion makes the identification of HOOH much more difficult than in ρ Oph A. As a result of having to consider the possible contamination by other molecules, we left the current detection status undecided. Based on observations with APEX, which is a 12 m diameter submillimetre telescope at 5100 m altitude on Llano Chajnantor in Chile. The telescope is operated by Onsala Space Observatory, Max-Planck-Institut für Radioastronomie (MPIfR), and European Southern Observatory (ESO).The final reduced data cube (FITS files) is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/583/A53

Advanced modern algebra part 2

CERN Document Server

Rotman, Joseph J

2017-01-01

This book is the second part of the new edition of Advanced Modern Algebra (the first part published as Graduate Studies in Mathematics, Volume 165). Compared to the previous edition, the material has been significantly reorganized and many sections have been rewritten. The book presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.

A q-deformed Lorentz algebra

International Nuclear Information System (INIS)

Schmidke, W.B.; Wess, J.; Muenchen Univ.; Zumino, B.; Lawrence Berkeley Lab., CA

1991-01-01

We derive a q-deformed version of the Lorentz algebra by deformating the algebra SL(2, C). The method is based on linear representations of the algebra on the complex quantum spinor space. We find that the generators usually identified with SL q (2, C) generate SU q (2) only. Four additional generators are added which generate Lorentz boosts. The full algebra of all seven generators and their coproduct is presented. We show that in the limit q→1 the generators are those of the classical Lorentz algebra plus an additional U(1). Thus we have a deformation of SL(2, C)xU(1). (orig.)

Introduction to algebraic quantum field theory

International Nuclear Information System (INIS)

Horuzhy, S.S.

1990-01-01

This volume presents a systematic introduction to the algebraic approach to quantum field theory. The structure of the contents corresponds to the way the subject has advanced. It is shown how the algebraic approach has developed from the purely axiomatic theory of observables via superselection rules into the dynamical formalism of fields and observables. Chapter one discusses axioms and their consequences -many of which are now classical theorems- and deals, in general, with the axiomatic theory of local observable algebras. The absence of field concepts makes this theory incomplete and, in chapter two, superselection rules are shown to be the key to the reconstruction of fields from observables. Chapter three deals with the algebras of Wightman fields, first unbounded operator algebras, then Von Neumann field algebras (with a special section on wedge region algebras) and finally local algebras of free and generalised free fields. (author). 447 refs.; 4 figs

Comments on N=4 superconformal algebras

International Nuclear Information System (INIS)

Rasmussen, J.

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)xU(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 vertical bar 2) current superalgebra. Replacing SL(2 vertical bar 2) with the coset SL(2 vertical bar 2)/U(1), results directly in the small N=4 superconformal algebra

The theory of algebraic numbers

CERN Document Server

Pollard, Harry

1998-01-01

An excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture. 1975 edition. References. List of Symbols. Index.

Quantum Heisenberg groups and Sklyanin algebras

International Nuclear Information System (INIS)

Andruskiewitsch, N.; Devoto, J.; Tiraboschi, A.

1993-05-01

We define new quantizations of the Heisenberg group by introducing new quantizations in the universal enveloping algebra of its Lie algebra. Matrix coefficients of the Stone-von Neumann representation are preserved by these new multiplications on the algebra of functions on the Heisenberg group. Some of the new quantizations provide also a new multiplication in the algebra of theta functions; we obtain in this way Sklyanin algebras. (author). 23 refs

Classification of simple flexible Lie-admissible algebras

International Nuclear Information System (INIS)

Okubo, S.; Myung, H.C.

1979-01-01

Let A be a finite-dimensional flexible Lie-admissible algebra over the complex field such that A - is a simple Lie algebra. It is shown that either A is itself a Lie algebra isomorphic to A - or A - is a Lie algebra of type A/sub n/ (n greater than or equal to 2). In the latter case, A is isomorphic to the algebra defined on the space of (n + 1) x (n + 1) traceless matrices with multiplication given by x * y = μxy + (1 - μ)yx - (1/(n + 100 Tr (xy) E where μ is a fixed scalar, xy denotes the matrix operators in Lie algebras which has been studied in theoretical physics. We also discuss a broader class of Lie algebras over arbitrary field of characteristic not equal to 2, called quasi-classical, which includes semisimple as well as reductive Lie algebras. For this class of Lie algebras, we can introduce a multiplication which makes the adjoint operator space into an associative algebra. When L is a Lie algebra with nondegenerate killing form, it is shown that the adjoint operator algebra of L in the adjoint representation becomes a commutative associative algebra with unit element and its dimension is 1 or 2 if L is simple over the complex field. This is related to the known result that a Lie algebra of type A/sub n/ (n greater than or equal to 2) alone has a nonzero completely symmetric adjoint operator in the adjoint representation while all other algebras have none. Finally, Lie-admissible algebras associated with bilinear form are investigated

ALMA Observations of the Archetypal “Hot Core” That Is Not: Orion-KL

International Nuclear Information System (INIS)

Orozco-Aguilera, M. T.; Zapata, Luis A.; Hirota, Tomoya; Qin, Sheng-Li; Masqué, Josep M

2017-01-01

We present sensitive high angular resolution (∼0.″1–0.″3) continuum Atacama Large Millimeter/Submillimeter Array (ALMA) observations of the archetypal hot core located in the Orion Kleinmann-Low (KL) region. The observations were made in five different spectral bands (bands 3, 6, 7, 8, and 9) covering a very broad range of frequencies (149–658 GHz). Apart from the well-known millimeter emitting objects located in this region (Orion Source I and BN), we report the first submillimeter detection of three compact continuum sources (ALMA1–3) in the vicinities of the Orion-KL hot molecular core. These three continuum objects have spectral indices between 1.47 and 1.56, and brightness temperatures between 100 and 200 K at 658 GHz, suggesting that we are seeing moderate, optically thick dust emission with possible grain growth. However, as these objects are not associated with warm molecular gas, and some of them are farther out from the molecular core, we thus conclude that they cannot heat the molecular core. This result favors the hypothesis that the hot molecular core in Orion-KL core is heated externally.

ALMA Observations of the Archetypal “Hot Core” That Is Not: Orion-KL

Energy Technology Data Exchange (ETDEWEB)

Orozco-Aguilera, M. T. [Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro 1, Tonantzintla, Puebla, México (Mexico); Zapata, Luis A. [Instituto de Radioastronomía y Astrofísica, UNAM, Apdo. Postal 3-72 (Xangari), 58089 Morelia, Michoacán, México (Mexico); Hirota, Tomoya [Mizusawa VLBI Observatory, National Astronomical Observatory of Japan, Osawa 2-21-1, Mitaka-shi, Tokyo 181-8588 (Japan); Qin, Sheng-Li [Department of Astronomy, Yunnan University, and Key Laboratory of Astroparticle Physics of Yunnan Province, Kunming 650091 (China); Masqué, Josep M, E-mail: lzapata@crya.unam.mx [Departamento de Astronomía, Universidad de Guanajuato, Apdo. Postal 144, 36000 Guanajuato, México (Mexico)

2017-09-20

We present sensitive high angular resolution (∼0.″1–0.″3) continuum Atacama Large Millimeter/Submillimeter Array (ALMA) observations of the archetypal hot core located in the Orion Kleinmann-Low (KL) region. The observations were made in five different spectral bands (bands 3, 6, 7, 8, and 9) covering a very broad range of frequencies (149–658 GHz). Apart from the well-known millimeter emitting objects located in this region (Orion Source I and BN), we report the first submillimeter detection of three compact continuum sources (ALMA1–3) in the vicinities of the Orion-KL hot molecular core. These three continuum objects have spectral indices between 1.47 and 1.56, and brightness temperatures between 100 and 200 K at 658 GHz, suggesting that we are seeing moderate, optically thick dust emission with possible grain growth. However, as these objects are not associated with warm molecular gas, and some of them are farther out from the molecular core, we thus conclude that they cannot heat the molecular core. This result favors the hypothesis that the hot molecular core in Orion-KL core is heated externally.

Quantitative Algebraic Reasoning

DEFF Research Database (Denmark)

Mardare, Radu Iulian; Panangaden, Prakash; Plotkin, Gordon

2016-01-01

We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We define an equality relation indexed by rationals: a =ε b which we think of as saying that “a is approximately equal to b up to an error of ε”. We have 4 interesting examples where we have a quantitative...... equational theory whose free algebras correspond to well known structures. In each case we have finitary and continuous versions. The four cases are: Hausdorff metrics from quantitive semilattices; pWasserstein metrics (hence also the Kantorovich metric) from barycentric algebras and also from pointed...

Anyons, deformed oscillator algebras and projectors

International Nuclear Information System (INIS)

Engquist, Johan

2009-01-01

We initiate an algebraic approach to the many-anyon problem based on deformed oscillator algebras. The formalism utilizes a generalization of the deformed Heisenberg algebras underlying the operator solution of the Calogero problem. We define a many-body Hamiltonian and an angular momentum operator which are relevant for a linearized analysis in the statistical parameter ν. There exists a unique ground state and, in spite of the presence of defect lines, the anyonic weight lattices are completely connected by the application of the oscillators of the algebra. This is achieved by supplementing the oscillator algebra with a certain projector algebra.

Alternative algebraic approaches in quantum chemistry

International Nuclear Information System (INIS)

Mezey, Paul G.

2015-01-01

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

Alternative algebraic approaches in quantum chemistry

Energy Technology Data Exchange (ETDEWEB)

Mezey, Paul G., E-mail: paul.mezey@gmail.com [Canada Research Chair in Scientific Modeling and Simulation, Department of Chemistry and Department of Physics and Physical Oceanography, Memorial University of Newfoundland, 283 Prince Philip Drive, St. John' s, NL A1B 3X7 (Canada)

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.

On graded algebras of global dimension 3

International Nuclear Information System (INIS)

Piontkovskii, D I

2001-01-01

Assume that a graded associative algebra A over a field k is minimally presented as the quotient algebra of a free algebra F by the ideal I generated by a set f of homogeneous elements. We study the following two extensions of A: the algebra F-bar=F/I oplus I/I 2 oplus ... associated with F with respect to the I-adic filtration, and the homology algebra H of the Shafarevich complex Sh(f,F) (which is a non-commutative version of the Koszul complex). We obtain several characterizations of algebras of global dimension 3. In particular, the A-algebra H in this case is free, and the algebra F-bar is isomorphic to the quotient algebra of a free A-algebra by the ideal generated by a so-called strongly free (or inert) set

Unipotent and nilpotent classes in simple algebraic groups and lie algebras

CERN Document Server

Liebeck, Martin W

2012-01-01

This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of...

Elements of mathematics algebra

CERN Document Server

Bourbaki, Nicolas

2003-01-01

This is a softcover reprint of the English translation of 1990 of the revised and expanded version of Bourbaki's, Algèbre, Chapters 4 to 7 (1981). This completes Algebra, 1 to 3, by establishing the theories of commutative fields and modules over a principal ideal domain. Chapter 4 deals with polynomials, rational fractions and power series. A section on symmetric tensors and polynomial mappings between modules, and a final one on symmetric functions, have been added. Chapter 5 was entirely rewritten. After the basic theory of extensions (prime fields, algebraic, algebraically closed, radical extension), separable algebraic extensions are investigated, giving way to a section on Galois theory. Galois theory is in turn applied to finite fields and abelian extensions. The chapter then proceeds to the study of general non-algebraic extensions which cannot usually be found in textbooks: p-bases, transcendental extensions, separability criterions, regular extensions. Chapter 6 treats ordered groups and fields and...

Brauer algebra of type F4

NARCIS (Netherlands)

Liu, S.

2012-01-01

We present an algebra related to the Coxeter group of type F4 which can be viewed as the Brauer algebra of type F4 and is obtained as a subalgebra of the Brauer algebra of type E6. We also describe some properties of this algebra.

Brauer algebras of type F4

NARCIS (Netherlands)

Liu, S.

2013-01-01

We present an algebra related to the Coxeter group of type F4 which can be viewed as the Brauer algebra of type F4 and is obtained as a subalgebra of the Brauer algebra of type E6. We also describe some properties of this algebra.

New examples of continuum graded Lie algebras

International Nuclear Information System (INIS)

Savel'ev, M.V.

1989-01-01

Several new examples of continuum graded Lie algebras which provide an additional elucidation of these algebras are given. Here, in particular, the Kac-Moody algebras, the algebra S 0 Diff T 2 of infinitesimal area-preserving diffeomorphisms of the torus T 2 , the Fairlie, Fletcher and Zachos sine-algebras, etc., are described as special cases of the cross product Lie algebras. 8 refs

Generalized Galilean algebras and Newtonian gravity

Science.gov (United States)

González, N.; Rubio, G.; Salgado, P.; Salgado, S.

2016-04-01

The non-relativistic versions of the generalized Poincaré algebras and generalized AdS-Lorentz algebras are obtained. These non-relativistic algebras are called, generalized Galilean algebras of type I and type II and denoted by GBn and GLn respectively. Using a generalized Inönü-Wigner contraction procedure we find that the generalized Galilean algebras of type I can be obtained from the generalized Galilean algebras type II. The S-expansion procedure allows us to find the GB5 algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref. [1] allows us to show that the nonrelativistic limit of the five dimensional Einstein-Chern-Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.

Circle Maps and C*-algebras

DEFF Research Database (Denmark)

Schmidt, Thomas Lundsgaard

such a map, generalising the transformation groupoid of a local homeomorphism first introduced by Renault in \\cite{re}. We conduct a detailed study of the relationship between the dynamics of $\\phi$, the properties of these groupoids, the structure of their corresponding reduced groupoid $C^*$-algebras, and......, for certain classes of maps, the K-theory of these algebras. When the map $\\phi$ is transitive, we show that the algebras $C^*_r(\\Gamma_\\phi)$ and $C^*_r(\\Gamma_\\phi^+)$ are purely infinite and satisfy the Universal Coefficient Theorem. Furthermore, we find necessary and sufficient conditions for simplicity...... of these algebras in terms of dynamical properties of $\\phi$. We proceed to consider the situation when the algebras are non-simple, and describe the primitive ideal spectrum in this case. We prove that any irreducible representation factors through the $C^*$-algebra of the reduction of the groupoid to the orbit...

The Boolean algebra of Galois algebras

Directory of Open Access Journals (Sweden)

Lianyong Xue

2003-02-01

Full Text Available Let B be a Galois algebra with Galois group G, Jg={b∈B|bx=g(xb for all x∈B} for each g∈G, and BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|g∈G}, e a nonzero element in Ba, and He={g∈G|eeg=e}. Then, a monomial e is characterized, and the Galois extension Be, generated by e with Galois group He, is investigated.

ORION: a web server for protein fold recognition and structure prediction using evolutionary hybrid profiles.

Science.gov (United States)

Ghouzam, Yassine; Postic, Guillaume; Guerin, Pierre-Edouard; de Brevern, Alexandre G; Gelly, Jean-Christophe

2016-06-20

Protein structure prediction based on comparative modeling is the most efficient way to produce structural models when it can be performed. ORION is a dedicated webserver based on a new strategy that performs this task. The identification by ORION of suitable templates is performed using an original profile-profile approach that combines sequence and structure evolution information. Structure evolution information is encoded into profiles using structural features, such as solvent accessibility and local conformation -with Protein Blocks-, which give an accurate description of the local protein structure. ORION has recently been improved, increasing by 5% the quality of its results. The ORION web server accepts a single protein sequence as input and searches homologous protein structures within minutes. Various databases such as PDB, SCOP and HOMSTRAD can be mined to find an appropriate structural template. For the modeling step, a protein 3D structure can be directly obtained from the selected template by MODELLER and displayed with global and local quality model estimation measures. The sequence and the predicted structure of 4 examples from the CAMEO server and a recent CASP11 target from the 'Hard' category (T0818-D1) are shown as pertinent examples. Our web server is accessible at http://www.dsimb.inserm.fr/ORION/.

Orion star-forming region - far-infrared and radio molecular observations

International Nuclear Information System (INIS)

Thronson, H.A. Jr.; Harper, D.A.; Bally, J.; Dragovan, M.; Mozurkewich, D.; Yerkes Observatory, Williams Bay, WI; ATandT Bell Labs., Holmdel, NJ; Chicago Uni., IL; E. O. Hulburt Center for Space Research, Washington, DC)

1986-01-01

New J = 1-0 CO and far-infrared maps of the Orion star-forming region are presented and discussed. The total infrared luminosity of the Orion star-forming ridge is 250,000 solar luminosities. The material that is emitting strongly at 60 microns is traced and found to be highly centrally concentrated. However, the majority of the extended emission from this region comes from dust that is ultimately heated by the visible Trapezium cluster stars. The luminosity of IRc 2, the most luminous member of the infrared cluster, is estimated to be 40,000-50,000 solar luminosities. A schematic drawing of the Ori MC 1 region is presented. 30 references

Flare stars of the Orion Nebula - spectra of an outburst

International Nuclear Information System (INIS)

Carter, B.D.; O'Mara, B.J.; Ross, J.E.

1988-01-01

For the first time, detailed, time-resolved spectra of a flare event of an Orion cluster flare star are presented. These spectra, covering ∼ λλ3600-4600, were obtained by using the Anglo-Australian Telescope with a fibre coupler to simultaneously monitor 23 flare stars in the region of the Orion Nebula. The flare spectra reveal continuous emission which filled in the photospheric Ca I 4226 A absorption, and hydrogen Balmer, Ca II H and K, He I 4026 A and He I 4471 A line emission. Overall, the spectral behaviour indicates similarities to strong outbursts of the classical dMe flare stars. (author)

Geometry of Spin: Clifford Algebraic Approach

Indian Academy of Sciences (India)

Then the various algebraic properties of Pauli matricesare studied as properties of matrix algebra. What has beenshown in this article is that Pauli matrices are a representationof Clifford algebra of spin and hence all the propertiesof Pauli matrices follow from the underlying algebra. Cliffordalgebraic approach provides a ...

Differential operators and W-algebra

International Nuclear Information System (INIS)

Vaysburd, I.; Radul, A.

1992-01-01

The connection between W-algebras and the algebra of differential operators is conjectured. The bosonized representation of the differential operator algebra with c=-2n and all the subalgebras are examined. The degenerate representations and null-state classifications for c=-2 are presented. (orig.)

Donaldson invariants in algebraic geometry

International Nuclear Information System (INIS)

Goettsche, L.

2000-01-01

In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)

Fractional supersymmetry and infinite dimensional lie algebras

International Nuclear Information System (INIS)

Rausch de Traubenberg, M.

2001-01-01

In an earlier work extensions of supersymmetry and super Lie algebras were constructed consistently starting from any representation D of any Lie algebra g. Here it is shown how infinite dimensional Lie algebras appear naturally within the framework of fractional supersymmetry. Using a differential realization of g this infinite dimensional Lie algebra, containing the Lie algebra g as a sub-algebra, is explicitly constructed

Polarimetry of the Orion population stars

Energy Technology Data Exchange (ETDEWEB)

Kopatskaya, E N; Shulov, O S

1978-01-01

The results of polarization observations are given for 44 stars of the Orion population selected from the list of Herbig and Rao (Astrophys. J., v. 174, pt. 1, pp 401-423(1972)). Photometric observations are also reported for a number of the stars. The distribution of the degrees of polarization is found to be approximated by the logarithmic-normal probability law. 1 figure, 2 tables.

Quantum algebra of N superspace

International Nuclear Information System (INIS)

Hatcher, Nicolas; Restuccia, A.; Stephany, J.

2007-01-01

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 κ-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

On criteria for algebraic independence of collections of functions satisfying algebraic difference relations

Directory of Open Access Journals (Sweden)

Hiroshi Ogawara

2017-01-01

Full Text Available This paper gives conditions for algebraic independence of a collection of functions satisfying a certain kind of algebraic difference relations. As applications, we show algebraic independence of two collections of special functions: (1 Vignéras' multiple gamma functions and derivatives of the gamma function, (2 the logarithmic function, \\(q\\-exponential functions and \\(q\\-polylogarithm functions. In a similar way, we give a generalization of Ostrowski's theorem.

Assessment of the Orion-SLS Interface Management Process in Achieving the EIA 731.1 Systems Engineering Capability Model Generic Practices Level 3 Criteria

Science.gov (United States)

Jellicorse, John J.; Rahman, Shamin A.

2016-01-01

NASA is currently developing the next generation crewed spacecraft and launch vehicle for exploration beyond earth orbit including returning to the Moon and making the transit to Mars. Managing the design integration of major hardware elements of a space transportation system is critical for overcoming both the technical and programmatic challenges in taking a complex system from concept to space operations. An established method of accomplishing this is formal interface management. In this paper we set forth an argument that the interface management process implemented by NASA between the Orion Multi-Purpose Crew Vehicle (MPCV) and the Space Launch System (SLS) achieves the Level 3 tier of the EIA 731.1 System Engineering Capability Model (SECM) for Generic Practices. We describe the relevant NASA systems and associated organizations, and define the EIA SECM Level 3 Generic Practices. We then provide evidence for our compliance with those practices. This evidence includes discussions of: NASA Systems Engineering Interface (SE) Management standard process and best practices; the tailoring of that process for implementation on the Orion to SLS interface; changes made over time to improve the tailored process, and; the opportunities to take the resulting lessons learned and propose improvements to our institutional processes and best practices. We compare this evidence against the practices to form the rationale for the declared SECM maturity level.

An algebra of reversible computation.

Science.gov (United States)

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.

On an extension of the Weil algebra

International Nuclear Information System (INIS)

Palev, Ch.

An extension of the Weil algebra Wsub(n), generated by an appropriate topology is considered. The topology is introduced in such a way that algebraic operations in Wsub(n) to be continuous. The algebraic operations in Wsub(n) are extended by a natural way to a complement, which is noted as an extended Weil algebra. It turns out that the last algebra contains isomorphically the Heisenberg group. By the same way an arbitrary enveloping algebra of a Lie group may be extended. The extended algebra will contain the initial Lie group. (S.P.)

Exponentiation and deformations of Lie-admissible algebras

International Nuclear Information System (INIS)

Myung, H.C.

1982-01-01

The exponential function is defined for a finite-dimensional real power-associative algebra with unit element. The application of the exponential function is focused on the power-associative (p,q)-mutation of a real or complex associative algebra. Explicit formulas are computed for the (p,q)-mutation of the real envelope of the spin 1 algebra and the Lie algebra so(3) of the rotation group, in light of earlier investigations of the spin 1/2. A slight variant of the mutated exponential is interpreted as a continuous function of the Lie algebra into some isotope of the corresponding linear Lie group. The second part of this paper is concerned with the representation and deformation of a Lie-admissible algebra. The second cohomology group of a Lie-admissible algebra is introduced as a generalization of those of associative and Lie algebras in the Hochschild and Chevalley-Eilenberg theory. Some elementary theory of algebraic deformation of Lie-admissible algebras is discussed in view of generalization of that of associative and Lie algebras. Lie-admissible deformations are also suggested by the representation of Lie-admissible algebras. Some explicit examples of Lie-admissible deformation are given in terms of the (p,q)-mutation of associative deformation of an associative algebra. Finally, we discuss Lie-admissible deformations of order one

Clifford algebras and the minimal representations of the 1D N-extended supersymmetry algebra

International Nuclear Information System (INIS)

Toppan, Francesco

2008-01-01

The Atiyah-Bott-Shapiro classification of the irreducible Clifford algebra is used to derive general properties of the minimal representations of the 1D N-Extended Supersymmetry algebra (the Z 2 -graded symmetry algebra of the Supersymmetric Quantum Mechanics) linearly realized on a finite number of fields depending on a real parameter t, the time. (author)

Contraction of graded su(2) algebra

International Nuclear Information System (INIS)

Patra, M.K.; Tripathy, K.C.

1989-01-01

The Inoenu-Wigner contraction scheme is extended to Lie superalgebras. The structure and representations of extended BRS algebra are obtained from contraction of the graded su(2) algebra. From cohomological consideration, we demonstrate that the graded su(2) algebra is the only superalgebra which, on contraction, yields the full BRS algebra. (orig.)

Atomic effect algebras with compression bases

International Nuclear Information System (INIS)

Caragheorgheopol, Dan; Tkadlec, Josef

2011-01-01

Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.

Operator theory, operator algebras and applications

CERN Document Server

Lebre, Amarino; Samko, Stefan; Spitkovsky, Ilya

2014-01-01

This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i) operator theory and harmonic analysis (singular integral operators with shifts; pseudodifferential operators, factorization of almost periodic matrix functions; inequalities; Cauchy type integrals; maximal and singular operators on generalized Orlicz-Morrey spaces; the Riesz potential operator; modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras; inner endomorphisms of some semi group, crossed products; C*-algebras generated by mappings which have finite orbits; Folner sequences in operator algebras; arithmetic aspect of C*_r SL(2); C*-algebras of singular integral operators; algebras of operator sequences) and (iii) mathematical physics (operator approach to diffraction from polygonal-conical screens; Poisson geo...

A twisted generalization of Novikov-Poisson algebras

OpenAIRE

Yau, Donald

2010-01-01

Hom-Novikov-Poisson algebras, which are twisted generalizations of Novikov-Poisson algebras, are studied. Hom-Novikov-Poisson algebras are shown to be closed under tensor products and several kinds of twistings. Necessary and sufficient conditions are given under which Hom-Novikov-Poisson algebras give rise to Hom-Poisson algebras.

Process Algebra and Markov Chains

NARCIS (Netherlands)

Brinksma, Hendrik; Hermanns, H.; Brinksma, Hendrik; Hermanns, H.; Katoen, Joost P.

This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study

Process algebra and Markov chains

NARCIS (Netherlands)

Brinksma, E.; Hermanns, H.; Brinksma, E.; Hermanns, H.; Katoen, J.P.

2001-01-01

This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study

Vertex ring-indexed Lie algebras

International Nuclear Information System (INIS)

Fairlie, David; Zachos, Cosmas

2005-01-01

Infinite-dimensional Lie algebras are introduced, which are only partially graded, and are specified by indices lying on cyclotomic rings. They may be thought of as generalizations of the Onsager algebra, but unlike it, or its sl(n) generalizations, they are not subalgebras of the loop algebras associated with sl(n). In a particular interesting case associated with sl(3), their indices lie on the Eisenstein integer triangular lattice, and these algebras are expected to underlie vertex operator combinations in CFT, brane physics, and graphite monolayers

Invariants of triangular Lie algebras

International Nuclear Information System (INIS)

Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman

2007-01-01

Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated

Q-systems as cluster algebras

International Nuclear Information System (INIS)

Kedem, Rinat

2008-01-01

Q-systems first appeared in the analysis of the Bethe equations for the XXX model and generalized Heisenberg spin chains (Kirillov and Reshetikhin 1987 Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Steklov. 160 211-21, 301). Such systems are known to exist for any simple Lie algebra and many other Kac-Moody algebras. We formulate the Q-system associated with any simple, simply-laced Lie algebras g in the language of cluster algebras (Fomin and Zelevinsky 2002 J. Am. Math. Soc. 15 497-529), and discuss the relation of the polynomiality property of the solutions of the Q-system in the initial variables, which follows from the representation-theoretical interpretation, to the Laurent phenomenon in cluster algebras (Fomin and Zelevinsky 2002 Adv. Appl. Math. 28 119-44)

Waterloo Workshop on Computer Algebra

CERN Document Server

Zima, Eugene; WWCA-2016; Advances in computer algebra : in honour of Sergei Abramov's' 70th birthday

2018-01-01

This book discusses the latest advances in algorithms for symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. It presents a collection of papers on original research topics from the Waterloo Workshop on Computer Algebra (WWCA-2016), a satellite workshop of the International Symposium on Symbolic and Algebraic Computation (ISSAC’2016), which was held at Wilfrid Laurier University (Waterloo, Ontario, Canada) on July 23–24, 2016.   This workshop and the resulting book celebrate the 70th birthday of Sergei Abramov (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow), whose highly regarded and inspirational contributions to symbolic methods have become a crucial benchmark of computer algebra and have been broadly adopted by many Computer Algebra systems.

Study on the Orion spiral arm structure by the statistical modelling method

International Nuclear Information System (INIS)

Basharina, T.S.; Pavlovskaya, E.D.; Filippova, A.A.

1980-01-01

A method of investigation of the spiral structure based on the statistical modelling methods is suggested. This method is used for the study of the Orion spiral arm. The maxima of density and the widths of the Orion arm in the direction of the areas considered for the longitude interval 55 deg - 187 deg are defined under the assumption of normal distribution of stars across the arm. The Sun is shown to be at the inner edge of the arm [ru

The Cuntz algebra Q_N and C*-algebras of product systems

DEFF Research Database (Denmark)

Hong, Jeong Hee; Larsen, Nadia S.; Szymanski, Wojciech

2011-01-01

We consider a product system over the multiplicative group semigroup N^x of Hilbert bimodules which is implicit in work of S. Yamashita and of the second named author. We prove directly, using universal properties, that the associated Nica-Toeplitz algebra is an extension of the C*-algebra Q...

Lectures on algebraic quantum field theory and operator algebras

International Nuclear Information System (INIS)

Schroer, Bert

2001-04-01

In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as why mathematicians are/should be interested in algebraic quantum field theory would be equally fitting. besides a presentation of the framework and the main results of local quantum physics these notes may serve as a guide to frontier research problems in mathematical. (author)

q-deformations of noncompact Lie (super-) algebras: The examples of q-deformed Lorentz, Weyl, Poincare' and (super-) conformal algebras

International Nuclear Information System (INIS)

Dobrev, V.K.

1992-01-01

We review and explain a canonical procedure for the q-deformation of the real forms G of complex Lie (super-) algebras associated with (generalized) Cartan matrices. Our procedure gives different q-deformations for the non-conjugate Cartan subalgebras of G. We give several in detail the q-deformed Lorentz and conformal (super-) algebras. The q-deformed conformal algebra contains as a subalgebra a q-deformed Poincare algebra and as Hopf subalgebras two conjugate 11-generator q-deformed Weyl algebras. The q-deformed Lorentz algebra in Hopf subalgebra of both Weyl algebras. (author). 24 refs

Ames Infusion Stories for NASA Annual Technology Report: Development of an Ablative 3D Quartz / Cyanate Ester Composite Multi-Functional Material for the Orion Spacecraft Compression Pad

Science.gov (United States)

Smith, Brandon; Jan, Darrell Leslie; Venkatapathy, Ethiraj

2015-01-01

Vehicles re-entering Earth's atmosphere require protection from the heat of atmospheric friction. The Orion Multi-Purpose Crew Vehicle (MPCV) has more demanding thermal protection system (TPS) requirements than the Low Earth Orbit (LEO) missions, especially in regions where the structural load passes through. The use of 2-dimensional laminate materials along with a metal insert, used in EFT1 flight test for the compression pad region, are deemed adequate but cannot be extended for Lunar return missions.

Assessing Algebraic Solving Ability: A Theoretical Framework

Science.gov (United States)

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…

Associative and Lie deformations of Poisson algebras

OpenAIRE

Remm, Elisabeth

2011-01-01

Considering a Poisson algebra as a non associative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this non associative algebra. This gives a natural interpretation of deformations which preserves the underlying associative structure and we study deformations which preserve the underlying Lie algebra.

Paragrassmann analysis and covariant quantum algebras

International Nuclear Information System (INIS)

Filippov, A.T.; Isaev, A.P.; Kurdikov, A.B.; Pyatov, P.N.

1993-01-01

This report is devoted to the consideration from the algebraic point of view the paragrassmann algebras with one and many paragrassmann generators Θ i , Θ p+1 i = 0. We construct the paragrassmann versions of the Heisenberg algebra. For the special case, this algebra is nothing but the algebra for coordinates and derivatives considered in the context of covariant differential calculus on quantum hyperplane. The parameter of deformation q in our case is (p+1)-root of unity. Our construction is nondegenerate only for even p. Taking bilinear combinations of paragrassmann derivatives and coordinates we realize generators for the covariant quantum algebras as tensor products of (p+1) x (p+1) matrices. (orig./HSI)

CLASSIFICATION OF 4-DIMENSIONAL GRADED ALGEBRAS

OpenAIRE

Armour, Aaron; Chen, Hui-Xiang; ZHANG, Yinhuo

2009-01-01

Let k be an algebraically closed field. The algebraic and geometric classification of finite dimensional algebras over k with ch(k) not equal 2 was initiated by Gabriel in [6], where a complete list of nonisomorphic 4-dimensional k-algebras was given and the number of irreducible components of the variety Alg(4) was discovered to be 5. The classification of 5-dimensional k-algebras was done by Mazzola in [10]. The number of irreducible components of the variety Alg(5) is 10. With the dimensio...

Banana Algebra: Compositional syntactic language extension

DEFF Research Database (Denmark)

Andersen, Jacob; Brabrand, Claus; Christiansen, David Raymond

2013-01-01

We propose an algebra of languages and transformations as a means of compositional syntactic language extension. The algebra provides a layer of high-level abstractions built on top of languages (captured by context-free grammars) and transformations (captured by constructive catamorphisms...... algebra as presented in the paper is implemented as the Banana Algebra Tool which may be used to syntactically extend languages in an incremental and modular fashion via algebraic composition of previously defined languages and transformations. We demonstrate and evaluate the tool via several kinds...

Linear algebra

CERN Document Server

Liesen, Jörg

2015-01-01

This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...

JB*-Algebras of Topological Stable Rank 1

Directory of Open Access Journals (Sweden)

Akhlaq A. Siddiqui

2007-01-01

Full Text Available In 1976, Kaplansky introduced the class JB*-algebras which includes all C*-algebras as a proper subclass. The notion of topological stable rank 1 for C*-algebras was originally introduced by M. A. Rieffel and was extensively studied by various authors. In this paper, we extend this notion to general JB*-algebras. We show that the complex spin factors are of tsr 1 providing an example of special JBW*-algebras for which the enveloping von Neumann algebras may not be of tsr 1. In the sequel, we prove that every invertible element of a JB*-algebra is positive in certain isotope of ; if the algebra is finite-dimensional, then it is of tsr 1 and every element of is positive in some unitary isotope of . Further, it is established that extreme points of the unit ball sufficiently close to invertible elements in a JB*-algebra must be unitaries and that in any JB*-algebras of tsr 1, all extreme points of the unit ball are unitaries. In the end, we prove the coincidence between the λ-function and λu-function on invertibles in a JB*-algebra.

(Super)conformal algebra on the (super)torus

International Nuclear Information System (INIS)

Mezincescu, L.; Nepomechie, R.I.; Zachos, C.K.

1989-01-01

A generalization of the Virasoro algebra has recently been introduced by Krichever and Novikov (KN). The KN algebra describes the algebra of general conformal transformations in a basis appropriate to a genus-g Riemann surface. We examine in detail the genus-one KN algebra, and find explicit expressions for the central extension. We, further, construct explicitly the superconformal algebra of the supertorus, which yields supersymmetric generalizations of the genus-one KN algebra. A novel feature of the odd-spin-structure case is that the algebra includes a central element which is anticommuting. We comment on possible applications to string theory. (orig.)

Spin-4 extended conformal algebras

International Nuclear Information System (INIS)

Kakas, A.C.

1988-01-01

We construct spin-4 extended conformal algebras using the second hamiltonian structure of the KdV hierarchy. In the presence of a U(1) current a family of spin-4 algebras exists but the additional requirement that the spin-1 and spin-4 currents commute fixes the algebra uniquely. (orig.)

Computer algebra applications

International Nuclear Information System (INIS)

Calmet, J.

1982-01-01

A survey of applications based either on fundamental algorithms in computer algebra or on the use of a computer algebra system is presented. Recent work in biology, chemistry, physics, mathematics and computer science is discussed. In particular, applications in high energy physics (quantum electrodynamics), celestial mechanics and general relativity are reviewed. (Auth.)

Nonlinear evolution equations and solving algebraic systems: the importance of computer algebra

International Nuclear Information System (INIS)

Gerdt, V.P.; Kostov, N.A.

1989-01-01

In the present paper we study the application of computer algebra to solve the nonlinear polynomial systems which arise in investigation of nonlinear evolution equations. We consider several systems which are obtained in classification of integrable nonlinear evolution equations with uniform rank. Other polynomial systems are related with the finding of algebraic curves for finite-gap elliptic potentials of Lame type and generalizations. All systems under consideration are solved using the method based on construction of the Groebner basis for corresponding polynomial ideals. The computations have been carried out using computer algebra systems. 20 refs

Filiform Lie algebras of order 3

Science.gov (United States)

Navarro, R. M.

2014-04-01

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.

Rudiments of algebraic geometry

CERN Document Server

Jenner, WE

2017-01-01

Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.

Applications of Computer Algebra Conference

CERN Document Server

Martínez-Moro, Edgar

2017-01-01

The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development.

Chiral algebras of class S

CERN Document Server

Beem, Christopher; Rastelli, Leonardo; van Rees, Balt C.

2015-01-01

Four-dimensional N=2 superconformal field theories have families of protected correlation functions that possess the structure of two-dimensional chiral algebras. In this paper, we explore the chiral algebras that arise in this manner in the context of theories of class S. The class S duality web implies nontrivial associativity properties for the corresponding chiral algebras, the structure of which is best summarized in the language of generalized topological quantum field theory. We make a number of conjectures regarding the chiral algebras associated to various strongly coupled fixed points.

Homotopy Theory of C*-Algebras

CERN Document Server

Ostvaer, Paul Arne

2010-01-01

Homotopy theory and C* algebras are central topics in contemporary mathematics. This book introduces a modern homotopy theory for C*-algebras. One basic idea of the setup is to merge C*-algebras and spaces studied in algebraic topology into one category comprising C*-spaces. These objects are suitable fodder for standard homotopy theoretic moves, leading to unstable and stable model structures. With the foundations in place one is led to natural definitions of invariants for C*-spaces such as homology and cohomology theories, K-theory and zeta-functions. The text is largely self-contained. It

Computational aspects of algebraic curves

CERN Document Server

Shaska, Tanush

2005-01-01

The development of new computational techniques and better computing power has made it possible to attack some classical problems of algebraic geometry. The main goal of this book is to highlight such computational techniques related to algebraic curves. The area of research in algebraic curves is receiving more interest not only from the mathematics community, but also from engineers and computer scientists, because of the importance of algebraic curves in applications including cryptography, coding theory, error-correcting codes, digital imaging, computer vision, and many more.This book cove

ORION-VIRCAT: a tool for mapping ICTV and NCBI taxonomies.

Science.gov (United States)

Valdivia-Granda, Willy; Larson, Francis

2009-01-01

Viruses, viroids and prions are the smallest infectious biological entities that depend on their host for replication. The number of pathogenic viruses is considerably large and their impact in human global health is well documented. Currently, the International Committee on the Taxonomy of Viruses (ICTV) has classified approximately 4379 virus species while the National Center for Biotechnology Information Viral Genomes Resource (NCBI-VGR) database has mapped 617 705 proteins to eight large taxonomic groups. Despite these efforts, an automated approach for mapping the ICTV master list and its officially accepted virus naming to the NCBI-VGR's taxonomical classification is not available. Due to metagenomic sequencing, it is likely that the discovery and naming of new viral species will increase by at least ten fold. Unfortunately, existing viral databases are not adequately prepared to scale, maintain and annotate automatically ultra-high throughput sequences and place this information into specific taxonomic categories. ORION-VIRCAT is a scalable and interoperable object-relational database designed to serve as a resource for the integration and verification of taxonomical classifications generated by the ICTV and NCBI-VGR. The current release (v1.0) of ORION-VIRCAT is implemented in PostgreSQL and it has been extended to ORACLE, MySQL and SyBase. ORION-VIRCAT automatically mapped and joined 617 705 entries from the NCBI-VGR to the viral naming of the ICTV. This detailed analysis revealed that 399 095 entries from the NCBI-VGR can be mapped to the ICTV classification and that one Order, 10 families, 35 genera and 503 species listed in the ICTV disagree with the the NCBI-VGR classification schema. Nevertheless, we were eable to correct several discrepancies mapping 234 000 additional entries.Database URL:http://www.orionbiosciences.com/research/orion-vircat.html.

The algebras of large N matrix mechanics

Energy Technology Data Exchange (ETDEWEB)

Halpern, M.B.; Schwartz, C.

1999-09-16

Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.

(L,M-Fuzzy σ-Algebras

Directory of Open Access Journals (Sweden)

Fu-Gui Shi

2010-01-01

Full Text Available The notion of (L,M-fuzzy σ-algebras is introduced in the lattice value fuzzy set theory. It is a generalization of Klement's fuzzy σ-algebras. In our definition of (L,M-fuzzy σ-algebras, each L-fuzzy subset can be regarded as an L-measurable set to some degree.

Explicit field realizations of W algebras

OpenAIRE

Wei, Shao-Wen; Liu, Yu-Xiao; Zhang, Li-Jie; Ren, Ji-Rong

2009-01-01

The fact that certain non-linear $W_{2,s}$ algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize $W_{2,s}$ algebras from linear $W_{1,2,s}$ algebras. In this paper, we first construct the explicit field realizations of linear $W_{1,2,s}$ algebras with double-scalar and double-spinor, respectively. Then, after a change of basis, the realizations of $W_{2,s}$ algebras are presented. The results show that all these realizations are Romans-type realiz...

Explicit field realizations of W algebras

International Nuclear Information System (INIS)

Wei Shaowen; Liu Yuxiao; Ren Jirong; Zhang Lijie

2009-01-01

The fact that certain nonlinear W 2,s algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize W 2,s algebras from linear W 1,2,s algebras. In this paper, we first construct the explicit field realizations of linear W 1,2,s algebras with double scalar and double spinor, respectively. Then, after a change of basis, the realizations of W 2,s algebras are presented. The results show that all these realizations are Romans-type realizations.

Hurwitz Algebras and the Octonion Algebra

Science.gov (United States)

Burdik, Čestmir; Catto, Sultan

2018-02-01

We explore some consequences of a theory of internal symmetries for elementary particles constructed on exceptional quantum mechanical spaces based on Jordan algebra formulation that admit exceptional groups as gauge groups.

Low-Frequency Carbon Recombination Lines in the Orion Molecular Cloud Complex

Science.gov (United States)

Tremblay, Chenoa D.; Jordan, Christopher H.; Cunningham, Maria; Jones, Paul A.; Hurley-Walker, Natasha

2018-05-01

We detail tentative detections of low-frequency carbon radio recombination lines from within the Orion molecular cloud complex observed at 99-129 MHz. These tentative detections include one alpha transition and one beta transition over three locations and are located within the diffuse regions of dust observed in the infrared at 100 μm, the Hα emission detected in the optical, and the synchrotron radiation observed in the radio. With these observations, we are able to study the radiation mechanism transition from collisionally pumped to radiatively pumped within the H ii regions within the Orion molecular cloud complex.

Distribution function of frequency of stellar flares in the Orion association

International Nuclear Information System (INIS)

Parsamyan, Eh.S.

1980-01-01

Using the chronology of discoveries of new flares and the chronology of confirmation i.e. the time distribution of second flares (Ambartsumian's method), the distribution function of frequency of flares on stars in the Orion association is obtained. A number of stars having different frequencies is also found. It is shown that flare stars with high flare frequency (ν -1 13sup(m). The quantities of flare stars in aggregates determined by two independent methods show that the number of flare stars in Orion association is about 1.5 times greater than in the Pleiades cluster [ru

On d -Dimensional Lattice (co)sine n -Algebra

International Nuclear Information System (INIS)

Yao Shao-Kui; Zhang Chun-Hong; Zhao Wei-Zhong; Ding Lu; Liu Peng

2016-01-01

We present the (co)sine n-algebra which is indexed by the d-dimensional integer lattice. Due to the associative operators, this generalized (co)sine n-algebra is the higher order Lie algebra for the n even case. The particular cases are the d-dimensional lattice sine 3 and cosine 5-algebras with the special parameter values. We find that the corresponding d-dimensional lattice sine 3 and cosine 5-algebras are the Nambu 3-algebra and higher order Lie algebra, respectively. The limiting case of the d-dimensional lattice (co)sine n-algebra is also discussed. Moreover we construct the super sine n-algebra, which is the super higher order Lie algebra for the n even case. (paper)

Pre-Algebra Lexicon.

Science.gov (United States)

Hayden, Dunstan; Cuevas, Gilberto

The pre-algebra lexicon is a set of classroom exercises designed to teach the technical words and phrases of pre-algebra mathematics, and includes the terms most commonly found in related mathematics courses. The lexicon has three parts, each with its own introduction. The first introduces vocabulary items in three groups forming a learning…

An Arithmetic-Algebraic Work Space for the Promotion of Arithmetic and Algebraic Thinking: Triangular Numbers

Science.gov (United States)

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…

n-ary algebras: a review with applications

International Nuclear Information System (INIS)

De Azcarraga, J A; Izquierdo, J M

2010-01-01

This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations are algebraic structures in which the two-entry Lie bracket has been replaced by a bracket with n entries. Each type of n-ary bracket satisfies a specific characteristic identity which plays the role of the Jacobi identity for Lie algebras. Particular attention will be paid to generalized Lie algebras, which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized Jacobi identity, and to Filippov (or n-Lie) algebras, which are defined by fully antisymmetric n-brackets that satisfy the Filippov identity. 3-Lie algebras have surfaced recently in multi-brane theory in the context of the Bagger-Lambert-Gustavsson model. As a result, Filippov algebras will be discussed at length, including the cohomology complexes that govern their central extensions and their deformations (it turns out that Whitehead's lemma extends to all semisimple n-Lie algebras). When the skewsymmetry of the Lie or n-Lie algebra bracket is relaxed, one is led to a more general type of n-algebras, the n-Leibniz algebras. These will be discussed as well, since they underlie the cohomological properties of n-Lie algebras. The standard Poisson structure may also be extended to the n-ary case. We shall review here the even generalized Poisson structures, whose generalized Jacobi identity reproduces the pattern of the generalized Lie algebras, and the Nambu-Poisson structures, which satisfy the Filippov identity and determine Filippov algebras. Finally, the recent work of Bagger-Lambert and Gustavsson on superconformal Chern-Simons theory will be briefly discussed. Emphasis will be made on the appearance of the 3-Lie algebra structure and on why the A 4 model may be formulated in terms of an ordinary Lie algebra, and on its Nambu bracket generalization. (topical

Frequency distribution function of stellar flares in the Orion association

International Nuclear Information System (INIS)

Parsamian, E.S.

1981-01-01

The temporal distributions of flare stars in the Orion association and the numbers of stars with different flare frequencies are determined by means of Ambartsumian's (1978) method, which uses the chronology of discovery of 'first' flares and the chronology of confirmations, i.e., the temporal distributions of 'repeated' flares. It is shown that flare stars with high flare frequency (not greater than 1000 hours) in the Pleiades are basically stars of low luminosity with M(U) not less than 13m. Two independent methods of determining the number of flare stars in the aggregates confirm that there are about 1.5 times more flare stars in the Orion association than in the Pleiades

Additive derivations on algebras of measurable operators

International Nuclear Information System (INIS)

Ayupov, Sh.A.; Kudaybergenov, K.K.

2009-08-01

Given a von Neumann algebra M we introduce the so-called central extension mix(M) of M. We show that mix(M) is a *-subalgebra in the algebra LS(M) of all locally measurable operators with respect to M, and this algebra coincides with LS(M) if and only if M does not admit type II direct summands. We prove that if M is a properly infinite von Neumann algebra then every additive derivation on the algebra mix(M) is inner. This implies that on the algebra LS(M), where M is a type I ∞ or a type III von Neumann algebra, all additive derivations are inner derivations. (author)

Families talen en algebra

NARCIS (Netherlands)

Asveld, P.R.J.

1976-01-01

Operaties op formele talen geven aanleiding tot bijbehorende operatoren op families talen. Bepaalde onderwerpen uit de algebra (universele algebra, tralies, partieel geordende monoiden) kunnen behulpzaam zijn in de studie van verzamelingen van dergelijke operatoren.

Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras

International Nuclear Information System (INIS)

Ammar, F; Makhlouf, A; Silvestrov, S

2010-01-01

In this paper we construct ternary q-Virasoro-Witt algebras which q-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using su(1, 1) enveloping algebra techniques. The ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a parameter and are not Nambu-Lie algebras for all but finitely many values of this parameter. For the parameter values for which the ternary Virasoro-Witt algebras are Nambu-Lie, the corresponding ternary q-Virasoro-Witt algebras constructed in this paper are also Hom-Nambu-Lie because they are obtained from the ternary Nambu-Lie algebras using the composition method. For other parameter values this composition method does not yield a Hom-Nambu-Lie algebra structure for q-Virasoro-Witt algebras. We show however, using a different construction, that the ternary Virasoro-Witt algebras of Curtright, Fairlie and Zachos, as well as the general ternary q-Virasoro-Witt algebras we construct, carry a structure of the ternary Hom-Nambu-Lie algebra for all values of the involved parameters.

Algebraic Methods to Design Signals

Science.gov (United States)

2015-08-27

to date on designing signals using algebraic and combinatorial methods. Mathematical tools from algebraic number theory, representation theory and... combinatorial objects in designing signals for communication purposes. Sequences and arrays with desirable autocorrelation properties have many...multiple access methods in mobile radio communication systems. We continue our mathematical framework based on group algebras, character theory

Assessing Elementary Algebra with STACK

Science.gov (United States)

Sangwin, Christopher J.

2007-01-01

This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…

Rotational emission-line spectrum of Orion A between 247 and 263 GHZ

International Nuclear Information System (INIS)

Blake, G.A.; Sutton, E.C.; Masson, C.R.; Phillips, T.G.

1986-01-01

Results are presented from a molecular line survey of the core of the Orion molecular cloud between 247 and 263 GHz. The spectrum contains a total of 243 resolvable lines from 23 different chemical species. When combined with the earlier survey of Orion from 215 to 247 GHz by Sutton et al (1985), the complete data set includes over 780 emission features from 29 distinct molecules. Of the 23 molecules detected in this survey, only NO, CCH, and HCO + were identified not in the lower frequency data

Homological methods, representation theory, and cluster algebras

CERN Document Server

Trepode, Sonia

2018-01-01

This text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands as a partial testimony to this new development. The courses are useful for any mathematician who would like to learn more about this rapidly developing field; the primary aim is to engage graduate students and young researchers. Prerequisites include knowledge of some noncommutative algebra or homological algebra. Homological algebra has always been considered as one of the main tools in the study of finite-dimensional algebras. The strong relationship with cluster algebras is more recent and has quickly established itself as one of the important highlights of today’s mathematical landscape. This connection has been fruitful to both areas—representation theory provides a categorification of cluster algebras, wh...

From simplicial Lie algebras and hypercrossed complexes to differential graded Lie algebras via 1-jets

OpenAIRE

Jurco, Branislav

2011-01-01

Let g be a simplicial Lie algebra with Moore complex Ng of length k. Let G be the simplicial Lie group integrating g, which is simply connected in each simplicial level. We use the 1-jet of the classifying space of G to construct, starting from g, a Lie k-algebra L. The so constructed Lie k-algebra L is actually a differential graded Lie algebra. The differential and the brackets are explicitly described in terms (of a part) of the corresponding k-hypercrossed complex structure of Ng. The res...

Classification and identification of Lie algebras

CERN Document Server

Snobl, Libor

2014-01-01

The purpose of this book is to serve as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address the problem of expressing a Lie algebra obtained in some arbitrary basis in a more suitable basis in which all essential features of the Lie algebra are directly visible. This includes algorithms accomplishing decomposition into a direct sum, identification of the radical and the Levi decomposition, and the computation of the nilradical and of the Casimir invariants. Examples are given for each algorithm. For low-dimensional Lie algebras this makes it possible to identify the given Lie algebra completely. The authors provide a representative list of all Lie algebras of dimension less or equal to 6 together with their important properties, including their Casimir invariants. The list is ordered in a way to make identification easy, using only basis independent properties of the Lie algebras. They also describe certain cl...

Sugawara operators for classical Lie algebras

CERN Document Server

Molev, Alexander

2018-01-01

The celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras. The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical \\mathcal{W}-algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations. An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the Harish-Chandra isomorphism connec...

Filiform Lie algebras of order 3

International Nuclear Information System (INIS)

Navarro, R. M.

2014-01-01

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

Algebraic Systems and Pushdown Automata

Science.gov (United States)

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.

Ready, Set, Algebra?

Science.gov (United States)

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,…

Block diagonalization for algebra's associated with block codes

NARCIS (Netherlands)

D. Gijswijt (Dion)

2009-01-01

htmlabstractFor a matrix *-algebra B, consider the matrix *-algebra A consisting of the symmetric tensors in the n-fold tensor product of B. Examples of such algebras in coding theory include the Bose-Mesner algebra and Terwilliger algebra of the (non)binary Hamming cube, and algebras arising in

Grassmann, super-Kac-Moody and super-derivation algebras

International Nuclear Information System (INIS)

Frappat, L.; Ragoucy, E.; Sorba, P.

1989-05-01

We study the cyclic cocycles of degree one on the Grassmann algebra and on the super-circle with N supersymmetries (i.e. the tensor product of the algebra of functions on the circle times a Grassmann algebra with N generators). They are related to central extensions of graded loop algebras (i.e. super-Kac-Moody algebras). The corresponding algebras of super-derivations have to be compatible with the cocycle characterizing the extension; we give a general method for determining these algebras and examine in particular the cases N = 1,2,3. We also discuss their relations with the Ademollo et al. algebras, and examine the possibility of defining new kinds of super-conformal algebras, which, for N > 1, generalize the N = 1 Ramond-Neveu-Schwarz algebra

Current algebra

International Nuclear Information System (INIS)

Jacob, M.

1967-01-01

The first three chapters of these lecture notes are devoted to generalities concerning current algebra. The weak currents are defined, and their main properties given (V-A hypothesis, conserved vector current, selection rules, partially conserved axial current,...). The SU (3) x SU (3) algebra of Gell-Mann is introduced, and the general properties of the non-leptonic weak Hamiltonian are discussed. Chapters 4 to 9 are devoted to some important applications of the algebra. First one proves the Adler- Weisberger formula, in two different ways, by either the infinite momentum frame, or the near-by singularities method. In the others chapters, the latter method is the only one used. The following topics are successively dealt with: semi leptonic decays of K mesons and hyperons, Kroll- Ruderman theorem, non leptonic decays of K mesons and hyperons ( ΔI = 1/2 rule), low energy theorems concerning processes with emission (or absorption) of a pion or a photon, super-convergence sum rules, and finally, neutrino reactions. (author) [fr

Linear algebra

CERN Document Server

Edwards, Harold M

1995-01-01

In his new undergraduate textbook, Harold M Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject

A type of loop algebra and the associated loop algebras

International Nuclear Information System (INIS)

Tam Honwah; Zhang Yufeng

2008-01-01

A higher-dimensional twisted loop algebra is constructed. As its application, a new Lax pair is presented, whose compatibility gives rise to a Liouville integrable hierarchy of evolution equations by making use of Tu scheme. One of the reduction cases of the hierarchy is an analogous of the well-known AKNS system. Next, the twisted loop algebra, furthermore, is extended to another higher dimensional loop algebra, from which a hierarchy of evolution equations with 11-potential component functions is obtained, whose reduction is just standard AKNS system. Especially, we prove that an arbitrary linear combination of the four Hamiltonian operators directly obtained from the recurrence relations is still a Hamiltonian operator. Therefore, the hierarchy with 11-potential functions possesses 4-Hamiltonian structures. Finally, an integrable coupling of the hierarchy is worked out

Extrapolating the Trends of Test Drop Data with Opening Shock Factor Calculations: the Case of the Orion Main and Drogue Parachutes Inflating to 1st Reefed Stage

Science.gov (United States)

Potvin, Jean; Ray, Eric

2017-01-01

We describe a new calculation of the opening shock factor C (sub k) characterizing the inflation performance of NASA's Orion spacecraft main and drogue parachutes opening under a reefing constraint (1st stage reefing), as currently tested in the Capsule Parachute Assembly System (CPAS) program. This calculation is based on an application of the Momentum-Impulse Theorem at low mass ratio (R (sub m) is less than 10 (sup -1)) and on an earlier analysis of the opening performance of drogues decelerating point masses and inflating along horizontal trajectories. Herein we extend the reach of the Theorem to include the effects of payload drag and gravitational impulse during near-vertical motion - both important pre-requisites for CPAS parachute analysis. The result is a family of C (sub k) versus R (sub m) curves which can be used for extrapolating beyond the drop-tested envelope. The paper proves this claim in the case of the CPAS Mains and Drogues opening while trailing either a Parachute Compartment Drop Test Vehicle or a Parachute Test Vehicle (an Orion capsule boiler plate). It is seen that in all cases the values of the opening shock factor can be extrapolated over a range in mass ratio that is at least twice that of the test drop data.

Spin-zero mesons and current algebras

International Nuclear Information System (INIS)

Wellner, M.

1977-01-01

Large chiral algebras, using the f and d coefficients of SU(3) can be constructed with spin-1/2 baryons. Such algebras have been found useful in some previous investigations. This article examines under what conditions similar or identical current algebras may be realized with spin-0 mesons. A curious lack of analogy emerges between meson and baryon currents. Second-class currents, made of mesons, are required in some algebras. If meson and baryon currents are to satisfy the same extended SU(3) algebra, four meson nonets are needed, in terms of which we give an explicit construction for the currents

Chiral algebras for trinion theories

International Nuclear Information System (INIS)

Lemos, Madalena; Peelaers, Wolfger

2015-01-01

It was recently understood that one can identify a chiral algebra in any four-dimensional N=2 superconformal theory. In this note, we conjecture the full set of generators of the chiral algebras associated with the T n theories. The conjecture is motivated by making manifest the critical affine module structure in the graded partition function of the chiral algebras, which is computed by the Schur limit of the superconformal index for T n theories. We also explicitly construct the chiral algebra arising from the T 4 theory. Its null relations give rise to new T 4 Higgs branch chiral ring relations.

The $W_{3}$ algebra modules, semi-infinite cohomology and BV algebras

CERN Document Server

Bouwknegt, Peter; Pilch, Krzysztof

1996-01-01

The noncritical D=4 W_3 string is a model of W_3 gravity coupled to two free scalar fields. In this paper we discuss its BRST quantization in direct analogy with that of the D=2 (Virasoro) string. In particular, we calculate the physical spectrum as a problem in BRST cohomology. The corresponding operator cohomology forms a BV-algebra. We model this BV-algebra on that of the polyderivations of a commutative ring on six variables with a quadratic constraint, or equivalently, on the BV-algebra of (polynomial) polyvector fields on the base affine space of SL(3,C). In this paper we attempt to present a complete summary of the progress made in these studies. [...

Normed algebras and the geometric series test

Directory of Open Access Journals (Sweden)

Robert Kantrowitz

2017-11-01

Full Text Available The purpose of this article is to survey a class of normed algebras that share many central features of Banach algebras, save for completeness. The likeness of these algebras to Banach algebras derives from the fact that the geometric series test is valid, whereas the lack of completeness points to the failure of the absolute convergence test for series in the algebra. Our main result is a compendium of conditions that are all equivalent to the validity of the geometric series test for commutative unital normed algebras. Several examples in the final section showcase some incomplete normed algebras for which the geometric series test is valid, and still others for which it is not.

Representations of affine Hecke algebras

CERN Document Server

Xi, Nanhua

1994-01-01

Kazhdan and Lusztig classified the simple modules of an affine Hecke algebra Hq (q E C*) provided that q is not a root of 1 (Invent. Math. 1987). Ginzburg had some very interesting work on affine Hecke algebras. Combining these results simple Hq-modules can be classified provided that the order of q is not too small. These Lecture Notes of N. Xi show that the classification of simple Hq-modules is essentially different from general cases when q is a root of 1 of certain orders. In addition the based rings of affine Weyl groups are shown to be of interest in understanding irreducible representations of affine Hecke algebras. Basic knowledge of abstract algebra is enough to read one third of the book. Some knowledge of K-theory, algebraic group, and Kazhdan-Lusztig cell of Cexeter group is useful for the rest

A modal characterization of Peirce algebras

NARCIS (Netherlands)

M. de Rijke (Maarten)

1995-01-01

textabstractPeirce algebras combine sets, relations and various operations linking the two in a unifying setting.This note offers a modal perspective on Peirce algebras.It uses modal logic to characterize the full Peirce algebras.

On δ-derivations of n-ary algebras

International Nuclear Information System (INIS)

Kaygorodov, Ivan B

2012-01-01

We give a description of δ-derivations of (n+1)-dimensional n-ary Filippov algebras and, as a consequence, of simple finite-dimensional Filippov algebras over an algebraically closed field of characteristic zero. We also give new examples of non-trivial δ-derivations of Filippov algebras and show that there are no non-trivial δ-derivations of the simple ternary Mal'tsev algebra M 8 .

Cluster algebras in mathematical physics

International Nuclear Information System (INIS)

Francesco, Philippe Di; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2014-01-01

This special issue of Journal of Physics A: Mathematical and Theoretical contains reviews and original research articles on cluster algebras and their applications to mathematical physics. Cluster algebras were introduced by S Fomin and A Zelevinsky around 2000 as a tool for studying total positivity and dual canonical bases in Lie theory. Since then the theory has found diverse applications in mathematics and mathematical physics. Cluster algebras are axiomatically defined commutative rings equipped with a distinguished set of generators (cluster variables) subdivided into overlapping subsets (clusters) of the same cardinality subject to certain polynomial relations. A cluster algebra of rank n can be viewed as a subring of the field of rational functions in n variables. Rather than being presented, at the outset, by a complete set of generators and relations, it is constructed from the initial seed via an iterative procedure called mutation producing new seeds successively to generate the whole algebra. A seed consists of an n-tuple of rational functions called cluster variables and an exchange matrix controlling the mutation. Relations of cluster algebra type can be observed in many areas of mathematics (Plücker and Ptolemy relations, Stokes curves and wall-crossing phenomena, Feynman integrals, Somos sequences and Hirota equations to name just a few examples). The cluster variables enjoy a remarkable combinatorial pattern; in particular, they exhibit the Laurent phenomenon: they are expressed as Laurent polynomials rather than more general rational functions in terms of the cluster variables in any seed. These characteristic features are often referred to as the cluster algebra structure. In the last decade, it became apparent that cluster structures are ubiquitous in mathematical physics. Examples include supersymmetric gauge theories, Poisson geometry, integrable systems, statistical mechanics, fusion products in infinite dimensional algebras, dilogarithm

The central extensions of Kac-Moody-Malcev algebras

International Nuclear Information System (INIS)

Osipov, E.P.

1989-01-01

The authors introduce a class of infinite-dimensional Kac-Moody-Malcev algebras. The Kac-Moody-Malcev algebras are the generalization of Lie algebras of Kac-Moody type to the Malcev algebras. They demonstrate that the central extensions of Kac-Moody-Malcev algebras are given by the same cocycles as in the case of Lie algebras. It is given a construction of Virasoro algebra in terms of bilinear combinations of currents satisfying the Kac-Moody-Malcev commutation relations. Thus, it is given the generalization of the Sugawara Construction to the case of Kac-Moody-Malcev algebras. Analogues of Kac-Moody-Malcev algebras may be also introduced in the case of arbitrary Riemann surface

Using Max-Plus Algebra for the Evaluation of Stochastic Process Algebra Prefixes

NARCIS (Netherlands)

Cloth, L.; de Alfaro, L.; Gilmore, S.; Bohnenkamp, H.C.; Haverkort, Boudewijn R.H.M.

2001-01-01

In this paper, the concept of complete finite prefixes for process algebra expressions is extended to stochastic models. Events are supposed to happen after a delay that is determined by random variables assigned to the preceding conditions. Max-plus algebra expressions are shown to provide an

The structure of relation algebras generated by relativizations

CERN Document Server

Givant, Steven R

1994-01-01

The foundation for an algebraic theory of binary relations was laid by De Morgan, Peirce, and Schröder during the second half of the nineteenth century. Modern development of the subject as a theory of abstract algebras, called "relation algebras", was undertaken by Tarski and his students. This book aims to analyze the structure of relation algebras that are generated by relativized subalgebras. As examples of their potential for applications, the main results are used to establish representation theorems for classes of relation algebras and to prove existence and uniqueness theorems for simple closures (i.e., for minimal simple algebras containing a given family of relation algebras as relativized subalgebras). This book is well written and accessible to those who are not specialists in this area. In particular, it contains two introductory chapters on the arithmetic and the algebraic theory of relation algebras. This book is suitable for use in graduate courses on algebras of binary relations or algebraic...

Linear-Algebra Programs

Science.gov (United States)

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.

P-commutative topological *-algebras

International Nuclear Information System (INIS)

Mohammad, N.; Thaheem, A.B.

1991-07-01

If P(A) denotes the set of all continuous positive functionals on a unital complete Imc *-algebra and S(A) the extreme points of P(A), and if the spectrum of an element χ Ε A coincides with the set {f(χ): f Ε S(A)}, then A is shown to be P-commutative. Moreover, if A is unital symmetric Frechet Q Imc *-algebra, then this spectral condition is, in fact, necessary. Also, an isomorphism theorem between symmetric Frechet P-commutative Imc *-algebras is established. (author). 12 refs

Matrices and linear algebra

CERN Document Server

Schneider, Hans

1989-01-01

Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it.This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related t

Generalized NLS hierarchies from rational W algebras

International Nuclear Information System (INIS)

Toppan, F.

1993-11-01

Finite rational W algebras are very natural structures appearing in coset constructions when a Kac-Moody subalgebra is factored out. The problem of relating these algebras to integrable hierarchies of equations is studied by showing how to associate to a rational W algebra its corresponding hierarchy. Two examples are worked out, the sl(2)/U(1) coset, leading to the Non-Linear Schroedinger hierarchy, and the U(1) coset of the Polyakov-Bershadsky W algebra, leading to a 3-field representation of the KP hierarchy already encountered in the literature. In such examples a rational algebra appears as algebra of constraints when reducing a KP hierarchy to a finite field representation. This fact arises the natural question whether rational algebras are always associated to such reductions and whether a classification of rational algebras can lead to a classification of the integrable hierarchies. (author). 19 refs

Some Aspects of -Units in BCK-Algebras

Directory of Open Access Journals (Sweden)

Hee Sik Kim

2012-01-01

Full Text Available We explore properties of the set of d-units of a -algebra. A property of interest in the study of -units in -algebras is the weak associative property. It is noted that many other -algebras, especially -algebras, are in fact weakly associative. The existence of -algebras which are not weakly associative is demonstrated. Moreover, the notions of a -integral domain and a left-injectivity are discussed.

Low-energy cosmic rays in the Orion region

DEFF Research Database (Denmark)

Pohl, M.

1998-01-01

The recently observed nuclear gamma-ray line emission from the Orion complex implies a high flux of low-energy cosmic rays (LECR) with unusual abundance. This cosmic ray component would dominate the energy density, pressure, and ionising power of cosmic rays, and thus would have a strong impact...

Bases in Lie and quantum algebras

International Nuclear Information System (INIS)

Ballesteros, A; Celeghini, E; Olmo, M A del

2008-01-01

Applications of algebras in physics are related to the connection of measurable observables to relevant elements of the algebras, usually the generators. However, in the determination of the generators in Lie algebras there is place for some arbitrary conventions. The situation is much more involved in the context of quantum algebras, where inside the quantum universal enveloping algebra, we have not enough primitive elements that allow for a privileged set of generators and all basic sets are equivalent. In this paper we discuss how the Drinfeld double structure underlying every simple Lie bialgebra characterizes uniquely a particular basis without any freedom, completing the Cartan program on simple algebras. By means of a perturbative construction, a distinguished deformed basis (we call it the analytical basis) is obtained for every quantum group as the analytical prolongation of the above defined Lie basis of the corresponding Lie bialgebra. It turns out that the whole construction is unique, so to each quantum universal enveloping algebra is associated one and only one bialgebra. In this way the problem of the classification of quantum algebras is moved to the classification of bialgebras. In order to make this procedure more clear, we discuss in detail the simple cases of su(2) and su q (2).

Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

Institute of Scientific and Technical Information of China (English)

2008-01-01

Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

On Deformations and Contractions of Lie Algebras

Directory of Open Access Journals (Sweden)

Marc de Montigny

2006-05-01

Full Text Available In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras. We first discuss low-dimensional Lie algebras and illustrate thereby that whereas for every contraction there exists a reverse deformation, the converse is not true in general. Also we note that some Lie algebras belonging to parameterized families are singled out by the irreversibility of deformations and contractions. After reminding that global deformations of the Witt, Virasoro, and affine Kac-Moody algebras allow one to retrieve Lie algebras of Krichever-Novikov type, we contract the latter to find new infinite dimensional Lie algebras.

A M2FS Spectroscopic Study of Low-mass Young Stars in Orion OB1

Science.gov (United States)

Kaleida, Catherine C.; Briceno, Cesar; Calvet, Nuria; Mateo, Mario L.; Hernandez, Jesus

2015-01-01

Surveys of pre-main sequence stars in the ~4-10 Myr range provide a window into the decline of the accretion phase of stars and the formation of planets. Nearby star clusters and stellar associations allow for the study of these young stellar populations all the way down to the lowest mass members. One of the best examples of nearby 4-10 Myr old stellar populations is the Orion OB1 association. The CIDA Variability Survey of Orion OB1 (CVSO - Briceño et al. 2001) has used the variability properties of low-mass pre-main-sequence (PMS) stars to identify hundreds of K and M-type stellar members of the Orion OB1 association, a number of them displaying IR-excess emission and thought to be representative of more evolved disk-bearing young stars. Characterizing these young, low-mass objects using spectroscopy is integral to understanding the accretion phase in young stars. We present preliminary results of a spectroscopic survey of candidate and confirmed Orion OB1 low-mass members taken during November 2014 and February 2014 using the Michigan/Magellan Fiber Spectrograph (M2FS), a PI instrument on the Magellan Clay Telescope (PI: M. Matteo). Target fields located in the off-cloud regions of Orion were identified in the CVSO, and observed using the low and high-resolution modes of M2FS. Both low and high-resolution spectra are needed in order to confirm membership and derive masses, ages, kinematics and accretion properties. Initial analysis of these spectra reveal many new K and M-type members of the Orion OB1 association in these low extinction, off-cloud areas. These are the more evolved siblings of the youngest stars still embedded in the molecular clouds, like those in the Orion Nebula Cluster. With membership and spectroscopic indicators of accretion we are building the most comprehensive stellar census of this association, enabling us to derive a robust estimate of the fraction of young stars still accreting at a various ages, a key constraint for the end of

Abundance of carbon and magnesium in the Orion nebula

International Nuclear Information System (INIS)

Perinotto, M.; Patriarchi, P.

1980-01-01

The Orion nebula has been observed in two positions with IUE (International Ultraviolet Explorer) in the low-resolution mode (approx.7 A) and in the spectral range 1150--3200 A. Emission lines of C II], C III], [O II], and He I have been measured and used to determine what is probably the first reliable abundance of carbon in H II regions. The logarithmic total abundance of carbon is found to be 8.4 close to the solar value. In contrast with the situation in the planetary nebula of similar excitation, IC 418, where the resonance Mg II lambda2800 line is observed to be relatively strong, in the Orion nebula the lambda2800 line is not detectable. an upper limit for the magnesium abundance of the order of 10 times smaller than in the Sun is suggested

Algebraic Description of Motion

Science.gov (United States)

Davidon, William C.

1974-01-01

An algebraic definition of time differentiation is presented and used to relate independent measurements of position and velocity. With this, students can grasp certain essential physical, geometric, and algebraic properties of motion and differentiation before undertaking the study of limits. (Author)

Enabling Spacecraft Formation Flying through Position Determination, Control and Enhanced Automation Technologies

Science.gov (United States)

Bristow, John; Bauer, Frank; Hartman, Kate; How, Jonathan

2000-01-01

Formation Flying is revolutionizing the way the space community conducts science missions around the Earth and in deep space. This technological revolution will provide new, innovative ways for the community to gather scientific information, share that information between space vehicles and the ground, and expedite the human exploration of space. Once fully matured, formation flying will result in numerous sciencecraft acting as virtual platforms and sensor webs, gathering significantly more and better science data than call be collected today. To achieve this goal, key technologies must be developed including those that address the following basic questions posed by the spacecraft: Where am I? Where is the rest of the fleet? Where do I need to be? What do I have to do (and what am I able to do) to get there? The answers to these questions and the means to implement those answers will depend oil the specific mission needs and formation configuration. However, certain critical technologies are common to most formations. These technologies include high-precision position and relative-position knowledge including Global Positioning System (GPS) mid celestial navigation; high degrees of spacecraft autonomy inter-spacecraft communication capabilities; targeting and control including distributed control algorithms, and high precision control thrusters and actuators. This paper provides an overview of a selection of the current activities NASA/DoD/Industry/Academia are working to develop Formation Flying technologies as quickly as possible, the hurdles that need to be overcome to achieve our formation flying vision, and the team's approach to transfer this technology to space. It will also describe several of the formation flying testbeds, such as Orion and University Nanosatellites, that are being developed to demonstrate and validate many of these innovative sensing and formation control technologies.

Deformation of the exterior algebra and the GLq (r, included in) algebra

International Nuclear Information System (INIS)

El Hassouni, A.; Hassouni, Y.; Zakkari, M.

1993-06-01

The deformation of the associative algebra of exterior forms is performed. This operation leads to a Y.B. equation. Its relation with the braid group B n-1 is analyzed. The correspondence of this deformation with the GL q (r, included in) algebra is developed. (author). 9 refs

The Universal Askey-Wilson Algebra

Directory of Open Access Journals (Sweden)

Paul Terwilliger

2011-07-01

Full Text Available In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3 and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension Δ of AW, obtained from AW by reinterpreting certain parameters as central elements in the algebra. We call Δ the universal Askey-Wilson algebra. We give a faithful action of the modular group PSL_2(Z on Δ as a group of automorphisms. We give a linear basis for Δ. We describe the center of Δ and the 2-sided ideal Δ[Δ,Δ]Δ. We discuss how Δ is related to the q-Onsager algebra.

Linear algebra

CERN Document Server

Stoll, R R

1968-01-01

Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand

Lie algebras

CERN Document Server

Jacobson, Nathan

1979-01-01

Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses.Chapter I introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Carlan's criterion and its

Basic algebra

CERN Document Server

Jacobson, Nathan

2009-01-01

A classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for two decades. Nathan Jacobson's books possess a conceptual and theoretical orientation, and in addition to their value as classroom texts, they serve as valuable references.Volume I explores all of the topics typically covered in undergraduate courses, including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. Its comprehensive treatment extends to such rigorous topics as L

Feature-Oriented Programming with Object Algebras

NARCIS (Netherlands)

B.C.d.S. Oliveira (Bruno); T. van der Storm (Tijs); A. Loh; W.R. Cook

2013-01-01

htmlabstractObject algebras are a new programming technique that enables a simple solution to basic extensibility and modularity issues in programming languages. While object algebras excel at defining modular features, the composition mechanisms for object algebras (and features) are still

Representations of fundamental groups of algebraic varieties

CERN Document Server

Zuo, Kang

1999-01-01

Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.

Located actions in process algebra with timing

NARCIS (Netherlands)

Bergstra, J.A.; Middelburg, C.A.

2004-01-01

We propose a process algebra obtained by adapting the process algebra with continuous relative timing from Baeten and Middelburg [Process Algebra with Timing, Springer, 2002, Chap. 4] to spatially located actions. This process algebra makes it possible to deal with the behaviour of systems with a

The Orion Nebula: The Jewel in the Sword

Science.gov (United States)

2001-01-01

Orion the Hunter is perhaps the best known constellation in the sky, well placed in the evening at this time of the year for observers in both the northern and southern hemispheres, and instantly recognisable. And for astronomers, Orion is surely one of the most important constellations, as it contains one of the nearest and most active stellar nurseries in the Milky Way, the galaxy in which we live. Here tens of thousands of new stars have formed within the past ten million years or so - a very short span of time in astronomical terms. For comparison: our own Sun is now 4,600 million years old and has not yet reached half-age. Reduced to a human time-scale, star formation in Orion would have been going on for just one month as compared to the Sun's 40 years. Just below Orion's belt, the hilt of his sword holds a great jewel in the sky, the beautiful Orion Nebula . Bright enough to be seen with the naked eye, a small telescope or even binoculars show the nebula to be a few tens of light-years' wide complex of gas and dust, illuminated by several massive and hot stars at its core, the famous Trapezium stars . However, the heart of this nebula also conceals a secret from the casual observer. There are in fact about one thousand very young stars about one million years old within the so-called Trapezium Cluster , crowded into a space less than the distance between the Sun and its nearest neighbour stars. The cluster is very hard to observe in visible light, but is clearly seen in the above spectacular image of this area ( ESO PR 03a/01 ), obtained in December 1999 by Mark McCaughrean (Astrophysical Institute Potsdam, Germany) and his collaborators [1] with the infrared multi-mode ISAAC instrument on the ESO Very Large Telescope (VLT) at Paranal (Chile). Many details are seen in the new ISAAC image ESO PR Photo 03b/01 ESO PR Photo 03b/01 [Preview - JPEG: 400 x 589 pix - 62k] [Normal - JPEG: 800 x 1178 pix - 648k] [Hires - JPEG: 1957 x 2881 pix - 2.7M] ESO PR Photo 03c

Lie Algebras Associated with Group U(n)

International Nuclear Information System (INIS)

Zhang Yufeng; Dong Huanghe; Honwah Tam

2007-01-01

Starting from the subgroups of the group U(n), the corresponding Lie algebras of the Lie algebra A 1 are presented, from which two well-known simple equivalent matrix Lie algebras are given. It follows that a few expanding Lie algebras are obtained by enlarging matrices. Some of them can be devoted to producing double integrable couplings of the soliton hierarchies of nonlinear evolution equations. Others can be used to generate integrable couplings involving more potential functions. The above Lie algebras are classified into two types. Only one type can generate the integrable couplings, whose Hamiltonian structure could be obtained by use of the quadratic-form identity. In addition, one condition on searching for integrable couplings is improved such that more useful Lie algebras are enlightened to engender. Then two explicit examples are shown to illustrate the applications of the Lie algebras. Finally, with the help of closed cycling operation relations, another way of producing higher-dimensional Lie algebras is given.

Smarandache hyper BCC-algebra

OpenAIRE

Ahadpanah, A.; Borumand Saeid, A.

2011-01-01

In this paper, we define the Smarandache hyper BCC-algebra, and Smarandache hyper BCC-ideals of type 1, 2, 3 and 4. We state and prove some theorems in Smarandache hyper BCC -algebras, and then we determine the relationships between these hyper ideals.

ASYS: a computer algebra package for analysis of nonlinear algebraic equations systems

International Nuclear Information System (INIS)

Gerdt, V.P.; Khutornoj, N.V.

1992-01-01

A program package ASYS for analysis of nonlinear algebraic equations based on the Groebner basis technique is described. The package is written in REDUCE computer algebra language. It has special facilities to treat polynomial ideals of positive dimension, corresponding to algebraic systems with infinitely many solutions. Such systems can be transformed to an equivalent set of subsystems with reduced number of variables in completely automatic way. It often allows to construct the explicit form of a solution set in many problems of practical importance. Some examples and results of comparison with the standard Reduce package GROEBNER and special-purpose systems FELIX and A1PI are given. 21 refs.; 2 tabs

The N=2 super-W3 algebra

International Nuclear Information System (INIS)

Romans, L.J.

1992-01-01

We present the complete structure of the N=2 super-W 3 algebra, a non-linear extended conformal algebra containing the usual N=2 superconformal algebra (with generators of spins 1, 3/2, 3/2 and 2) and a higher-spin multiplet of generators with spins 2, 5/2, 5/2 and 3. We investigate various sub-algebras and related algebras, and find necessary conditions upon possible unitary representations of the algebra. In particular, the central charge c is restricted to two discrete series, one ascending and one descending to a common accumulation point c=6. The results suggest that the algebra is realised in certain (compact or non-compact) Kazama-Suzuki coset models, including a c=9 model proposed by Bars based on SU(2, 1)/U(2). (orig.)

C2H observations toward the Orion Bar

NARCIS (Netherlands)

Nagy, Z.; Ossenkopf, V.; Van der Tak, F. F. S.; Faure, A.; Makai, Z.; Bergin, E. A.

Context. The ethynyl radical (C2H) is one of the first radicals to be detected in the interstellar medium. Its higher rotational transitions have recently become available with the Herschel Space Observatory. Aims: We aim to constrain the physical parameters of the C2H emitting gas toward the Orion

Tracing the Origins of Nitrogen Bearing Organics Toward Orion KL with Alma

Science.gov (United States)

Carroll, Brandon; Crockett, Nathan; Wilkins, Olivia H.; Bergin, Edwin; Blake, Geoffrey

2017-06-01

A comprehensive analysis of a broadband 1.2 THz wide spectral survey of the Orion Kleinmann-Low nebula (Orion KL) has shown that nitrogen bearing complex organics trace systematically hotter gas than O-bearing organics toward this source. The origin of this O/N dichotomy remains a mystery. If complex molecules originate from grain surfaces, N-bearing species may be more difficult to remove from grain surfaces than O-bearing organics. Theoretical studies, however, have shown that hot (T=300 K) gas phase chemistry can produce high abundances of N-bearing organics while suppressing the formation of O-bearing complex molecules. In order to distinguish these distinct formation pathways we have obtained extremely high angular resolution observations of methyl cyanide (CH_3CN) using the Atacama Large Millimeter/Submillimeter Array (ALMA) toward Orion KL. By simultaneously imaging ^{13}CH_3CN and CH_2DCN we map the temperature structure and D/H ratio of CH_3CN. We will present updated results of these observations and discuss their implications for the formation of N-bearing organics in the interstellar medium.

Intracluster dust, circumstellar shells, and the wavelength dependence of polarization in orion

International Nuclear Information System (INIS)

Breger, M.

1977-01-01

The wavelength dependence of polarization of 21 polarized stars near the Orion Nebula has been measured. Most stars fit the standard interstellar law. The wavelength of maximum linear polarization, lambda/sub max/, ranges from normal values to 0.71μm. The polarimetric, spectroscopic, and photometric data support a normal reddening law (Rapprox. =3) for most Orion stars, and present evidence for unusually large grain sizes in front of some Orion stars. For the stars BR 545 and BR 885 large values of lambda/sub max/ are associated with unusually large values of total to selective extinction.A division of the observed polarization into intracluster dust and circumstellar shell components shows that the presence of shells does not usually lead to linear polarization in the optical wavelength region. Also, no association of polarization with known light variability could be found. The nature of the intracluster dust clouds is discussed briefly.The results of searches for circular polarization as well as short-period variability are presented in two appendices

Quantization and representation theory of finite W algebras

International Nuclear Information System (INIS)

Boer, J. de; Tjin, T.

1993-01-01

In this paper we study the finitely generated algebras underlying W algebras. These so called 'finite W algebras' are constructed as Poisson reductions of Kirillov Poisson structures on simple Lie algebras. The inequivalent reductions are labeled by the inequivalent embeddings of sl 2 into the simple Lie algebra in question. For arbitrary embeddings a coordinate free formula for the reduced Poisson structure is derived. We also prove that any finite W algebra can be embedded into the Kirillov Poisson algebra of a (semi)simple Lie algebra (generalized Miura map). Furthermore it is shown that generalized finite Toda systems are reductions of a system describing a free particle moving on a group manifold and that they have finite W symmetry. In the second part we BRST quantize the finite W algebras. The BRST cohomoloy is calculated using a spectral sequence (which is different from the one used by Feigin and Frenkel). This allows us to quantize all finite W algebras in one stroke. Examples are given. In the last part of the paper we study the representation theory of finite W algebras. It is shown, using a quantum inversion of the generalized Miura transformation, that the representations of finite W algebras can be constructed from the representations of a certain Lie subalgebra of the original simple Lie algebra. As a byproduct of this we are able to construct the Fock realizations of arbitrary finite W algebras. (orig.)

Periodic light variations of young stars U X Orion and S U Auriga

International Nuclear Information System (INIS)

Minikulov, N.Kh.; Abdulloev, S.Kh.

2007-01-01

The light curves of young variable stars U X Orion and S U Auriga are created from archive data of Institute of Astrophysics of the Academy of Sciences of the Republic of Tajikistan and other sources. It is established that periodic light variations of young stars U X Orion and S U Auriga occurs to duration of 36.4 and 29.8 years, accordingly. It is supposed that such periodic light variations are connected with existence a planetary system around these stars

Finite W-algebras and intermediate statistics

International Nuclear Information System (INIS)

Barbarin, F.; Ragoucy, E.; Sorba, P.

1995-01-01

New realizations of finite W-algebras are constructed by relaxing the usual constraint conditions. Then finite W-algebras are recognized in the Heisenberg quantization recently proposed by Leinaas and Myrheim, for a system of two identical particles in d dimensions. As the anyonic parameter is directly associated to the W-algebra involved in the d=1 case, it is natural to consider that the W-algebra framework is well adapted for a possible generalization of the anyon statistics. ((orig.))

Quantized Matrix Algebras and Quantum Seeds

DEFF Research Database (Denmark)

Jakobsen, Hans Plesner; Pagani, Chiara

2015-01-01

We determine explicitly quantum seeds for classes of quantized matrix algebras. Furthermore, we obtain results on centres and block diagonal forms of these algebras. In the case where is an arbitrary root of unity, this further determines the degrees.......We determine explicitly quantum seeds for classes of quantized matrix algebras. Furthermore, we obtain results on centres and block diagonal forms of these algebras. In the case where is an arbitrary root of unity, this further determines the degrees....

Simple Lie algebras and Dynkin diagrams

International Nuclear Information System (INIS)

Buccella, F.

1983-01-01

The following theorem is studied: in a simple Lie algebra of rank p there are p positive roots such that all the other n-3p/2 positive roots are linear combinations of them with integer non negative coefficients. Dykin diagrams are built by representing the simple roots with circles and drawing a junction between the roots. Five exceptional algebras are studied, focusing on triple junction algebra, angular momentum algebra, weights of the representation, antisymmetric tensors, and subalgebras

Algebra, Geometry and Mathematical Physics Conference

CERN Document Server

Paal, Eugen; Silvestrov, Sergei; Stolin, Alexander

2014-01-01

This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers a...

Basic algebraic topology and its applications

CERN Document Server

Adhikari, Mahima Ranjan

2016-01-01

This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. T...

L_∞ algebras and field theory

International Nuclear Information System (INIS)

Hohm, Olaf; Zwiebach, Barton

2017-01-01

We review and develop the general properties of L_∞ algebras focusing on the gauge structure of the associated field theories. Motivated by the L_∞ homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the L_∞ structure of general gauge invariant perturbative field theories. We sketch such formulations for non-abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an L_∞ algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full L_∞ algebra for the interacting theory. The analysis suggests that L_∞ algebras provide a classification of perturbative gauge invariant classical field theories. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Lie algebra of conformal Killing–Yano forms

International Nuclear Information System (INIS)

Ertem, Ümit

2016-01-01

We provide a generalization of the Lie algebra of conformal Killing vector fields to conformal Killing–Yano forms. A new Lie bracket for conformal Killing–Yano forms that corresponds to slightly modified Schouten–Nijenhuis bracket of differential forms is proposed. We show that conformal Killing–Yano forms satisfy a graded Lie algebra in constant curvature manifolds. It is also proven that normal conformal Killing–Yano forms in Einstein manifolds also satisfy a graded Lie algebra. The constructed graded Lie algebras reduce to the graded Lie algebra of Killing–Yano forms and the Lie algebras of conformal Killing and Killing vector fields in special cases. (paper)

Constructing Meanings and Utilities within Algebraic Tasks

Science.gov (United States)

Ainley, Janet; Bills, Liz; Wilson, Kirsty

2004-01-01

The Purposeful Algebraic Activity project aims to explore the potential of spreadsheets in the introduction to algebra and algebraic thinking. We discuss two sub-themes within the project: tracing the development of pupils' construction of meaning for variable from arithmetic-based activity, through use of spreadsheets, and into formal algebra,…

Algebraic groups and their birational invariants

CERN Document Server

Voskresenskiĭ, V E

2011-01-01

Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, R-equivalence, projective toric varieties, invariants of finite transformation groups, and index-formulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading.

The classical limit of W-algebras

International Nuclear Information System (INIS)

Figueroa-O'Farrill, J.M.; Ramos, E.

1992-01-01

We define and compute explicitly the classical limit of the realizations of W n appearing as hamiltonian structures of generalized KdV hierarchies. The classical limit is obtained by taking the commutative limit of the ring of pseudodifferential operators. These algebras - denoted w n - have free field realizations in which the generators are given by the elementary symmetric polynomials in the free fields. We compute the algebras explicitly and we show that they are all reductions of a new algebra w KP , which is proposed as the universal classical W-algebra for the w n series. As a deformation of this algebra we also obtain w 1+∞ , the classical limit of W 1+∞ . (orig.)

Higher regulators, algebraic

CERN Document Server

Bloch, Spencer J

2000-01-01

This book is the long-awaited publication of the famous Irvine lectures. Delivered in 1978 at the University of California at Irvine, these lectures turned out to be an entry point to several intimately-connected new branches of arithmetic algebraic geometry, such as regulators and special values of L-functions of algebraic varieties, explicit formulas for them in terms of polylogarithms, the theory of algebraic cycles, and eventually the general theory of mixed motives which unifies and underlies all of the above (and much more). In the 20 years since, the importance of Bloch's lectures has not diminished. A lucky group of people working in the above areas had the good fortune to possess a copy of old typewritten notes of these lectures. Now everyone can have their own copy of this classic work.

Complex algebraic geometry

CERN Document Server

Kollár, János

1997-01-01

This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.

Basic algebraic geometry, v.2

CERN Document Server

Shafarevich, Igor Rostislavovich

1994-01-01

Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of al...