Cowings, Patricia S; Toscano, William B; Reschke, Millard F; Tsehay, Addis
2018-03-02
The National Aeronautics and Space Administration (NASA) has identified a potential risk of spatial disorientation, motion sickness, and degraded performance to astronauts during re-entry and landing of the proposed Orion crew vehicle. The purpose of this study was to determine if a physiological training procedure, Autogenic-Feedback Training Exercise (AFTE), can mitigate these adverse effects. Fourteen men and six women were assigned to two groups (AFTE, no-treatment Control) matched for motion sickness susceptibility and gender. All subjects received a standard rotating chair test to determine motion sickness susceptibility; three training sessions on a manual performance task; and four exposures in the rotating chair (Orion tests) simulating angular accelerations of the crew vehicle during re-entry. AFTE subjects received 2 h of training before Orion tests 2, 3, and 4. Motion sickness symptoms, task performance, and physiological measures were recorded on all subjects. Results showed that the AFTE group had significantly lower symptom scores when compared to Controls on test 2 (p = .05), test 3 (p = .03), and test 4 (p = .02). Although there were no significant group differences on task performance, trends showed that AFTE subjects were less impaired than Controls. Heart rate change scores (20 rpm minus baseline) of AFTE subjects indicated significantly less reactivity on Test 4 compared to Test 1 (10.09 versus 16.59, p = .02), while Controls did not change significantly across tests. Results of this study indicate that AFTE may be an effective countermeasure for mitigating spatial disorientation and motion sickness in astronauts. Copyright © 2018. Published by Elsevier B.V.
Spacecraft Charging Considerations and Design Efforts for the Orion Crew Module
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
Cowings, Patricia S.; Toscano, William B.; Reschke, Millard F.; Gebreyesus, Fiyori; Rocha, Christopher
2017-01-01
NASA has identified a potential risk of spatial disorientation to future astronauts during re-entry of the proposed Orion spacecraft. The purpose of this study was to determine if a 6-hour physiological training procedure, Autogenic-Feedback Training Exercise (AFTE), can mitigate these effects. Twenty subjects were assigned to two groups (AFTE and Control) matched for motion sickness susceptibility and gender. All subjects received a standard rotating chair test to determine motion sickness susceptibility; three training sessions on a manual performance task; and four exposures to a simulated Orion re-entry test in the rotating chair. Treatment subjects were given two hours of AFTE training before each Orion test. A diagnostic scale was used to evaluate motion sickness symptom severity. Results showed that 2 hours of AFTE significantly reduced motion sickness symptoms during the second Orion test. AFTE subjects were able to maintain lower heart rates and skin conductance levels and other responses than the control group subjects during subsequent tests. Trends show that performance was less degraded for AFTE subjects. The results of this study indicate that astronauts could benefit from receiving at least 2 hours of preflight AFTE. In addition, flight crews could benefit further by practicing physiologic self-regulation using mobile devices.
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.
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
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
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.
Crew Exploration Vehicle (CEV) (Orion) Occupant Protection
Currie-Gregg, Nancy J.; Gernhardt, Michael L.; Lawrence, Charles; Somers, Jeffrey T.
2016-01-01
Dr. Nancy J. Currie, of the NASA Engineering and Safety Center (NESC), Chief Engineer at Johnson Space Center (JSC), requested an assessment of the Crew Exploration Vehicle (CEV) occupant protection as a result of issues identified by the Constellation Program and Orion Project. The NESC, in collaboration with the Human Research Program (HRP), investigated new methods associated with occupant protection for the Crew Exploration Vehicle (CEV), known as Orion. The primary objective of this assessment was to investigate new methods associated with occupant protection for the CEV, known as Orion, that would ensure the design provided minimal risk to the crew during nominal and contingency landings in an acceptable set of environmental and spacecraft failure conditions. This documents contains the outcome of the NESC assessment. NASA/TM-2013-217380, "Application of the Brinkley Dynamic Response Criterion to Spacecraft Transient Dynamic Events." supercedes this document.
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
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 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.
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.
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.)
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.
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
Avionics System Architecture for the NASA Orion Vehicle
Baggerman, Clint; McCabe, Mary; Verma, Dinesh
2009-01-01
It has been 30 years since the National Aeronautics and Space Administration (NASA) last developed a crewed spacecraft capable of launch, on-orbit operations, and landing. During that time, aerospace avionics technologies have greatly advanced in capability, and these technologies have enabled integrated avionics architectures for aerospace applications. The inception of NASA s Orion Crew Exploration Vehicle (CEV) spacecraft offers the opportunity to leverage the latest integrated avionics technologies into crewed space vehicle architecture. The outstanding question is to what extent to implement these advances in avionics while still meeting the unique crewed spaceflight requirements for safety, reliability and maintainability. Historically, aircraft and spacecraft have very similar avionics requirements. Both aircraft and spacecraft must have high reliability. They also must have as much computing power as possible and provide low latency between user control and effecter response while minimizing weight, volume, and power. However, there are several key differences between aircraft and spacecraft avionics. Typically, the overall spacecraft operational time is much shorter than aircraft operation time, but the typical mission time (and hence, the time between preventive maintenance) is longer for a spacecraft than an aircraft. Also, the radiation environment is typically more severe for spacecraft than aircraft. A "loss of mission" scenario (i.e. - the mission is not a success, but there are no casualties) arguably has a greater impact on a multi-million dollar spaceflight mission than a typical commercial flight. Such differences need to be weighted when determining if an aircraft-like integrated modular avionics (IMA) system is suitable for a crewed spacecraft. This paper will explore the preliminary design process of the Orion vehicle avionics system by first identifying the Orion driving requirements and the difference between Orion requirements and those of
Orion Powered Flight Guidance Burn Options for Near Term Exploration
Fill, Tom; Goodman, John; Robinson, Shane
2018-01-01
NASA's Orion exploration spacecraft will fly more demanding mission profiles than previous NASA human flight spacecraft. Missions currently under development are destined for cislunar space. The EM-1 mission will fly unmanned to a Distant Retrograde Orbit (DRO) around the Moon. EM-2 will fly astronauts on a mission to the lunar vicinity. To fly these missions, Orion requires powered flight guidance that is more sophisticated than the orbital guidance flown on Apollo and the Space Shuttle. Orion's powered flight guidance software contains five burn guidance options. These five options are integrated into an architecture based on a proven shuttle heritage design, with a simple closed-loop guidance strategy. The architecture provides modularity, simplicity, versatility, and adaptability to future, yet-to-be-defined, exploration mission profiles. This paper provides a summary of the executive guidance architecture and details the five burn options to support both the nominal and abort profiles for the EM-1 and EM-2 missions.
Crew Exploration Vehicle (CEV) (Orion) Occupant Protection. Part 1; Appendices
Currie-Gregg, Nancy J.; Gernhardt, Michael L.; Lawrence, Charles; Somers, Jeffrey T.
2016-01-01
Dr. Nancy J. Currie, of the NASA Engineering and Safety Center (NESC), Chief Engineer at Johnson Space Center (JSC), requested an assessment of the Crew Exploration Vehicle (CEV) occupant protection as a result of issues identified by the Constellation Program and Orion Project. The NESC, in collaboration with the Human Research Program (HRP), investigated new methods associated with occupant protection for the Crew Exploration Vehicle (CEV), known as Orion. The primary objective of this assessment was to investigate new methods associated with occupant protection for the CEV, known as Orion, that would ensure the design provided minimal risk to the crew during nominal and contingency landings in an acceptable set of environmental and spacecraft failure conditions. This documents contains the appendices to the NESC assessment report. NASA/TM-2013-217380, Application of the Brinkley Dynamic Response Criterion to Spacecraft Transient Dynamic Events supersedes this document.
Orion Handling Qualities During ISS Rendezvous and Docking
Hart, Jeremy J.; Stephens, J. P.; Spehar, P.; Bilimoria, K.; Foster, C.; Gonzalex, R.; Sullivan, K.; Jackson, B.; Brazzel, J.; Hart, J.
2011-01-01
The Orion spacecraft was designed to rendezvous with multiple vehicles in low earth orbit (LEO) and beyond. To perform the required rendezvous and docking task, Orion must provide enough control authority to perform coarse translational maneuvers while maintaining precision to perform the delicate docking corrections. While Orion has autonomous docking capabilities, it is expected that final approach and docking operations with the International Space Station (ISS) will initially be performed in a manual mode. A series of evaluations was conducted by NASA and Lockheed Martin at the Johnson Space Center to determine the handling qualities (HQ) of the Orion spacecraft during different docking and rendezvous conditions using the Cooper-Harper scale. This paper will address the specifics of the handling qualities methodology, vehicle configuration, scenarios flown, data collection tools, and subject ratings and comments. The initial Orion HQ assessment examined Orion docking to the ISS. This scenario demonstrates the Translational Hand Controller (THC) handling qualities of Orion. During this initial assessment, two different scenarios were evaluated. The first was a nominal docking approach to a stable ISS, with Orion initializing with relative position dispersions and a closing rate of approximately 0.1 ft/sec. The second docking scenario was identical to the first, except the attitude motion of the ISS was modeled to simulate a stress case ( 1 degree deadband per axis and 0.01 deg/sec rate deadband per axis). For both scenarios, subjects started each run on final approach at a docking port-to-port range of 20 ft. Subjects used the THC in pulse mode with cues from the docking camera image, window views, and range and range rate data displayed on the Orion display units. As in the actual design, the attitude of the Orion vehicle was held by the automated flight control system at 0.5 degree deadband per axis. Several error sources were modeled including Reaction
Vertex algebras and algebraic curves
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...
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 ...
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.
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
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.
Bally, J.
2008-12-01
The Orion star formation complex is the nearest region of on-going star formation that continues to produce both low and high mass stars. Orion is discussed in the larger context of star formation in the Solar vicinity over the last 100 Myr. The Orion complex is located on the far side of the Gould's Belt system of clouds and young stars through which our Solar system is drifting. A review is given of the overall structure and properties of the Orion star forming complex, the best studied OB association. Over the last 12 Myr, Orion has given birth to at least ten thousand stars contained in a half dozen sub-groups and short-lived clusters. The Orion OB association has been the source of several massive, high-velocity run-away stars, including μ Columbae and AE Aurigae. Some of Orion's most massive members died in supernova explosions that created the 300 pc diameter Orion / Eridanus super-bubble whose near wall may be as close as 180 pc. The combined effects of UV radiation, stellar winds, and supernovae have impacted surviving molecular clouds in Orion. The large Orion A, IC 2118 molecular clouds and dozens of smaller clouds strewn throughout the interior of the superbubble have cometary shapes pointing back towards the center of the Orion OB association. Most are forming stars in the compressed layers facing the bubble interior.
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 ...
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.
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.)
Orion Ammonia Boiler System Preflight Test Preparations
Levitt, Julia L.
2017-01-01
The Environmental Controls and Life Support Systems (ECLSS) branch at Kennedy Space Center (KSC) is currently undergoing preparations for ground testing of the Orion Multi-Purpose Crew Vehicle (MPCV) to prepare its subsystems for EM-1 (Exploration Mission-1). EM-1, Orions second unmanned flight, is a three-week long lunar mission during which the vehicle will complete a 6-day retrograde lunar orbit before returning to Earth. This paper focuses on the work done during the authors 16-week internship with the Mechanical Engineering Branch of KSCs Engineering Directorate. The authors project involved assisting with the preparations for testing the Orion MPCVs ammonia boiler system. The purpose of the ammonia boiler system is to keep the spacecraft sufficiently cool during the reentry portion of its mission, from service module (SM) separation to post-landing. This system is critical for keeping both the spacecraft (avionics and electronics) and crew alive during reentry, thus a successful test of the system is essential to the success of EM-1. XXXX The author was able to draft a detailed outline of the procedure for the ammonia system functional test. More work will need to be done on the vehicle power-up and power-down portions of the procedure, but the ammonia system testing portion of the procedure is thorough and includes vehicle test configurations, vehicle commands, and GSE. The author was able to compile a substantial list of questions regarding the ammonia system functional test with the help of her mentors. A significant number of these questions were answered in the teleconferences with Lockheed Martin.
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
A personal airbag system for the Orion Crew Exploration Vehicle
Do, Sydney; de Weck, Olivier
2012-12-01
Airbag-based methods for crew impact attenuation have been highlighted as a potential simple, lightweight means of enabling safe land-landings for the Orion Crew Exploration Vehicle, and the next generation of ballistic shaped spacecraft. To investigate the feasibility of this concept during a nominal 7.62 m/s Orion landing, a full-scale personal airbag system 24% lighter than the Orion baseline has been developed, and subjected to 38 drop tests on land. Through this effort, the system has demonstrated the ability to maintain the risk of injury to an occupant during a 7.85 m/s, 0° impact angle land-landing to within the NASA specified limit of 0.5%. In accomplishing this, the personal airbag system concept has been proven to be feasible. Moreover, the obtained test results suggest that by implementing anti-bottoming airbags to prevent direct contact between the system and the landing surface, the system performance during landings with 0° impact angles can be further improved, by at least a factor of two. Additionally, a series of drop tests from the nominal Orion impact angle of 30° indicated that severe injury risk levels would be sustained beyond impact velocities of 5 m/s. This is a result of the differential stroking of the airbags within the system causing a shearing effect between the occupant seat structure and the spacecraft floor, removing significant stroke from the airbags.
NASA Planning for Orion Multi-Purpose Crew Vehicle Ground Operations
Letchworth, Gary; Schlierf, Roland
2011-01-01
The NASA Orion Ground Processing Team was originally formed by the Kennedy Space Center (KSC) Constellation (Cx) Project Office's Orion Division to define, refine and mature pre-launch and post-landing ground operations for the Orion human spacecraft. The multidisciplined KSC Orion team consisted of KSC civil servant, SAIC, Productivity Apex, Inc. and Boeing-CAPPS engineers, project managers and safety engineers, as well as engineers from Constellation's Orion Project and Lockheed Martin Orion Prime contractor. The team evaluated the Orion design configurations as the spacecraft concept matured between Systems Design Review (SDR), Systems Requirement Review (SRR) and Preliminary Design Review (PDR). The team functionally decomposed prelaunch and post-landing steps at three levels' of detail, or tiers, beginning with functional flow block diagrams (FFBDs). The third tier FFBDs were used to build logic networks and nominal timelines. Orion ground support equipment (GSE) was identified and mapped to each step. This information was subsequently used in developing lower level operations steps in a Ground Operations Planning Document PDR product. Subject matter experts for each spacecraft and GSE subsystem were used to define 5th - 95th percentile processing times for each FFBD step, using the Delphi Method. Discrete event simulations used this information and the logic network to provide processing timeline confidence intervals for launch rate assessments. The team also used the capabilities of the KSC Visualization Lab, the FFBDs and knowledge of the spacecraft, GSE and facilities to build visualizations of Orion pre-launch and postlanding processing at KSC. Visualizations were a powerful tool for communicating planned operations within the KSC community (i.e., Ground Systems design team), and externally to the Orion Project, Lockheed Martin spacecraft designers and other Constellation Program stakeholders during the SRR to PDR timeframe. Other operations planning
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.
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.
Ascoli, Peter A.; Haddock, Michael H.
2014-01-01
An Orion Crew Module Service Module Structural Weight and Center of Gravity Simulator and a Vehicle Motion Simulator Hoist Structure for Orion Service Module Umbilical Testing were designed during a summer 2014 internship in Kennedy Space Centers Structures and Mechanisms Design Branch. The simulator is a structure that supports ballast, which will be integrated into an existing Orion mock-up to simulate the mass properties of the Exploration Mission-1 flight vehicle in both fueled and unfueled states. The simulator mimics these configurations through the use of approximately 40,000 lbf of steel and water ballast, and a steel support structure. Draining four water tanks, which house the water ballast, transitions the simulator from the fueled to unfueled mass properties. The Ground Systems Development and Operations organization will utilize the simulator to verify and validate equipment used to maneuver and transport the Orion spacecraft in its fueled and unfueled configurations. The second design comprises a cantilevered tripod hoist structure that provides the capability to position a large Orion Service Module Umbilical in proximity to the Vehicle Motion Simulator. The Ground Systems Development and Operations organization will utilize the Vehicle Motion Simulator, with the hoist structure attached, to test the Orion Service Module Umbilical for proper operation prior to installation on the Mobile Launcher. Overall, these two designs provide NASA engineers viable concepts worthy of fabricating and placing into service to prepare for the launch of Orion in 2017.
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.
Linear Algebra and Smarandache Linear Algebra
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...
Simple Sensitivity Analysis for Orion GNC
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.
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
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
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
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)
Orion's Powered Flight Guidance Burn Options for Near Term Exploration Missions
Fill, Thomas; Goodman, John; Robinson, Shane
2018-01-01
NASA's Orion exploration spacecraft will fly more demanding mission profiles than previous NASA human flight spacecraft. Missions currently under development are destined for cislunar space. The EM-1 mission will fly unmanned to a Distant Retrograde Orbit (DRO) around the Moon. EM-2 will fly astronauts on a mission to the lunar vicinity. To fly these missions, Orion requires powered flight guidance that is more sophisticated than the orbital guidance flown on Apollo and the Space Shuttle. Orion's powered flight guidance software contains five burn guidance options. These five options are integrated into an architecture based on a proven shuttle heritage design, with a simple closed-loop guidance strategy. The architecture provides modularity, simplicity, versatility, and adaptability to future, yet-to-be-defined, exploration mission profiles. This paper provides a summary of the executive guidance architecture and details the five burn options to support both the nominal and abort profiles for the EM-1 and EM-2 missions.
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)
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...
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
VISION - Vienna survey in Orion. I. VISTA Orion A Survey
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
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
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
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
Indian Academy of Sciences (India)
tion - 6. How Architectural Features Affect. Building During Earthquakes? C VRMurty. 48 Turbulence and Dispersion. K 5 Gandhi. BOOK REVIEWS. 86 Algebraic Topology. Siddhartha Gadgil. Front Cover. - .. ..-.......... -. Back Cover. Two-dimensional vertical section through a turbulent plume. (Courtesy: G S Shat, CAOS, IISc.).
Indian Academy of Sciences (India)
Deligne, Mumford and Artin [DM, Ar2]) and consider algebraic stacks, then we can cons- truct the 'moduli ... the moduli scheme and the moduli stack of vector bundles. First I will give ... 1–31. © Printed in India. 1 ...... Cultura, Spain. References.
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
Algebraic characterizations of measure algebras
Czech Academy of Sciences Publication Activity Database
Jech, Thomas
2008-01-01
Roč. 136, č. 4 (2008), s. 1285-1294 ISSN 0002-9939 R&D Projects: GA AV ČR IAA100190509 Institutional research plan: CEZ:AV0Z10190503 Keywords : Von - Neumann * sequential topology * Boolean-algebras * Souslins problem * Submeasures Subject RIV: BA - General Mathematics Impact factor: 0.584, year: 2008
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.)
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
Orion Absolute Navigation System Progress and Challenges
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
Mulligan, Jeffrey B.
2017-01-01
A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. The difficulty addressed here is the fact that, because of metamerism, we cannot know with certainty the spectrum that produced a particular color solely on the basis of sensory data. Knowledge of the spectrum is not required to compute additive mixture of colors, but is critical for subtractive (multiplicative) mixture. Therefore, we cannot predict with certainty the multiplicative interactions between colors based solely on sensory data. There are two potential applications of a color algebra: first, to aid modeling phenomena of human visual perception, such as color constancy and transparency; and, second, to provide better models of the interactions of lights and surfaces for computer graphics rendering.
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
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.
Automation Interfaces of the Orion GNC Executive Architecture
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.
A Comparison Between Orion Automated and Space Shuttle Rendezvous Techniques
Ruiz, Jose O,; Hart, Jeremy
2010-01-01
The Orion spacecraft will replace the space shuttle and will be the first human spacecraft since the Apollo program to leave low earth orbit. This vehicle will serve as the cornerstone of a complete space transportation system with a myriad of mission requirements necessitating rendezvous to multiple vehicles in earth orbit, around the moon and eventually beyond . These goals will require a complex and robust vehicle that is, significantly different from both the space shuttle and the command module of the Apollo program. Historically, orbit operations have been accomplished with heavy reliance on ground support and manual crew reconfiguration and monitoring. One major difference with Orion is that automation will be incorporated as a key element of the man-vehicle system. The automated system will consist of software devoted to transitioning between events based on a master timeline. This effectively adds a layer of high level sequencing that moves control of the vehicle from one phase to the next. This type of automated control is not entirely new to spacecraft since the shuttle uses a version of this during ascent and entry operations. During shuttle orbit operations however many of the software modes and hardware switches must be manually configured through the use of printed procedures and instructions voiced from the ground. The goal of the automation scheme on Orion is to extend high level automation to all flight phases. The move towards automation represents a large shift from current space shuttle operations, and so these new systems will be adopted gradually via various safeguards. These include features such as authority-to-proceed, manual down modes, and functional inhibits. This paper describes the contrast between the manual and ground approach of the space shuttle and the proposed automation of the Orion vehicle. I will introduce typical orbit operations that are common to all rendezvous missions and go on to describe the current Orion automation
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)
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.
Bliss, Gilbert Ames
1933-01-01
This book, immediately striking for its conciseness, is one of the most remarkable works ever produced on the subject of algebraic functions and their integrals. The distinguishing feature of the book is its third chapter, on rational functions, which gives an extremely brief and clear account of the theory of divisors.... A very readable account is given of the topology of Riemann surfaces and of the general properties of abelian integrals. Abel's theorem is presented, with some simple applications. The inversion problem is studied for the cases of genus zero and genus unity. The chapter on t
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)
'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
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 ...
Orion GN&C Fault Management System Verification: Scope And Methodology
Brown, Denise; Weiler, David; Flanary, Ronald
2016-01-01
In order to ensure long-term ability to meet mission goals and to provide for the safety of the public, ground personnel, and any crew members, nearly all spacecraft include a fault management (FM) system. For a manned vehicle such as Orion, the safety of the crew is of paramount importance. The goal of the Orion Guidance, Navigation and Control (GN&C) fault management system is to detect, isolate, and respond to faults before they can result in harm to the human crew or loss of the spacecraft. Verification of fault management/fault protection capability is challenging due to the large number of possible faults in a complex spacecraft, the inherent unpredictability of faults, the complexity of interactions among the various spacecraft components, and the inability to easily quantify human reactions to failure scenarios. The Orion GN&C Fault Detection, Isolation, and Recovery (FDIR) team has developed a methodology for bounding the scope of FM system verification while ensuring sufficient coverage of the failure space and providing high confidence that the fault management system meets all safety requirements. The methodology utilizes a swarm search algorithm to identify failure cases that can result in catastrophic loss of the crew or the vehicle and rare event sequential Monte Carlo to verify safety and FDIR performance requirements.
Grätzer, George
1979-01-01
Universal Algebra, heralded as ". . . the standard reference in a field notorious for the lack of standardization . . .," has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science. Each chapter is followed by an extensive list of exercises and problems. The "state of the art" account also includes new appendices (with contributions from B. Jónsson, R. Quackenbush, W. Taylor, and G. Wenzel) and a well-selected additional bibliography of over 1250 papers and books which makes this a fine work for students, instructors, and researchers in the field. "This book will certainly be, in the years to come, the basic reference to the subject." --- The American Mathematical Monthly (First Edition) "In this reviewer's opinion [the author] has more than succeeded in his aim. The problems at the end of each chapter are well-chosen; there are more than 650 of them. The book is especially sui...
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 ...
Executive Summary of Propulsion on the Orion Abort Flight-Test Vehicles
Jones, Daniel S.; Brooks, Syri J.; Barnes, Marvin W.; McCauley, Rachel J.; Wall, Terry M.; Reed, Brian D.; Duncan, C. Miguel
2012-01-01
The National Aeronautics and Space Administration Orion Flight Test Office was tasked with conducting a series of flight tests in several launch abort scenarios to certify that the Orion Launch Abort System is capable of delivering astronauts aboard the Orion Crew Module to a safe environment, away from a failed booster. The first of this series was the Orion Pad Abort 1 Flight-Test Vehicle, which was successfully flown on May 6, 2010 at the White Sands Missile Range in New Mexico. This report provides a brief overview of the three propulsive subsystems used on the Pad Abort 1 Flight-Test Vehicle. An overview of the propulsive systems originally planned for future flight-test vehicles is also provided, which also includes the cold gas Reaction Control System within the Crew Module, and the Peacekeeper first stage rocket motor encased within the Abort Test Booster aeroshell. Although the Constellation program has been cancelled and the operational role of the Orion spacecraft has significantly evolved, lessons learned from Pad Abort 1 and the other flight-test vehicles could certainly contribute to the vehicle architecture of many future human-rated space launch vehicles
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...
Feasibility Study of an Airbag-Based Crew Impact Attenuation System for the Orion MPCV
Do, Sydney; deWeck, Olivier
2011-01-01
Airbag-based methods for crew impact attenuation have been highlighted as a potential lightweight means of enabling safe land-landings for the Orion Multi-Purpose Crew Vehicle, and the next generation of ballistic shaped spacecraft. To investigate the performance feasibility of this concept during a nominal 7.62m/s Orion landing, a full-scale personal airbag system 24% lighter than the Orion baseline has been developed, and subjected to 38 drop tests on land. Through this effort, the system has demonstrated the ability to maintain the risk of injury to an occupant during a 7.85m/s, 0 deg. impact angle land-landing to within the NASA specified limit of 0.5%. In accomplishing this, the airbag-based crew impact attenuation concept has been proven to be feasible. Moreover, the obtained test results suggest that by implementing anti-bottoming airbags to prevent direct contact between the system and the landing surface, the system performance during landings with 0 deg impact angles can be further improved, by at least a factor of two. Additionally, a series of drop tests from the nominal Orion impact angle of 30 deg indicated that severe injury risk levels would be sustained beyond impact velocities of 5m/s. This is a result of the differential stroking of the airbags within the system causing a shearing effect between the occupant seat structure and the spacecraft floor, removing significant stroke from the airbags.
Said-Houari, Belkacem
2017-01-01
This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...
The Yoneda algebra of a K2 algebra need not be another K2 algebra
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.
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.
Introduction to relation algebras relation algebras
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 ...
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
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.
White, Molly E.; Hyatt, Andrew J.
2016-01-01
The Orion Multi-Purpose Crew Vehicle (MPCV) Reaction Control System (RCS) is critical to guide the vehicle along the desired trajectory during re--entry. However, this system has a significant impact on the convective heating environment to the spacecraft. Heating augmentation from the jet interaction (JI) drives thermal protection system (TPS) material selection and thickness requirements for the spacecraft. This paper describes the heating environment from the RCS on the afterbody of the Orion MPCV during Orion's first flight test, Exploration Flight Test 1 (EFT-1). These jet plumes interact with the wake of the crew capsule and cause an increase in the convective heating environment. Not only is there widespread influence from the jet banks, there may also be very localized effects. The firing history during EFT-1 will be summarized to assess which jet bank interaction was measured during flight. Heating augmentation factors derived from the reconstructed flight data will be presented. Furthermore, flight instrumentation across the afterbody provides the highest spatial resolution of the region of influence of the individual jet banks of any spacecraft yet flown. This distribution of heating augmentation across the afterbody will be derived from the flight data. Additionally, trends with possible correlating parameters will be investigated to assist future designs and ground testing programs. Finally, the challenges of measuring JI, applying this data to future flights and lessons learned will be discussed.
Orion Multi-Purpose Crew Vehicle Solving and Mitigating the Two Main Cluster Pendulum Problem
Ali, Yasmin; Sommer, Bruce; Troung, Tuan; Anderson, Brian; Madsen, Christopher
2017-01-01
The Orion Multi-purpose Crew Vehicle (MPCV) Orion spacecraft will return humans from beyond earth's orbit, including Mars and will be required to land 20,000 pounds of mass safely in the ocean. The parachute system nominally lands under 3 main parachutes, but the system is designed to be fault tolerant and land under 2 main parachutes. During several of the parachute development tests, it was observed that a pendulum, or swinging, motion could develop while the Crew Module (CM) was descending under two parachutes. This pendulum effect had not been previously predicted by modeling. Landing impact analysis showed that the landing loads would double in some places across the spacecraft. The CM structural design limits would be exceeded upon landing if this pendulum motion were to occur. The Orion descent and landing team was faced with potentially millions of dollars in structural modifications and a severe mass increase. A multidisciplinary team was formed to determine root cause, model the pendulum motion, study alternate canopy planforms and assess alternate operational vehicle controls & operations providing mitigation options resulting in a reliability level deemed safe for human spaceflight. The problem and solution is a balance of risk to a known solution versus a chance to improve the landing performance for the next human-rated spacecraft.
Quantum cluster algebras and quantum nilpotent algebras
Goodearl, Kenneth R.; Yakimov, Milen T.
2014-01-01
A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197
Orion Optical Navigation Progress Toward Exploration Mission 1
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.
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...
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
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.
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
Simple Sensitivity Analysis for Orion Guidance Navigation and Control
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.
Murdin, P.
2000-11-01
(the Hunter; abbrev. Ori, gen. Orionis; area 594 sq. deg.) An equatorial constellation which lies between Taurus and Monoceros, and culminates at midnight in mid-December. Its origin dates back to Sumerian times, when it was identified with the hero Gilgamesh and his fight against the Bull of Heaven (represented by Taurus), but today it is associated with the son of Poseidon, in Greek mythology, ...
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
The Gas-Surface Interaction of a Human-Occupied Spacecraft with a Near-Earth Object
Farrell, W. M.; Hurley, D. M.; Poston, M. J.; Zimmerman, M. I.; Orlando, T. M.; Hibbitts, C. A.; Killen, R. M.
2016-01-01
NASA's asteroid redirect mission (ARM) will feature an encounter of the human-occupied Orion spacecraft with a portion of a near- Earth asteroid (NEA) previously placed in orbit about the Moon by a capture spacecraft. Applying a shuttle analog, we suggest that the Orion spacecraft should have a dominant local water exosphere, and that molecules from this exosphere can adsorb onto the NEA. The amount of adsorbed water is a function of the defect content of the NEA surface, with retention of shuttle-like water levels on the asteroid at 10(exp 15) H2O's/m2 for space weathered regolith at T approximately 300 K.
Generalized EMV-Effect Algebras
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.
Space astrophysical observatory 'Orion-2'
International Nuclear Information System (INIS)
Gurzadyan, G.A.; Jarakyan, A.L.; Krmoyan, M.N.; Kashin, A.L.; Loretsyan, G.M.; Ohanesyan, J.B.
1976-01-01
Ultraviolet spectrograms of a large number of faint stars up to 13sup(m) were obtained in the wavelengths 2000-5000 A by means of the space observatory 'Orion-2' installed in the spaceship 'Soyuz-13' with two spacemen on board. The paper deals with a description of the operation modes of this observatory, the designs and basic schemes of the scientific and auxiliary device and the method of combining the work of the flight engineer and the automation system of the observatory itself. It also treats of the combination of the particular parts of 'Orion-2' observatory on board the spaceship and the measures taken to provide for its normal functioning in terms of the space flight. A detailed description is given of the optical, electrical and mechanical schemes of the devices - meniscus telescope with an objective prism, stellar diffraction spectrographs, single-coordinate and two-coordinate stellar and solar transducers, control panel, control systems, etc. The paper also provides the functional scheme of astronavigation, six-wheel stabilization, the design of mounting (assembling) the stabilized platform carrying the telescopes and the drives used in it. Problems relating to the observation program in orbit, the ballistic provision of initial data, and control of the operation of the observatory are also dealt with. In addition, the paper carries information of the photomaterials used, the methods of their energy calibration, standardization and the like. Matters of pre-start tests of apparatus, the preparation of the spacemen for conducting astronomical observations with the given devices, etc. are likewise dwelt on. The paper ends with a brief survey of the results obtained and the elaboration of the observed material. (Auth.)
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.
Rudiments of algebraic geometry
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.
Sellmaier, Florian; Schmidhuber, Michael
2015-01-01
The book describes the basic concepts of spaceflight operations, for both, human and unmanned missions. The basic subsystems of a space vehicle are explained in dedicated chapters, the relationship of spacecraft design and the very unique space environment are laid out. Flight dynamics are taught as well as ground segment requirements. Mission operations are divided into preparation including management aspects, execution and planning. Deep space missions and space robotic operations are included as special cases. The book is based on a course held at the German Space Operation Center (GSOC).
Cylindric-like algebras and algebraic logic
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.
Categories and Commutative Algebra
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.
Evolution of Orion Mission Design for Exploration Mission 1 and 2
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.
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)
Combinatorial commutative algebra
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.
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
NASA Alternative Orion Small Cell Battery Design Support
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
Orion Optical Navigation Progress Toward Exploration: Mission 1
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
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
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)
Algorithms in Algebraic Geometry
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
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.
Lectures on algebraic statistics
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.
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)
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
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
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.)
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.
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
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
Hurwitz Algebras and the Octonion Algebra
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.
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
Linear algebra meets Lie algebra: the Kostant-Wallach theory
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.
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)
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
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.
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.
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...
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...
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.)
Kennedy Space Center Orion Processing Team Planning for Ground Operations
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
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?
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.
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.
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
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
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.
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
Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra
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
Differential Hopf algebra structures on the universal enveloping algebra ofa Lie algebra
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
On-Board Rendezvous Targeting for Orion
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.
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)
Algebraic monoids, group embeddings, and algebraic combinatorics
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...
(Quasi-)Poisson enveloping algebras
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.
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,…
Learning Activity Package, Algebra.
Evans, Diane
A set of ten teacher-prepared Learning Activity Packages (LAPs) in beginning algebra and nine in intermediate algebra, these units cover sets, properties of operations, number systems, open expressions, solution sets of equations and inequalities in one and two variables, exponents, factoring and polynomials, relations and functions, radicals,…
Herriott, Scott R.; Dunbar, Steven R.
2009-01-01
The common understanding within the mathematics community is that the role of the college algebra course is to prepare students for calculus. Though exceptions are emerging, the curriculum of most college algebra courses and the content of most textbooks on the market both reflect that assumption. This article calls that assumption into question…
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.
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…
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.)
Algebraic Description of Motion
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)
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.
Elements of mathematics algebra
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...
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
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
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.
Anderson, Grant A. (Inventor)
2012-01-01
A spacecraft radiator system designed to provide structural support to the spacecraft. Structural support is provided by the geometric "crescent" form of the panels of the spacecraft radiator. This integration of radiator and structural support provides spacecraft with a semi-monocoque design.
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
Layers in the Central Orion Nebula
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.
System Level Analysis of a Water PCM HX Integrated into Orion's Thermal Control System
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.
System Level Analysis of a Water PCM HX Integrated Into Orion's Thermal Control System Abstract
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.
Cluster algebras bases on vertex operator algebras
Czech Academy of Sciences Publication Activity Database
Zuevsky, Alexander
2016-01-01
Roč. 30, 28-29 (2016), č. článku 1640030. ISSN 0217-9792 Institutional support: RVO:67985840 Keywords : cluster alegbras * vertex operator algebras * Riemann surfaces Subject RIV: BA - General Mathematics Impact factor: 0.736, year: 2016 http://www.worldscientific.com/doi/abs/10.1142/S0217979216400300
Algebraic K-theory and algebraic topology
Energy Technology Data Exchange (ETDEWEB)
Berrick, A J [Department of Mathematics, National University of Singapore (Singapore)
2003-09-15
This contribution treats the various topological constructions of Algebraic K-theory together with the underlying homotopy theory. Topics covered include the plus construction together with its various ramifications and applications, Topological Hochschild and Cyclic Homology as well as K-theory of the ring of integers.
An introduction to algebraic geometry and algebraic groups
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
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...
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
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...
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
Adaptive algebraic reconstruction technique
International Nuclear Information System (INIS)
Lu Wenkai; Yin Fangfang
2004-01-01
Algebraic reconstruction techniques (ART) are iterative procedures for reconstructing objects from their projections. It is proven that ART can be computationally efficient by carefully arranging the order in which the collected data are accessed during the reconstruction procedure and adaptively adjusting the relaxation parameters. In this paper, an adaptive algebraic reconstruction technique (AART), which adopts the same projection access scheme in multilevel scheme algebraic reconstruction technique (MLS-ART), is proposed. By introducing adaptive adjustment of the relaxation parameters during the reconstruction procedure, one-iteration AART can produce reconstructions with better quality, in comparison with one-iteration MLS-ART. Furthermore, AART outperforms MLS-ART with improved computational efficiency
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
Configuring the Orion Guidance, Navigation, and Control Flight Software for Automated Sequencing
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
Profinite algebras and affine boundedness
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...
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.
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
Indian Academy of Sciences (India)
algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.
Axler, Sheldon
2015-01-01
This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions. No prerequisites are assumed other than the ...
Algebraic Semantics for Narrative
Kahn, E.
1974-01-01
This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)
Leamer, Micah J.
2004-01-01
Let K be a field and Q a finite directed multi-graph. In this paper I classify all path algebras KQ and admissible orders with the property that all of their finitely generated ideals have finite Groebner bases. MS
Differential Hopf algebra structures on the Universal Enveloping Algebra of a Lie Algebra
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 EFT-1 Catalytic Tile Experiment Overview and Flight Measurements
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.
International Nuclear Information System (INIS)
Waldron, A.K.; Joshi, G.C.
1992-01-01
By considering representation theory for non-associative algebras the fundamental adjoint representations of the octonion algebra is constructed. It is then shown how these representations by associative matrices allow a consistent octonionic gauge theory to be realized. It was found that non-associativity implies the existence of new terms in the transformation laws of fields and the kinetic term of an octonionic Lagrangian. 13 refs
Institute of Scientific and Technical Information of China (English)
Antonio AIZPURU; Antonio GUTI(E)RREZ-D(A)VILA
2004-01-01
In this paper we will study some families and subalgebras ( ) of ( )(N) that let us characterize the unconditional convergence of series through the weak convergence of subseries ∑i∈A xi, A ∈ ( ).As a consequence, we obtain a new version of the Orlicz-Pettis theorem, for Banach spaces. We also study some relationships between algebraic properties of Boolean algebras and topological properties of the corresponding Stone spaces.
Polynomials in algebraic analysis
Multarzyński, Piotr
2012-01-01
The concept of polynomials in the sense of algebraic analysis, for a single right invertible linear operator, was introduced and studied originally by D. Przeworska-Rolewicz \\cite{DPR}. One of the elegant results corresponding with that notion is a purely algebraic version of the Taylor formula, being a generalization of its usual counterpart, well known for functions of one variable. In quantum calculus there are some specific discrete derivations analyzed, which are right invertible linear ...
Intermediate algebra & analytic geometry
Gondin, William R
1967-01-01
Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system
Currents on Grassmann algebras
International Nuclear Information System (INIS)
Coquereaux, R.; Ragoucy, E.
1993-09-01
Currents are defined on a Grassmann algebra Gr(N) with N generators as distributions on its exterior algebra (using the symmetric wedge product). The currents are interpreted in terms of Z 2 -graded Hochschild cohomology and closed currents in terms of cyclic cocycles (they are particular multilinear forms on Gr(N)). An explicit construction of the vector space of closed currents of degree p on Gr(N) is given by using Berezin integration. (authors). 10 refs
Introduction to abstract algebra
Nicholson, W Keith
2012-01-01
Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."-Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately be
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={bÃ¢ÂˆÂˆB|bx=g(xbÃ¢Â€Â‰for allÃ¢Â€Â‰xÃ¢ÂˆÂˆB} for each gÃ¢ÂˆÂˆG, and BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|gÃ¢ÂˆÂˆG}, e a nonzero element in Ba, and He={gÃ¢ÂˆÂˆG|eeg=e}. Then, a monomial e is characterized, and the Galois extension Be, generated by e with Galois group He, is investigated.
Orion: Design of a system for assured low-cost human access to space
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.
Lunar Entry Downmode Options for Orion
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.
Application of Terrestrial Environments in Orion Assessments
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.
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
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.
Molecular hydrogen jets from the Orion nebula
International Nuclear Information System (INIS)
Taylor, K.N.R.; Storey, J.W.V.; Zealey, W.J.
1984-01-01
In an attempt to understand the relationship of the recently discovered complex of Herbig Haro objects in Orion to the IR sources in this region, the authors have carried out a survey of the molecular hydrogen S(1) line distribution. The observations have led to the discovery of a previously unsuspected structure of finger-like filaments of H 2 emission extending radially outwards from a common centre at IRC9. (author)
ORION - A Global Approach to Waste Management.
Heinzelmann, Elsbeth
2015-01-01
In the ORION project supported by the European Commission, 20 partners work together to manage organic waste from agro-food industries. The goal is to develop a small, automatic and user-friendly digestion machine to facilitate the domestic on-site treatment of a wide range of organic waste from around 100 and up to 5000 tonnes per year at low cost and with limited maintenance. Simon Crelier at the HES-SO Valais/Wallis is part of the network.
Lightning Protection for the Orion Space Vehicle
Scully, Robert
2015-01-01
The Orion space vehicle is designed to requirements for both direct attachment and indirect effects of lightning. Both sets of requirements are based on a full threat 200kA strike, in accordance with constraints and guidelines contained in SAE ARP documents applicable to both commercial and military aircraft and space vehicles. This paper describes the requirements as levied against the vehicle, as well as the means whereby the design shows full compliance.
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
Special set linear algebra and special set fuzzy linear algebra
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...
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...
Hecke algebras with unequal parameters
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...
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.
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.
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
Algebra II workbook for dummies
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
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 ...
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...
Interactions Between Representation Ttheory, Algebraic Topology and Commutative Algebra
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...
Quantum cluster algebra structures on quantum nilpotent algebras
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.
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)
Algebraic quantum field theory
International Nuclear Information System (INIS)
Foroutan, A.
1996-12-01
The basic assumption that the complete information relevant for a relativistic, local quantum theory is contained in the net structure of the local observables of this theory results first of all in a concise formulation of the algebraic structure of the superselection theory and an intrinsic formulation of charge composition, charge conjugation and the statistics of an algebraic quantum field theory. In a next step, the locality of massive particles together with their spectral properties are wed for the formulation of a selection criterion which opens the access to the massive, non-abelian quantum gauge theories. The role of the electric charge as a superselection rule results in the introduction of charge classes which in term lead to a set of quantum states with optimum localization properties. Finally, the asymptotic observables of quantum electrodynamics are investigated within the framework of algebraic quantum field theory. (author)
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.
Launey, Warwick De
2011-01-01
Combinatorial design theory is a source of simply stated, concrete, yet difficult discrete problems, with the Hadamard conjecture being a prime example. It has become clear that many of these problems are essentially algebraic in nature. This book provides a unified vision of the algebraic themes which have developed so far in design theory. These include the applications in design theory of matrix algebra, the automorphism group and its regular subgroups, the composition of smaller designs to make larger designs, and the connection between designs with regular group actions and solutions to group ring equations. Everything is explained at an elementary level in terms of orthogonality sets and pairwise combinatorial designs--new and simple combinatorial notions which cover many of the commonly studied designs. Particular attention is paid to how the main themes apply in the important new context of cocyclic development. Indeed, this book contains a comprehensive account of cocyclic Hadamard matrices. The book...
Peternell, Thomas; Schneider, Michael; Schreyer, Frank-Olaf
1992-01-01
The Bayreuth meeting on "Complex Algebraic Varieties" focussed on the classification of algebraic varieties and topics such as vector bundles, Hodge theory and hermitian differential geometry. Most of the articles in this volume are closely related to talks given at the conference: all are original, fully refereed research articles. CONTENTS: A. Beauville: Annulation du H(1) pour les fibres en droites plats.- M. Beltrametti, A.J. Sommese, J.A. Wisniewski: Results on varieties with many lines and their applications to adjunction theory.- G. Bohnhorst, H. Spindler: The stability of certain vector bundles on P(n) .- F. Catanese, F. Tovena: Vector bundles, linear systems and extensions of (1).- O. Debarre: Vers uns stratification de l'espace des modules des varietes abeliennes principalement polarisees.- J.P. Demailly: Singular hermitian metrics on positive line bundles.- T. Fujita: On adjoint bundles of ample vector bundles.- Y. Kawamata: Moderate degenerations of algebraic surfaces.- U. Persson: Genus two fibra...
Wadsworth, A R
2017-01-01
This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups); rings (including basic ideal theory and factorization in integral domains and Gauss's Theorem); linear algebra (emphasizing linear transformations, including canonical forms); and fields (including Galois theory). Hints to many problems are also included.
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.
Olver, Peter J
2018-01-01
This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics. Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the un...
Blyth, T S
2002-01-01
Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be of particular interest to readers:...
Deo, Satya
2018-01-01
This book presents the first concepts of the topics in algebraic topology such as the general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in greater detail. Originally published in 2003, this book has become one of the seminal books. Now, in the completely revised and enlarged edition, the book discusses the rapidly developing field of algebraic topology. Targeted to undergraduate and graduate students of mathematics, the prerequisite for this book is minimal knowledge of linear algebra, group theory and topological spaces. The book discusses about the relevant concepts and ideas in a very lucid manner, providing suitable motivations and illustrations. All relevant topics are covered, including the classical theorems like the Brouwer’s fixed point theorem, Lefschetz fixed point theorem, Borsuk-Ulam theorem, Brouwer’s separation theorem and the theorem on invariance of the domain. Most of the exercises are elementary, but sometimes chal...
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.)
Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction
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…
Converting nested algebra expressions into flat algebra expressions
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
On Associative Conformal Algebras of Linear Growth
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 ...
Computer Program For Linear Algebra
Krogh, F. T.; Hanson, R. J.
1987-01-01
Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.
Algebra for Gifted Third Graders.
Borenson, Henry
1987-01-01
Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)
Gradings on simple Lie algebras
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.
Tensor spaces and exterior algebra
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.
Dynamical systems and linear algebra
Colonius, Fritz (Prof.)
2007-01-01
Dynamical systems and linear algebra / F. Colonius, W. Kliemann. - In: Handbook of linear algebra / ed. by Leslie Hogben. - Boca Raton : Chapman & Hall/CRC, 2007. - S. 56,1-56,22. - (Discrete mathematics and its applications)
Projector bases and algebraic spinors
International Nuclear Information System (INIS)
Bergdolt, G.
1988-01-01
In the case of complex Clifford algebras a basis is constructed whose elements satisfy projector relations. The relations are sufficient conditions for the elements to span minimal ideals and hence to define algebraic spinors
Contractions of quantum algebraic structures
International Nuclear Information System (INIS)
Doikou, A.; Sfetsos, K.
2010-01-01
A general framework for obtaining certain types of contracted and centrally extended algebras is reviewed. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Polynomial Heisenberg algebras
International Nuclear Information System (INIS)
Carballo, Juan M; C, David J Fernandez; Negro, Javier; Nieto, Luis M
2004-01-01
Polynomial deformations of the Heisenberg algebra are studied in detail. Some of their natural realizations are given by the higher order susy partners (and not only by those of first order, as is already known) of the harmonic oscillator for even-order polynomials. Here, it is shown that the susy partners of the radial oscillator play a similar role when the order of the polynomial is odd. Moreover, it will be proved that the general systems ruled by such kinds of algebras, in the quadratic and cubic cases, involve Painleve transcendents of types IV and V, respectively
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
Weiss, Edwin
1998-01-01
Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate's thesis).Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract te
Partially ordered algebraic systems
Fuchs, Laszlo
2011-01-01
Originally published in an important series of books on pure and applied mathematics, this monograph by a distinguished mathematician explores a high-level area in algebra. It constitutes the first systematic summary of research concerning partially ordered groups, semigroups, rings, and fields. The self-contained treatment features numerous problems, complete proofs, a detailed bibliography, and indexes. It presumes some knowledge of abstract algebra, providing necessary background and references where appropriate. This inexpensive edition of a hard-to-find systematic survey will fill a gap i
Hohn, Franz E
2012-01-01
This complete and coherent exposition, complemented by numerous illustrative examples, offers readers a text that can teach by itself. Fully rigorous in its treatment, it offers a mathematically sound sequencing of topics. The work starts with the most basic laws of matrix algebra and progresses to the sweep-out process for obtaining the complete solution of any given system of linear equations - homogeneous or nonhomogeneous - and the role of matrix algebra in the presentation of useful geometric ideas, techniques, and terminology.Other subjects include the complete treatment of the structur
Principles of algebraic geometry
Griffiths, Phillip A
1994-01-01
A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special top
Energy Technology Data Exchange (ETDEWEB)
Christian, J M; McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Materials and Physics Research Centre, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P, E-mail: j.christian@salford.ac.u [Departamento de Teoria de la Senal y Comunicaciones e Ingenieria Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)
2010-02-26
We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.
Endomorphisms of graph algebras
DEFF Research Database (Denmark)
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA D...... that the restriction to the diagonal MASA of an automorphism which globally preserves both D_E and the core AF-subalgebra eventually commutes with the corresponding one-sided shift. Secondly, we exhibit several properties of proper endomorphisms, investigate invertibility of localized endomorphisms both on C...
Algebraic curves and cryptography
Murty, V Kumar
2010-01-01
It is by now a well-known paradigm that public-key cryptosystems can be built using finite Abelian groups and that algebraic geometry provides a supply of such groups through Abelian varieties over finite fields. Of special interest are the Abelian varieties that are Jacobians of algebraic curves. All of the articles in this volume are centered on the theme of point counting and explicit arithmetic on the Jacobians of curves over finite fields. The topics covered include Schoof's \\ell-adic point counting algorithm, the p-adic algorithms of Kedlaya and Denef-Vercauteren, explicit arithmetic on
Kendig, Keith
2015-01-01
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th
International Nuclear Information System (INIS)
Christian, J M; McDonald, G S; Chamorro-Posada, P
2010-01-01
We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.
Hogben, Leslie
2013-01-01
With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters.New to the Second EditionSeparate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of
Algebra & trigonometry I essentials
REA, Editors of
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. Algebra & Trigonometry I includes sets and set operations, number systems and fundamental algebraic laws and operations, exponents and radicals, polynomials and rational expressions, eq
Algebra & trigonometry super review
2012-01-01
Get all you need to know with Super Reviews! Each Super Review is packed with in-depth, student-friendly topic reviews that fully explain everything about the subject. The Algebra and Trigonometry Super Review includes sets and set operations, number systems and fundamental algebraic laws and operations, exponents and radicals, polynomials and rational expressions, equations, linear equations and systems of linear equations, inequalities, relations and functions, quadratic equations, equations of higher order, ratios, proportions, and variations. Take the Super Review quizzes to see how much y
Linear Algebra Thoroughly Explained
Vujičić, Milan
2008-01-01
Linear Algebra Thoroughly Explained provides a comprehensive introduction to the subject suitable for adoption as a self-contained text for courses at undergraduate and postgraduate level. The clear and comprehensive presentation of the basic theory is illustrated throughout with an abundance of worked examples. The book is written for teachers and students of linear algebra at all levels and across mathematics and the applied sciences, particularly physics and engineering. It will also be an invaluable addition to research libraries as a comprehensive resource book for the subject.
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.)
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
In the Shadow of Pennhurst: The Orion Community.
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…
The theory of algebraic numbers
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.
Innovative Approach for Developing Spacecraft Interior Acoustic Requirement Allocation
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 Fencing on the Orion Heatshield
Alunni, Antonella I.; Gokcen, Tahir
2016-01-01
This paper presents recession measurements of arc-jet test articles that simulate an ablator with gap filler and were exposed to various heating profiles. Results were used to derive empirically-based differential recession models used for the baseline sizing of the Orion block heatshield architecture. The profile test conditions represent different local flight environments associated with different regions of the heatshield. Recession measurements were collected during and after arc-jet tests, and the results were used to observe the heating profiles’ effect on differential recession. Arc-jet tests were conducted at the Aerodynamic Heating Facility at NASA Ames Research Center.
The dynamical evolution of the Orion Trapezium
Allen, C.; Costero, R.; Ruelas-Mayorga, A.; Sánchez, L.
2018-01-01
Using recent observational data on transverse and radial velocities of the bright Orion Trapezium stars we study the dynamical evolution of ensembles of systems mimicking the Trapezium. To this end we perform numerical N-body integrations using the observed planar positions and velocities, the radial velocities, and random z-positions for all components. We include perturbations in these quantities compatible with the observational errors. We discuss the dynamical outcome of the evolution of such systems and the properties of the resulting binaries.
Orion infrared nebula/molecular cloud
International Nuclear Information System (INIS)
Zuckerman, B.; Palmer, P.
1975-01-01
Observational and theoretical studies of the Orion Nebula and the associated molecular clouds have greatly increased our understanding of this and other regions in which star formation is taking place. Fundamental questions remain unanswered; and in this Letter we address three of them: (1) the chemical composition of the molecular cloud, (2) its internal motions, and (3) the role of magnetic fields in its evolution. We show that the gas phase chemistry and internal motions in one part of the cloud are distinctly different from those in the rest of the cloud, and two recent estimates of the magnetic field strengths are very uncertain. (auth)
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.)
An algebra of reversible computation.
Wang, Yong
2016-01-01
We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules: basic reversible processes algebra, algebra of reversible communicating processes, recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.
Thomys, Janus; Zhang, Xiaohong
2013-01-01
We describe weak-BCC-algebras (also called BZ-algebras) in which the condition (x∗y)∗z = (x∗z)∗y is satisfied only in the case when elements x, y belong to the same branch. We also characterize ideals, nilradicals, and nilpotent elements of such algebras. PMID:24311983
Assessing Elementary Algebra with STACK
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…
Process Algebra and Markov Chains
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
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
Algebraic Methods to Design Signals
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
Orion FSW V and V and Kedalion Engineering Lab Insight
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.
Bergstra, J.A.; Middelburg, C.A.
2015-01-01
We add probabilistic features to basic thread algebra and its extensions with thread-service interaction and strategic interleaving. Here, threads represent the behaviours produced by instruction sequences under execution and services represent the behaviours exhibited by the components of execution
Indian Academy of Sciences (India)
BOOK REVIEW ... To the Indian reader, the word discourse, evokes a respected ... I dug a bit deeper with Google trans- late, and ... published in a journal of mathematics educa- tion. ... The article on Shafarevich's work elsewhere ... goal then, is to develop the basics of algebra in ... ometric Greeks, and works like a magician.
Thinking Visually about Algebra
Baroudi, Ziad
2015-01-01
Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…
The algebraic collective model
International Nuclear Information System (INIS)
Rowe, D.J.; Turner, P.S.
2005-01-01
A recently proposed computationally tractable version of the Bohr collective model is developed to the extent that we are now justified in describing it as an algebraic collective model. The model has an SU(1,1)xSO(5) algebraic structure and a continuous set of exactly solvable limits. Moreover, it provides bases for mixed symmetry collective model calculations. However, unlike the standard realization of SU(1,1), used for computing beta wave functions and their matrix elements in a spherical basis, the algebraic collective model makes use of an SU(1,1) algebra that generates wave functions appropriate for deformed nuclei with intrinsic quadrupole moments ranging from zero to any large value. A previous paper focused on the SO(5) wave functions, as SO(5) (hyper-)spherical harmonics, and computation of their matrix elements. This paper gives analytical expressions for the beta matrix elements needed in applications of the model and illustrative results to show the remarkable gain in efficiency that is achieved by using such a basis in collective model calculations for deformed nuclei
Benjamin, Carl; And Others
Presented are student performance objectives, a student progress chart, and assignment sheets with objective and diagnostic measures for the stated performance objectives in College Algebra I. Topics covered include: sets; vocabulary; linear equations; inequalities; real numbers; operations; factoring; fractions; formulas; ratio, proportion, and…
Swan, R G
1968-01-01
From the Introduction: "These notes are taken from a course on algebraic K-theory [given] at the University of Chicago in 1967. They also include some material from an earlier course on abelian categories, elaborating certain parts of Gabriel's thesis. The results on K-theory are mostly of a very general nature."
Bergstra, J.A.; Baeten, J.C.M.
1993-01-01
The real time process algebra of Baeten and Bergstra [Formal Aspects of Computing, 3, 142-188 (1991)] is extended to real space by requiring the presence of spatial coordinates for each atomic action, in addition to the required temporal attribute. It is found that asynchronous communication
Commutative algebra with a view toward algebraic geometry
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...
Federal Laboratory Consortium — FUNCTION: Provides the capability to correct unbalances of spacecraft by using dynamic measurement techniques and static/coupled measurements to provide products of...
Operator algebras and topology
International Nuclear Information System (INIS)
Schick, T.
2002-01-01
These notes, based on three lectures on operator algebras and topology at the 'School on High Dimensional Manifold Theory' at the ICTP in Trieste, introduce a new set of tools to high dimensional manifold theory, namely techniques coming from the theory of operator algebras, in particular C*-algebras. These are extensively studied in their own right. We will focus on the basic definitions and properties, and on their relevance to the geometry and topology of manifolds. A central pillar of work in the theory of C*-algebras is the Baum-Connes conjecture. This is an isomorphism conjecture, as discussed in the talks of Luck, but with a certain special flavor. Nevertheless, it has important direct applications to the topology of manifolds, it implies e.g. the Novikov conjecture. In the first chapter, the Baum-Connes conjecture will be explained and put into our context. Another application of the Baum-Connes conjecture is to the positive scalar curvature question. This will be discussed by Stephan Stolz. It implies the so-called 'stable Gromov-Lawson-Rosenberg conjecture'. The unstable version of this conjecture said that, given a closed spin manifold M, a certain obstruction, living in a certain (topological) K-theory group, vanishes if and only M admits a Riemannian metric with positive scalar curvature. It turns out that this is wrong, and counterexamples will be presented in the second chapter. The third chapter introduces another set of invariants, also using operator algebra techniques, namely L 2 -cohomology, L 2 -Betti numbers and other L 2 -invariants. These invariants, their basic properties, and the central questions about them, are introduced in the third chapter. (author)
Advanced modern algebra part 2
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.
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.)
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
Chandra Finds X-ray Star Bonanza in the Orion Nebula
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
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...
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...
76 FR 22865 - Action Affecting Export Privileges; Orion Air, S.L. and Syrian Pearl Airlines
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...
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)
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.
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
Goembel, L.
2003-12-01
We are currently developing a flight prototype Spacecraft Charge Monitor (SCM) with support from NASA's Small Business Innovation Research (SBIR) program. The device will use a recently proposed high energy-resolution electron spectroscopic technique to determine spacecraft floating potential. The inspiration for the technique came from data collected by the Atmosphere Explorer (AE) satellites in the 1970s. The data available from the AE satellites indicate that the SCM may be able to determine spacecraft floating potential to within 0.1 V under certain conditions. Such accurate measurement of spacecraft charge could be used to correct biases in space plasma measurements. The device may also be able to measure spacecraft floating potential in the solar wind and in orbit around other planets.
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
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.
Bochnak, Jacek; Roy, Marie-Françoise
1998-01-01
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
Directory of Open Access Journals (Sweden)
María Carolina Spinel G.
1990-01-01
Con esta base, en posteriores artículos de divulgación, presentaremos algunas aplicaciones que muestren la ventaja de su empleo en la descripción de sistema físico. Dado el amplio conocimiento que se tiene de los espacios vectoriales. La estructura y propiedades del algebra de Clifford suele presentarse con base en los elementos de un espacio vectorial. En esta dirección, en la sección 2 se define la notación y se describe la estructura de un algebra de Clifford Gn, introduciendo con detalle las operaciones básicas entre los elementos del álgebra. La sección 3 se dedica a describir una base tensorial de Gn.
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
Indian Academy of Sciences (India)
project of the Spanish Ministerio de Educación y Ciencia MTM2007-60333. References. [1] Calderón A J, On split Lie algebras with symmetric root systems, Proc. Indian. Acad. Sci (Math. Sci.) 118(2008) 351–356. [2] Calderón A J, On split Lie triple systems, Proc. Indian. Acad. Sci (Math. Sci.) 119(2009). 165–177.
Lee, Jaehoon; Wilczek, Frank
2013-11-27
Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.
Beigie, Darin
2014-01-01
Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…
Fundamentals of linear algebra
Dash, Rajani Ballav
2008-01-01
FUNDAMENTALS OF LINEAR ALGEBRA is a comprehensive Text Book, which can be used by students and teachers of All Indian Universities. The Text has easy, understandable form and covers all topics of UGC Curriculum. There are lots of worked out examples which helps the students in solving the problems without anybody's help. The Problem sets have been designed keeping in view of the questions asked in different examinations.
Algebras of Information States
Czech Academy of Sciences Publication Activity Database
Punčochář, Vít
2017-01-01
Roč. 27, č. 5 (2017), s. 1643-1675 ISSN 0955-792X R&D Projects: GA ČR(CZ) GC16-07954J Institutional support: RVO:67985955 Keywords : information states * relational semantics * algebraic semantics * intuitionistic logic * inquisitive disjunction Subject RIV: AA - Philosophy ; Religion OBOR OECD: Philosophy, History and Philosophy of science and technology Impact factor: 0.909, year: 2016
International Nuclear Information System (INIS)
Todorov, Ivan
2010-12-01
Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particular, in now fashionable theoretical speculations on neutrino masses. It has a more mathematical flavour than the over twenty-six-year-old Introduction to Majorana masses [M84] and includes historical notes and biographical data on past participants in the story. (author)
Algebra & trigonometry II essentials
REA, Editors of
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. Algebra & Trigonometry II includes logarithms, sequences and series, permutations, combinations and probability, vectors, matrices, determinants and systems of equations, mathematica
Lutfiyya, Lutfi A
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. Modern Algebra includes set theory, operations, relations, basic properties of the integers, group theory, and ring theory.
Blyth, T S
2002-01-01
Most of the introductory courses on linear algebra develop the basic theory of finite dimensional vector spaces, and in so doing relate the notion of a linear mapping to that of a matrix. Generally speaking, such courses culminate in the diagonalisation of certain matrices and the application of this process to various situations. Such is the case, for example, in our previous SUMS volume Basic Linear Algebra. The present text is a continuation of that volume, and has the objective of introducing the reader to more advanced properties of vector spaces and linear mappings, and consequently of matrices. For readers who are not familiar with the contents of Basic Linear Algebra we provide an introductory chapter that consists of a compact summary of the prerequisites for the present volume. In order to consolidate the student's understanding we have included a large num ber of illustrative and worked examples, as well as many exercises that are strategi cally placed throughout the text. Solutions to the ex...
Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.
1999-01-01
This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.
Infrared reflection nebulae in Orion Molecular Cloud
International Nuclear Information System (INIS)
Pendleton, Y.; Werner, M.W.; Capps, R.; Lester, D.; Hawaii Univ., Honolulu; Texas Univ., Austin)
1986-01-01
New observations of Orion Molecular Cloud 2 have been made from 1 to 100 microns using the NASA Infrared Telescope Facility and the Kuiper Airborne Observatory. An extensive program of polarimetry, photometry, and spectrophotometry has shown that the extended emission regions associated with two of the previously known near-infrared sources, IRS 1 and IRS 4, are infrared reflection nebulae, and that the compact sources IRS 1 and IRS 4 are the main luminosity sources in the cloud. The constraints from the far-infrared observations and an analysis of the scattered light from the IRS 1 nebula show that OMC-2/IRS 1 can be characterized by L of 500 solar luminosities or less and T of roughly 1000 K. The near-infrared albedo of the grains in the IRS 1 nebula is greater than 0.08. 27 references
On the Nature of Orion Source I
Báez-Rubio, A.; Jiménez-Serra, I.; Martín-Pintado, J.; Zhang, Q.; Curiel, S.
2018-01-01
The Kleinmann–Low nebula in Orion, the closest region of massive star formation, harbors Source I, whose nature is under debate. Knowledge of this source may have profound implications for our understanding of the energetics of the hot core in Orion KL since it might be the main heating source in the region. The spectral energy distribution of this source in the radio is characterized by a positive spectral index close to 2, which is consistent with (i) thermal bremsstrahlung emission of ionized hydrogen gas produced by a central massive protostar, or (ii) photospheric bremsstrahlung emission produced by electrons when deflected by the interaction with neutral and molecular hydrogen like Mira-like variable stars. If ionized hydrogen gas were responsible for the observed continuum emission, its modeling would predict detectable emission from hydrogen radio recombination lines (RRLs). However, our SMA observations were obtained with a high enough sensitivity to rule out that the radio continuum emission arises from a dense hypercompact H II region because the H26α line would have been detected, in contrast with our observations. To explain the observational constraints, we investigate further the nature of the radio continuum emission from source I. We have compared available radio continuum data with the predictions from our upgraded non-LTE 3D radiative transfer model, MOdel for REcombination LInes, to show that radio continuum fluxes and sizes can only be reproduced by assuming both dust and bremsstrahlung emission from neutral gas. The dust emission contribution is significant at ν ≥ 43 GHz. In addition, our RRL peak intensity predictions for the ionized metals case are consistent with the nondetection of Na and K RRLs at millimeter and submillimeter wavelengths.
HIERARCHICAL FRAGMENTATION OF THE ORION MOLECULAR FILAMENTS
International Nuclear Information System (INIS)
Takahashi, Satoko; Ho, Paul T. P.; Su, Yu-Nung; Teixeira, Paula S.; Zapata, Luis A.
2013-01-01
We present a high angular resolution map of the 850 μm continuum emission of the Orion Molecular Cloud-3 (OMC 3) obtained with the Submillimeter Array (SMA); the map is a mosaic of 85 pointings covering an approximate area of 6.'5 × 2.'0 (0.88 × 0.27 pc). We detect 12 spatially resolved continuum sources, each with an H 2 mass between 0.3-5.7 M ☉ and a projected source size between 1400-8200 AU. All the detected sources are on the filamentary main ridge (n H 2 ≥10 6 cm –3 ), and analysis based on the Jeans theorem suggests that they are most likely gravitationally unstable. Comparison of multi-wavelength data sets indicates that of the continuum sources, 6/12 (50%) are associated with molecular outflows, 8/12 (67%) are associated with infrared sources, and 3/12 (25%) are associated with ionized jets. The evolutionary status of these sources ranges from prestellar cores to protostar phase, confirming that OMC-3 is an active region with ongoing embedded star formation. We detect quasi-periodical separations between the OMC-3 sources of ≈17''/0.035 pc. This spatial distribution is part of a large hierarchical structure that also includes fragmentation scales of giant molecular cloud (≈35 pc), large-scale clumps (≈1.3 pc), and small-scale clumps (≈0.3 pc), suggesting that hierarchical fragmentation operates within the Orion A molecular cloud. The fragmentation spacings are roughly consistent with the thermal fragmentation length in large-scale clumps, while for small-scale cores it is smaller than the local fragmentation length. These smaller spacings observed with the SMA can be explained by either a helical magnetic field, cloud rotation, or/and global filament collapse. Finally, possible evidence for sequential fragmentation is suggested in the northern part of the OMC-3 filament.
Assessing Algebraic Solving Ability: A Theoretical Framework
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
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.
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.)
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
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.
Categorical Algebra and its Applications
1988-01-01
Categorical algebra and its applications contain several fundamental papers on general category theory, by the top specialists in the field, and many interesting papers on the applications of category theory in functional analysis, algebraic topology, algebraic geometry, general topology, ring theory, cohomology, differential geometry, group theory, mathematical logic and computer sciences. The volume contains 28 carefully selected and refereed papers, out of 96 talks delivered, and illustrates the usefulness of category theory today as a powerful tool of investigation in many other areas.
Fractionated Spacecraft Architectures Seeding Study
National Research Council Canada - National Science Library
Mathieu, Charlotte; Weigel, Annalisa
2006-01-01
.... Models were developed from a customer-centric perspective to assess different fractionated spacecraft architectures relative to traditional spacecraft architectures using multi-attribute analysis...
Spacecraft momentum control systems
Leve, Frederick A; Peck, Mason A
2015-01-01
The goal of this book is to serve both as a practical technical reference and a resource for gaining a fuller understanding of the state of the art of spacecraft momentum control systems, specifically looking at control moment gyroscopes (CMGs). As a result, the subject matter includes theory, technology, and systems engineering. The authors combine material on system-level architecture of spacecraft that feature momentum-control systems with material about the momentum-control hardware and software. This also encompasses material on the theoretical and algorithmic approaches to the control of space vehicles with CMGs. In essence, CMGs are the attitude-control actuators that make contemporary highly agile spacecraft possible. The rise of commercial Earth imaging, the advances in privately built spacecraft (including small satellites), and the growing popularity of the subject matter in academic circles over the past decade argues that now is the time for an in-depth treatment of the topic. CMGs are augmented ...
Spacecraft Material Outgassing Data
National Aeronautics and Space Administration — This compilation of outgassing data of materials intended for spacecraft use were obtained at the Goddard Space Flight Center (GSFC), utilizing equipment developed...
Spacecraft Fire Safety Demonstration
National Aeronautics and Space Administration — The objective of the Spacecraft Fire Safety Demonstration project is to develop and conduct large-scale fire safety experiments on an International Space Station...
Quick spacecraft charging primer
International Nuclear Information System (INIS)
Larsen, Brian Arthur
2014-01-01
This is a presentation in PDF format which is a quick spacecraft charging primer, meant to be used for program training. It goes into detail about charging physics, RBSP examples, and how to identify charging.
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.
Applications of Computer Algebra Conference
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 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.
Computational aspects of algebraic curves
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 European Service Module (ESM) Development, Integration and Qualification Status
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.
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
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
Project Orion, Environmental Control and Life Support System Integrated Studies
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.
Deployable Brake for Spacecraft
Rausch, J. R.; Maloney, J. W.
1987-01-01
Aerodynamic shield that could be opened and closed proposed. Report presents concepts for deployable aerodynamic brake. Brake used by spacecraft returning from high orbit to low orbit around Earth. Spacecraft makes grazing passes through atmosphere to slow down by drag of brake. Brake flexible shield made of woven metal or ceramic withstanding high temperatures created by air friction. Stored until needed, then deployed by set of struts.
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)
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)
Abstract Algebra to Secondary School Algebra: Building Bridges
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…
Galois Theory of Differential Equations, Algebraic Groups and Lie Algebras
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.
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.
A modal characterization of Peirce algebras
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.
Quantum deformation of the affine transformation algebra
International Nuclear Information System (INIS)
Aizawa, N.; Sato, Haru-Tada
1994-01-01
We discuss a quantum deformation of the affine transformation algebra in one-dimensional space. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators. (orig.)
DEFF Research Database (Denmark)
Høyrup, Jens
with basic Assyriology but otherwise philological details are avoided. All of these texts are from the second half of the Old Babylonian period, that is, 1800–1600 BCE. It is indeed during this period that the “algebraic” discipline, and Babylonian mathematics in general, culminates. Even though a few texts...... particular culture. Finally, it describes the origin of the discipline and its impact in later mathematics, not least Euclid’s geometry and genuine algebra as created in medieval Islam and taken over in European medieval and Renaissance mathematics....
Algebraic topology and concurrency
DEFF Research Database (Denmark)
Fajstrup, Lisbeth; Raussen, Martin; Goubault, Eric
2006-01-01
We show in this article that some concepts from homotopy theory, in algebraic topology,are relevant for studying concurrent programs. We exhibit a natural semantics of semaphore programs, based on partially ordered topological spaces, which are studied up to “elastic deformation” or homotopy...... differences between ordinary and directed homotopy through examples. We also relate the topological view to a combinatorial view of concurrent programs closer to transition systems, through the notion of a cubical set. Finally we apply some of these concepts to the proof of the safeness of a two...
Clark, Allan
1984-01-01
This concise, readable, college-level text treats basic abstract algebra in remarkable depth and detail. An antidote to the usual surveys of structure, the book presents group theory, Galois theory, and classical ideal theory in a framework emphasizing proof of important theorems.Chapter I (Set Theory) covers the basics of sets. Chapter II (Group Theory) is a rigorous introduction to groups. It contains all the results needed for Galois theory as well as the Sylow theorems, the Jordan-Holder theorem, and a complete treatment of the simplicity of alternating groups. Chapter III (Field Theory)
Corrochano, Eduardo Bayro
2010-01-01
This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; int
Lopez, Cesar
2014-01-01
MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Linear Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving an introduction to
Hazewinkel, M
2008-01-01
Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it i
The Unitality of Quantum B-algebras
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.
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
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
Star Formation in the Orion Nebula Cluster
Palla, Francesco; Stahler, Steven W.
1999-11-01
We study the record of star formation activity within the dense cluster associated with the Orion Nebula. The bolometric luminosity function of 900 visible members is well matched by a simplified theoretical model for cluster formation. This model assumes that stars are produced at a constant rate and distributed according to the field-star initial mass function. Our best-fit age for the system, within this framework, is 2×106 yr. To undertake a more detailed analysis, we present a new set of theoretical pre-main-sequence tracks. These cover all masses from 0.1 to 6.0 Msolar, and start from a realistic stellar birthline. The tracks end along a zero-age main-sequence that is in excellent agreement with the empirical one. As a further aid to cluster studies, we offer an heuristic procedure for the correction of pre-main-sequence luminosities and ages to account for the effects of unresolved binary companions. The Orion Nebula stars fall neatly between our birthline and zero-age main-sequence in the H-R diagram. All those more massive than about 8 Msolar lie close to the main sequence, as also predicted by theory. After accounting for the finite sensitivity of the underlying observations, we confirm that the population between 0.4 and 6.0 Msolar roughly follows a standard initial mass function. We see no evidence for a turnover at lower masses. We next use our tracks to compile stellar ages, also between 0.4 and 6.0 Msolar. Our age histogram reveals that star formation began at a low level some 107 yr ago and has gradually accelerated to the present epoch. The period of most active formation is indeed confined to a few×106 yr, and has recently ended with gas dispersal from the Trapezium. We argue that the acceleration in stellar births, which extends over a wide range in mass, reflects the gravitational contraction of the parent cloud spawning this cluster.
Graded associative conformal algebras of finite type
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...
Linear Algebra and Image Processing
Allali, Mohamed
2010-01-01
We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)
Templates for Linear Algebra Problems
Bai, Z.; Day, D.; Demmel, J.; Dongarra, J.; Gu, M.; Ruhe, A.; Vorst, H.A. van der
1995-01-01
The increasing availability of advanced-architecture computers is having a very signicant eect on all spheres of scientic computation, including algorithm research and software development in numerical linear algebra. Linear algebra {in particular, the solution of linear systems of equations and
Differential Equation over Banach Algebra
Kleyn, Aleks
2018-01-01
In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.
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.
General distributions in process algebra
Katoen, Joost P.; d' Argenio, P.R.; Brinksma, Hendrik; Hermanns, H.; Katoen, Joost P.
2001-01-01
This paper is an informal tutorial on stochastic process algebras, i.e., process calculi where action occurrences may be subject to a delay that is governed by a (mostly continuous) random variable. Whereas most stochastic process algebras consider delays determined by negative exponential
Tilting-connected symmetric algebras
Aihara, Takuma
2010-01-01
The notion of silting mutation was introduced by Iyama and the author. In this paper we mainly study silting mutation for self-injective algebras and prove that any representation-finite symmetric algebra is tilting-connected. Moreover we give some sufficient conditions for a Bongartz-type Lemma to hold for silting objects.
Algebraic study of chiral anomalies
Indian Academy of Sciences (India)
2012-06-14
Jun 14, 2012 ... They form a group G which acts on the (affine) space of ... The curvature F of A is defined by (notice that in this paper the bracket is defined ... This purely algebraic formulation easily extends to the consideration of the Lie algebra of vector .... namely the case of perturbatively renormalizable theories in four ...
Logarithmic residues in Banach algebras
H. Bart (Harm); T. Ehrhardt; B. Silbermann
1994-01-01
textabstractLet f be an analytic Banach algebra valued function and suppose that the contour integral of the logarithmic derivative f′f-1 around a Cauchy domain D vanishes. Does it follow that f takes invertible values on all of D? For important classes of Banach algebras, the answer is positive. In
Modular specifications in process algebra
R.J. van Glabbeek (Rob); F.W. Vaandrager (Frits)
1987-01-01
textabstractIn recent years a wide variety of process algebras has been proposed in the literature. Often these process algebras are closely related: they can be viewed as homomorphic images, submodels or restrictions of each other. The aim of this paper is to show how the semantical reality,
Galois Connections for Flow Algebras
DEFF Research Database (Denmark)
Filipiuk, Piotr; Terepeta, Michal Tomasz; Nielson, Hanne Riis
2011-01-01
to the approach taken by Monotone Frameworks and other classical analyses. We present a generic framework for static analysis based on flow algebras and program graphs. Program graphs are often used in Model Checking to model concurrent and distributed systems. The framework allows to induce new flow algebras...
The Algebra of Complex Numbers.
LePage, Wilbur R.
This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…
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)
Learning Algebra from Worked Examples
Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.
2014-01-01
For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…
Covariant representations of nuclear *-algebras
International Nuclear Information System (INIS)
Moore, S.M.
1978-01-01
Extensions of the Csup(*)-algebra theory for covariant representations to nuclear *-algebra are considered. Irreducible covariant representations are essentially unique, an invariant state produces a covariant representation with stable vacuum, and the usual relation between ergodic states and covariant representations holds. There exist construction and decomposition theorems and a possible relation between derivations and covariant representations
Practical algebraic renormalization
International Nuclear Information System (INIS)
Grassi, Pietro Antonio; Hurth, Tobias; Steinhauser, Matthias
2001-01-01
A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over non-invariant counterterms is translated into a practical computational method. We provide a detailed introduction into the handling of the Slavnov-Taylor and Ward-Takahashi identities in the standard model both in the conventional and the background gauge. Explicit examples for their practical derivation are presented. After a brief introduction into the Quantum Action Principle the conventional algebraic method which allows for the restoration of the functional identities is discussed. The main point of our approach is the optimization of this procedure which results in an enormous reduction of the calculational effort. The counterterms which have to be computed are universal in the sense that they are independent of the regularization scheme. The method is explicitly illustrated for two processes of phenomenological interest: QCD corrections to the decay of the Higgs boson into two photons and two-loop electroweak corrections to the process B→X s γ
Internet Technology on Spacecraft
Rash, James; Parise, Ron; Hogie, Keith; Criscuolo, Ed; Langston, Jim; Powers, Edward I. (Technical Monitor)
2000-01-01
The Operating Missions as Nodes on the Internet (OMNI) project has shown that Internet technology works in space missions through a demonstration using the UoSAT-12 spacecraft. An Internet Protocol (IP) stack was installed on the orbiting UoSAT-12 spacecraft and tests were run to demonstrate Internet connectivity and measure performance. This also forms the basis for demonstrating subsequent scenarios. This approach provides capabilities heretofore either too expensive or simply not feasible such as reconfiguration on orbit. The OMNI project recognized the need to reduce the risk perceived by mission managers and did this with a multi-phase strategy. In the initial phase, the concepts were implemented in a prototype system that includes space similar components communicating over the TDRS (space network) and the terrestrial Internet. The demonstration system includes a simulated spacecraft with sample instruments. Over 25 demonstrations have been given to mission and project managers, National Aeronautics and Space Administration (NASA), Department of Defense (DoD), contractor technologists and other decisions makers, This initial phase reached a high point with an OMNI demonstration given from a booth at the Johnson Space Center (JSC) Inspection Day 99 exhibition. The proof to mission managers is provided during this second phase with year 2000 accomplishments: testing the use of Internet technologies onboard an actual spacecraft. This was done with a series of tests performed using the UoSAT-12 spacecraft. This spacecraft was reconfigured on orbit at very low cost. The total period between concept and the first tests was only 6 months! On board software was modified to add an IP stack to support basic IP communications. Also added was support for ping, traceroute and network timing protocol (NTP) tests. These tests show that basic Internet functionality can be used onboard spacecraft. The performance of data was measured to show no degradation from current
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...
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
Waterloo Workshop on Computer Algebra
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.
Elements of algebraic coding systems
Cardoso da Rocha, Jr, Valdemar
2014-01-01
Elements of Algebraic Coding Systems is an introductory text to algebraic coding theory. In the first chapter, you'll gain inside knowledge of coding fundamentals, which is essential for a deeper understanding of state-of-the-art coding systems. This book is a quick reference for those who are unfamiliar with this topic, as well as for use with specific applications such as cryptography and communication. Linear error-correcting block codes through elementary principles span eleven chapters of the text. Cyclic codes, some finite field algebra, Goppa codes, algebraic decoding algorithms, and applications in public-key cryptography and secret-key cryptography are discussed, including problems and solutions at the end of each chapter. Three appendices cover the Gilbert bound and some related derivations, a derivation of the Mac- Williams' identities based on the probability of undetected error, and two important tools for algebraic decoding-namely, the finite field Fourier transform and the Euclidean algorithm f...
Representations of affine Hecke algebras
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
Mechanical Design of Spacecraft
1962-01-01
In the spring of 1962, engineers from the Engineering Mechanics Division of the Jet Propulsion Laboratory gave a series of lectures on spacecraft design at the Engineering Design seminars conducted at the California Institute of Technology. Several of these lectures were subsequently given at Stanford University as part of the Space Technology seminar series sponsored by the Department of Aeronautics and Astronautics. Presented here are notes taken from these lectures. The lectures were conceived with the intent of providing the audience with a glimpse of the activities of a few mechanical engineers who are involved in designing, building, and testing spacecraft. Engineering courses generally consist of heavily idealized problems in order to allow the more efficient teaching of mathematical technique. Students, therefore, receive a somewhat limited exposure to actual engineering problems, which are typified by more unknowns than equations. For this reason it was considered valuable to demonstrate some of the problems faced by spacecraft designers, the processes used to arrive at solutions, and the interactions between the engineer and the remainder of the organization in which he is constrained to operate. These lecture notes are not so much a compilation of sophisticated techniques of analysis as they are a collection of examples of spacecraft hardware and associated problems. They will be of interest not so much to the experienced spacecraft designer as to those who wonder what part the mechanical engineer plays in an effort such as the exploration of space.
Orion Boiler Plate Airdrop Test System
Machin, Ricardo A.; Evans, Carol T.
2013-01-01
On the 29th of February 2012 the Orion Capsule Parachute Assembly System (CPAS) project attempted to perform an airdrop test of a boilerplate test article for the second time. The first attempt (Cluster Development Test 2, July 2008) to deliver a similar boilerplate from a C-17 using the Low Velocity Air Drop (LVAD) technique resulted in the programmer parachute failing to properly inflate, the test article failing to achieve the desired test initiation conditions, and the test article a total loss. This paper will pick up where the CDT-2 failure investigation left off, describing the test technique that was adopted, and outline the modeling that was performed to gain confidence that the second attempt would be successful. The second boiler plate test (Cluster Development Test 3-3) was indeed a complete success and has subsequently been repeated several times, allowing the CPAS project to proceed with the full scale system level development testing required to integrate the hardware to the first Entry Flight Test vehicle as well as go into the Critical Design Review with minimum risk and a mature design.
Ultraviolet and Infrared Correlation Studies in Orion
Directory of Open Access Journals (Sweden)
Bose Lakshmi S.
2015-09-01
Full Text Available We have studied the variation of diffuse ultraviolet (UV radiation in the northern part of the Orion constellation using a set of eight areas of the GALEX All-Sky Imaging Survey in the far and near UV. Different components of diffuse UV radiation, like dust scattered emission and H2 fluorescence, were quantified and separated after removing the point sources and the foreground emission in each of the fields. Then the dependence of the individual UV components on the infrared 100 μm dust emission was studied. We did not find any positive correlation between the diffuse-UV and IR-100 micron intensities, probably due to the high optical depth of the region or the entire dust column not contributing to the diffuse UV radiation. However, in the far UV we noticed the presence of an excess emission in addition to the dust scattered radiation, which is clearly absent in the near UV. This excess emission, identified as the H2 fluorescence, is produced by the Trapezium stars in the surrounding molecular clouds. We also compare our results with those of previous studies in the region, based on Far Ultraviolet Spectroscopic Explorer (FUSE observations.
(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.
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
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.)
Spacecraft Attitude Determination
DEFF Research Database (Denmark)
Bak, Thomas
This thesis describes the development of an attitude determination system for spacecraft based only on magnetic field measurements. The need for such system is motivated by the increased demands for inexpensive, lightweight solutions for small spacecraft. These spacecraft demands full attitude...... determination based on simple, reliable sensors. Meeting these objectives with a single vector magnetometer is difficult and requires temporal fusion of data in order to avoid local observability problems. In order to guaranteed globally nonsingular solutions, quaternions are generally the preferred attitude...... is a detailed study of the influence of approximations in the modeling of the system. The quantitative effects of errors in the process and noise statistics are discussed in detail. The third contribution is the introduction of these methods to the attitude determination on-board the Ørsted satellite...
Revamping Spacecraft Operational Intelligence
Hwang, Victor
2012-01-01
The EPOXI flight mission has been testing a new commercial system, Splunk, which employs data mining techniques to organize and present spacecraft telemetry data in a high-level manner. By abstracting away data-source specific details, Splunk unifies arbitrary data formats into one uniform system. This not only reduces the time and effort for retrieving relevant data, but it also increases operational visibility by allowing a spacecraft team to correlate data across many different sources. Splunk's scalable architecture coupled with its graphing modules also provide a solid toolset for generating data visualizations and building real-time applications such as browser-based telemetry displays.
Dips spacecraft integration issues
International Nuclear Information System (INIS)
Determan, W.R.; Harty, R.B.
1988-01-01
The Department of Energy, in cooperation with the Department of Defense, has recently initiated the dynamic isotope power system (DIPS) demonstration program. DIPS is designed to provide 1 to 10 kW of electrical power for future military spacecraft. One of the near-term missions considered as a potential application for DIPS was the boost surveillance and tracking system (BSTS). A brief review and summary of the reasons behind a selection of DIPS for BSTS-type missions is presented. Many of these are directly related to spacecraft integration issues; these issues will be reviewed in the areas of system safety, operations, survivability, reliability, and autonomy
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
Lie algebra in quantum physics by means of computer algebra
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...
Head First Algebra A Learner's Guide to Algebra I
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
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)
Meijer, Alko R
2016-01-01
This textbook provides an introduction to the mathematics on which modern cryptology is based. It covers not only public key cryptography, the glamorous component of modern cryptology, but also pays considerable attention to secret key cryptography, its workhorse in practice. Modern cryptology has been described as the science of the integrity of information, covering all aspects like confidentiality, authenticity and non-repudiation and also including the protocols required for achieving these aims. In both theory and practice it requires notions and constructions from three major disciplines: computer science, electronic engineering and mathematics. Within mathematics, group theory, the theory of finite fields, and elementary number theory as well as some topics not normally covered in courses in algebra, such as the theory of Boolean functions and Shannon theory, are involved. Although essentially self-contained, a degree of mathematical maturity on the part of the reader is assumed, corresponding to his o...
Hestenes, David
2015-01-01
This small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about far-reaching change in the future. At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions, tensors and differential forms. It provides a unified approach covering all these areas and thus leads to a very efficient ‘toolkit’ for use in physical problems including quantum mechanics, classical mechanics, electromagnetism and relativity (both special and general) – only one mathematical system needs to be learned and understood, and one can use it at levels which extend right through to current research topics in each of these areas. These same techniques, in the form of the ‘Geometric Algebra’, can be applied in many areas of engineering, robotics and computer science, with no changes necessary – it is the same underlying mathematics, a...
Current algebra for parafields
International Nuclear Information System (INIS)
Palev, Ch.D.
1976-01-01
Within the framework of the Lagrangean QFT a generalization of canonical commutation and anticommutation relations in terms of three-linear commutation relations, corresponding to the parastatistics, s discussed. A detailed derivation of these three-linear relations for a set of parafermi fields is presented. Then for a Lagrangean, depending of a family of parabose fields and a family of paraferm fields, is shown that the fundamental hypothesis of current algebra is valid. In other words, the currents corresponding to the linear gauge transformations are found to meet the commutation relation: [Jsub(f)sup(0)(x), Jsub(g)sup(0)]sub(x 0 =y 0 ) = -idelta(x vector - y vector)Jsub([f,g])sup(0) (x), where Jsub(f)sup(0) is a time component of the current, corresponding to transformation f. (S.P.)
Applications of computer algebra
1985-01-01
Today, certain computer software systems exist which surpass the computational ability of researchers when their mathematical techniques are applied to many areas of science and engineering. These computer systems can perform a large portion of the calculations seen in mathematical analysis. Despite this massive power, thousands of people use these systems as a routine resource for everyday calculations. These software programs are commonly called "Computer Algebra" systems. They have names such as MACSYMA, MAPLE, muMATH, REDUCE and SMP. They are receiving credit as a computational aid with in creasing regularity in articles in the scientific and engineering literature. When most people think about computers and scientific research these days, they imagine a machine grinding away, processing numbers arithmetically. It is not generally realized that, for a number of years, computers have been performing non-numeric computations. This means, for example, that one inputs an equa tion and obtains a closed for...
Pérez López, César
2014-01-01
MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Matrix Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. Starting with a look at symbolic and numeric variables, with an emphasis on vector and matrix variables, you will go on to examine functions and operations that support vectors and matrices as arguments, including those based on analytic parent functions. Computational methods for finding eigenvalues and eigenvectors of matrices are detailed, leading to various matrix decompositions. Applications such as change of bases, the classification of quadratic forms and ...
Distances, Kinematics, And Structure Of The Orion Complex
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
Mapping young stellar populations towards Orion with Gaia DR1
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.
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 .
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
Macdonald index and chiral algebra
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.)
1996-01-01
Handbook of Algebra defines algebra as consisting of many different ideas, concepts and results. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. Each chapter of the book combines some of the features of both a graduate-level textbook and a research-level survey. This book is divided into eight sections. Section 1A focuses on linear algebra and discusses such concepts as matrix functions and equations and random matrices. Section 1B cover linear d
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
Introduction to applied algebraic systems
Reilly, Norman R
2009-01-01
This upper-level undergraduate textbook provides a modern view of algebra with an eye to new applications that have arisen in recent years. A rigorous introduction to basic number theory, rings, fields, polynomial theory, groups, algebraic geometry and elliptic curves prepares students for exploring their practical applications related to storing, securing, retrieving and communicating information in the electronic world. It will serve as a textbook for an undergraduate course in algebra with a strong emphasis on applications. The book offers a brief introduction to elementary number theory as
International Nuclear Information System (INIS)
Barbarin, F.; Sorba, P.; Ragoucy, E.
1996-01-01
The property of some finite W algebras to be the commutant of a particular subalgebra of a simple Lie algebra G is used to construct realizations of G. When G ≅ so (4,2), unitary representations of the conformal and Poincare algebras are recognized in this approach, which can be compared to the usual induced representation technique. When G approx=(2, R), the anyonic parameter can be seen as the eigenvalue of a W generator in such W representations of G. The generalization of such properties to the affine case is also discussed in the conclusion, where an alternative of the Wakimoto construction for sl(2) k is briefly presented. (authors)
Lectures on Algebraic Geometry I
Harder, Gunter
2012-01-01
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern metho
Lie Algebras and Integrable Systems
International Nuclear Information System (INIS)
Zhang Yufeng; Mei Jianqin
2012-01-01
A 3 × 3 matrix Lie algebra is first introduced, its subalgebras and the generated Lie algebras are obtained, respectively. Applications of a few Lie subalgebras give rise to two integrable nonlinear hierarchies of evolution equations from their reductions we obtain the nonlinear Schrödinger equations, the mKdV equations, the Broer-Kaup (BK) equation and its generalized equation, etc. The linear and nonlinear integrable couplings of one integrable hierarchy presented in the paper are worked out by casting a 3 × 3 Lie subalgebra into a 2 × 2 matrix Lie algebra. Finally, we discuss the elliptic variable solutions of a generalized BK equation. (general)
Study guide for college algebra
Snow, James W; Shapiro, Arnold
1981-01-01
Study Guide for College Algebra is a supplemental material for the basic text, College Algebra. Its purpose is to make the learning of college algebra and trigonometry easier and enjoyable.The book provides detailed solutions to exercises found in the text. Students are encouraged to use the study guide as a learning tool during the duration of the course, a reviewer prior to an exam, a reference book, and as a quick overview before studying a section of the text. The Study Guide and Solutions Manual consists of four major components: basic concepts that should be learned from each unit, what
Kolman, Bernard; Levitan, Michael L
1985-01-01
Test Bank for College Algebra, Second Edition is a supplementary material for the text, College Algebra, Second Edition. The book is intended for use by mathematics teachers.The book contains standard tests for each chapter in the textbook. Each set of test aims to evaluate the level of understanding the student has achieved during the course. The answers for each chapter test and the final exam are found at the end of the book.Mathematics teachers teaching college algebra will find the book very useful.
Coxeter groups and Hopf algebras
Aguiar, Marcelo
2011-01-01
An important idea in the work of G.-C. Rota is that certain combinatorial objects give rise to Hopf algebras that reflect the manner in which these objects compose and decompose. Recent work has seen the emergence of several interesting Hopf algebras of this kind, which connect diverse subjects such as combinatorics, algebra, geometry, and theoretical physics. This monograph presents a novel geometric approach using Coxeter complexes and the projection maps of Tits for constructing and studying many of these objects as well as new ones. The first three chapters introduce the necessary backgrou
Algebraic and stochastic coding theory
Kythe, Dave K
2012-01-01
Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes.
Linear operators in Clifford algebras
International Nuclear Information System (INIS)
Laoues, M.
1991-01-01
We consider the real vector space structure of the algebra of linear endomorphisms of a finite-dimensional real Clifford algebra (2, 4, 5, 6, 7, 8). A basis of that space is constructed in terms of the operators M eI,eJ defined by x→e I .x.e J , where the e I are the generators of the Clifford algebra and I is a multi-index (3, 7). In particular, it is shown that the family (M eI,eJ ) is exactly a basis in the even case. (orig.)
Introduction to algebra and trigonometry
Kolman, Bernard
1981-01-01
Introduction to Algebra and Trigonometry provides a complete and self-contained presentation of the fundamentals of algebra and trigonometry.This book describes an axiomatic development of the foundations of algebra, defining complex numbers that are used to find the roots of any quadratic equation. Advanced concepts involving complex numbers are also elaborated, including the roots of polynomials, functions and function notation, and computations with logarithms. This text also discusses trigonometry from a functional standpoint. The angles, triangles, and applications involving triangles are
Constructing Meanings and Utilities within Algebraic Tasks
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,…
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.
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.)
Located actions in process algebra with timing
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
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.
Strongly \\'etale difference algebras and Babbitt's decomposition
Tomašić, Ivan; Wibmer, Michael
2015-01-01
We introduce a class of strongly \\'{e}tale difference algebras, whose role in the study of difference equations is analogous to the role of \\'{e}tale algebras in the study of algebraic equations. We deduce an improved version of Babbitt's decomposition theorem and we present applications to difference algebraic groups and the compatibility problem.
Particle-like structure of Lie algebras
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.
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.
The Centroid of a Lie Triple Algebra
Directory of Open Access Journals (Sweden)
Xiaohong Liu
2013-01-01
Full Text Available General results on the centroids of Lie triple algebras are developed. Centroids of the tensor product of a Lie triple algebra and a unitary commutative associative algebra are studied. Furthermore, the centroid of the tensor product of a simple Lie triple algebra and a polynomial ring is completely determined.
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 ...
HERSCHEL MEASUREMENTS OF MOLECULAR OXYGEN IN ORION
International Nuclear Information System (INIS)
Goldsmith, Paul F.; Chen, Jo-Hsin; Li Di; Liseau, Rene; Black, John H.; Bell, Tom A.; Hollenbach, David; Kaufman, Michael J.; Lis, Dariusz C.; Melnick, Gary; Neufeld, David; Pagani, Laurent; Encrenaz, Pierre; Snell, Ronald; Benz, Arnold O.; Bruderer, Simon; Bergin, Edwin; Caselli, Paola; Caux, Emmanuel; Falgarone, Edith
2011-01-01
We report observations of three rotational transitions of molecular oxygen (O 2 ) in emission from the H 2 Peak 1 position of vibrationally excited molecular hydrogen in Orion. We observed the 487 GHz, 774 GHz, and 1121 GHz lines using the Heterodyne Instrument for the Far Infrared on the Herschel Space Observatory, having velocities of 11 km s -1 to 12 km s -1 and widths of 3 km s -1 . The beam-averaged column density is N(O 2 ) = 6.5 x 10 16 cm -2 , and assuming that the source has an equal beam-filling factor for all transitions (beam widths 44, 28, and 19''), the relative line intensities imply a kinetic temperature between 65 K and 120 K. The fractional abundance of O 2 relative to H 2 is (0.3-7.3) x 10 -6 . The unusual velocity suggests an association with a ∼5'' diameter source, denoted Peak A, the Western Clump, or MF4. The mass of this source is ∼10 M sun and the dust temperature is ≥150 K. Our preferred explanation of the enhanced O 2 abundance is that dust grains in this region are sufficiently warm (T ≥ 100 K) to desorb water ice and thus keep a significant fraction of elemental oxygen in the gas phase, with a significant fraction as O 2 . For this small source, the line ratios require a temperature ≥180 K. The inferred O 2 column density ≅5 x 10 18 cm -2 can be produced in Peak A, having N(H 2 ) ≅ 4 x 10 24 cm -2 . An alternative mechanism is a low-velocity (10-15 km s -1 ) C-shock, which can produce N(O 2 ) up to 10 17 cm -2 .
Orion Absolute Navigation System Progress and Challenge
Holt, Greg N.; D'Souza, Christopher
2012-01-01
The absolute navigation design of NASA's Orion vehicle is described. It 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 onboard measurements in a Near-Earth or Mid-Earth environment consist of GPS pseudo-range and delta-range, 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, and cold start are discussed as are strategies for whole and partial state updates as well as covariance considerations. Strategies are given for dealing with latent measurements and high-rate propagation using multi-rate architecture. The details of the rate groups and the data ow between the elements is discussed and evaluated.
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....
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)
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.)
Pre-Algebra Essentials For Dummies
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
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
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
Orion: a glimpse of hope in life span extension?
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)).
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
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.
ORION - Crew Module Side Hatch: Proof Pressure Test Anomaly Investigation
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.
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...
A non-equilibrium ortho-to-para ratio of water in the Orion PDR
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
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
Connections between algebra, combinatorics, and geometry
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...
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
Representations of fundamental groups of algebraic varieties
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.
Asymptotic aspect of derivations in Banach algebras
Directory of Open Access Journals (Sweden)
Jaiok Roh
2017-02-01
Full Text Available Abstract We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.
Pure homology of algebraic varieties
Weber, Andrzej
2003-01-01
We show that for a complete complex algebraic variety the pure component of homology coincides with the image of intersection homology. Therefore pure homology is topologically invariant. To obtain slightly more general results we introduce "image homology" for noncomplete varieties.
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
Classical theory of algebraic numbers
Ribenboim, Paulo
2001-01-01
Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem These were the starting points for the theory of algebraic numbers, developed in the classical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many others This theory, enriched with more recent contributions, is of basic importance in the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptography This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples The Introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields Part One is devoted to residue classes and quadratic residues In Part Two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, iner...
The algebraic geometry of multimonopoles
International Nuclear Information System (INIS)
Nahm, W.
1982-11-01
Multimonopole solutions of the Bogomolny equation are treated by a transform to an ordinary differential equation. The solution of this equation yields algebraic curves and holomorphic line bundles over them. (orig.)
Algebraic study of chiral anomalies
Indian Academy of Sciences (India)
Chiral anomalies; gauge theories; bundles; connections; quantum ﬁeld ... The algebraic structure of chiral anomalies is made globally valid on non-trivial bundles by the introduction of a ﬁxed background connection. ... Current Issue : Vol.
Cartooning in Algebra and Calculus
Moseley, L. Jeneva
2014-01-01
This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.
Klumpp, A. R.; Lawson, C. L.
1988-01-01
Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.
Computational linear and commutative algebra
Kreuzer, Martin
2016-01-01
This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the Linear Algebra of the Third Millennium, developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems. This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is not available at all. The authors continue to prese...
Algebraic structure of chiral anomalies
International Nuclear Information System (INIS)
Stora, R.
1985-09-01
I will describe first the algebraic aspects of chiral anomalies, exercising however due care about the topological delicacies. I will illustrate the structure and methods in the context of gauge anomalies and will eventually make contact with results obtained from index theory. I will go into two sorts of generalizations: on the one hand, generalizing the algebraic set up yields e.g. gravitational and mixed gauge anomalies, supersymmetric gauge anomalies, anomalies in supergravity theories; on the other hand most constructions applied to the cohomologies which characterize anomalies easily extend to higher cohomologies. Section II is devoted to a description of the general set up as it applies to gauge anomalies. Section III deals with a number of algebraic set ups which characterize more general types of anomalies: gravitational and mixed gauge anomalies, supersymmetric gauge anomalies, anomalies in supergravity theories. It also includes brief remarks on σ models and a reminder on the full BRST algebra of quantized gauge theories
On the spatial distributions of dense cores in Orion B
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.
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)
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
Hopf algebras and topological recursion
International Nuclear Information System (INIS)
Esteves, João N
2015-01-01
We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293–309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347–452). (paper)
Nineteen papers on algebraic semigroups
Aizenshtat, A Ya; Podran, N E; Ponizovskii, IS; Shain, BM
1988-01-01
This volume contains papers selected by leading specialists in algebraic semigroups in the U.S., the United Kingdom, and Australia. Many of the papers strongly influenced the development of algebraic semigroups, but most were virtually unavailable outside the U.S.S.R. Written by some of the most prominent Soviet researchers in the field, the papers have a particular emphasis on semigroups of transformations. Boris Schein of the University of Arkansas is the translator.
Distribution theory of algebraic numbers
Yang, Chung-Chun
2008-01-01
The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions Algebraic numbers Algebraic geometry Height functions The abc-conjecture Roth''s theorem Subspace theorems Vojta''s conjectures L-functions.
Algebraic Systems and Pushdown Automata
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.
Hurlbert, Kathryn Miller
2009-01-01
In the 21st century, the National Aeronautics and Space Administration (NASA), the Russian Federal Space Agency, the National Space Agency of Ukraine, the China National Space Administration, and many other organizations representing spacefaring nations shall continue or newly implement robust space programs. Additionally, business corporations are pursuing commercialization of space for enabling space tourism and capital business ventures. Future space missions are likely to include orbiting satellites, orbiting platforms, space stations, interplanetary vehicles, planetary surface missions, and planetary research probes. Many of these missions will include humans to conduct research for scientific and terrestrial benefits and for space tourism, and this century will therefore establish a permanent human presence beyond Earth s confines. Other missions will not include humans, but will be autonomous (e.g., satellites, robotic exploration), and will also serve to support the goals of exploring space and providing benefits to Earth s populace. This section focuses on thermal management systems for human space exploration, although the guiding principles can be applied to unmanned space vehicles as well. All spacecraft require a thermal management system to maintain a tolerable thermal environment for the spacecraft crew and/or equipment. The requirements for human rating and the specified controlled temperature range (approximately 275 K - 310 K) for crewed spacecraft are unique, and key design criteria stem from overall vehicle and operational/programatic considerations. These criteria include high reliability, low mass, minimal power requirements, low development and operational costs, and high confidence for mission success and safety. This section describes the four major subsystems for crewed spacecraft thermal management systems, and design considerations for each. Additionally, some examples of specialized or advanced thermal system technologies are presented
Wörz-Busekros, Angelika
1980-01-01
The purpose of these notes is to give a rather complete presentation of the mathematical theory of algebras in genetics and to discuss in detail many applications to concrete genetic situations. Historically, the subject has its origin in several papers of Etherington in 1939- 1941. Fundamental contributions have been given by Schafer, Gonshor, Holgate, Reiers¢l, Heuch, and Abraham. At the moment there exist about forty papers in this field, one survey article by Monique Bertrand from 1966 based on four papers of Etherington, a paper by Schafer and Gonshor's first paper. Furthermore Ballonoff in the third section of his book "Genetics and Social Structure" has included four papers by Etherington and Reiers¢l's paper. Apparently a complete review, in par ticular one comprising more recent results was lacking, and it was difficult for students to enter this field of research. I started to write these notes in spring 1978. A first german version was finished at the end of that year. Further revision and tran...
Chirivì, Rocco; Dvornicich, Roberto
2017-01-01
Questo libro – primo di due volumi - presenta oltre 250 esercizi scelti di algebra ricavati dai compiti d'esame dei corsi di Aritmetica tenuti dagli autori all'Università di Pisa. Ogni esercizio viene presentato con una o più soluzioni accuratamente redatte con linguaggio e notazioni uniformi. Caratteristica distintiva del libro è che gli esercizi proposti sono tutti diversi uno dall'altro e le soluzioni richiedono sempre una piccola idea originale; ciò rende il libro unico nel genere. Gli argomenti di questo primo volume sono: principio d'induzione, combinatoria, congruenze, gruppi abeliani, anelli commutativi, polinomi, estensioni di campi, campi finiti. Il libro contiene inoltre una dettagliata sezione di richiami teorici e può essere usato come libro di riferimento per lo studio. Una serie di esercizi preliminari introduce le tecniche principali da usare per confrontarsi con i testi d'esame proposti. Il volume è rivolto a tutti gli studenti del primo anno dei corsi di laur ea in Matematica e Inf...
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.)
Approximation of complex algebraic numbers by algebraic numbers of bounded degree
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...
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...
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.)
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
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.
Homological methods, representation theory, and cluster algebras
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...
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
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
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.
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
ORION-the Omega Remote Interactive On-line System
Russell, R D; Levratt, B; Lipps, H; Sparrman, P
1974-01-01
ORION is a system which permits the manipulation of files, records and characters, remote job submittal and retrieval of output files including the direct loading of remote on-line computers. The system uses the computer hardware of the OMEGA project at CERN and is designed to assist researchers in development and debugging of their programs. (10 refs).
Protostar Evolution in the Orion Nebula Cluster (ONC)
Sanchez, Michael Allan
2018-01-01
We present our preliminary analysis of the protostars within the Orion Nebula Cluster (ONC). We developed a pipeline to identify protostars in the ONC using the IRAC instrument aboard Spitzer. We verified our photometric measurements with the catalog provided by Megeath et al. (2012). We then classified the protostar evolution stages (0/I, Flatt, II, and III) based on their spectral slope.
ORION - the OMEGA Remote Interactive On-line System
Russell, R D; Krieger, M
1973-01-01
ORION is a system which permits the manipulation of files, records and characters, remote job submittal and retrieval of output files including the direct loading of remote on-line computers. The system uses the computer hardware of the OMEGA project at CERN, and is designed to assist researchers in development and debugging of their programs.
C2H observations toward the Orion Bar
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
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...
Orion, a high efficiency 4π neutron detector
International Nuclear Information System (INIS)
Crema, E.; Piasecki, E.; Wang, X.M.; Doubre, H.; Galin, J.; Guerreau, D.; Pouthas, J.; Saint-Laurent, F.
1990-01-01
In intermediate energy heavy ion collisions the multiplicity of emitted neutrons is strongly connected to energy dissipation and to impact parameter. We present the 4π detector ORION, a high efficiency liquid scintillator detector which permits to get information on the multiplicity of neutrons measured event-wise and on the spatial distribution of these neutrons [fr
Apollo 16 Lunar Module 'Orion' at the Descartes landing site
1972-01-01
The Apollo 16 Lunar Module 'Orion' is part of the lunar scene at the Descartes landing site, as seen in the reproduction taken from a color television transmission made by the color TV camera mounted on the Lunar Roving Vehicle. Note the U.S. flag deployed on the left. This picture was made during the second Apollo 16 extravehicular activity (EVA-2).
Assessment of the Use of Nanofluids in Spacecraft Active Thermal Control Systems
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.
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....
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.
Principles of linear algebra with Mathematica
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,
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
Discrete event systems in dioid algebra and conventional algebra
Declerck, Philippe
2013-01-01
This book concerns the use of dioid algebra as (max, +) algebra to treat the synchronization of tasks expressed by the maximum of the ends of the tasks conditioning the beginning of another task - a criterion of linear programming. A classical example is the departure time of a train which should wait for the arrival of other trains in order to allow for the changeover of passengers.The content focuses on the modeling of a class of dynamic systems usually called "discrete event systems" where the timing of the events is crucial. Events are viewed as sudden changes in a process which i
Spacecraft exploration of asteroids
International Nuclear Information System (INIS)
Veverka, J.; Langevin, Y.; Farquhar, R.; Fulchignoni, M.
1989-01-01
After two decades of spacecraft exploration, we still await the first direct investigation of an asteroid. This paper describes how a growing international interest in the solar system's more primitive bodies should remedy this. Plans are under way in Europe for a dedicated asteroid mission (Vesta) which will include multiple flybys with in situ penetrator studies. Possible targets include 4 Vesta, 8 Flora and 46 Hestia; launch its scheduled for 1994 or 1996. In the United States, NASA plans include flybys of asteroids en route to outer solar system targets
Spacecraft rendezvous and docking
DEFF Research Database (Denmark)
Jørgensen, John Leif
1999-01-01
The phenomenons and problems encountered when a rendezvous manoeuvre, and possible docking, of two spacecrafts has to be performed, have been the topic for numerous studies, and, details of a variety of scenarios has been analysed. So far, all solutions that has been brought into realization has...... been based entirely on direct human supervision and control. This paper describes a vision-based system and methodology, that autonomously generates accurate guidance information that may assist a human operator in performing the tasks associated with both the rendezvous and docking navigation...
Fogel, L. J.; Calabrese, P. G.; Walsh, M. J.; Owens, A. J.
1982-01-01
Ways in which autonomous behavior of spacecraft can be extended to treat situations wherein a closed loop control by a human may not be appropriate or even possible are explored. Predictive models that minimize mean least squared error and arbitrary cost functions are discussed. A methodology for extracting cyclic components for an arbitrary environment with respect to usual and arbitrary criteria is developed. An approach to prediction and control based on evolutionary programming is outlined. A computer program capable of predicting time series is presented. A design of a control system for a robotic dense with partially unknown physical properties is presented.
Endomorphisms of the Cuntz algebras
DEFF Research Database (Denmark)
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
This mainly expository article is devoted to recent advances in the study of dynamical aspects of the Cuntz algebras O_n, n
Quantum algebras in nuclear structure
International Nuclear Information System (INIS)
Bonatsos, D.; Daskaloyannis, C.
1995-01-01
Quantum algebras is a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction through the necessary mathematical tools (q-numbers, q-analysis, q-oscillators, q-algebras), the su q (2) rotator model and its extensions, the construction of deformed exactly soluble models (Interacting Boson Model, Moszkowski model), the use of deformed bosons in the description of pairing correlations, and the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies, which underline the structure of superdeformed and hyperdeformed nuclei are discussed in some details. A brief description of similar applications to molecular structure and an outlook are also given. (author) 2 Tabs., 324 Refs
Clifford Algebras and magnetic monopoles
International Nuclear Information System (INIS)
Recami, E.
1987-01-01
It is known that the introduction of magnetic monopolies in electromagnetism does still present formal problems from the point of view of classical field theory. The author attempts to overcome at least some of them by making recourse to the Clifford Algebra formalism. In fact, while the events of a two-dimensional Minkowski space-time M(1,1) are sufficiently well represented by ordinary Complex Numbers, when dealing with the events of the four-dimensional Minkowski space M(1,3)identical to M/sub 4/ one has of course to look for hypercomplex numbers or, more generally, for the elements of a Clifford Algebra. The author uses the Clifford Algebras in terms of ''multivectors'', and in particular by Hestenes' language, which suits space-time quite well. He recalls that the Clifford product chiγ is the sum of the internal product chi . γ and of the wedge product chiΛγ
Zorn algebra in general relativity
International Nuclear Information System (INIS)
Oliveira, C.G.; Maia, M.D.
The covariant differential properties of the split Cayley subalgebra of local real quaternion tetrads is considered. Referred to this local quaternion tetrad several geometrical objects are given in terms of Zorn-Weyl matrices. Associated to a pair of real null vectors we define two-component spinor fields over the curved space and the associated Zorn-Weyl matrices which satisfy the Dirac equation written in terms of the Zorn algebra. The formalism is generalized by considering a field of complex tetrads defining a Hermitian second rank tensor. The real part of this tensor describes the gravitational potentials and the imaginary part the electromagnetic potentials in the Lorentz gauge. The motion of a charged spin zero test body is considered. The Zorn-Weyl algebra associated to this generalized formalism has elements belonging to the full octonion algebra [pt
Topics in quaternion linear algebra
Rodman, Leiba
2014-01-01
Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses...
Algebraic geometry and effective lagrangians
International Nuclear Information System (INIS)
Martinec, E.J.; Chicago Univ., IL
1989-01-01
N=2 supersymmetric Landau-Ginsburg fixed points describe nonlinear models whose target spaces are algebraic varieties in certain generalized projective spaces; the defining equation is precisely the zero set of the superpotential, considered as a condition in the projective space. The ADE classification of modular invariants arises as the classification of projective descriptions of P 1 ; in general, the hierarchy of fixed points is conjectured to be isomorphic to the classification of quasihomogeneous singularities. The condition of vanishing first Chern class is an integrality condition on the Virasoro central charge; the central charge is determined by the superpotential. The operator algebra is given by the algebra of Wick contractions of perturbations of the superpotential. (orig.)
Dynamical systems of algebraic origin
Schmidt, Klaus
1995-01-01
Although much of classical ergodic theory is concerned with single transformations and one-parameter flows, the subject inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multidimensional symmetry groups. However, the wealth of concrete and natural examples which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. The purpose of this book is to help remedy this scarcity of explicit examples by introducing a class of continuous Zd-actions diverse enough to exhibit many of the new phenomena encountered in the transition from Z to Zd, but which nevertheless lends itself to systematic study: the Zd-actions by automorphisms of compact, abelian groups. One aspect of these actions, not surprising in itself but quite striking in its extent and depth nonetheless, is the connection with commutative algebra and arithmetical algebraic geometry. The algebraic framework resulting...
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
Neutrosophic filters in BE-algebras
Directory of Open Access Journals (Sweden)
Akbar Rezaei
2015-12-01
Full Text Available Inthispaper, weintroducethenotionof(implicativeneutrosophicfilters in BE-algebras. The relation between implicative neutrosophic filters and neutrosophic filters is investigated and we show that in self distributive BE-algebras these notions are equivalent.
Hopf algebra structures in particle physics
International Nuclear Information System (INIS)
Weinzierl, Stefan
2004-01-01
In the recent years, Hopf algebras have been introduced to describe certain combinatorial properties of quantum field theories. I give a basic introduction to these algebras and review some occurrences in particle physics. (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
Computer Algebra Systems in Undergraduate Instruction.
Small, Don; And Others
1986-01-01
Computer algebra systems (such as MACSYMA and muMath) can carry out many of the operations of calculus, linear algebra, and differential equations. Use of them with sketching graphs of rational functions and with other topics is discussed. (MNS)
Quantum Groupoids Acting on Semiprime Algebras
Directory of Open Access Journals (Sweden)
Inês Borges
2011-01-01
Full Text Available Following Linchenko and Montgomery's arguments we show that the smash product of an involutive weak Hopf algebra and a semiprime module algebra, satisfying a polynomial identity, is semiprime.
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)
Equationally Noetherian property of Ershov algebras
Dvorzhetskiy, Yuriy
2014-01-01
This article is about equationally Noetherian and weak equationally Noetherian property of Ershov algebras. Here we show two canonical forms of the system of equations over Ershov algebras and two criteria of equationally Noetherian and weak equationally Noetherian properties.
Generalized Galilean algebras and Newtonian gravity
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.
Current algebra, baryons and quark confinement
International Nuclear Information System (INIS)
Witten, E.
1983-01-01
It is shown that ordinary baryons can be understood as solitons in current algebra effective lagrangiangs. The formation of color flux tubes can also be seen in current algebra, under certain conditions. (orig.)
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
Colored Quantum Algebra and Its Bethe State
International Nuclear Information System (INIS)
Wang Jin-Zheng; Jia Xiao-Yu; Wang Shi-Kun
2014-01-01
We investigate the colored Yang—Baxter equation. Based on a trigonometric solution of colored Yang—Baxter equation, we construct a colored quantum algebra. Moreover we discuss its algebraic Bethe ansatz state and highest wight representation. (general)
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
Applied matrix algebra in the statistical sciences
Basilevsky, Alexander
2005-01-01
This comprehensive text offers teachings relevant to both applied and theoretical branches of matrix algebra and provides a bridge between linear algebra and statistical models. Appropriate for advanced undergraduate and graduate students. 1983 edition.
Indian Academy of Sciences (India)
Abstract. Order unit property of a positive element in a *-algebra is defined. It is proved that precisely projections satisfy this order theoretic property. This way, unital hereditary *-subalgebras of a *-algebra are characterized.
On extensions of superconformal algebras
International Nuclear Information System (INIS)
Nagi, Jasbir
2005-01-01
Starting from vector fields that preserve a differential form on a Riemann sphere with Grassmann variables, one can construct a superconformal algebra by considering central extensions of the algebra of vector fields. In this paper, the N=4 case is analyzed closely, where the presence of weight zero operators in the field theory forces the introduction of noncentral extensions. How this modifies the existing field theory, representation theory, and Gelfand-Fuchs constructions is discussed. It is also discussed how graded Riemann sphere geometry can be used to give a geometrical description of the central charge in the N=1 theory
Computational triadic algebras of signs
Energy Technology Data Exchange (ETDEWEB)
Zadrozny, W. [T.J. Watson Research Center, Yorktown Heights, NY (United States)
1996-12-31
We present a finite model of Peirce`s ten classes of signs. We briefly describe Peirce`s taxonomy of signs; we prove that any finite collection of signs can be extended to a finite algebra of signs in which all interpretants are themselves being interpreted; and we argue that Peirce`s ten classes of signs can be defined using constraints on algebras of signs. The paper opens the possibility of defining multimodal cognitive agents using Peirce`s classes of signs, and is a first step towards building a computational logic of signs based on Peirce`s taxonomies.
Surface defects and chiral algebras
Energy Technology Data Exchange (ETDEWEB)
Córdova, Clay [School of Natural Sciences, Institute for Advanced Study,1 Einstein Dr, Princeton, NJ 08540 (United States); Gaiotto, Davide [Perimeter Institute for Theoretical Physics,31 Caroline St N, Waterloo, ON N2L 2Y5 (Canada); Shao, Shu-Heng [School of Natural Sciences, Institute for Advanced Study,1 Einstein Dr, Princeton, NJ 08540 (United States)
2017-05-26
We investigate superconformal surface defects in four-dimensional N=2 superconformal theories. Each such defect gives rise to a module of the associated chiral algebra and the surface defect Schur index is the character of this module. Various natural chiral algebra operations such as Drinfeld-Sokolov reduction and spectral flow can be interpreted as constructions involving four-dimensional surface defects. We compute the index of these defects in the free hypermultiplet theory and Argyres-Douglas theories, using both infrared techniques involving BPS states, as well as renormalization group flows onto Higgs branches. In each case we find perfect agreement with the predicted characters.
Fusion algebra and fusing matrices
International Nuclear Information System (INIS)
Gao Yihong; Li Miao; Yu Ming.
1989-09-01
We show that the Wilson line operators in topological field theories form a fusion algebra. In general, the fusion algebra is a relation among the fusing (F) matrices. In the case of the SU(2) WZW model, some special F matrix elements are found in this way, and the remaining F matrix elements are then determined up to a sign. In addition, the S(j) modular transformation of the one point blocks on the torus is worked out. Our results are found to agree with those obtained from the quantum group method. (author). 24 refs
Automorphisms of the Cuntz algebras
DEFF Research Database (Denmark)
Conti, Roberto; Szymanski, Wojciech
2011-01-01
We survey recent results on endomorphisms and especially on automorphisms of the Cuntz algebras, with a special emphasis on the structure of the Weyl group. We discuss endomorphisms globally preserving the diagonal MASA and their corresponding actions. In particular, we investigate those endomorp......We survey recent results on endomorphisms and especially on automorphisms of the Cuntz algebras, with a special emphasis on the structure of the Weyl group. We discuss endomorphisms globally preserving the diagonal MASA and their corresponding actions. In particular, we investigate those...
Tracing a planar algebraic curve
International Nuclear Information System (INIS)
Chen Falai; Kozak, J.
1994-09-01
In this paper, an algorithm that determines a real algebraic curve is outlined. Its basic step is to divide the plane into subdomains that include only simple branches of the algebraic curve without singular points. Each of the branches is then stably and efficiently traced in the particular subdomain. Except for the tracing, the algorithm requires only a couple of simple operations on polynomials that can be carried out exactly if the coefficients are rational, and the determination of zeros of several polynomials of one variable. (author). 5 refs, 4 figs
Introduction to computational linear algebra
Nassif, Nabil; Erhel, Jocelyne
2015-01-01
Introduction to Computational Linear Algebra introduces the reader with a background in basic mathematics and computer programming to the fundamentals of dense and sparse matrix computations with illustrating examples. The textbook is a synthesis of conceptual and practical topics in ""Matrix Computations."" The book's learning outcomes are twofold: to understand state-of-the-art computational tools to solve matrix computations problems (BLAS primitives, MATLAB® programming) as well as essential mathematical concepts needed to master the topics of numerical linear algebra. It is suitable for s
Invariants of generalized Lie algebras
International Nuclear Information System (INIS)
Agrawala, V.K.
1981-01-01
Invariants and invariant multilinear forms are defined for generalized Lie algebras with arbitrary grading and commutation factor. Explicit constructions of invariants and vector operators are given by contracting invariant forms with basic elements of the generalized Lie algebra. The use of the matrix of a linear map between graded vector spaces is emphasized. With the help of this matrix, the concept of graded trace of a linear operator is introduced, which is a rich source of multilinear forms of degree zero. To illustrate the use of invariants, a characteristic identity similar to that of Green is derived and a few Racah coefficients are evaluated in terms of invariants
Regular algebra and finite machines
Conway, John Horton
2012-01-01
World-famous mathematician John H. Conway based this classic text on a 1966 course he taught at Cambridge University. Geared toward graduate students of mathematics, it will also prove a valuable guide to researchers and professional mathematicians.His topics cover Moore's theory of experiments, Kleene's theory of regular events and expressions, Kleene algebras, the differential calculus of events, factors and the factor matrix, and the theory of operators. Additional subjects include event classes and operator classes, some regulator algebras, context-free languages, communicative regular alg
Algebraic geometry and theta functions
Coble, Arthur B
1929-01-01
This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and