Varieties Generated by Standard BL-algebras
Czech Academy of Sciences Publication Activity Database
Haniková, Zuzana
2014-01-01
Roč. 31, č. 1 (2014), s. 15-33 ISSN 0167-8094 R&D Projects: GA ČR GAP202/10/1826 Institutional research plan: CEZ:AV0Z10300504 Institutional support: RVO:67985807 Keywords : substructural logic * fuzzy logic * BL * standard BL-algebra * variety of algebras Subject RIV: BA - General Mathematics Impact factor: 0.621, year: 2014
Implementing the Standards: Teaching Informal Algebra.
Schultz, James E.
1991-01-01
Presents suggestions for developing algebraic concepts beginning in the early grades to develop a gradual building from informal to formal algebraic concepts that progresses over the K-12 curriculum. Includes suggestions for representing relationships, solving equations, employing meaningful applications of algebra, and using of technology. (MDH)
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
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
DOE Standard: Fire protection design criteria
Energy Technology Data Exchange (ETDEWEB)
1999-07-01
The development of this Standard reflects the fact that national consensus standards and other design criteria do not comprehensively or, in some cases, adequately address fire protection issues at DOE facilities. This Standard provides supplemental fire protection guidance applicable to the design and construction of DOE facilities and site features (such as water distribution systems) that are also provided for fire protection. It is intended to be used in conjunction with the applicable building code, National Fire Protection Association (NFPA) Codes and Standards, and any other applicable DOE construction criteria. This Standard replaces certain mandatory fire protection requirements that were formerly in DOE 5480.7A, ``Fire Protection``, and DOE 6430.1A, ``General Design Criteria``. It also contains the fire protection guidelines from two (now canceled) draft standards: ``Glove Box Fire Protection`` and ``Filter Plenum Fire Protection``. (Note: This Standard does not supersede the requirements of DOE 5480.7A and DOE 6430.1A where these DOE Orders are currently applicable under existing contracts.) This Standard, along with the criteria delineated in Section 3, constitutes the basic criteria for satisfying DOE fire and life safety objectives for the design and construction or renovation of DOE facilities.
DOE Standard: Fire protection design criteria
International Nuclear Information System (INIS)
1999-07-01
The development of this Standard reflects the fact that national consensus standards and other design criteria do not comprehensively or, in some cases, adequately address fire protection issues at DOE facilities. This Standard provides supplemental fire protection guidance applicable to the design and construction of DOE facilities and site features (such as water distribution systems) that are also provided for fire protection. It is intended to be used in conjunction with the applicable building code, National Fire Protection Association (NFPA) Codes and Standards, and any other applicable DOE construction criteria. This Standard replaces certain mandatory fire protection requirements that were formerly in DOE 5480.7A, ''Fire Protection'', and DOE 6430.1A, ''General Design Criteria''. It also contains the fire protection guidelines from two (now canceled) draft standards: ''Glove Box Fire Protection'' and ''Filter Plenum Fire Protection''. (Note: This Standard does not supersede the requirements of DOE 5480.7A and DOE 6430.1A where these DOE Orders are currently applicable under existing contracts.) This Standard, along with the criteria delineated in Section 3, constitutes the basic criteria for satisfying DOE fire and life safety objectives for the design and construction or renovation of DOE facilities
Nonreactor nuclear facilities: Standards and criteria guide
International Nuclear Information System (INIS)
Brynda, W.J.; Scarlett, C.H.; Tanguay, G.E.; Lobner, P.R.
1986-09-01
This guide is a source document that identifies standards, codes, and guides that address the nuclear safety considerations pertinent to nuclear facilities as defined in DOE 5480.1A, Chapter V, ''Safety of Nuclear Facilities.'' The guidance and criteria provided is directed toward areas of safety usually addressed in a Safety Analysis Report. The areas of safety include, but are not limited to, siting, principal design criteria and safety system design guidelines, radiation protection, accident analysis, conduct of operations, and quality assurance. The guide is divided into two sections: general guidelines and appendices. Those guidelines that are broadly applicable to most nuclear facilities are presented in the general guidelines. Guidelines specific to the various types or categories of nuclear facilities are presented in the appendices. These facility-specific appendices provide guidelines and identify standards and criteria that should be considered in addition to, or in lieu of, the general guidelines. 25 figs., 62 tabs
Nonreactor nuclear facilities: standards and criteria guide
International Nuclear Information System (INIS)
Brynda, W.J.; Junker, L.; Karol, R.C.; Lobner, P.R.; Goldman, L.A.
1981-09-01
This guide is a source document that identifies standards, codes, and guides that address the nuclear safety considerations pertinent to nuclear facilities as defined in DOE Order 5480.1, Chapter V, Safety of Nuclear Facilities. The guidance and criteria provided are directed toward areas of safety usually addressed in a Safety Analysis Report. The areas of safety include, but are not limited to, siting, principal design criteria and safety system design guidelines, radiation protection, accident analysis, and quality assurance. The guide is divided into two sections: general guidelines and appendices. Those guidelines that are broadly applicable to most nuclear facilities are presented in the general guidelines. These general guidelines may have limited applicability to subsurface facilities such as waste repositories. Guidelines specific to the various types or categories of nuclear facilities are presented in the appendices. These facility-specific appendices provide guidelines and identify standards and criteria that should be considered in addition to, or in lieu of, the general guidelines
A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers
Czech Academy of Sciences Publication Activity Database
Jiránek, P.; Strakoš, Zdeněk; Vohralík, M.
2010-01-01
Roč. 32, č. 3 (2010), s. 1567-1590 ISSN 1064-8275 R&D Projects: GA AV ČR IAA100300802 Grant - others:GA ČR(CZ) GP201/09/P464 Institutional research plan: CEZ:AV0Z10300504 Keywords : second-order elliptic partial differential equation * finite volume method * a posteriori error estimates * iterative methods for linear algebraic systems * conjugate gradient method * stopping criteria Subject RIV: BA - General Mathematics Impact factor: 3.016, year: 2010
Aerosol exposure: Concepts, criteria, standards and applications
International Nuclear Information System (INIS)
Vincent, James H
2009-01-01
This paper places Inhaled Particles X in the context of the whole sequence of such symposia, going back to the first one in 1961. It draws together some of the essential principles that have been learned since that earlier meeting about the nature of exposure and exposure assessment and thus provides a framework by which to integrate the new knowledge presented at this latest one. In the process, the importance of understanding the formal definition of aerosol exposure is stressed, including the distinction between exposure intensity and exposure history, and how that relates to some measure of cumulative dose which, in turn, may be linked with knowledge about intrinsic toxicity, etc. This then leads to a definition of exposure standards, and the important ingredients of criteria, sampling and limit values. A summary is provided of the current set of particle size-selective criteria that have been widely agreed in the international occupational and environmental health community. Some ideas are presented about how this set might be expanded for certain applications, the important case of ultrafine aerosols being one of them.
Combinatorics of transformations from standard to non-standard bases in Brauer algebras
International Nuclear Information System (INIS)
Chilla, Vincenzo
2007-01-01
Transformation coefficients between standard bases for irreducible representations of the Brauer centralizer algebra B f (x) and split bases adapted to the B f 1 (x) x B f 2 (x) subset of B f (x) subalgebra (f 1 + f 2 = f) are considered. After providing the suitable combinatorial background, based on the definition of the i-coupling relation on nodes of the subduction grid, we introduce a generalized version of the subduction graph which extends the one given in Chilla (2006 J. Phys. A: Math. Gen. 39 7657) for symmetric groups. Thus, we can describe the structure of the subduction system arising from the linear method and give an outline of the form of the solution space. An ordering relation on the grid is also given and then, as in the case of symmetric groups, the choices of the phases and of the free factors governing the multiplicity separations are discussed
Warner, Seth
1990-01-01
Standard text provides an exceptionally comprehensive treatment of every aspect of modern algebra. Explores algebraic structures, rings and fields, vector spaces, polynomials, linear operators, much more. Over 1,300 exercises. 1965 edition.
Distinguishing Standard SBL-algebras with Involutive Negations by Propositional Formulas
Czech Academy of Sciences Publication Activity Database
Haniková, Zuzana; Savický, Petr
2008-01-01
Roč. 54, č. 6 (2008), s. 579-596 ISSN 0942-5616 R&D Projects: GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10300504 Keywords : fuzzy logic * strict basic logic * continuous t-norm * standard SBL-algebra * involutive negation Subject RIV: BA - General Mathematics Impact factor: 0.459, year: 2008
Comparison of Araoye's criteria with standard electrocardiographic ...
African Journals Online (AJOL)
Background: Left ventricular hypertrophy (LVH) is a major risk factor for cardiovascular morbidity and mortality. Various electrocardiographic (ECG) criteria for LHV give poorer performance in black subjects when compared with white subjects. Araoye proposed a code system for improved ECG diagnosis of LVH in blacks.
New applications of graded Lie algebras to Lie algebras, generalized Lie algebras and cohomology
Pinczon, Georges; Ushirobira, Rosane
2005-01-01
We give new applications of graded Lie algebras to: identities of standard polynomials, deformation theory of quadratic Lie algebras, cyclic cohomology of quadratic Lie algebras, $2k$-Lie algebras, generalized Poisson brackets and so on.
Safety Criteria and Standards for Bearing Capacity of Foundation
Directory of Open Access Journals (Sweden)
Yanlong Li
2017-01-01
Full Text Available This paper focuses on the evaluation standards of factor of safety for foundation stability analysis. The problem of foundation stability is analyzed via the methods of risk analysis of engineering structures and reliability-based design, and the factor of safety for foundation stability is determined by using bearing capacity safety-factor method (BSFM and strength safety-factor method (SSFM. Based on a typical example, the admissible factors of safety were calibrated with a target reliability index specified in relevant standards. Two safety criteria and their standards of bearing capacity of foundation for these two methods (BSFM and SSFM were established. The universality of the safety criteria and their standards for foundation reliability was verified based on the concept of the ratio of safety margin (RSM.
Criteria and standards for radiation therapy (megavoltage) in southeastern Michigan
International Nuclear Information System (INIS)
1979-01-01
The criteria and standards presented in this document provide the basis for the review of proposals to establish, expand or alter institutionally-based radiation therapy services, the criteria developed should provide sufficient guidance to the Plan Implementation Committee of CHPC-SEM to enable it to accomplish the following: Assure the existence of sufficient treatment capacity to serve the identified radiation therapy needs of the Southeastern Michigan community; Assure the residents of Southeastern Michigan of reasonable access to radiation therapy services; Assure that the radiation therapy services offered are of good quality; Avoid unnecessary and wasteful duplication of radiation therapy equipment and services; and promote the effective operation of the health care system in Southeastern Michigan. These criteria and standards also should provide guidance to providers who may consider initiating a new radiation therapy service or altering an existing service or program
Standardization of growth and fermentation criteria of Lasiodiplodia ...
African Journals Online (AJOL)
Standardization of growth and fermentation criteria of Lasiodiplodia theobromae for production of jasmonic acid. PC Dhandhukia, VR Thakkar. Abstract. Aim of the study was to examine the enhanced growth supporting conditions and production of jasmonic acid (JA) by Lasiodiplodia theobromae in liquid cultures.
On criteria for examining analysis quality with standard reference material
International Nuclear Information System (INIS)
Yang Huating
1997-01-01
The advantages and disadvantages and applicability of some criteria for examining analysis quality with standard reference material are discussed. The combination of the uncertainties of the instrument examined and the reference material should be determined on the basis of specific situations. Without the data of the instrument's uncertainty, it would be applicable to substitute the standard deviation multiplied by certain times for the uncertainty. The result of the examining should not result in more error reported in routine measurements than it really is. Over strict examining should also be avoided
Standard guide for design criteria for plutonium gloveboxes
American Society for Testing and Materials. Philadelphia
2009-01-01
1.1 This guide defines criteria for the design of glovebox systems to be used for the handling of plutonium in any chemical or physical form or isotopic composition or when mixed with other elements or compounds. Not included in the criteria are systems auxiliary to the glovebox systems such as utilities, ventilation, alarm, and waste disposal. Also not addressed are hot cells or open-face hoods. The scope of this guide excludes specific license requirements relating to provisions for criticality prevention, hazards control, safeguards, packaging, and material handling. Observance of this guide does not relieve the user of the obligation to conform to all federal, state, and local regulations for design and construction of glovebox systems. 1.2 The values stated in SI units are to be regarded as the standard. The values given in parentheses are for information only. 1.3 This standard does not purport to address all of the safety problems, if any, associated with its use. It is the responsibility of the user...
DEFF Research Database (Denmark)
Anton, Karin; Vestergaard, Inge
2013-01-01
The analysis shows differences in definition of apssive house criterias. It also communicates issues os the passive house concept that are nor completely transferred by the Norwegian passive house standard.......The analysis shows differences in definition of apssive house criterias. It also communicates issues os the passive house concept that are nor completely transferred by the Norwegian passive house standard....
Algebraic partial Boolean algebras
Smith, D
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...
78 FR 38735 - Autopsy Performance Criteria: Standards, Guidelines and Best Practices
2013-06-27
... DEPARTMENT OF JUSTICE Office of Justice Programs [OJP (NIJ) Docket No. 1626] Autopsy Performance Criteria: Standards, Guidelines and Best Practices AGENCY: National Institute of Justice, DOJ. ACTION... entitled, ``Autopsy Performance Criteria: Standards, Guidelines and Best Practices''. The opportunity to...
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
29 CFR 1630.10 - Qualification standards, tests, and other selection criteria.
2010-07-01
... DISABILITIES ACT § 1630.10 Qualification standards, tests, and other selection criteria. It is unlawful for a covered entity to use qualification standards, employment tests or other selection criteria that screen..., on the basis of disability, unless the standard, test or other selection criteria, as used by the...
Samuel V. Glass; Stanley D. Gatland II; Kohta Ueno; Christopher J. Schumacher
2017-01-01
ASHRAE Standard 160, Criteria for Moisture-Control Design Analysis in Buildings, was published in 2009. The standard sets criteria for moisture design loads, hygrothermal analysis methods, and satisfactory moisture performance of the building envelope. One of the evaluation criteria specifies conditions necessary to avoid mold growth. The current standard requires that...
29 CFR 1630.7 - Standards, criteria, or methods of administration.
2010-07-01
... Standards, criteria, or methods of administration. It is unlawful for a covered entity to use standards, criteria, or methods of administration, which are not job-related and consistent with business necessity... 29 Labor 4 2010-07-01 2010-07-01 false Standards, criteria, or methods of administration. 1630.7...
Algebraic partial Boolean algebras
Smith, Derek
2003-04-01
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 Script 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 A5 sublattice. Finally, we characterize the rays of B(T) when T consists of the rays spanning the minimal vectors of the root lattice E8.
Algebraic partial Boolean algebras
Energy Technology Data Exchange (ETDEWEB)
Smith, Derek [Math Department, Lafayette College, Easton, PA 18042 (United States)
2003-04-04
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{sub 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{sub 8}.
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
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.
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.
Beilinson, Alexander
2004-01-01
Chiral algebras form the primary algebraic structure of modern conformal field theory. Each chiral algebra lives on an algebraic curve, and in the special case where this curve is the affine line, chiral algebras invariant under translations are the same as well-known and widely used vertex algebras. The exposition of this book covers the following topics: the "classical" counterpart of the theory, which is an algebraic theory of non-linear differential equations and their symmetries; the local aspects of the theory of chiral algebras, including the study of some basic examples, such as the ch
Common Risk Criteria Standards for National Test Ranges
2016-08-01
someone acted with negligence. The reasonable person acts sensibly, does things without serious delay, and takes proper but not excessive precautions...provides a common set of range safety policies, risk criteria, and guidelines for managing risk to people and assets during manned and unmanned...involuntary acceptance) and mission-essential personnel (MEP) (voluntary acceptance), excluding people in the launch or reentry vehicle; b. Debris injury
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…
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......_E of C*(E). Our results pertain both automorphisms and proper endomorphisms. Firstly, the Weyl group and the restricted Weyl group of a graph C*-algebra are introduced and investigated. In particular, criteria of outerness for automorphisms in the restricted Weyl group are found. We also show...
[Measurement of CO diffusion capacity (II): Standardization and quality criteria].
Salcedo Posadas, A; Villa Asensi, J R; de Mir Messa, I; Sardón Prado, O; Larramona, H
2015-08-01
The diffusion capacity is the technique that measures the ability of the respiratory system for gas exchange, thus allowing a diagnosis of the malfunction of the alveolar-capillary unit. The most important parameter to assess is the CO diffusion capacity (DLCO). New methods are currently being used to measure the diffusion using nitric oxide (NO). There are other methods for measuring diffusion, although in this article the single breath technique is mainly referred to, as it is the most widely used and best standardized. Its complexity, its reference equations, differences in equipment, inter-patient variability and conditions in which the DLCO is performed, lead to a wide inter-laboratory variability, although its standardization makes this a more reliable and reproductive method. The practical aspects of the technique are analyzed, by specifying the recommendations to carry out a suitable procedure, the calibration routine, calculations and adjustments. Clinical applications are also discussed. An increase in the transfer of CO occurs in diseases in which there is an increased volume of blood in the pulmonary capillaries, such as in the polycythemia and pulmonary hemorrhage. There is a decrease in DLCO in patients with alveolar volume reduction or diffusion defects, either by altered alveolar-capillary membrane (interstitial diseases) or decreased volume of blood in the pulmonary capillaries (pulmonary embolism or primary pulmonary hypertension). Other causes of decreased or increased DLCO are also highlighted. Copyright © 2014 Asociación Española de Pediatría. Published by Elsevier España, S.L.U. All rights reserved.
Sierra, Juan C; Buela-Casal, Gualberto; Bermúdez, María P; Santos-Iglesias, Pablo
2009-02-01
Sex differences in criteria and standards of scientific and teaching productivity of Spanish teaching staff. The aim of this study is to analyze differences in university teachers' opinion about the criteria and standards of scientific and teaching productivity, as well as the minimum number of criteria to be accredited as an Associate Professor or Professor. For this purpose, two representative samples of Spanish university teachers (97% interval confidence and 3% estimation error) were polled. These samples were made up of 960 male and 329 female university teachers. Results show that there are important gender differences. Females show a higher level of demand to achieve accreditation than do males. Thus, females are more demanding in more than 43% of the criteria to be accredited as an Associate Professor and in 54% of the criteria to be accredited as a Professor, compared to males. On the contrary, males only score higher than females in one of the criteria (articles published in the Journal Citation Reports).
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...
2013-04-04
... Water Quality Standards; Withdrawal of Certain Federal Water Quality Criteria Applicable to California... aquatic life water quality criteria applicable to waters of New Jersey, Puerto Rico, and California's San Francisco Bay. In 1992, EPA promulgated the National Toxics Rule or NTR to establish numeric water quality...
2011-08-03
...] Medicare Program; Evaluation Criteria and Standards for Quality Improvement Program Contracts (10th... evaluate the effectiveness and efficiency of Quality Improvement Organizations (QIOs) that will enter into... and efficient performance of contract obligations by the Quality Improvement Organizations (QIOs), and...
Development of criteria and standards for management of low-level radioactive waste
International Nuclear Information System (INIS)
Grey, A.E.; Falconer, K.L.
1980-08-01
The basic need for criteria and standards for radioactive waste management is to ensure compliance with Federal and State regulations applicable to this activity. In addition, criteria and standards can establish the parameters by which a radioactive waste disposal site is selected, the form in which the waste is to be disposed, how a disposal site is to be operated, and how that site is to be closed when it reaches the end of its useful life. For developing criteria and standards, this report discusses the nature of low-level radioactive waste and the role government agencies play in regulating its management. It describes subject areas for which criteria and standards could be developed, current and evolving requirements, and future suggested analyses
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.
Planar algebra of the subgroup-subfactor
Indian Academy of Sciences (India)
G in terms of operator matrices. We also obtain an identification between the planar algebra of the fixed algebra sub- factor RG ⊂ RH and the G-invariant planar subalgebra of the planar algebra of the 'flip' of ⋆n. Keywords. Planar algebras; subfactors; standard invariant. 1. Introduction. For every pair H ⊂ G of finite groups, ...
2011-03-25
... Criteria for Ag and Urban Water Management Plans AGENCY: Bureau of Reclamation, Interior. ACTION: Notice of availability. SUMMARY: The ``Standard Criteria for Agricultural and Urban Water Management Plans'' (Criteria... (Reclamation) developed and published the Criteria. The Criteria apply to any Water Management Plans (Plans...
Leibniz Algebras and Lie Algebras
Directory of Open Access Journals (Sweden)
Geoffrey Mason
2013-10-01
Full Text Available This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear pairing taking values in the Leibniz kernel.
Izmerov, N F; Denisov, É I; Adeninskaia, E E; Gorblianskiĭ, Iu Iu
2014-01-01
The objective of the present paper was to review international and national standards for the criteria of assessment of the noise-induced occupational loss of hearing. The importance of healthy hearing for the occupational safety is emphasized which implies the necessity of the more rigorous criteria for hearing conservation in the workers engaged in the noisy technological environment compared with those for the general population. A rationale for the development of the standard program of hearing conservation in the workers engaged in the noisy technological environment is proposed including hygienic norms and rules or national state standards.
What are the attributes of a good standard and associated criteria?
International Nuclear Information System (INIS)
Allentuck, J.
1987-01-01
The Department of Energy (DOE) Standards and Criteria (S and C) provide the framework upon which Office of Security Evaluations (OSE) inspections of safeguards and security at DOE facilities are conducted. The S and C were created to assure that inspections are comprehensive, standardized to the extent possible and accurately reported in meaningful terms, and that assessments are objective. With these goals in mind, the desirable attributes of a standard and its associated criteria are relevance, inspectability, and limited need for inspector judgement. 1 fig
Kim, Ha-Young; Shin, Sang-Wan
2014-01-01
PURPOSE The aim of this review was to analyze the evaluation criteria on mandibular implant overdentures through a systematic review and suggest standardized evaluation criteria. MATERIALS AND METHODS A systematic literature search was conducted by PubMed search strategy and hand-searching of relevant journals from included studies considering inclusion and exclusion criteria. Randomized clinical trials (RCT) and clinical trial studies comparing attachment systems on mandibular implant overdentures until December, 2011 were selected. Twenty nine studies were finally selected and the data about evaluation methods were collected. RESULTS Evaluation criteria could be classified into 4 groups (implant survival, peri-implant tissue evaluation, prosthetic evaluation, and patient satisfaction). Among 29 studies, 21 studies presented implant survival rate, while any studies reporting implant failure did not present cumulative implant survival rate. Seventeen studies evaluating peri-implant tissue status presented following items as evaluation criteria; marginal bone level (14), plaque Index (13), probing depth (8), bleeding index (8), attachment gingiva level (8), gingival index (6), amount of keratinized gingiva (1). Eighteen studies evaluating prosthetic maintenance and complication also presented following items as evaluation criteria; loose matrix (17), female detachment (15), denture fracture (15), denture relining (14), abutment fracture (14), abutment screw loosening (11), and occlusal adjustment (9). Atypical questionnaire (9), Visual analog scales (VAS) (4), and Oral Health Impact Profile (OHIP) (1) were used as the format of criteria to evaluate patients satisfaction in 14 studies. CONCLUSION For evaluation of implant overdenture, it is necessary to include cumulative survival rate for implant evaluation. It is suggested that peri-implant tissue evaluation criteria include marginal bone level, plaque index, bleeding index, probing depth, and attached gingiva
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.
[Reappraisal of the standard method (Light's criteria) for identifying pleural exudates].
Porcel, José M; Peña, José M; Vicente de Vera, Carmina; Esquerda, Aureli
2006-02-18
Light's criteria remain the best method for separating pleural exudates from transudates. We assessed their operating characteristics, as well as those resulting from omitting the pleural fluid to serum lactate dehydrogenase (LDH) ratio from the original criteria (abbreviated Light criteria), in a large series of patients. We also searched for the best combination of pleural fluid parameters, including protein, LDH and cholesterol that identify exudates. We conducted a retrospective study of 1,490 consecutive patients with pleural effusion who underwent a diagnostic thoracentesis. There were 1,192 exudates and 298 transudates. Sensitivity, specificity, area under ROC curve, and odds ratio for both individual and combined pleural fluid parameters were calculated. Light's criteria yielded 97.5% sensitivity and 80% specificity. Both abbreviated Light criteria (sensitivity: 95.4%; specificity: 83.3%) and the combined use in an "or" rule of pleural fluid protein and LDH (sensitivity: 95.4%; specificity: 80,2%) had similar discriminative properties than standard criteria. Diagnostic separation of pleural effusions into exudates or transudates can be done effectively thorough the abbreviated Light criteria when the serum LDH value is not available. On the other hand, if venipuncture wants to be avoided (an unusual circumstance) the combination of pleural fluid protein and LDH represents an alternative to Light's criteria.
International Nuclear Information System (INIS)
Odesskii, A V
2002-01-01
This survey is devoted to associative Z ≥0 -graded algebras presented by n generators and n(n-1)/2 quadratic relations and satisfying the so-called Poincare-Birkhoff-Witt condition (PBW-algebras). Examples are considered of such algebras, depending on two continuous parameters (namely, on an elliptic curve and a point on it), that are flat deformations of the polynomial ring in n variables. Diverse properties of these algebras are described, together with their relations to integrable systems, deformation quantization, moduli spaces, and other directions of modern investigations
National Research Council Canada - National Science Library
Hartshorne, Robin
1977-01-01
.... 141 BECKERIWEISPFENNINGIKREDEL. Grabner Bases. A Computational Approach to Commutative Algebra. 142 LANG. Real and Functional Analysis. 3rd ed. 143 DOOB. Measure Theory. 144 DENNIS/FARB. Noncommutat...
Directory of Open Access Journals (Sweden)
Stuart J. McLaren
2013-12-01
Full Text Available An evaluation of 28 commercially available toys imported into New Zealand revealed that 21% of these toys do not meet the acoustic criteria in the ISO standard, ISO 8124-1:2009 Safety of Toys, adopted by Australia and New Zealand as AS/NZS ISO 8124.1:2010. While overall the 2010 standard provided a greater level of protection than the earlier 2002 standard, there was one high risk toy category where the 2002 standard provided greater protection. A secondary set of toys from the personal collections of children known to display atypical methods of play with toys, such as those with autism spectrum disorders (ASD, was part of the evaluation. Only one of these toys cleanly passed the 2010 standard, with the remainder failing or showing a marginal-pass. As there is no tolerance level stated in the standards to account for interpretation of data and experimental error, a value of +2 dB was used. The findings of the study indicate that the current standard is inadequate in providing protection against excessive noise exposure. Amendments to the criteria have been recommended that apply to the recently adopted 2013 standard. These include the integration of the new approaches published in the recently amended European standard (EN 71 on safety of toys.
Setting standards for CSR : a comparative case study on criteria-formulating organizations
Ingenbleek, P.T.M.; Binnekamp, M.H.A.; Goddijn, S.T.
2007-01-01
Though criteria-formulating organizations (CFOs) ¿ organizations in which business and community stakeholders cooperate to formulate standards for ethical issues ¿ play an important role in the relationship between firms and society, they receive scant attention from CSR researchers. Adopting an
American National Standard: fire-protection program criteria for research reactors
International Nuclear Information System (INIS)
Anon.
1981-01-01
This standard provides criteria for a fire protection program for research reactor facilities and for the reactor safety-related systems included in those facilities. It stresses preservation of the capability to achieve and maintain safe shutdown of the reactor, and includes consideration of both direct fire hazards and indirect or consequential hazards
African Journals Online (AJOL)
Tadesse
Department of Mathematics, Faculty of Computer and Mathematical Sciences, Addis Ababa. University, Addis Ababa, Ethiopia(*drkvenkateswarlu@gmail.com, **berhanufk@yahoo.co.uk). ABSTRACT. In this paper we introduce the concept of implicative algebras which is an equivalent definition of lattice implication algebra ...
African Journals Online (AJOL)
Tadesse
metric space. Also we prove that every implicative algebra can be made into a regular. Autometrized Algebra of Swamy (1964) (see theorem 2.9). We recall the definition of Xu (1993). Defintion [2]: Let (L,∨,∧,0,1) be a bounded lattice with order reversing involution. “ ' ”and a binary operation → satisfying the following ...
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...
Linden, Michael; Muschalla, Beate
2012-09-01
There is a general consensus that diagnoses for mental disorders should be based on criteria and algorithms as given in ICD or DSM. Standardized clinical interviews are recommended as diagnostic methods. In ICD and DSM, much emphasis is put on algorithms, while the underlying criteria get much less attention. The question is how valid are the criteria that are collected by structured diagnostic interviews. 209 patients from a cardiology inpatient unit were interviewed with the Mini International Neuropsychiatric Interview (MINI). 32 (15.3%) were diagnosed as suffering from a major depressive episode or dysthymia. Additionally, a thorough clinical examination was done by a psychiatric expert in 15 patients. The standardized diagnosis of present major depression was reaffirmed in one. In total, four patients were suffering from some kind of depressive disorder presently or life time. Two patients were suffering from anxiety disorders, two from adjustment disorders, and four from different types of organic brain disorders. Most important, there are 3 out of 15 who are not mentally ill. Our observations show that standardized diagnostic interviews cannot be used to make specific differential diagnoses, but rather catch unspecific syndromes. This is partly due to the fact that the wording, definition, and understanding of the underlying criteria is rather vague. This is an even greater problem if there is any somatic comorbidity. In the revision of ICD and DSM, a glossary of psychopathological terms and guidelines for the training of clinicians should be included.
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
Fine, Henry Burchard
2005-01-01
At the beginning of the twentieth century, college algebra was taught differently than it is nowadays. There are many topics that are now part of calculus or analysis classes. Other topics are covered only in abstract form in a modern algebra class on field theory. Fine's College Algebra offers the reader a chance to learn the origins of a variety of topics taught in today's curriculum, while also learning valuable techniques that, in some cases, are almost forgotten. In the early 1900s, methods were often emphasized, rather than abstract principles. In this book, Fine includes detailed discus
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
Holme, Audun
1988-01-01
This volume presents selected papers resulting from the meeting at Sundance on enumerative algebraic geometry. The papers are original research articles and concentrate on the underlying geometry of the subject.
McKeague, Charles P
1986-01-01
Elementary Algebra, Third Edition focuses on the basic principles, operations, and approaches involved in elementary algebra. The book first ponders on the basics, linear equations and inequalities, and graphing and linear systems. Discussions focus on the elimination method, solving linear systems by graphing, word problems, addition property of equality, solving linear equations, linear inequalities, addition and subtraction of real numbers, and properties of real numbers. The text then takes a look at exponents and polynomials, factoring, and rational expressions. Topics include reducing ra
McKeague, Charles P
1981-01-01
Elementary Algebra 2e, Second Edition focuses on the basic principles, operations, and approaches involved in elementary algebra. The book first tackles the basics, linear equations and inequalities, and graphing and linear systems. Discussions focus on the substitution method, solving linear systems by graphing, solutions to linear equations in two variables, multiplication property of equality, word problems, addition property of equality, and subtraction, addition, multiplication, and division of real numbers. The manuscript then examines exponents and polynomials, factoring, and rational e
Spratt, Susan E; Pereira, Katherine; Granger, Bradi B; Batch, Bryan C; Phelan, Matthew; Pencina, Michael; Miranda, Marie Lynn; Boulware, Ebony; Lucas, Joseph E; Nelson, Charlotte L; Neely, Benjamin; Goldstein, Benjamin A; Barth, Pamela; Richesson, Rachel L; Riley, Isaretta L; Corsino, Leonor; McPeek Hinz, Eugenia R; Rusincovitch, Shelley; Green, Jennifer; Barton, Anna Beth; Kelley, Carly; Hyland, Kristen; Tang, Monica; Elliott, Amanda; Ruel, Ewa; Clark, Alexander; Mabrey, Melanie; Morrissey, Kay Lyn; Rao, Jyothi; Hong, Beatrice; Pierre-Louis, Marjorie; Kelly, Katherine; Jelesoff, Nicole
2017-04-01
We assessed the sensitivity and specificity of 8 electronic health record (EHR)-based phenotypes for diabetes mellitus against gold-standard American Diabetes Association (ADA) diagnostic criteria via chart review by clinical experts. We identified EHR-based diabetes phenotype definitions that were developed for various purposes by a variety of users, including academic medical centers, Medicare, the New York City Health Department, and pharmacy benefit managers. We applied these definitions to a sample of 173 503 patients with records in the Duke Health System Enterprise Data Warehouse and at least 1 visit over a 5-year period (2007-2011). Of these patients, 22 679 (13%) met the criteria of 1 or more of the selected diabetes phenotype definitions. A statistically balanced sample of these patients was selected for chart review by clinical experts to determine the presence or absence of type 2 diabetes in the sample. The sensitivity (62-94%) and specificity (95-99%) of EHR-based type 2 diabetes phenotypes (compared with the gold standard ADA criteria via chart review) varied depending on the component criteria and timing of observations and measurements. Researchers using EHR-based phenotype definitions should clearly specify the characteristics that comprise the definition, variations of ADA criteria, and how different phenotype definitions and components impact the patient populations retrieved and the intended application. Careful attention to phenotype definitions is critical if the promise of leveraging EHR data to improve individual and population health is to be fulfilled. © The Author 2016. Published by Oxford University Press on behalf of the American Medical Informatics Association. All rights reserved. For Permissions, please email: journals.permissions@oup.com
International Nuclear Information System (INIS)
Patel, K.; Charron, M.; Hoberman, A.; Brown, M.L.; Rogers, K.D.
1993-01-01
A set of criteria was developed to standardize assessment of DMSA renal scintigraphy which were performed to evaluate children for acute pyelonephritis and renal scarring. This study was undertaken to assess intra-and interobserver vriability in the interpretation of DMSA renal scintigraphy using these criteria. Renal contours and parenchyma were assessed in three zones. Contours were assessed as normal or abnormal and parenchymal defects were evaluated in terms of character, shape and degree in three regions (upper and lower pole and midzone). Two nuclear medicine physicians blindly reviewed 57 DMSA scintigraphy on two occasions each. Disagreement of each observer's evaluation of the same scintigraphy on two different occasions was described as intraobserver variability, and the comparison between readings by each of the two observers was described as interobserver variability. High levels of intra- (95.9% and 90.6% respectively, p<0.05) and interobserver agreement (84.4%, p<0.05) were demonstrated. There were minor differences in inconsistencies between the two kidneys of different kidney zones. We conclude that standardization of criteria resulted in higher intra- and interobserver consistency in interpretation of DMSA scintigraphy. (orig.)
Objectives, standards and criteria for radioactive waste disposal in the European Community
International Nuclear Information System (INIS)
Orlowski, S.; Schaller, K.H.
1989-01-01
The present report, edited by a working group within the framework of the European Commission research programme on radioactive waste management and disposal, reviews the objectives, standards and criteria for radioactive waste disposal in the European Community with a view to identifying common features and differences in the regulatory frameworks of its Member States. Suggestions for possible harmonization are made. A few common general principles form the basis for legal and regulatory measures. These principles apply to and are discussed for the following: radiation protection (with the systems of dose limitation and control), ethical and sociological questions, environmental and natural resources protection, and nuclear safeguards. A description is given of the implementation of common principles, standards and requirements at Community level, in line with requirements laid down in the European Community Treaties, and in international conventions and recommendations. This is followed by a review of the implementation of basic criteria by national safety authorities. Regulatory measures and national policies, and the approaches used in devising criteria are discussed for both near-surface disposal of low-level waste, and for deep geological disposal of waste in continental geological formations. Finally, the roles and duties of the operators of radioactive waste facilities are reported. More detailed information on particular aspects is presented in the annexes
Wang, Tieyu; Zhou, Yunqiao; Bi, Cencen; Lu, Yonglong; He, Guizhen; Giesy, John P
2017-07-01
There is a need to formulate water environment standards (WESs) from the current water quality criteria (WQC) in China. To this end, we briefly summarize typical mechanisms applied in several countries with longer histories of developing WESs, and three limitations to formulating WESs in China were identified. After analyzing the feasibility factors including economic development, scientific support capability and environmental policies, we realized that China is still not ready for a complete change from its current nation-wide unified WES system to a local-standard-based system. Thus, we proposed a framework for transformation from WQC to WESs in China. The framework consists of three parts, including responsibilities, processes and policies. The responsibilities include research authorization, development of guidelines, and collection of information, at both national and local levels; the processes include four steps and an impact factor system to establish water quality standards; and the policies include seven specific proposals. Copyright © 2016. Published by Elsevier B.V.
International Nuclear Information System (INIS)
Hsue, S.T.; Stewart, J.E.; Sampson, T.E.; Butler, G.W.; Rudy, C.R.; Rinard, P.M.
1997-10-01
For certification and measurement control, nondestructive assay (NDA) instruments and methods used for verification measurements of special nuclear materials (SNMs) require calibrations based on certified reference materials (CRMs), or working reference materials (WRMs), traceable to the national system of measurements, and adequately characteristic of the unknowns. The Department of Energy Office of Safeguards and Security is sponsoring production of a comprehensive guide to preparation of NDA standards. The scope of the report includes preparation criteria, current availability of CRMs and WRMs, practical considerations for preparation and characterization, and an extensive bibliography. In preparing the report, based primarily on experience at Los Alamos, they have found that standards preparation is highly dependent on the particular NDA method being applied. They therefore include sections that contain information specific to commonly used neutron and gamma-ray NDA techniques. They also present approaches that are alternatives to, or minimize requirements for physical standards
Energy Technology Data Exchange (ETDEWEB)
Hsue, S.T.; Stewart, J.E.; Sampson, T.E.; Butler, G.W.; Rudy, C.R.; Rinard, P.M.
1997-10-01
For certification and measurement control, nondestructive assay (NDA) instruments and methods used for verification measurements of special nuclear materials (SNMs) require calibrations based on certified reference materials (CRMs), or working reference materials (WRMs), traceable to the national system of measurements, and adequately characteristic of the unknowns. The Department of Energy Office of Safeguards and Security is sponsoring production of a comprehensive guide to preparation of NDA standards. The scope of the report includes preparation criteria, current availability of CRMs and WRMs, practical considerations for preparation and characterization, and an extensive bibliography. In preparing the report, based primarily on experience at Los Alamos, they have found that standards preparation is highly dependent on the particular NDA method being applied. They therefore include sections that contain information specific to commonly used neutron and gamma-ray NDA techniques. They also present approaches that are alternatives to, or minimize requirements for physical standards.
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
Bell, Eric T
1927-01-01
The central topic of this book is the presentation of the author's principle of arithmetical paraphrases, which won him the BÃ´cher Prize in 1924. This general principle served to unify and extend many isolated results in the theory of numbers. The author successfully provides a systematic attempt to find a unified theory for each of various classes of related important problems in the theory of numbers, including its interrelations with algebra and analysis. This book will be of interest to advanced students in various branches of mathematics, including number theory, abstract algebra, ellipti
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
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
A Term-Graph Syntax for Algebras over Multisets
Gadducci, Fabio
Earlier papers argued that term graphs play for the specification of relation-based algebras the same role that standard terms play for total algebras. The present contribution enforces the claim by showing that term graphs are a sound and complete representation for multiset algebras, i.e., algebras whose operators are interpreted over multisets.
International Nuclear Information System (INIS)
Hultcrantz, K.
1999-04-01
The co-organisers of the International Symposium on Health and Environmental Criteria and Standards for Radioactive Waste Disposal are pleased to present these proceedings. This Symposium succeeded in bringing together a wide range of participants and perspectives in order to address in a common forum the technical and non-technical issues related to long-term storage of radioactive waste. The papers presented herein reflect both the diversity of the participants and the complexity of the issues addressed. The sessions, panels, and papers developed for the symposium focused on some of the daunting challenges posed by long-term isolation and storage of high level radioactive waste. Panel sessions addressed the basic principles of criteria and standards, the context of the risks involved, and an overview of relevant philosophical, social, and ethical issues. Paper sessions considered national laws, policies and experiences; criteria formulation; environmental protection; compliance; human intrusion; and fundamental philosophical, social, and ethical issues. The presentations stimulated lively discussion and debate, and the contributors received valuable feedback. The interplay between technical and social aspects reflected in some papers and in the discussion highlights the changing role of the public in radioactive waste issues. The average citizen has become more aware of and more involved in radioactive waste matters in recent years. Solutions that were previously analysed through a technological lens are now being viewed in a much broader perspective that better addresses the concerns of local communities as well as national and international interests. Public involvement must begin earlier, last longer, and improve in quality so as to create an ongoing dialogue and debate rather than cycles of dictates and discord. The symposium has offered suggestions as to how government, industry, and the public can foster a broader dialogue on the formulation and
International Nuclear Information System (INIS)
Stewart, J.E.; Hsue, S.T.; Sampson, T.E.
1997-01-01
For certification and measurement control, nondestructive assay (NDA) instruments and methods used for verification measurement of special nuclear materials (SNMs) require calibrations based on certified reference materials (CRMs), or working reference materials (WRMs), traceable to the national system of measurements, and adequately characteristic of the unknowns. The Department of Energy Office of Safeguards and Security is sponsoring production of a comprehensive guide to preparation of NDA standards. The scope of the report includes preparation criteria, current availability of CRMs and WRMs, practical considerations for preparation and characterization, and an extensive bibliography. In preparing the report, based primarily on experience at Los Alamos, we have found that standards preparation is highly dependent on the particular NDA method being applied. We therefore include sections that contain information specific to commonly used neutron and gamma-ray NDA techniques. 16 refs., 4 figs., 2 tabs
Oliver, Bob; Pawałowski, Krzystof
1991-01-01
As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.
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.).
The development and significance of the DOE Safeguards and Security standards and criteria
International Nuclear Information System (INIS)
Toman, J.
1987-01-01
In October 1985, the DOE Assistant Secretary for Defense Programs created a task force to develop inspection standards and criteria for Safeguards and Security. These standards and criteria (S/C) would provide the DOE Inspection and Evaluation (I and E) teams with the guidance needed to assess the security posture of DOE's nuclear and other important facilities. The Lawrence Livermore National Laboratory was designated the lead management organization for the structuring, administration, and execution of the overall task force effort and appointed the Executive Secretary. The Office of Security Evaluations (OSE) became the responsible DOE organization, and its Director assumed the role of Chairman of the Task Force Executive Committee. At its peak, the Task Force consisted of approximately 200 people who were considered to be experts in eight major topical areas. The composition of the experts was almost evenly divided between DOE and contractor employees. The collective wisdom of these experts was used in a consensus process to develop the S/C that are now published in draft form. These S/C have been used in more than ten inspections since May 1986 with much success. This paper discusses the process used to achieve the desired end result and the significance of the Task Force's accomplishments
International Nuclear Information System (INIS)
Dickson, H.W.
1978-08-01
A review of existing health and safety standards and guidelines has been undertaken to assist in the development of criteria for the decontamination and decommissioning of property contaminated with radioactive material. During the early years of development of the nuclear program in the United States, a number of sites were used which became contaminated with radioactive material. Many of these sites are no longer useful for nuclear activities, and the U.S. DOE desires to develop criteria for the management of these sites for future uses. Radiation protection standards promulgated by ICRP, NCRP, and ANSI have been considered. Government regulations, from the Code of Federal Regulations and the legal codes of various states, as well as regulatory guidelines with specific application to decommissioning of nuclear facilities also have been reviewed. In addition, recommendations of other scientific organizations such as the National Academy of Sciences/National Research Council Advisory Committee on the Biological Effects of Ionizing Radiations and the United Nations Scientific Committee on the Effects of Atomic Radiation were considered. Finally, a few specific recommendations and discussions from current literature were included. 28 references
Classification of flexible composition algebras, I
Energy Technology Data Exchange (ETDEWEB)
Okubo, S.
1982-06-01
The following theorem has been proven. Let A be a finite-dimensional flexible composition algebra over a field F of characteristic not equal to 2, and not equal to 3. Then, A must be either a Hurwitz, or a para-Hurwitz, or a pseudo-octonion algebra. If the field F is of characteristic 2, then the dimension of a composition algebra is arbitrary in contrast to the standard dimensionality of 1, 2, 4, or 8. Finally, it is shown that any finite-dimensional flexible composition algebra over a field F of any characteristic is automatically a Malcev-admissible algebra.
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
Gorga, M P; Neely, S T; Dorn, P A
1999-08-01
1) To describe distortion product otoacoustic emission (DPOAE) test performance when a priori response criteria are applied to a large set of DPOAE data. 2) To describe DPOAE test performance when multifrequency definitions of auditory function are used. 3) To determine DPOAE test performance when a single decision regarding auditory status is made for an ear, based on DPOAE data from several frequencies. 4) To compare univariate and multivariate test performance when multifrequency gold standard definitions and response criteria are applied to DPOAE data. DPOAE and audiometric data were analyzed from 1267 ears of 806 subjects. These data were evaluated for three different frequency combinations (2, 3, 4 kHz; 2, 3, 4, 6 kHz; 1.5, 2, 3, 4, 6 kHz). DPOAE data were collected for each of the f2 frequencies listed above, using primary levels (L1/L2) of 65/55 dB SPL and a primary ratio (f2/f1) of 1.22. Sensitivity and specificity were evaluated for signal to noise ratios (SNRs) of 3, 6, and 9 dB, which are in common clinical use. In addition, test performance was evaluated using clinical decision theory, following the convention we have used in previous reports on otoacoustic emission test performance. Both univariate and multivariate analyses techniques were applied to the data. In addition to evaluating DPOAE test performance for the case when audiometric and f2 frequency were equal, multifrequency gold standards and multifrequency criterion responses were evaluated. Three new gold standards were used to assess test performance: average pure-tone thresholds, extrema thresholds that took into account both the magnitude of the loss and the number of frequencies at which hearing loss existed, and a combination of the two. These new gold standards were applied to each of the three frequency groups described above. As expected, SNR criteria of 3, 6, and 9 dB never resulted in perfect DPOAE test performance. Even the most stringent of these criteria (9 dB SNR) did not result
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.
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
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.
[Mechanism for transformation of environmental criteria into environmental standards in China].
Bi, Cen-Cen; Wang, Tie-Yu; Lü, Yong-Long
2012-12-01
In order to provide scientific basis for developing more reasonable and effective environmental standards (ESs), China has taken its own environmental criteria (EC) research strategy in recent years. For the purpose of developing a transformation mechanism from EC to ESs suitable for China, current EC and ESs in China were compared with those in some developed countries, such as the USA, Canada and Australia. Four common characteristics of transformation from EC to ESs in developed countries and corresponding problems in China were drawn through the comparison, based on which a framework for transformation from EC to ESs was established. The framework was composed by three parts: (1) relevant national and local agencies and responsibilities; (2) steps for transformation including affecting factors and their interactions; (3) and policies for solving current problems in China.
Varieties of integrative scholarship: why rules of evidence, criteria, and standards matter.
McGaghie, William C
2015-03-01
Integrative scholarship involves the aggregation of data and evidence in a way that allows the research community to comprehend and value the connections and perspectives that unite isolated facts and research studies. Integrative scholarship summarizes data, enlightens and informs readers broadly, and sets the stage for subsequent research. This article describes five approaches to integrative scholarship--narrative, systematic, scoping, critical-realist, open peer commentary--and argues that each approach uses different methods and rules of evidence to combine data and report their meaning. Different forms of integrative scholarship use methods, criteria, and standards that are matched to the integrative approach and data being evaluated. There is no one best strategy to conduct or judge integrative scholarship. Researchers who perform integrative scholarship should openly express the values that underlie their work.
Directory of Open Access Journals (Sweden)
Marcelo Roberto Pereira Freitas
2011-09-01
Full Text Available Objective: To compare the prognosis estimated by standardprognostic criteria versus the prognosis estimated by the OncotypeDX. Methods: A retrospective study was performed on 22 patientswith positive estrogen receptor, early-stage breast cancer whohad an Oncotype DX recurrence score available. Results: Kappavalue between Oncotype DX and standard prognostic criteriawas: Adjuvant! (K = 0.091, Adjuvant! (Transbig (K = 0.182 andNational Comprehensive Cancer Network (K = 0.091. The Fisher’sexact test did not show correlation between Oncotype and standardprognostic criteria. Conclusion: Standard prognostic criteria showedno correlation with Oncotype DX.
Energy Technology Data Exchange (ETDEWEB)
Tychyj-Pinel, Christelle [Service de Medecine Nucleaire, Hospices Civils de Lyon, Centre Hospitalier Lyon Sud, Pierre-Benite (France); Ricard, Fabien [Service de Medecine Nucleaire, Hospices Civils de Lyon, Centre Hospitalier Lyon Sud, Pierre-Benite (France); Universite de Lyon, Faculte de Medecine, UCB Lyon 1, Lyon (France); Fulham, Michael [Royal Prince Alfred Hospital, Department of PET and Nuclear Medicine, Sydney (Australia); University of Sydney, Sydney Medical School, Sydney (Australia); Fournier, Marion [Centre Hospitalier Lyon Sud, The Lymphoma Academic Research Organisation (LYSARC), Pierre-Benite (France); Meignan, Michel [CHU Henri Mondor, Medicine Nucleaire, Creteil (France); Lamy, Thierry [Service d' Hematologie, CHU, Rennes (France); Vera, Pierre [Centre Henri Becquerel, Service de Medecine Nucleaire, Rouen (France); Rouen University, QuantIF (Litis EA4108), Rouen (France); Salles, Gilles [Universite de Lyon, Faculte de Medecine, UCB Lyon 1, Lyon (France); Service d' Hematologie, Hospices Civils de Lyon, Centre Hospitalier Lyon Sud, Pierre-Benite (France); Trotman, Judith [University of Sydney, Sydney Medical School, Sydney (Australia); Concord Hospital, Department of Haematology, Concord, NSW (Australia)
2014-03-15
We aimed to compare the standardized central review of {sup 18}F-fluorodeoxyglucose (FDG) positron emission tomography (PET)/CT scans performed after induction therapy for follicular lymphoma (FL) in the PRIMA study (Salles et al., Lancet 377:42-51, 2011; Trotman et al., J Clin Oncol 29:3194-3200, 2011) to scan review at local centres. PET/CT scans were independently evaluated by two nuclear medicine physicians using the 2007 International Harmonization Project (IHP) criteria (Cheson et al., J Clin Oncol 25:579-586, 2007; Juweid et al., J Clin Oncol 25:571-578, 2007; Shankar et al., J Nucl Med 47:1059-1066, 2006) and Deauville 5-point scale (5PS) criteria (Meignan et al., Leuk Lymphoma 50:1257-1260, 2009; Meignan et al., Leuk Lymphoma 51:2171-2180, 2010; Barrington et al., Eur J Nucl Med Mol Imaging 37:1824-1833, 2010). PET/CT status was compared with prospectively recorded patient outcomes. Central evaluation was performed on 119 scans. At diagnosis, 58 of 59 were recorded as positive, with a mean maximum standardized uptake value (SUV{sub max}) of 11.7 (range 4.6-35.6). There was no significant association between baseline SUV{sub max} and progression-free survival (PFS). Sixty post-induction scans were interpreted using both the IHP criteria and 5PS. Post-induction PET-positive status failed to predict progression when applying the IHP criteria [p = 0.14; hazard ratio (HR) 1.9; 95 % confidence interval (CI) 0.8-4.6] or 5PS with a cut-off ≥3 (p = 0.12; HR 2.0; 95 % CI 0.8-4.7). However, when applying the 5PS with a cut-off ≥4, there was a significantly inferior 42-month PFS in PET-positive patients of 25.0 % (95 % CI 3.7-55.8 %) versus 61.4 % (95 % CI 45.4-74.1 %) in PET-negative patients (p = 0.01; HR 3.1; 95 % CI 1.2-7.8). The positive predictive value (PPV) of post-induction PET with this liver cut-off was 75 %. The 42-month PFS for patients remaining PET-positive by local assessment was 31.1 % (95 % CI 10.2-55.0 %) vs 64.6 % (95 % CI 47.0-77.6 %) for PET
Iachello, F
1995-01-01
1. The Wave Mechanics of Diatomic Molecules. 2. Summary of Elements of Algebraic Theory. 3. Mechanics of Molecules. 4. Three-Body Algebraic Theory. 5. Four-Body Algebraic Theory. 6. Classical Limit and Coordinate Representation. 8. Prologue to the Future. Appendices. Properties of Lie Algebras; Coupling of Algebras; Hamiltonian Parameters
Design and validation of standardized clinical and functional remission criteria in schizophrenia
Directory of Open Access Journals (Sweden)
Mosolov SN
2014-01-01
Full Text Available Sergey N Mosolov,1 Andrey V Potapov,1 Uriy V Ushakov,2 Aleksey A Shafarenko,1 Anastasiya B Kostyukova11Department of Mental Disorders Therapy, Moscow Research Institute of Psychiatry, Moscow, Russia; 2Moscow Psychiatric Outpatient Services #21, Moscow, RussiaBackground: International Remission Criteria (IRC for schizophrenia were developed recently by a group of internationally known experts. The IRC detect only 10%–30% of cases and do not cover the diversity of forms and social functioning. Our aim was to design a more applicable tool and validate its use – the Standardized Clinical and Functional Remission Criteria (SCFRC.Methods: We used a 6-month follow-up study of 203 outpatients from two Moscow centers and another further sample of stable patients from a 1-year controlled trial of atypical versus typical medication. Diagnosis was confirmed by International Classification of Diseases Version 10 (ICD10 criteria and the Mini-International Neuropsychiatric Interview (MINI. Patients were assessed by the Positive and Negative Syndrome Scale, including intensity threshold, and further classified using the Russian domestic remission criteria and the level of social and personal functioning, according to the Personal and Social Performance Scale (PSP. The SCFRC were formulated and were validated by a data reanalysis on the first population sample and on a second independent sample (104 patients and in an open-label prospective randomized 12-month comparative study of risperidone long-acting injectable (RLAI versus olanzapine.Results: Only 64 of the 203 outpatients (31.5% initially met the IRC, and 53 patients (26.1% met the IRC after 6 months, without a change in treatment. Patients who were in remission had episodic and progressive deficit (39.6%, or remittent (15% paranoid schizophrenia, or schizoaffective disorder (17%. In addition, 105 patients of 139 (51.7%, who did not meet symptomatic IRC, remained stable within the period. Reanalysis of
Casimir elements of epsilon Lie algebras
International Nuclear Information System (INIS)
Scheunert, M.
1982-10-01
The classical framework for investigating the Casimir elements of a Lie algebra is generalized to the case of an epsilon Lie algebra L. We construct the standard L-module isomorphism of the epsilon-symmetric algebra of L onto its enveloping algebra and we introduce the Harish-Chandra homomorphism. In case the generators of L can be written in a canonical two-index form, we construct the associated standard sequence of Casimir elements and derive a formula for their eigenvalues in an arbitrary highest weight module. (orig.)
Mahé, Louis; Roy, Marie-Françoise
1992-01-01
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...
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.
Singh, Rajinder P; Farney, Alan C; Rogers, Jeffrey; Gautreaux, Michael; Reeves-Daniel, Amber; Hartmann, Erica; Doares, William; Iskandar, Samy; Adams, Patricia; Stratta, Robert J
2011-01-01
Hypertension may be a either a cause or an effect of kidney disease. Although hypertension is an important component of the expanded criteria donor definition, risks of transplanting deceased donor kidneys from hypertensive standard criteria donors (SCD) are less well understood. Retrospective single-center study in all adult patients who received a deceased donor kidney transplant from a SCD to evaluate the role of donor hypertension as a pre-transplant risk factor for death-censored graft loss (DCGL) and renal function. From October 2001 through May 2008, 297 kidney transplants were performed from donation after brain death SCDs. A total of 47 (15.8%) grafts were lost, including 19 (6.4%) deaths with functioning grafts. Univariate analysis of death-censored cases (n = 278) identified history of donor hypertension, cold ischemia time (CIT) >30 h, and African American (AA) recipients as significant pre-transplant risk factors predictive for DCGL at five yr follow-up (mean 38 months, all p hypertension (relative risk 2.2, p = 0.04) to be a significant risk factor for DCGL, whereas CIT >30 h and AA recipient ethnicity showed only trends toward DCGL. Renal function as determined by serum creatinine levels was significantly higher in recipients of hypertensive compared with non-hypertensive SCD kidneys at all time points out to 48 months follow-up and the disparity in renal function increased over time. Transplanting SCD kidneys from hypertensive donors is associated with worse graft function and an increased risk of graft loss. © 2011 John Wiley & Sons A/S.
International Nuclear Information System (INIS)
Nha, Hyunchul; Kim, Jaewan
2006-01-01
We derive a class of inequalities, from the uncertainty relations of the su(1,1) and the su(2) algebra in conjunction with partial transposition, that must be satisfied by any separable two-mode states. These inequalities are presented in terms of the su(2) operators J x =(a † b+ab † )/2, J y =(a † b-ab † )/2i, and the total photon number a +N b >. They include as special cases the inequality derived by Hillery and Zubairy [Phys. Rev. Lett. 96, 050503 (2006)], and the one by Agarwal and Biswas [New J. Phys. 7, 211 (2005)]. In particular, optimization over the whole inequalities leads to the criterion obtained by Agarwal and Biswas. We show that this optimal criterion can detect entanglement for a broad class of non-Gaussian entangled states, i.e., the su(2) minimum-uncertainty states. Experimental schemes to test the optimal criterion are also discussed, especially the one using linear optical devices and photodetectors
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
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 ...
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...
Generalized Hermitian Algebras
Foulis, David J.; Pulmannová, Sylvia
2009-05-01
We refer to the real Jordan Banach algebra of bounded Hermitian operators on a Hilbert space as a Hermitian algebra. In this paper we define and launch a study of a class of generalized Hermitian (GH) algebras. Among the examples of GH-algebras are ordered special Jordan algebras, JW-algebras, and AJW-algebras, but unlike these more restricted cases, a GH-algebra is not necessarily a Banach space and its lattice of projections is not necessarily complete. In this paper we develop the basic theory of GH-algebras, identify their unit intervals as effect algebras, and observe that their projection lattices are sigma-complete orthomodular lattices. We show that GH-algebras are spectral order-unit spaces and that they admit a substantial spectral theory.
Universal enveloping algebras for Malcev color algebras
de-la-Concepción, Daniel
2015-01-01
In this paper we give a construction of the universal enveloping algebra of a Malcev algebra in categories of group algebra comodules with a symmetry given by a bicharacter of the group. A particular example of such categories is the category of super vector spaces.
Visualizing automorphisms of graph algebras
DEFF Research Database (Denmark)
Avery, James Emil; Johansen, Rune; Szymanski, Wojciech
2018-01-01
Graph C*-algebras have been celebrated as C*-algebras that can be seen, because many important properties may be determined by looking at the underlying graph. This paper introduces the permutation graph for a permutative endomorphism of a graph C*-algebra as a labeled directed multigraph...... that gives a visual representation of the endomorphism and facilitates computations. Combinatorial criteria have previously been developed for deciding when such an endomorphism is an automorphism, but here the question is reformulated in terms of the permutation graph and new proofs are given. Furthermore......, it is shown how to use permutation graphs to efficiently generate exhaustive collections of permutative automorphisms. Permutation graphs provide a natural link to the textile systems representing induced endomorphisms on the edge shift of the given graph, and this allows the powerful tools of the theory...
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...
On Realization of Generalized Effect Algebras
Paseka, Jan
2012-12-01
A well-known fact is that there is a finite orthomodular lattice with an order determining set of states which is not representable in the standard quantum logic, the lattice L(H) of all closed subspaces of a separable complex Hilbert space. We show that a generalized effect algebra is representable in the operator generalized effect algebra G(H) of effects of a complex Hilbert space H iff it has an order determining set of generalized states. This extends the corresponding results for effect algebras of Riečanová and Zajac. Further, any operator generalized effect algebra G(H) possesses an order determining set of generalized states.
Algebra I textbook for students of mathematics
Gorodentsev, Alexey L
2016-01-01
This book is the first volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them. The course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra, representation theory, category theory, commutative algebra, Galois theory, and algebraic geometry – topics that are often overlooked in standard undergraduate courses. This textbook is based on courses the author has conducted at the Independent University of Moscow and at the Faculty of Mathematics in the Higher School of Economics. The main content is complemented by a wealth of exercises for class discussion, some of which include comments and hints, as well as problems for independent study.
Algebra II textbook for students of mathematics
Gorodentsev, Alexey L
2017-01-01
This book is the second volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them. The course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra, representation theory, category theory, commutative algebra, Galois theory, and algebraic geometry – topics that are often overlooked in standard undergraduate courses. This textbook is based on courses the author has conducted at the Independent University of Moscow and at the Faculty of Mathematics in the Higher School of Economics. The main content is complemented by a wealth of exercises for class discussion, some of which include comments and hints, as well as problems for independent study.
Indian Academy of Sciences (India)
Introduction and preliminaries. The class of Malcev algebras contains one of the Lie algebras and so a question arises whether some known results on Lie algebras can be extended to the framework of Malcev algebras (see [4, 7, 9, 10]). In the present paper, we are interested in studying the structure of arbitrary Malcev ...
Embeddings of Heyting Algebras
Jongh, D.H.J. de; Visser, A.
In this paper we study embeddings of Heyting Algebras. It is pointed out that such embeddings are naturally connected with Derived Rules. We compare the Heyting Algebras embeddable in the Heyting Algebra of the Intuitionistic Propositional Calculus (IPC), i.e. the free Heyting Algebra on countably
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 ...
Planar algebra of the subgroup-subfactor
Indian Academy of Sciences (India)
The crucial step in this identification is an exhibition of a model for the basic construction tower, and thereafter of the standard invariant of R ⋊ H ⊂ R ⋊ G in terms of operator matrices. We also obtain an identification between the planar algebra of the fixed algebra subfactor R G ⊂ R H and the -invariant planar subalgebra ...
An Inquiry-Based Linear Algebra Class
Wang, Haohao; Posey, Lisa
2011-01-01
Linear algebra is a standard undergraduate mathematics course. This paper presents an overview of the design and implementation of an inquiry-based teaching material for the linear algebra course which emphasizes discovery learning, analytical thinking and individual creativity. The inquiry-based teaching material is designed to fit the needs of a…
Just Say Yes to Early Algebra!
Stephens, Ana; Blanton, Maria; Knuth, Eric; Isler, Isil; Gardiner, Angela Murphy
2015-01-01
Mathematics educators have argued for some time that elementary school students are capable of engaging in algebraic thinking and should be provided with rich opportunities to do so. Recent initiatives like the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) have taken up this call by reiterating the place of early algebra in…
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
Supersymmetry algebra cohomology. I. Definition and general structure
International Nuclear Information System (INIS)
Brandt, Friedemann
2010-01-01
This paper concerns standard supersymmetry algebras in diverse dimensions, involving bosonic translational generators and fermionic supersymmetry generators. A cohomology related to these supersymmetry algebras, termed supersymmetry algebra cohomology, and corresponding 'primitive elements' are defined by means of a BRST (Becchi-Rouet-Stora-Tyutin)-type coboundary operator. A method to systematically compute this cohomology is outlined and illustrated by simple examples.
Schwarz maps of algebraic linear ordinary differential equations
Sanabria Malagón, Camilo
2017-12-01
A linear ordinary differential equation is called algebraic if all its solution are algebraic over its field of definition. In this paper we solve the problem of finding closed form solution to algebraic linear ordinary differential equations in terms of standard equations. Furthermore, we obtain a method to compute all algebraic linear ordinary differential equations with rational coefficients by studying their associated Schwarz map through the Picard-Vessiot Theory.
Goldmann, H
1990-01-01
The first part of this monograph is an elementary introduction to the theory of Fréchet algebras. Important examples of Fréchet algebras, which are among those considered, are the algebra of all holomorphic functions on a (hemicompact) reduced complex space, and the algebra of all continuous functions on a suitable topological space.The problem of finding analytic structure in the spectrum of a Fréchet algebra is the subject of the second part of the book. In particular, the author pays attention to function algebraic characterizations of certain Stein algebras (= algebras of holomorphic functions on Stein spaces) within the class of Fréchet algebras.
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...
Review of proposed EPA ambient lead criteria standard document. Final report. Task assignment No. 10
Energy Technology Data Exchange (ETDEWEB)
1984-03-04
The proposed October 1983 EPA ambient lead criteria document, Air Quality Criteria for Lead is reviewed from the perspective of DOE's policies and programs and addresses potential impacts on energy production and energy-intensive industries. Following an introduction, the study is organized in five subsequent sections. Section 2.0 addresses environmental and health effects of exposure to lead. Section 3.0 reviews sources of lead emissions. Section 4.0 presents information on lead concentrations in ambient air. Section 5.0 examines dose-effect relationships among lead emissions, ambient air concentrations and blood lead levels. Section 6.0 presents Radian's evaluation of the regulatory implications of the criteria document and the information it provides. 10 figures, 11 tables.
29 CFR 1904.9 - Recording criteria for cases involving medical removal under OSHA standards.
2010-07-01
... under OSHA standards. 1904.9 Section 1904.9 Labor Regulations Relating to Labor (Continued) OCCUPATIONAL... removal under OSHA standards. (a) Basic requirement. If an employee is medically removed under the medical surveillance requirements of an OSHA standard, you must record the case on the OSHA 300 Log. (b) Implementation...
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
Osborn, J
1989-01-01
During the academic year 1987-1988 the University of Wisconsin in Madison hosted a Special Year of Lie Algebras. A Workshop on Lie Algebras, of which these are the proceedings, inaugurated the special year. The principal focus of the year and of the workshop was the long-standing problem of classifying the simple finite-dimensional Lie algebras over algebraically closed field of prime characteristic. However, other lectures at the workshop dealt with the related areas of algebraic groups, representation theory, and Kac-Moody Lie algebras. Fourteen papers were presented and nine of these (eight research articles and one expository article) make up this volume.
Causal structure and algebraic classification of non-dissipative linear optical media
International Nuclear Information System (INIS)
Schuller, Frederic P.; Witte, Christof; Wohlfarth, Mattias N.R.
2010-01-01
In crystal optics and quantum electrodynamics in gravitational vacua, the propagation of light is not described by a metric, but an area metric geometry. In this article, this prompts us to study conditions for linear electrodynamics on area metric manifolds to be well-posed. This includes an identification of the timelike future cones and their duals associated to an area metric geometry, and thus paves the ground for a discussion of the related local and global causal structures in standard fashion. In order to provide simple algebraic criteria for an area metric manifold to present a consistent spacetime structure, we develop a complete algebraic classification of area metric tensors up to general transformations of frame. This classification, valuable in its own right, is then employed to prove a theorem excluding the majority of algebraic classes of area metrics as viable spacetimes. Physically, these results classify and drastically restrict the viable constitutive tensors of non-dissipative linear optical media.
Relation between dual S-algebras and BE-algebras
Directory of Open Access Journals (Sweden)
Arsham Borumand Saeid
2015-05-01
Full Text Available In this paper, we investigate the relationship between dual (Weak Subtraction algebras, Heyting algebras and BE-algebras. In fact, the purpose of this paper is to show that BE-algebra is a generalization of Heyting algebra and dual (Weak Subtraction algebras. Also, we show that a bounded commutative self distributive BE-algebra is equivalent to the Heyting algebra.
Matt, Susan B.; Maheady, Donna; Fleming, Susan E.
2015-01-01
Across the globe, students with disabilities have been increasing in prevalence in higher education settings. In the twenty-first century the struggle to include individuals with disabilities into nursing schools and workplaces continues in different parts of the world. Historically, entry criteria in nursing schools have been based on essential…
CASL, the Common Algebraic Specification Language
DEFF Research Database (Denmark)
Mossakowski, Till; Haxthausen, Anne Elisabeth; Sannella, Donald
2008-01-01
CASL is an expressive specification language that has been designed to supersede many existing algebraic specification languages and provide a standard. CASL consists of several layers, including basic (unstructured) specifications, structured specifications and architectural specifications...
Ornelas, J; Routt, E; Kallis, P; Lev-Tov, H
2018-04-01
The use of complementary and alternative medicine (CAM) is increasing in Western countries, including in the area of dermatology. However, Western healthcare providers have not integrated CAM into regular practice owing to a lack of reliable data supporting its use. To encourage high-quality research related to the use of CAM and specifically herbal interventions, the CONsolidated Standards Of Reporting Trials (CONSORT) extension criteria on reporting herbal interventions (hCONSORT) were published in 2006. To evaluate the adherence of randomized controlled trials (RCTs) investigating herbal interventions for acne, atopic dermatitis (AD) and psoriasis to the hCONSORT criteria. A comprehensive search of the PubMed, Embase and Cochrane Library databases was conducted. RCTs published between 2009 and 2014 assessing therapeutic outcomes of plant-based interventions for acne, AD or psoriasis were included. Investigators determined the number of unique hCONSORT criteria satisfied per report. anova was used to examine differences in scores by disease entity. The vast majority of reviewed studies reported reports based on language and lack of assessment of overall adherence to CONSORT criteria. Our data indicate lack of adherence to hCONSORT extension criteria. Adherence to hCONSORT guidelines should be encouraged in order to provide high-quality reporting of research on herbal interventions in dermatology. Doing so may ease the integration of CAM into conventional medical practice and provide actionable data to providers. © 2017 British Association of Dermatologists.
Munoz, Cesar; Butler, Ricky; Narkawicz, Anthony; Maddalon, Jeffrey; Hagen, George
2010-01-01
Distributed approaches for conflict resolution rely on analyzing the behavior of each aircraft to ensure that system-wide safety properties are maintained. This paper presents the criteria method, which increases the quality and efficiency of a safety assurance analysis for distributed air traffic concepts. The criteria standard is shown to provide two key safety properties: safe separation when only one aircraft maneuvers and safe separation when both aircraft maneuver at the same time. This approach is complemented with strong guarantees of correct operation through formal verification. To show that an algorithm is correct, i.e., that it always meets its specified safety property, one must only show that the algorithm satisfies the criteria. Once this is done, then the algorithm inherits the safety properties of the criteria. An important consequence of this approach is that there is no requirement that both aircraft execute the same conflict resolution algorithm. Therefore, the criteria approach allows different avionics manufacturers or even different airlines to use different algorithms, each optimized according to their own proprietary concerns.
Algebraic isotopy in genetics.
Campos, T M; Holgate, P
1987-01-01
It is shown that many of the algebras arising in nonselective genetics are isotopes of the algebras for particularly simple systems of inheritance. Moreover, interesting aspects of the structure are preserved under the relevant isotopies.
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.
Proposals for new standardized general diagnostic criteria for the secondary headaches
DEFF Research Database (Denmark)
Olesen, J; Steiner, T; Bousser, M-G
2009-01-01
Headache classification is a dynamic process through clinical testing and re-testing of current and proposed criteria. After publication of the second edition of the International Classification of Headache Disorders (ICHD-II), need arose for revisions in the classification of medication overuse...... into the internet-based version of the appendix of ICHD-II. During 2009 the Classification Committee will apply the general criteria to all the specific types of secondary headaches. These, and other changes, will be included in a revision of the entire classification entitled ICHD-IIR, expected to be published...... in 2010. ICHD-IIR will be printed and posted on the website and will be the official classification of the International Headache Society. Unfortunately, it will be necessary to translate ICHD-IIR into the many languages of the world, but the good news is that no major changes to the headache...
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.
Algebraic statistics computational commutative algebra in statistics
Pistone, Giovanni; Wynn, Henry P
2000-01-01
Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics. It begins with an introduction to Gröbner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case with new application to coherent systems in reliability and two level factorial designs. The work paves the way, in the last two chapters, for the application of computer algebra to discrete probability and statistical modelling through the important concept of an algebraic statistical model.As the first book on the subject, Algebraic Statistics presents many opportunities for spin-off research and applications and should become a landmark work welcomed by both the statistical community and its relatives in mathematics and computer science.
Indian Academy of Sciences (India)
We study the structure of split Malcev algebras of arbitrary dimension over an algebraically closed field of characteristic zero. We show that any such algebras is of the form M = U + ∑ j I j with U a subspace of the abelian Malcev subalgebra and any I j a well described ideal of satisfying [ I j , I k ] = 0 if ≠ .
Foundations of algebraic geometry
Weil, A
1946-01-01
This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Energy Technology Data Exchange (ETDEWEB)
Volterra, L.; De Nava, V.; Mancini, L. [Istituto Superiore di Sanita`, Rome (Italy). Lab. di Igiene Ambientale
1998-12-31
The report concerns two Italian laws, n.130/92 and 131/92 derived from the EEC directives n. 659/78 and 923/91 concerning water quality respectively for freshwater and for marine water suitable for shellfish. The meaning of each parameter, included in the two laws, is explained considering that their purpose is protection and promotion of aquatic life. This review was originated by a request that Ministry of the Environment directed to the `Istituto Superiore of Sanita` to supply information necessary for a possible definition of lacking standards and to draw up appropriate monitoring plans. [Italiano] Il rapporto si riferisce a due decreti, il numero 130/92 e il 131/92 recepiti dalle direttive comunitarie 659/78 e 923/91 riguardanti rispettivamente la qualita` delle acque dolci che richiedono protezione e miglioramento per la vita dei pesci e i requisiti di qualita` delle acque per la molluschiocoltura. Si elencano isignificati dei singoli parametri introdotti nelle due normative il cui scopo e` quello di proteggere e favorire lo sviluppo della vita acquatica in ambienti di acqua dolce e marina. La rassegna e` nata da una richiesta formulata all`Istituto Superiore di Sanita` da parte del Ministero dell`Ambiente per fornire indicazioni necessarie per la eventuale definizione degli standard mancanti ed indirizzi per la formulazione di idonei piani di sorveglianza.
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
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
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
International Nuclear Information System (INIS)
Kainberger, Franz; Pokieser, Peter; Imhof, Herwig; Czembirek, Heinrich; Fruehwald, Franz
2002-01-01
Guidelines can be regarded as special forms of algorithms and have been shown to be useful tools for supporting medical decision making. With the Council Directive 97/43/Euratom recommendations concerning referral criteria for medical exposure have to be implemented into national law of all EU member states. The time- and cost-consuming efforts of developing, implementing, and updating such guidelines are balanced by the acceptance in clinical practice and eventual better health outcomes. Clearly defined objectives with special attention drawn on national and regional differences among potential users, support from organisations with expertise in evidence-based medicine, separated development of the evidence component and the recommendations component, and large-scale strategies for distribution and implementation are necessary. Editors as well as users of guidelines for referral criteria have to be aware which expectations can be met and which cannot be fulfilled with this instrument; thus, dealing with guidelines requires a new form of ''diagnostic reasoning'' based on medical ethics. (orig.)
International Nuclear Information System (INIS)
Kang, Tae Wook; Rhim, Hyun Chul; Lee, Min Woo; Kim, Young Sun; Choi, Dongil; Lim, Hyo Keun
2014-01-01
To perform a systematic review of compliance with standardized terminology and reporting criteria for radiofrequency (RF) tumor ablation, proposed by the International Working Group on Image-Guided Tumor Ablation in 2003, in the published reports. Literature search in the PubMed database was performed using index keywords, PubMed limit system, and eligibility criteria. The entire content of each article was reviewed to assess the terminology used for procedure terms, imaging findings, therapeutic efficacy, follow-up, and complications. Accuracy of the terminology and the use of alternative terms instead of standard terminology were analyzed. In addition, disparities in accuracy of terminology in articles according to the medical specialty and the type of radiology journal were evaluated. Among the articles (n = 308) included in this study, the accuracy of the terms 'procedure or session', 'treatment', 'index tumor', 'ablation zone', 'technical success', 'primary technique effectiveness rate', 'secondary technique effectiveness rate', 'local tumor progression', 'major complication', and 'minor complication' was 97% (298/307), 97% (291/300), 8% (25/307), 65% (103/159), 55% (52/94), 33% (42/129), 94% (17/18), 45% (88/195), 99% (79/80), and 100% (77/77), respectively. The overall accuracy of each term showed a tendency to improve over the years. The most commonly used alternative terms for 'technical success' and 'local tumor progression' were 'complete ablation' and 'local (tumor) recurrence', respectively. The accuracy of terminology in articles published in radiology journals was significantly greater than that of terminology in articles published in non-radiology journals, especially in Radiology and The Journal of Vascular and Interventional Radiology. The proposal for standardization of terminology and reporting criteria for RF tumor ablation has been gaining support according to the recently published scientific reports, especially in the field of radiology
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
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
Discrete Minimal Surface Algebras
Directory of Open Access Journals (Sweden)
Joakim Arnlind
2010-05-01
Full Text Available We consider discrete minimal surface algebras (DMSA as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sl_n (any semi-simple Lie algebra providing a trivial example by itself. A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.
Park, K-H; Sandor, G K; Kim, Y-D
2016-01-01
The purpose of this study was to compare the postoperative stability following bimaxillary surgery performed either with or without preoperative orthodontic treatment, in class III malocclusion patients. These patients were enrolled using standardized inclusion criteria. Forty patients with a class III malocclusion were included in this retrospective study. Inclusion criteria were class III malocclusion with and without premolar extraction, stability. With respect to postsurgical changes, significant differences were observed in the changes for the vertical reference plane to the posterior nasal spine, horizontal reference plane to B-point, and occlusal plane angle in both groups. No statistically significant differences in the relapse rates were observed between the two groups. No significant differences were observed between the two groups in terms of the postoperative stability. Copyright © 2015 International Association of Oral and Maxillofacial Surgeons. Published by Elsevier Ltd. All rights reserved.
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.
40 CFR 260.34 - Standards and criteria for non-waste determinations.
2010-07-01
... WASTES (CONTINUED) HAZARDOUS WASTE MANAGEMENT SYSTEM: GENERAL Rulemaking Petitions § 260.34 Standards and... determination that a hazardous secondary material is not discarded and therefore not a solid waste. The... determination for hazardous secondary material which is reclaimed in a continuous industrial process if the...
Standard for design criteria for decommissioning of nuclear fuel reprocessing plants
International Nuclear Information System (INIS)
Graham, H.B.
1976-01-01
This paper was developed by the ANSI Standards Committee N46. Deactivation or shutdown followed by continued operation on the same site does not constitute decommissioning. It is felt that abandonment with entombment of the highly radioactive parts of the plant is the only economically feasible alternative
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.
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.
AT -algebras and extensions of AT-algebras
Indian Academy of Sciences (India)
algebra by an AT-algebra and E has real rank zero, then E is an AT-algebra if and only if the index maps are both zero. Accordingly, in this paper, we attempt to describe a characterization of an extension E of an AT-algebra by an AF-algebra if E ...
Donor selection criteria for liver transplantation in Argentina: are current standards too rigorous?
Dirchwolf, Melisa; Ruf, Andrés E; Biggins, Scott W; Bisigniano, Liliana; Hansen Krogh, Daniela; Villamil, Federico G
2015-02-01
Organ shortage is the major limitation for the growth of deceased donor liver transplant worldwide. One strategy to ameliorate this problem is to maximize the liver utilization rate. To assess predictors of liver utilization in Argentina. The national database was used to analyze transplant activity in 2010. Donor, recipient, and transplant variables were evaluated as predictors of graft utilization of number of rejected donor offers before grafting and with the occurrence of primary nonfunction (PNF) or early post-transplant mortality (EM). Of the 582 deceased donors, 293 (50.3%) were recovered for liver transplant. Variables associated with the nonrecovery of the liver were age ≥46 years, umbilical perimeter ≥92 cm, organ procurement outside Gran Buenos Aires, AST ≥42 U/l and ALT ≥29 U/l. The median number of rejected offers before grafting was 4, and in 71 patients (25%), there were ≥13. The only independent predictor for the occurrence of PNF (3.4%) or EM (5.2%) was the recipient's emergency status. During 2010 in Argentina, the liver was recovered in only half of donors. The low incidence of PNF and EM and the characteristics of the nonrecovered liver donors suggest that organ acceptance criteria should be less rigorous. © 2014 Steunstichting ESOT.
Yoneda algebras of almost Koszul algebras
Indian Academy of Sciences (India)
a left (2, hQ − 2)-Koszul algebra (see Definition 2.1 below), and the Yoneda algebra of. A is isomorphic to a twisted ... is quadratic if R is a subspace of V ⊗ V . The quadratic dual A! of A is defined to be. T (V ∗)/(R⊥) .... (Q, ρ) is a stable bound quiver of Loewy length p + 1, and the Nakayama translation on. Q0 is induced by a ...
International Nuclear Information System (INIS)
Pisarev, V.V.; Tsybizov, I.S.
1976-01-01
Radioactive products discharge into natural water streams results in the necessity to regulate nuclear power plant discharges to ensure radiation safety (RS) for population using a river and surrounding river territory. To ensure RS it is necessary to set scientific-founded standards of permissible discharge level of liquid radioactive wastes (LRW) from nuclear power plant assuring observance of hygienic requirements for surface water puring. Volume of permissible LRW discharge into river systems must be set both with provision for concrete physical-geographycal conditions, specficity of utilizing the river and river valley and social-economical peculiarities of crtical population groups. The value of permissible LRW discharge into river systems is determined by three criterion groups: radiological, ecological and hydrological ones. By means of radiological group the internal and external irradiation doses for the whole body and its separate organs are set and RS of population is determined. Ecological criteria include a number of parameters (coefficients of accumulation, distribution and transition) determining quantitative ratios between radioactive element contents in water and separate links of biological chains: soil/water, fish/water, vegetables/water and others. Hydrological criteria determine the degree of waste dilution in rivers, control radioactive contamination of flood-lands areas and in common with ecological criteria determine radionuclide contents in soil and food products. A method of determining average annual values of LRW dilution in river waters is presented [ru
Atkinson, Kayla M; Koenka, Alison C; Sanchez, Carmen E; Moshontz, Hannah; Cooper, Harris
2015-03-01
A complete description of the literature search, including the criteria used for the inclusion of reports after they have been located, used in a research synthesis or meta-analysis is critical if subsequent researchers are to accurately evaluate and reproduce a synthesis' methods and results. Based on previous guidelines and new suggestions, we present a set of focused and detailed standards for reporting the methods used in a literature search. The guidelines cover five search strategies: reference database searches, journal and bibliography searches, searches of the reference lists of reports, citation searches, and direct contact searches. First, we bring together all the unique recommendations made in existing guidelines for research synthesis. Second, we identify gaps in reporting standards for search strategies. Third, we address these gaps by providing new reporting recommendations. Our hope is to facilitate successful evaluation and replication of research synthesis results. Copyright © 2014 John Wiley & Sons, Ltd.
International Nuclear Information System (INIS)
Hernandez Caceres, Jose Luis; Hong, Rolando; Martinez Ortiz, Carlos; Sautie Castellanos, Miguel; Valdes, Kiria; Guevara Erra, Ramon
2004-10-01
Under the assumption of even point mutation pressure on the DNA strand, rates for transitions from one amino acid into another were assessed. Nearly 25% of all mutations were silent. About 48% of the mutations from a given amino acid stream either into the same amino acid or into an amino acid of the same class. These results suggest a great stability of the Standard Genetic Code respect to mutation load. Concepts from chemical equilibrium theory are applicable into this case provided that mutation rate constants are given. It was obtained that unequal synonymic codon usage may lead to changes in the equilibrium concentrations. Data from real biological species showed that several amino acids are close to the respective equilibrium concentration. However in all the cases the concentration of leucine nearly doubled its equilibrium concentration, whereas for the stop command (Term) it was about 10 times lower. The overall distance from equilibrium for a set of species suggests that eukaryotes are closer to equilibrium than prokaryotes, and the HIV virus was closest to equilibrium among 15 species. We obtained that contemporary species are closer to the equilibrium than the Last Universal Common Ancestor (LUCA) was. Similarly, nonpreserved regions in proteins are closer to equilibrium than the preserved ones. We suggest that this approach can be useful for exploring some aspects of biological evolution in the framework of Standard Genetic Code properties. (author)
Pilot test of ANSI draft standard N13.29 environmental dosimetry -- Performance criteria for testing
Energy Technology Data Exchange (ETDEWEB)
Klemic, G.; Shebell, P.; Monetti, M.; Raccah, F. [Dept. of Energy, New York, NY (United States). Environmental Measurement Lab.; Shobe, J.; Lamperti, P.; Soares, C. [National Inst. of Standards and Technology, Gaithersburg, MD (United States); Sengupta, S. [Brookhaven National Lab., Upton, NY (United States)
1998-09-01
American National Standards Institute Draft N13.29 describes performance tests for environmental radiation dosimetry providers. If approved it would be the first step toward applying the types of performance testing now required in personnel dosimetry to environmental radiation monitoring. The objective of this study was to pilot test the draft standard, before it undergoes final balloting, on a small group of dosimetry providers that were selected to provide a mix of facility types, thermoluminescent dosimeter designs and monitoring program applications. The first phase of the pilot test involved exposing dosimeters to laboratory photon, beta, and x-ray sources at routine and accident dose levels. In the second phase, dosimeters were subjected to ninety days of simulated environmental conditions in an environmental chamber that cycled through extremes of temperature and humidity. Two out of seven participants passed all categories of the laboratory testing phase, and all seven passed the environmental test phase. While some relatively minor deficiencies were uncovered in the course of the pilot test, the results show that draft N13.29 describes useful tests that could be appropriate for environmental dosimetry providers. An appendix to this report contains recommendations that should be addressed by the N13.29 working group before draft N13.29 is submitted for balloting.
Evolution algebras and their applications
Tian, Jianjun Paul
2008-01-01
Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to some further research topics.
International Nuclear Information System (INIS)
Labutin, Timur A.; Zaytsev, Sergey M.; Popov, Andrey M.; Seliverstova, Irina V.; Bozhenko, Sergey E.; Zorov, Nikita B.
2013-01-01
The use of the reference line of an internal standard in LIBS is a usual way to eliminate or reduce the fluctuations of plasma parameters from pulse to pulse as well as from sample to sample. Thermodynamic criterion, i.e. closeness of excitation potentials of the analytical line and the reference one, is often used to select an appropriate reference line. In this work, we propose an alternative criterion based on searching the best correlated pairs of lines under the variations of laser energy. Two criteria were compared for high-alloy steels and soils of different origins. The discrepancy among the values of plasma temperature calculated from Fe I, Mn I and Cr I transitions was found under the conditions of slightly changed laser fluence on steel samples. On the other hand, the agreement between plasma temperatures, obtained for Fe I and Mn I transitions, was demonstrated in plasma on soil samples. Calibration results obtained for manganese in steels and lead in soils show that thermodynamic criterion can be an appropriate way for choosing an internal standard only under LTE conditions. Two lines of Mn I at 403.07 nm and 404.14 nm and Pb I at 405.78 nm were the analytical lines for the quantification of manganese in steels and lead in soils, respectively. The use of the correlative criterion seems to be suitable for internal standardization under LTE or non-LTE conditions. Probable limitations of the correlative criterion and its possibilities to identify weak lines are discussed in the article. - Highlights: • Novel criterion for internal standard selection, based on the correlation of analytical line and reference one • Comparison of correlation and thermodynamic criteria • Correlation analysis of the spectrum can be useful for atomic line identification. • Correlation approach can be used in LTE and non-LTE conditions
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...
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.)
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...
Endramawan, T.; Sifa, A.
2018-02-01
The purpose of this research is to know the type of discontinuity of SMAW welding result and to determine acceptance criteria based on American Society of Mechanical Engineer (ASME) standard. Material used is mild steel 98,71% Fe and 0,212% C with hardness 230 VHN with specimen diameter 20 cm and thickness 1.2 cm which is welded use SMAW butt joint with electrode for rooting LB 52U diameter 2.6 mm, current 70 Ampere and voltage 380 volt, filler used LB 5218 electrode diameter 3.2 mm with current 80 Ampere and 380 volt. The method used to analyze the welded with non destructive test dye penetrant (PT) method to see indication on the surface of the object and Ultrasonic (UT) to see indication on the sub and inner the surface of the object, the result is discontinuity recorded and analyzed and then the discontinuity is determine acceptance criteria based on the American Society of Mechanical Engineer (ASME) standards. The result show the discontinuity of porosity on the surface of the welded and inclusion on sub material used ultrasonic test, all indication on dye penetrant or ultrasonic test if there were rejected of result of welded that there must be gouging on part which rejected and then re-welding.
Standard criteria and methods to assess the reclamation of native vegetation on mined land
International Nuclear Information System (INIS)
Humphries, R.N.; Benyon, P.R.
1999-01-01
There is currently much interest in the re-establishment of native (semi-natural) vegetation in mineral workings in the UK. It is expected that future planning consents will have conditions attached which require evidence that the proposed communities have been achieved. At present there is no standard approach. This paper describes a formal sample based method which enables assessment of plant community, species richness and species of particular interest at any point in time and their course of development. The method is illustrated by use of data collected for sown grassland on a restored opencast coal site in South Wales. Further development work is likely to be necessary and comparison with other recently recommended methods is suggested
Developing glovebox robotics to meet the national robot safety standard and nuclear safety criteria
International Nuclear Information System (INIS)
McMahon, T.T.; Sievers, R.H.
1991-09-01
Development of a glove box based robotic system by the Lawrence Livermore National Laboratory (LLNL) is reported. Safety issues addressed include planning to meet the special constraints of operations within a hazardous material glove box and with hostile environments, compliance with the current and draft national robotic system safety standards, and eventual satisfaction of nuclear material handling requirements. Special attention has been required for the revision to the robot and control system models which antedate adoption of the present national safety standard. A robotic test bed, using non-radioactive surrogates is being activated at the Lawrence Livermore National Laboratory to develop the material handling system and the process interfaces for future special nuclear material processing applications. Part of this effort is to define, test, and revise adequate safety controls to ensure success when the system is eventually deployed at a DOE site. The current system is primarily for demonstration and testing, but will evolve into the baseline configuration from which the production system is to be derived. This results in special hazards associated with research activities which may not be present on a production line. Nuclear safety is of paramount importance and has been successfully addressed for 50 years in the DOE weapons production complex. It carries its particular requirements for robot systems and manual operations, as summarized below: Criticality must be avoided (materials cannot consolidate or accumulate to approach a critical mass). Radioactive materials must be confined. The public and workers must be protected from accountable radiation exposure. Nuclear material must be readily retrievable. Nuclear safety must be conclusively demonstrated through hazards analysis. 7 refs
Introduction to abstract algebra
Smith, Jonathan D H
2008-01-01
Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles. A Quick Introduction to Algebra The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. The author also uses equivalence relations to introduc
Berryman, Doris L.
The suggested standards and evaluative criteria are designed to assist hospitals and other residential institutions in evaluating recreation services provided to residents, primarily children and youth. Described are the development of the standards and the rating instrument, guidelines for using the standards, evaluation and scoring procedures,…
Kurosh, A G; Stark, M; Ulam, S
1965-01-01
Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University. The book starts with the basics of algebra. The text briefly describes the theory of sets, binary relations, equivalence relations, partial ordering, minimum condition, and theorems equivalent to the axiom of choice. The text gives the definition of binary algebraic operation and the concepts of groups, groupoids, and semigroups. The book examines the parallelism between the theory of groups and the theory of rings; such examinations show the
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
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.
Albert, A A
1939-01-01
The first three chapters of this work contain an exposition of the Wedderburn structure theorems. Chapter IV contains the theory of the commutator subalgebra of a simple subalgebra of a normal simple algebra, the study of automorphisms of a simple algebra, splitting fields, and the index reduction factor theory. The fifth chapter contains the foundation of the theory of crossed products and of their special case, cyclic algebras. The theory of exponents is derived there as well as the consequent factorization of normal division algebras into direct factors of prime-power degree. Chapter VI con
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
Comparison of melatonin products against USP's nutritional supplements standards and other criteria.
Hahm, H; Kujawa, J; Augsburger, L
1999-01-01
To evaluate and compare the quality of a sample of melatonin products, as measured by the United States Pharmacopeial Convention (USP) General Tests and Assays for Nutritional Supplements (other than Microbial Limits) and certain other tests. Five immediate-release, two sublingual, and two controlled-release products were randomly gathered from a health food store, groceries, and pharmacies in the Baltimore-Washington metropolitan area. Weight variation, disintegration (not applicable for controlled-release products), and drug dissolution, based on USP standards. Twelve-hour dissolution profiles were obtained from the controlled-release products. All tablets were also evaluated for friability following the USP procedure and for hardness following unofficial procedures. All products passed the weight variation test. Two products showed excessive friability. Three immediate-release products failed both the disintegration and the dissolution tests. One of the three products demonstrated a threefold difference in hardness. One controlled-release product released 90% of melatonin in four hours in the dissolution test; the other released 90% of its content in 12 hours. Some products showed evidence of poor formulation and/or poor quality control as indicated by excessive friability, failure to disintegrate and dissolve, and excessive variation in hardness. In vitro release profiles of the two controlled-release products were substantially different. The poor quality of some supplements should be a concern to consumers and health care providers.
National Research Council Canada - National Science Library
2003-01-01
... (SJMAC-DEM) to test the Ammunition Peculiar Equipment (APE) 1995 NIR Propellant Analyzer, to MIL-STD-398, "Military Standard Shields, Operational for Ammunition Operations, Criteria for Design of and Tests for Acceptance...
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...
International Nuclear Information System (INIS)
Elgohary, M.; Saudy, A.; Orbovic, N.; Dejan, D.
2006-01-01
With the surging interest in new build nuclear all over the world and a permanent interest in earthquake resistance of nuclear plants, there is a need to quantify the safety margins in nuclear buildings design in comparison to conventional buildings in order to increase the public confidence in the safety of nuclear power plants. Nuclear (CAN3-N289 series) and conventional (NBCC 2005) seismic standards have different approaches regarding the design of civil structures. The origin of the differences lays in the safety philosophy behind the seismic nuclear and conventional standards. Conventional seismic codes contain the minimal requirement destined primarily to safeguard against major structural failure and loss of life. It doesn't limit damage to a certain acceptable degree or maintain function. Nuclear seismic code requires that structures, systems and components important to safety, withstand the effects of earthquakes. The requirement states that for equipment important to safety, both integrity and functionality should be ascertained. The seismic hazard is generally defined on the basis of the annual probability of exceedence (return period). There is a major difference on the return period and the confidence level for design earthquakes between the conventional and the nuclear seismic standards. The seismic design criteria of conventional structures are based on the use of Force Modification Factors to take into account the energy dissipation by incursion in non-elastic domain and the reserve of strength. The use of such factors to lower intentionally the seismic input is consistent with the safety philosophy of the conventional seismic standard which is the 'non collapse' rather than the integrity and/or the operability of the structures or components. Nuclear seismic standard requires that the structure remain in the elastic domain; energy dissipation by incursion in non-elastic domain is not allowed for design basis earthquake conditions. This is
Learning abstract algebra with ISETL
Dubinsky, Ed
1994-01-01
Most students in abstract algebra classes have great difficulty making sense of what the instructor is saying. Moreover, this seems to remain true almost independently of the quality of the lecture. This book is based on the constructivist belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities which will establish an experiential base for any future verbal explanation. No less, they need to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies as well as on the substantial experience of the authors in teaching astract algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the mathlike programming language ISETL; the main tool for reflections is work in teams of 2-4 students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics...
Bär, Christian; Becker, Christian
In this chapter we will collect those basic concepts and facts related to C*-algebras that will be needed later on. We give complete proofs. In Sects. 1, 2, 3, and 6 we follow closely the presentation in [1]. For more information on C*-algebras, see, e.g. [2-6].
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.
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.)
Indian Academy of Sciences (India)
Discourses on Algebra. Rajaram Nityananda. Discourses on Algebra. Igor R Shafarevich. Narosa Publishing. Pages: 273, Price in India: | 1750. To the Indian reader, the word discourse, evokes a respected figure interpreting divine wisdom to common folk in an accessible fash- ion. I dug a bit deeper with Google trans-.
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)
International Nuclear Information System (INIS)
Talon, M.
1987-01-01
The algebraic set up for anomalies, a la Stora, is reviewed. Then a brief account is provided of the work of M. Dubois Violette, M. Talon, C. Viallet, in which the general algebraic solution to the consistency conditions is described. 34 references
Directory of Open Access Journals (Sweden)
Juliana P. Santos
2015-12-01
Full Text Available In Latin American, there is currently a regional action with the main purposes of putting the concept of severe neonatal morbidity in practice and formulating proposals for interventions. A general overview of neonatal health conditions, including morbidity and mortality, is provided to update regional knowledge on the topic. An example of the development and implementation of the concept of maternal near miss is also provided, followed by results from a systematic review covering all previously published studies on Neonatal Near Miss. Finally, some proposals for building a common concept on the topic and for launching a prospective surveillance study are presented. A Neonatal Near Miss is a neonate who had a severe morbidity (organ dysfunction or failure but who survived this condition within the first 27 days of life. The pragmatic criteria recommended to be used are as follows: birth weight below 1700 g, Apgar score below 7 at 5 minutes of life and gestational age below 33 weeks. As a proxy for organ dysfunction, the following management criteria are also confirmed: parenteral therapeutic antibiotics; nasal continuous positive airway pressure; any intubation during the first 27 days of life; phototherapy within the first 24 h of life; cardiopulmonary resuscitation; the use of vasoactive drugs, anticonvulsants, surfactants, blood products and steroids for refractory hypoglycemia and any surgical procedure. Although this study starts from a regional perspective, this topic is clearly globally relevant. All nations, especially low and middle-income countries, could benefit from the proposed standardization.
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...
Algebra task sheets : grades pk-2
Reed, Nat
2009-01-01
For grades PK-2, our Common Core State Standards-based resource meets the algebraic concepts addressed by the NCTM standards and encourages the students to learn and review the concepts in unique ways. Each task sheet is organized around a central problem taken from real-life experiences of the students.
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
International Nuclear Information System (INIS)
1977-01-01
Minimum standards and guidelines to be applied by State agencies and New Jersey health systems agencies in the examination of certificate-of-need applications and in the development of planning activities for radiation oncology units in health care facilities are presented. Radiation oncology is a medical discipline devoted to education and research in the use of ionizing radiation for the treatment of neoplastic disease. The proper application of radiation can be directed at either curative or palliative intent. It is an important and effective technique for the management of cancer. Radiotherapy equipment in clinical use is divided into four main categories: superficial, orthovoltage, megavoltage, and treatment planning facilities. Particular attention is given to megavoltage equipment which emits or generates rays over 1,000 kilovolts. These high energy rays effect better penetration of human tissue and are skin-sparing in nature, thus allowing for better tumor-to- skin dose ratios. The regionalization of megavoltage therapy services is discussed. Data on hospital megavoltage facilities in New Jersey for 1974, 1975, and 1976 are provided. The standards and guidelines pertain to utilization, personnel, and general criteria. A form for use by megavoltage radiation therapy units is appended
Algebra Survival Guide A Conversational Handbook for the Thoroughly Befuddled
Rappaport, Josh
2011-01-01
If you think algebra has to be boring, confusing and unrelated to anything in the real world, think again! Written in a humorous, conversational style, this book gently nudges students toward success in pre-algebra and Algebra I. With its engaging question/answer format and helpful practice problems, glossary and index, it is ideal for homeschoolers, tutors and students striving for classroom excellence. It features funky icons and lively cartoons by award-winning Santa Fe artist Sally BlakemoreThe Algebra Survival Guide is the winner of a Paretns' Choice award, and it meets the Standards 2000
BLAS- BASIC LINEAR ALGEBRA SUBPROGRAMS
Krogh, F. T.
1994-01-01
The Basic Linear Algebra Subprogram (BLAS) library is a collection of FORTRAN callable routines for employing standard techniques in performing the basic operations of numerical linear algebra. The BLAS library was developed to provide a portable and efficient source of basic operations for designers of programs involving linear algebraic computations. The subprograms available in the library cover the operations of dot product, multiplication of a scalar and a vector, vector plus a scalar times a vector, Givens transformation, modified Givens transformation, copy, swap, Euclidean norm, sum of magnitudes, and location of the largest magnitude element. Since these subprograms are to be used in an ANSI FORTRAN context, the cases of single precision, double precision, and complex data are provided for. All of the subprograms have been thoroughly tested and produce consistent results even when transported from machine to machine. BLAS contains Assembler versions and FORTRAN test code for any of the following compilers: Lahey F77L, Microsoft FORTRAN, or IBM Professional FORTRAN. It requires the Microsoft Macro Assembler and a math co-processor. The PC implementation allows individual arrays of over 64K. The BLAS library was developed in 1979. The PC version was made available in 1986 and updated in 1988.
Non-unique factorizations algebraic, combinatorial and analytic theory
Geroldinger, Alfred
2006-01-01
From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory. Focused efforts over the past few decades have wrought a great number and variety of results. However, these remain dispersed throughout the vast literature. For the first time, Non-Unique Factorizations: Algebraic, Combinatorial, and Analytic Theory offers a look at the present state of the theory in a single, unified resource.Taking a broad look at the algebraic, combinatorial, and analytic fundamentals, this book derives factorization results and applies them in concrete arithmetical situations using appropriate transfer principles. It begins with a basic introduction that can be understood with knowledge of standard basic algebra. The authors then move to the algebraic theory of monoids, arithmetic theory of monoids, the structure of sets of lengths, additive group theory, arithmetical invariants, and the arithmetic of Krull monoids. They also provide a s...
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
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
Orthogonal symmetries and Clifford algebras
Indian Academy of Sciences (India)
algebra over a field K, can be regarded as the Clifford algebra of a suitable nondegenerate quadratic form q over the base field K. In [13], such a form q is also explicitly constructed. The Grassmann algebra (or the exterior algebra) may also be regarded as the Clifford alge- bra of the null (totally isotropic) quadratic form.
Coreflections in Algebraic Quantum Logic
Jacobs, Bart; Mandemaker, Jorik
2012-07-01
Various generalizations of Boolean algebras are being studied in algebraic quantum logic, including orthomodular lattices, orthomodular po-sets, orthoalgebras and effect algebras. This paper contains a systematic study of the structure in and between categories of such algebras. It does so via a combination of totalization (of partially defined operations) and transfer of structure via coreflections.
On algebraic time-derivative estimation and deadbeat state reconstruction
DEFF Research Database (Denmark)
Reger, Johann; Jouffroy, Jerome
2009-01-01
This paper places into perspective the so-called algebraic time-derivative estimation method recently introduced by Fliess and co-authors with standard results from linear statespace theory for control systems. In particular, it is shown that the algebraic method can essentially be seen...
Introduction to Algebra Curriculum Guide, Grade 8, 1987. Bulletin 1802.
Louisiana State Dept. of Education, Baton Rouge. Div. of Academic Programs.
Because of the high incidence of failure in algebra I among ninth-grade students, the Louisiana State Board of Elementary and Secondary Education requested the development of this guide with the intention of providing a good pre-algebra foundation. The purposes of the guide are to recognize standards that involve the application of mathematical…
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 ...
Özen, Kahraman Esen; Tosun, Murat
2018-01-01
In this study, we define the elliptic biquaternions and construct the algebra of elliptic biquaternions over the elliptic number field. Also we give basic properties of elliptic biquaternions. An elliptic biquaternion is in the form A0 + A1i + A2j + A3k which is a linear combination of {1, i, j, k} where the four components A0, A1, A2 and A3 are elliptic numbers. Here, 1, i, j, k are the quaternion basis of the elliptic biquaternion algebra and satisfy the same multiplication rules which are satisfied in both real quaternion algebra and complex quaternion algebra. In addition, we discuss the terms; conjugate, inner product, semi-norm, modulus and inverse for elliptic biquaternions.
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)
Deficiently extremal Gorenstein algebras
Indian Academy of Sciences (India)
Thus, R/I is a Cohen–. Macaulay algebra of Type 1, and hence R/I is Gorenstein. In view of Theorem 2.1, R/I is a nearly (or 1-deficient) extremal Gorenstein algebra. We now shall describe a result of Bruns and Hibi [1] which characterizes the Stanley–. Reisner rings having 2-pure but not 2-linear resolutions. Theorem 2.3.
Intermediate algebra a textworkbook
McKeague, Charles P
1985-01-01
Intermediate Algebra: A Text/Workbook, Second Edition focuses on the principles, operations, and approaches involved in intermediate algebra. The publication first takes a look at basic properties and definitions, first-degree equations and inequalities, and exponents and polynomials. Discussions focus on properties of exponents, polynomials, sums, and differences, multiplication of polynomials, inequalities involving absolute value, word problems, first-degree inequalities, real numbers, opposites, reciprocals, and absolute value, and addition and subtraction of real numbers. The text then ex
Beginning algebra a textworkbook
McKeague, Charles P
1985-01-01
Beginning Algebra: A Text/Workbook, Second Edition focuses on the principles, operations, and approaches involved in algebra. The publication first elaborates on the basics, linear equations and inequalities, and graphing and linear systems. Discussions focus on solving linear systems by graphing, elimination method, graphing ordered pairs and straight lines, linear and compound inequalities, addition and subtraction of real numbers, and properties of real numbers. The text then examines exponents and polynomials, factoring, and rational expressions. Topics include multiplication and division
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
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
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
The 'golden' algebraic equations
International Nuclear Information System (INIS)
Stakhov, A.; Rozin, B.
2006-01-01
The special case of the (p + 1)th degree algebraic equations of the kind x p+1 = x p + 1 (p = 1, 2, 3, ?) is researched in the present article. For the case p = 1, the given equation is reduced to the well-known Golden Proportion equation x 2 = x + 1. These equations are called the golden algebraic equations because the golden p-proportions τ p , special irrational numbers that follow from Pascal's triangle, are their roots. A research on the general properties of the roots of the golden algebraic equations is carried out in this article. In particular, formulas are derived for the golden algebraic equations that have degree greater than p + 1. There is reason to suppose that algebraic equations derived by the authors in the present article will interest theoretical physicists. For example, these algebraic equations could be found in the research of the energy relationships within the structures of many compounds and physical particles. For the case of butadiene (C 4 H 6 ), this fact is proved by the famous physicist Richard Feynman
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.
Real division algebras and other algebras motivated by physics
Energy Technology Data Exchange (ETDEWEB)
Benkart, G.; Osborn, J.M.
1981-02-01
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.
Kac-Moody algebra is not hidden symmetry of chiral models
International Nuclear Information System (INIS)
Devchand, C.; Schiff, J.
1997-01-01
A detailed examination of the infinite dimensional loop algebra of hidden symmetry transformations of the Principal Chiral Model reveals it to have a structure differing from a standard centreless Kac-Moody algebra. A new infinite dimensional Abelian symmetry algebra is shown to preserve a symplectic form on the space of solutions. (author). 15 refs
Bensaci, Mekki; Flanagan, Shawn; Sandison, Taylor
2018-03-01
For effective antibacterial therapy, physicians require qualitative test results using susceptibility breakpoints provided by clinical microbiology laboratories. This article summarizes the key components used to establish the Clinical Laboratory Standards Institute (CLSI) breakpoints for tedizolid. First, in vitro studies using recent surveillance and clinical trial isolates ascertained minimal inhibitory concentration (MIC) distributions against pertinent organisms, including staphylococci, streptococci, and enterococci. Studies in animal models of infection determined rates of antibacterial efficacy and survival following administration of tedizolid phosphate at doses equivalent to those in humans. Pharmacokinetic and pharmacodynamic analyses examined the relationship between plasma concentrations and MICs against the target organism. Finally, clinical trials assessed clinical and microbiologic outcomes by MIC. All these data were evaluated and combined to obtain the ratified CLSI susceptibility criteria for tedizolid of ≤0.5μg/mL for Staphylococcus aureus, Streptococcus pyogenes, Streptococcus agalactiae, and Enterococcus faecalis and ≤0.25μg/mL for Streptococcus anginosus group. Copyright © 2017 Elsevier Inc. All rights reserved.
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...
H∞-control for the Wiener algebra
Iftime, Orest; Zwart, Hans; Martins de Carvalho, J.L.; Fontes, F.A.C.C.; de Pinho, M.D.R.
2001-01-01
We provide necessary and sufficient conditions for the solvability of the standard H∞-suboptimal control problem for systems with the transfer function in a subalgebra of the quotient field of the Wiener algebra. These conditions are formulated in terms of the existence of two J-spectral
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
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
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.
A first graduate course in abstract algebra
Wickless, WJ
2004-01-01
Since abstract algebra is so important to the study of advanced mathematics, it is critical that students have a firm grasp of its principles and underlying theories before moving on to further study. To accomplish this, they require a concise, accessible, user-friendly textbook that is both challenging and stimulating. A First Graduate Course in Abstract Algebra is just such a textbook.Divided into two sections, this book covers both the standard topics (groups, modules, rings, and vector spaces) associated with abstract algebra and more advanced topics such as Galois fields, noncommutative rings, group extensions, and Abelian groups. The author includes review material where needed instead of in a single chapter, giving convenient access with minimal page turning. He also provides ample examples, exercises, and problem sets to reinforce the material. This book illustrates the theory of finitely generated modules over principal ideal domains, discusses tensor products, and demonstrates the development of det...
n-ary algebras: a review with applications
International Nuclear Information System (INIS)
De Azcarraga, J A; Izquierdo, J M
2010-01-01
This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations are algebraic structures in which the two-entry Lie bracket has been replaced by a bracket with n entries. Each type of n-ary bracket satisfies a specific characteristic identity which plays the role of the Jacobi identity for Lie algebras. Particular attention will be paid to generalized Lie algebras, which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized Jacobi identity, and to Filippov (or n-Lie) algebras, which are defined by fully antisymmetric n-brackets that satisfy the Filippov identity. 3-Lie algebras have surfaced recently in multi-brane theory in the context of the Bagger-Lambert-Gustavsson model. As a result, Filippov algebras will be discussed at length, including the cohomology complexes that govern their central extensions and their deformations (it turns out that Whitehead's lemma extends to all semisimple n-Lie algebras). When the skewsymmetry of the Lie or n-Lie algebra bracket is relaxed, one is led to a more general type of n-algebras, the n-Leibniz algebras. These will be discussed as well, since they underlie the cohomological properties of n-Lie algebras. The standard Poisson structure may also be extended to the n-ary case. We shall review here the even generalized Poisson structures, whose generalized Jacobi identity reproduces the pattern of the generalized Lie algebras, and the Nambu-Poisson structures, which satisfy the Filippov identity and determine Filippov algebras. Finally, the recent work of Bagger-Lambert and Gustavsson on superconformal Chern-Simons theory will be briefly discussed. Emphasis will be made on the appearance of the 3-Lie algebra structure and on why the A 4 model may be formulated in terms of an ordinary Lie algebra, and on its Nambu bracket generalization. (topical
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)
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...
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)
Jarvis, Frazer
2014-01-01
The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic. Algebraic Number Theory takes the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the fi...
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.
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:...
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.
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.
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...
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 ...
Atomistic and orthoatomistic effect algebras
Tkadlec, Josef
2008-05-01
We characterize atomistic effect algebras, prove that a weakly orthocomplete Archimedean atomic effect algebra is orthoatomistic and present an example of an orthoatomistic orthomodular poset that is not weakly orthocomplete.
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)
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.)
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
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
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
Artin, Emil
2007-01-01
The present text was first published in 1947 by the Courant Institute of Mathematical Sciences of New York University. Published under the title Modern Higher Algebra. Galois Theory, it was based on lectures by Emil Artin and written by Albert A. Blank. This volume became one of the most popular in the series of lecture notes published by Courant. Many instructors used the book as a textbook, and it was popular among students as a supplementary text as well as a primary textbook. Because of its popularity, Courant has republished the volume under the new title Algebra with Galois Theory.
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.
Pseudo Algebraically Closed Extensions
Bary-Soroker, Lior
2009-07-01
This PhD deals with the notion of pseudo algebraically closed (PAC) extensions of fields. It develops a group-theoretic machinery, based on a generalization of embedding problems, to study these extensions. Perhaps the main result is that although there are many PAC extensions, the Galois closure of a proper PAC extension is separably closed. The dissertation also contains the following subjects. The group theoretical counterpart of pseudo algebraically closed extensions, the so-called projective pairs. Applications to seemingly unrelated subjects, e.g., an analog of Dirichlet's theorem about primes in arithmetic progression for polynomial rings in one variable over infinite fields.
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
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
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
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
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
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
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.
Homomorphisms between C∗ -algebra extensions
Indian Academy of Sciences (India)
C∗. -algebra extensions, Ext groups do not classify extension algebras. So one has to study the isomorphism equivalence of extensions. In fact, a homomorphism between two extension algebras may not map the essential ideal into the other in general, so we have to consider properties of extension homomorphisms.
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.
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
International Nuclear Information System (INIS)
Curtright, Thomas L.; Fairlie, David B.; Zachos, Cosmas K.
2008-01-01
A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations
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…
Energy Technology Data Exchange (ETDEWEB)
Zheng, Nina [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Zhou, Nan [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Fridley, David [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2012-03-01
This report presents a technical review of international minimum energy performance standards (MEPS), voluntary and mandatory energy efficiency labels and test procedures for five products being considered for new or revised MEPS in China: copy machines, external power supply, LED displays, residential gas cooktops and flat-screen televisions. For each product, an overview of the scope of existing international standards and labeling programs, energy values and energy performance metrics and description and detailed summary table of criteria and procedures in major test standards are presented.
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...
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...
Fan, Yun; Zheng, Y L
2000-01-01
This volume is based on the lectures given by the authors at Wuhan University and Hubei University in courses on abstract algebra. It presents the fundamental concepts and basic properties of groups, rings, modules and fields, including the interplay between them and other mathematical branches and applied aspects.
Indian Academy of Sciences (India)
from India, I will describe mainly some work in four topics with which I am familiar: Moduli problem of vector bundles (and the related geometric invariant theory), the work of. CPRamanujam, Frobenius split varieties and algebraic .... One important series of works, by Seshadri in collaboration with V Lakshmibai, C Musili, and.
Indian Academy of Sciences (India)
To the Indian reader, the word discourse, evokes a respected figure interpreting divine wisdom to common folk in an accessible fash- ion. I dug a bit deeper with Google trans- late, and found that the original Russian ti- tle of Shafarevich's book was more like Se- lected Chapters of Algebra and that it was first published in a ...
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
Gudder, Stan
2004-08-01
We define a special type of additive map J on an effect algebra E called a compression. We call J(1) the focus of J and if p is the focus of a compression then p is called a projection. The set of projections in E is denoted by P(E). A compression J is direct if J( a) ≤ a for all a ɛ E. We show that direct compressions are equivalent to projections onto components of cartesian products. An effect algebra E is said to be compressible if every compression on E is uniquely determined by its focus and every compression on E has a supplement. We define and characterize the commutant C(p) of a projection p and show that a compression with focus p is direct if and only if C(p) = E. We show that P(E) is an orthomodular poset. It is proved that the cartesian product of effect algebras is compressible if and only if each component is compressible. We then consider compressible sequential effect algebras, Lüders maps and conditional probabilities.
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,…
Algebraic Thinking through Origami.
Higginson, William; Colgan, Lynda
2001-01-01
Describes the use of paper folding to create a rich environment for discussing algebraic concepts. Explores the effect that changing the dimensions of two-dimensional objects has on the volume of related three-dimensional objects. (Contains 13 references.) (YDS)
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.
16 CFR 1616.35 - Use of alternate apparatus, procedures, or criteria for testing under the standard.
2010-01-01
... SAFETY COMMISSION FLAMMABLE FABRICS ACT REGULATIONS STANDARD FOR THE FLAMMABILITY OF CHILDREN'S SLEEPWEAR... converter) initially introducing items subject to the Standard into commerce to group items into production units, and to test samples from each production unit. See 16 CFR 1616.4. The Standard prescribes an...
16 CFR 1615.35 - Use of alternate apparatus, procedures, or criteria for testing under the standard.
2010-01-01
... SAFETY COMMISSION FLAMMABLE FABRICS ACT REGULATIONS STANDARD FOR THE FLAMMABILITY OF CHILDREN'S SLEEPWEAR... converter) initially introducing items subject to the Standard into commerce to group items into production units, and to test samples from each production unit. See 16 CFR 1615.4 (b), (c) and (d). The Standard...
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.
Barth, John; Burk, Zona Sharp; Serfass, Richard; Harms, Barbara Ann; Houlihan, G. Thomas; Anderson, Gerald; Farley, Raymond P.; Rigsby, Ken; O'Rourke, John
This document, one of a series of reports, focuses on the adoption of principles of quality management, originally developed by W. Edwards Deming, and the Baldrige Criteria for use in education. These processes and tools for systemic organizational management, when comprehensively applied, produce performance excellence and continuous improvement.…
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
Basic math and pre-algebra for dummies
Zegarelli, Mark
2014-01-01
Tips for simplifying tricky basic math and pre-algebra operations Whether you're a student preparing to take algebra or a parent who wants or needs to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you'll build necessary math skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations. Explanations and practical examples that mirror today's teaching methodsRelevant cultural vernacular and referencesStandard For Dummies materials that
Jack, Clifford R; Barkhof, Frederik; Bernstein, Matt A; Cantillon, Marc; Cole, Patricia E; DeCarli, Charles; Dubois, Bruno; Duchesne, Simon; Fox, Nick C; Frisoni, Giovanni B; Hampel, Harald; Hill, Derek LG; Johnson, Keith; Mangin, Jean-François; Scheltens, Philip; Schwarz, Adam J; Sperling, Reisa; Suhy, Joyce; Thompson, Paul M; Weiner, Michael; Foster, Norman L
2012-01-01
Background The promise of Alzheimer’s disease (AD) biomarkers has led to their incorporation in new diagnostic criteria and in therapeutic trials; however, significant barriers exist to widespread use. Chief among these is the lack of internationally accepted standards for quantitative metrics. Hippocampal volumetry is the most widely studied quantitative magnetic resonance imaging (MRI) measure in AD and thus represents the most rational target for an initial effort at standardization. Methods and Results The authors of this position paper propose a path toward this goal. The steps include: 1) Establish and empower an oversight board to manage and assess the effort, 2) Adopt the standardized definition of anatomic hippocampal boundaries on MRI arising from the EADC-ADNI hippocampal harmonization effort as a Reference Standard, 3) Establish a scientifically appropriate, publicly available Reference Standard Dataset based on manual delineation of the hippocampus in an appropriate sample of subjects (ADNI), and 4) Define minimum technical and prognostic performance metrics for validation of new measurement techniques using the Reference Standard Dataset as a benchmark. Conclusions Although manual delineation of the hippocampus is the best available reference standard, practical application of hippocampal volumetry will require automated methods. Our intent is to establish a mechanism for credentialing automated software applications to achieve internationally recognized accuracy and prognostic performance standards that lead to the systematic evaluation and then widespread acceptance and use of hippocampal volumetry. The standardization and assay validation process outlined for hippocampal volumetry is envisioned as a template that could be applied to other imaging biomarkers. PMID:21784356
Free Malcev algebra of rank three
Kornev, Alexandr
2011-01-01
We find a basis of the free Malcev algebra on three free generators over a field of characteristic zero. The specialty and semiprimity of this algebra are proved. In addition, we prove the decomposability of this algebra into subdirect sum of the free Lie algebra rank three and the free algebra of rank three of variety of Malcev algebras generated by a simple seven-dimensional Malcev algebra.
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.
Jacobson-Witt algebras and Lie-admissible algebras
International Nuclear Information System (INIS)
Tomber, M.L.
1981-01-01
For any field PHI of characteristics p > 0 and integer m greater than or equal to 1, there is a Jacobson-Witt algebra which is a Lie algebra. In this paper, all flexible Lie-admissible algebras U, such that U - is a Jacobson-Witt algebra W/sub m/(p), are determined. For any W/sub m/(p), p > 2 there is exactly one such U and it is isomorphic to W/sub m/(p). There are two non-isomorphic algebras U such that U - is isomorphic to W 1 (2), and there are no algebras U with U - isomorphic to W/sub m/(2), m > 1
Energy Technology Data Exchange (ETDEWEB)
Fridley, David; Zheng, Nina; Zhou, Nan
2010-06-01
Since the late 1970s, energy labeling programs and mandatory energy performance standards have been used in many different countries to improve the efficiency levels of major residential and commercial equipment. As more countries and regions launch programs covering a greater range of products that are traded worldwide, greater attention has been given to harmonizing the specific efficiency criteria in these programs and the test methods for measurements. For example, an international compact fluorescent light (CFL) harmonization initiative was launched in 2006 to focus on collaboration between Australia, China, Europe and North America. Given the long history of standards and labeling programs, most major energy-consuming residential appliances and commercial equipment are already covered under minimum energy performance standards (MEPS) and/or energy labels. For these products, such as clothes washers and CFLs, harmonization may still be possible when national MEPS or labeling thresholds are revised. Greater opportunity for harmonization exists in newer energy-consuming products that are not commonly regulated but are under consideration for new standards and labeling programs. This may include commercial products such as water dispensers and vending machines, which are only covered by MEPS or energy labels in a few countries or regions. As China continues to expand its appliance standards and labeling programs and revise existing standards and labels, it is important to learn from recent international experiences with efficiency criteria and test procedures for the same products. Specifically, various types of standards and labeling programs already exist in North America, Europe and throughout Asia for products in China's 2010 standards and labeling programs, namely clothes washers, water dispensers, vending machines and CFLs. This report thus examines similarities and critical differences in energy efficiency values, test procedure specifications and
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
Algebra, Arithmetic, and Geometry
Tschinkel, Yuri
2009-01-01
The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont
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.
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.
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)
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.
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
Directory of Open Access Journals (Sweden)
Sadık Çağlar
2009-04-01
Full Text Available Forest roads are one of the inevitable infrastructures in conducting forestry operations. Around 1000 km under standardized forest roads have been largely repaired in addition to construction of 1000 km new forest roads in Turkey. Implementing uniform road gradient along the road sections is very important in terms of transportation techniques and safety, as well as the geometrical standardizations of the forest road. In this study, current road standards, longitudinal gradient values and their limitations in forest road constructions recommended by Food and Agriculture Organization of the United Nations (FAO and some Europe Union (EU countries were examined. Firstly, the forest road standards and their gradient values have been defined in Turkish forest road construction practices. Afterwards, the forest road standards and the gradient values applied by FAO and some EU countries were presented, and finally, the specifications were examined by comparing them with the current practices in Turkish forestry.
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...
Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras
Paseka, Jan; Riečanová, Zdenka
2010-12-01
We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L. Moreover, if L is complete then L is (o)-topological. Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated.
Krňávek, Jan; Kühr, Jan
2011-12-01
Basic algebras are a generalization of MV-algebras, also including orthomodular lattices and lattice effect algebras. A pre-ideal of a basic algebra is a non-empty subset that is closed under the addition ⊕ and downwards closed with respect to the underlying order. In this paper, we study the pre-ideal lattices of algebras in a particular subclass of basic algebras which are closer to MV-algebras than basic algebras in general. We also prove that finite members of this subclass are exactly finite MV-algebras.
An Algebraic Specification of the Semantic Web
Ksystra, Katerina; Triantafyllou, Nikolaos; Stefaneas, Petros; Frangos, Panayiotis
2011-01-01
We present a formal specification of the Semantic Web, as an extension of the World Wide Web using the well known algebraic specification language CafeOBJ. Our approach allows the description of the key elements of the Semantic Web technologies, in order to give a better understanding of the system, without getting involved with their implementation details that might not yet be standardized. This specification is part of our work in progress concerning the modeling the Social Semantic Web.
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.)
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.
Directory of Open Access Journals (Sweden)
A. Ghahramani
2007-04-01
Full Text Available Background and Aims Permit to work (PTW system as an operational control methods, is an accepted system for control of maintenance activities hazards in chemical industries. The main objective of this study was degree of conformity analysis between existing situation of PTW system and audit criteria. Methods In this cross - sectional study, PTW system was audited in an oil and gas extracting industry by checklist. Results Major nonconformities include outdating of system legal and regulation, non existence of permit for majority of dangerous activities, unidentified training needs, incomplete identification and risk assessment of maintenance hazards before doing them, unspecified inspection and survey frequencies during works and nonexistence of scheduled auditing for the system. Conclusion PTW audit results showed that there is a noticeable gap between audit criteria and audit evidences. So that the examined system had nonconformities in all of the checklist sections; system, training and competency, permit, coordination and monitoring.
"Lost chains" in algebraic models
Fortunato, L.; de Graaf, W. A.
2011-03-01
The algebraic structure of some of the simplest algebraic models u(2), u(3) and u(4), widely used in several branches of physics either as toy models or as working instruments, are reanalyzed under a new perspective that releases the requirement that chains should terminate or pass through the angular momentum algebra. Unitary algebras are non-semisimple, therefore we first apply the Levi-Malcev decomposition. Then we use the theory of weighted Dynkin diagrams to identify conjugacy classes of A1 ~ su(2) ~ so(3) subalgebras: a complete classification of new angular momentum non conserving (AMNC) dynamical symmetries follows that we substantiate with examples.
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.
Introduction to algebraic independence theory
Philippon, Patrice
2001-01-01
In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.
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
Directory of Open Access Journals (Sweden)
Krasae-In Aracha
2016-01-01
Full Text Available Sustainable development has been a great challenge to the building and construction industry for decades. There have been many initiatives and attempts to create sustainability for the industry through the concept of the Green Building certificate in order to reduce the impact to environment and society while promoting better living conditions of the people involved in the project. This paper aims to examine all three aspects of sustainability; economy, environment and society, in the building and construction industry by proposing new criteria for the green building certificate. This will create opportunities for the community based handicraft building products to be specified and purchased to be used in the modern building and construction industry and share the economic value to the community.
The planar algebra of a semisimple and cosemisimple Hopf algebra
Indian Academy of Sciences (India)
M. Senthilkumar (Newgen Imaging) 1461 1996 Oct 15 13:05:22
[TngGlk] Etingof Pavel and Gelaki Shlomo, On finite-dimensional semisimple and cosemisimple Hopf algebras in positive characteristic. Int. Math. Res. Notices,. 16 (1998) 851–864. [DasKdy] Das Paramita and Vijay Kodiyalam, Planar algebras and the Ocneanu–. Szymanski theorem, Proc. AMS, 133 (2005) 2751–2759.
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.
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)
There is a growing interest in the application of human-associated fecal sourceidentification quantitative real-time PCR (qPCR) technologies for water quality management. The transition from a research tool to a standardized protocol requires a high degree of confidence in data q...
Algebraic K-theory of generalized schemes
DEFF Research Database (Denmark)
Anevski, Stella Victoria Desiree
Nikolai Durov has developed a generalization of conventional scheme theory in which commutative algebraic monads replace commutative unital rings as the basic algebraic objects. The resulting geometry is expressive enough to encompass conventional scheme theory, tropical algebraic geometry and ge...
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.)
Algebraic K-theory of generalized schemes
DEFF Research Database (Denmark)
Anevski, Stella Victoria Desiree
Nikolai Durov has developed a generalization of conventional scheme theory in which commutative algebraic monads replace commutative unital rings as the basic algebraic objects. The resulting geometry is expressive enough to encompass conventional scheme theory, tropical algebraic geometry...
Burchill, Susan A; Beiske, Klaus; Shimada, Hiroyuki; Ambros, Peter F; Seeger, Robert; Tytgat, Godelieve A M; Brock, Penelope R; Haber, Michelle; Park, Julie R; Berthold, Frank
2017-04-01
The current study was conducted to expedite international standardized reporting of bone marrow disease in children with neuroblastoma and to improve equivalence of care. A multidisciplinary International Neuroblastoma Response Criteria Bone Marrow Working Group was convened by the US National Cancer Institute in January 2012 with representation from Europe, North America, and Australia. Practical transferable recommendations to standardize the reporting of bone marrow disease were developed. To the authors' knowledge, the current study is the first to comprehensively present consensus criteria for the collection, analysis, and reporting of the percentage area of bone marrow parenchyma occupied by tumor cells in trephine-biopsies. The quantitative analysis of neuroblastoma content in bone marrow aspirates by immunocytology and reverse transcriptase-quantitative polymerase chain reaction are revised. The inclusion of paired-like homeobox 2b (PHOX2B) for immunohistochemistry and reverse transcriptase-quantitative polymerase chain reaction is recommended. Recommendations for recording bone marrow response are provided. The authors endorse the quantitative assessment of neuroblastoma cell content in bilateral core needle biopsies-trephines and aspirates in all children with neuroblastoma, with the exception of infants, in whom the evaluation of aspirates alone is advised. It is interesting to note that 5% disease is accepted as an internationally achievable level for disease assessment. The quantitative assessment of neuroblastoma cells is recommended to provide data from which evidence-based numerical criteria for the reporting of bone marrow response can be realized. This is particularly important in the minimal disease setting and when neuroblastoma detection in bone marrow is intermittent, where clinical impact has yet to be validated. The wide adoption of these harmonized criteria will enhance the ability to compare outcomes from different trials and facilitate
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
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
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...
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
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
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
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...
On Derivations of Operator Algebras with Involution
Directory of Open Access Journals (Sweden)
Širovnik Nejc
2014-12-01
Full Text Available The purpose of this paper is to prove the following result. Let X be a complex Hilbert space, let L(X be an algebra of all bounded linear operators on X and let A(X ⊂ L(X be a standard operator algebra, which is closed under the adjoint operation. Suppose there exists a linear mapping D : A(X → L(X satisfying the relation 2D(AA*A = D(AA*A + AA*D(A + D(AA*A + AD(A*A for all A ∈ A(X. In this case, D is of the form D(A = [A,B] for all A ∈ A(X and some fixed B ∈ L(X, which means that D is a derivation.
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...
Ultraproducts of von Neumann algebras
DEFF Research Database (Denmark)
Ando, Hiroshi; Haagerup, Uffe
2014-01-01
We study several notions of ultraproducts of von Neumann algebras from a unified viewpoint. In particular, we show that for a sigma-finite von Neumann algebra M , the ultraproduct MωMω introduced by Ocneanu is a corner of the ultraproduct ∏ωM∏ωM introduced by Groh and Raynaud. Using...
Orthogonal symmetries and Clifford algebras
Indian Academy of Sciences (India)
a universal property of the even Clifford algebra in §3. ..... symmetry if σ2 = id. In the literature, such maps are sometimes also called “orthogonal involutions” (cf. Ch. III, §5 of [4]). We have, however, preferred to use the former ...... [7] Helmstetter J and Micali A, Quadratic mappings and Clifford algebras (Basel: Birkhäuser.
Six Lectures on Commutative Algebra
Elias, J; Miro-Roig, Rosa Maria; Zarzuela, Santiago
2009-01-01
Interest in commutative algebra has surged over the years. In order to survey and highlight the developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. This title offers a synthesis of the lectures presented at the Summer School
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
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.)
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.
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…
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,
Linear Algebra and Linear Models
Indian Academy of Sciences (India)
Linear Algebra and Linear. Models. Kalyan Das. Linear Algebra and linear Models. (2nd Edn) by R P Bapat. Hindustan Book Agency, 1999 pp.xiii+180, Price: Rs.135/-. This monograph provides an introduction to the basic aspects of the theory oflinear estima- tion and that of testing linear hypotheses. The primary objective ...
Quantum Observables and Effect Algebras
Dvurečenskij, Anatolij
2017-11-01
We study observables on monotone σ-complete effect algebras. We find conditions when a spectral resolution implies existence of the corresponding observable. We characterize sharp observables of a monotone σ-complete homogeneous effect algebra using its orthoalgebraic skeleton. In addition, we study compatibility in orthoalgebras and we show that every orthoalgebra satisfying RIP is an orthomodular poset.
Algebraic study of chiral anomalies
Indian Academy of Sciences (India)
2012-06-14
Jun 14, 2012 ... Abstract. The algebraic structure of chiral anomalies is made globally valid on non-trivial bundles ... Editor's Note: †Reproduced with kind permission from Springer Science+Business Media: Algebraic study of chiral anoma- ..... We shall see in the sequel several examples in which this ambiguity helps.
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.
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
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
(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.
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.)
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.)
Universal enveloping Lie Rota-Baxter algebra of preLie and post-Lie algebras
Gubarev, Vsevolod
2017-01-01
Universal enveloping Lie Rota-Baxter algebras of pre-Lie and post-Lie algebras are constructed. It is proved that the pairs of varieties (Lie Rota-Baxter algebras of zero weight,preLie algebras) and (Lie Rota-Baxter algebras of nonzero weight,post-Lie algebras) are PBW-pairs and the variety of Lie Rota-Baxter algebras is not Schreier.
2016-01-01
Objective In low-resource settings, obstructed labour is strongly associated with severe maternal morbidity and intrapartum asphyxia, and consequently maternal and perinatal deaths. This study evaluated the impact of a criteria-based audit of the diagnosis and management of obstructed labour in a low-resource setting. Methods A baseline criteria-based audit was conducted from October 2013 to March 2014, followed by a workshop in which stakeholders gave feedback on interventions agreed upon to improve obstetric care. The implemented interventions included but were not limited to introducing standard guidelines for diagnosis and management of obstructed labour, agreeing on mandatory review by specialist for cases that are assigned caesarean section, re-training and supervision on use and interpretation of partograph and, strengthening team work between doctors, mid-wives and theatre staff. After implementing these interventions in March, a re-audit was performed from July 2015 to November, 2015, and the results were compared to those of the baseline audit. Results Two hundred and sixty deliveries in the baseline survey and 250 deliveries in the follow-up survey were audited. Implementing the new criteria improved the diagnosis from 74% to 81% (p = 0.049) and also the management of obstructed labour from 4.2% at baseline audit to 9.2% at re-audit (p = 0.025). Improved detection of prolonged labour through heightened observation of regular contractions, protracted cervical dilatation, protracted descent of presenting part, arrested cervical dilation, and severe moulding contributed to improved standards of diagnosis (all p labour using available resources. Some of the observed changes in practice were of modest magnitude implying demand for further improvements, while sustaining those already put in place. PMID:27893765
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)
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.)
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...
Energy Technology Data Exchange (ETDEWEB)
2017-08-01
AMG is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the BoomerAMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL and is very similar to the AMG2013 benchmark with additional optimizations. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem with a 27-point stencil, which can be scaled up and is designed to solve a very large problem. A second problem simulates a time dependent problem, in which successively various smnllcr systems are solved.
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...
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.
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
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.)
Quantum algebras as quantizations of dual Poisson–Lie groups
International Nuclear Information System (INIS)
Ballesteros, Ángel; Musso, Fabio
2013-01-01
A systematic computational approach for the explicit construction of any quantum Hopf algebra (U z (g), Δ z ) starting from the Lie bialgebra (g, δ) that gives the first-order deformation of the coproduct map Δ z is presented. The procedure is based on the well-known ‘quantum duality principle’, namely the fact that any quantum algebra can be viewed as the quantization of the unique Poisson–Lie structure (G*, Λ g ) on the dual group G*, which is obtained by exponentiating the Lie algebra g* defined by the dual map δ*. From this perspective, the coproduct for U z (g) is just the pull-back of the group law for G*, and the Poisson analogues of the quantum commutation rules for U z (g) are given by the unique Poisson–Lie structure Λ g on G* whose linearization is the Poisson analogue of the initial Lie algebra g. This approach is shown to be a very useful technical tool in order to solve the Lie bialgebra quantization problem explicitly since, once a Lie bialgebra (g, δ) is given, the full dual Poisson–Lie group (G*, Λ) can be obtained either by applying standard Poisson–Lie group techniques or by implementing the algorithm presented here with the aid of symbolic manipulation programs. As a consequence, the quantization of (G*, Λ) will give rise to the full U z (g) quantum algebra, provided that ordering problems are appropriately fixed through the choice of certain local coordinates on G* whose coproduct fulfils a precise ‘quantum symmetry’ property. The applicability of this approach is explicitly demonstrated by reviewing the construction of several instances of quantum deformations of physically relevant Lie algebras such as sl(2,R), the (2+1) anti-de Sitter algebra so(2, 2) and the Poincaré algebra in (3+1) dimensions. (paper)
Translating cosmological special relativity into geometric algebra
Horn, Martin Erik
2012-11-01
Geometric algebra and Clifford algebra are important tools to describe and analyze the physics of the world we live in. Although there is enormous empirical evidence that we are living in four dimensional spacetime, mathematical worlds of higher dimensions can be used to present the physical laws of our world in an aesthetical and didactical more appealing way. In physics and mathematics education we are therefore confronted with the question how these high dimensional spaces should be taught. But as an immediate confrontation of students with high dimensional compactified spacetimes would expect too much from them at the beginning of their university studies, it seems reasonable to approach the mathematics and physics of higher dimensions step by step. The first step naturally is the step from four dimensional spacetime of special relativity to a five dimensional spacetime world. As a toy model for this artificial world cosmological special relativity, invented by Moshe Carmeli, can be used. This five dimensional non-compactified approach describes a spacetime which consists not only of one time dimension and three space dimensions. In addition velocity is regarded as a fifth dimension. This model very probably will not represent physics correctly. But it can be used to discuss and analyze the consequences of an additional dimension in a clear and simple way. Unfortunately Carmeli has formulated cosmological special relativity in standard vector notation. Therefore a translation of cosmological special relativity into the mathematical language of Grassmann and Clifford (Geometric algebra) is given and the physics of cosmological special relativity is discussed.
A Verified Algebra for Linked Data
Directory of Open Access Journals (Sweden)
Ross Horne
2011-07-01
Full Text Available A foundation is investigated for the application of loosely structured data on the Web. This area is often referred to as Linked Data, due to the use of URIs in data to establish links. This work focuses on emerging W3C standards which specify query languages for Linked Data. The approach is to provide an abstract syntax to capture Linked Data structures and queries, which are then internalised in a process calculus. An operational semantics for the calculus specifies how queries, data and processes interact. A labelled transition system is shown to be sound with respect to the operational semantics. Bisimulation over the labelled transition system is used to verify an algebra over queries. The derived algebra is a contribution to the application domain. For instance, the algebra may be used to rewrite a query to optimise its distribution across a cluster of servers. The framework used to provide the operational semantics is powerful enough to model related calculi for the Web.
Evdokimova, Maria; Glazunov, Gennady; Yakovlev, Aleksandr
2017-04-01
The basis for development of standards for soil quality is based on the assessment of their resistance to external influences. The main criterion for assessing the environmental sustainability of soils and lands is the ability to perform their ecological functions (Nkonya et al, 2011, 2013; Costanza et al, 2014, Dobrovolsky and Nikitin, 1990; Yakovlev, Evdokimova, 2011). The limiting value of indicators of the state of the environment (physical, chemical, biological and other) corresponds to the value at which stability of environmental components is preserved (the ability to heal itself). Tht threshold for effect of stressor should be identified by the methods of bioindication and biotesting. The analysis obtained by these methods aimed to identify the highest indicator values of physical or chemical (concentration or dose of the stressor) effects, which have not yet fairly established negative changes in the organism, population of organisms or community. Using a theoretical model (Yakovlev et al, 2009, Gendugov., 2013) the problem of finding the threshold concentration is reduced to the finding of the singular points characterizing macroscopic "kinetics" of response in the phase space of dependence of the response rate upon the impact indicator. Singular points are determined by the analysis of derivatives. The theoretical model allows to calculate the singular points of the model (six of them), one of which, the maximum point corresponds to the highest concentration of the stressor at which it had no adverse effects on the test organisms. This point corresponds to the lowest concentration of the stressor at which it has no longer a stimulatory (hormesis) effect. Six singular points divide the whole range of stressors values (concentration) on seven bands with a unique range for each set of values of "macrokinetic" indicators of the living cells response to the impact of the stressor (concentration). Thus, the use of theoretical equations allowed us 1) to
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....
Topological Ã-algebras with CÃ-enveloping algebras II
Indian Academy of Sciences (India)
subalgebra and contained in the crossed product *-algebra *(, , ) satisfies ()=*(, , ). If G = R , if is an -invariant dense Frechet ∗-subalgebra of such that () = , and if the action on is -tempered, smooth and by continuous ...
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
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.)
Homology theory on algebraic varieties
Wallace, Andrew H
1958-01-01
Homology Theory on Algebraic Varieties, Volume 6 deals with the principles of homology theory in algebraic geometry and includes the main theorems first formulated by Lefschetz, one of which is interpreted in terms of relative homology and another concerns the Poincaré formula. The actual details of the proofs of these theorems are introduced by geometrical descriptions, sometimes aided with diagrams. This book is comprised of eight chapters and begins with a discussion on linear sections of an algebraic variety, with emphasis on the fibring of a variety defined over the complex numbers. The n
Clifford algebraic symmetries in physics
International Nuclear Information System (INIS)
Salingaros, N.
1986-01-01
This paper reviews the following appearances of Clifford algebras in theoretical physics: statistical mechanics; general relativity; quantum electrodynamics; internal symmetries; the vee product; classical electrodynamics; charged-particle motion; and the Lorentz group. It is concluded that the power of the Clifford-algebraic description resides in its ability to perform representation-free calculations which are generalizations of the traditional vector algebra and that this considerable computational asset, in combination with the intrinsic symmetry, provides a practical framework for much of theoretical physics. 5 references
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.
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
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
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
Abstract algebra an introduction with applications
Robinson, Derek JS
2015-01-01
This is the second edition of the introduction to abstract algebra. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. There is ample material here for a two semester course in abstract algebra.
Homomorphisms of certain Banach function algebras
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
. } < ∞ is denoted by Lipα(X, d). These algebras are called Lipschitz algebras of order α and were first studied by Sherbert. The Lipschitz algebras Lipα(X, d) for α ≤ 1 are natural. Banach function algebras on X under the norm f α = f X + pα(f ) ...
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.
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.)
Teacher Quality and Teaching Quality of 7th-Grade Algebra I Honors Teachers
Perez, Barbara
2013-01-01
With more and more focus on accountability, algebra achievement has become a major focus of math curriculum developers. In many states, students are expected to pass standardized Algebra achievement tests in order to satisfy graduation requirements. The purpose of this study was to identify teacher qualities and teaching qualities linked to…
Hilbert isometries and maximal deviation preserving maps on JB-algebras
Roelands, Mark; Wortel, Marten
2017-01-01
In this paper we characterize the surjective linear variation norm isometries on JB-algebras. Variation norm isometries are precisely the maps that preserve the maximal deviation, the quantum analogue of the standard deviation, which plays an important role in quantum statistics. Consequently, we characterize the Hilbert's metric isometries on cones in JB-algebras.
AT -algebras and extensions of AT-algebras
Indian Academy of Sciences (India)
and E has real rank zero, then E is an AT-algebra if and only if the index maps are both zero. Accordingly, in this ... It is well-known that two extensions with the same index are isomorphic as C. ∗. -algebras. We call these .... where each Bi = I (Ei) is a direct sum of K. By Lemma 2.3, I (E) = B. Without loss of generality, we may ...
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)
Topological أ-algebras with Cأ-enveloping algebras II
Indian Academy of Sciences (India)
A with the locally convex inductive limit topology t is a locally m-convex Q-algebra satisfying EًKnc. A ق ¼ EًKAق ¼ A. (3) If A has a countable bounded approximate identity, then ًKnc. A ; tق is an LFQ-algebra. In general KA 6¼ Knc. A , though KA Knc. A . Now KA has been interpreted as a non- commutative analogue of CcًXق.
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
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...
Klumpp, A. R.; Lawson, C. L.
1988-01-01
Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.
Cartooning in Algebra and Calculus
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.
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...
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...
Completeness of algebraic CPS simulations
Directory of Open Access Journals (Sweden)
Ali Assaf
2012-07-01
Full Text Available The algebraic lambda calculus and the linear algebraic lambda calculus are two extensions of the classical lambda calculus with linear combinations of terms. They arise independently in distinct contexts: the former is a fragment of the differential lambda calculus, the latter is a candidate lambda calculus for quantum computation. They differ in the handling of application arguments and algebraic rules. The two languages can simulate each other using an algebraic extension of the well-known call-by-value and call-by-name CPS translations. These simulations are sound, in that they preserve reductions. In this paper, we prove that the simulations are actually complete, strengthening the connection between the two languages.
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
A characterisation of algebraic exactness
Garner, Richard
2011-01-01
An algebraically exact category in one that admits all of the limits and colimits which every variety of algebras possesses and every forgetful functor between varieties preserves, and which verifies the same interactions between these limits and colimits as hold in any variety. Such categories were studied by Ad\\'amek, Lawvere and Rosick\\'y: they characterised them as the categories with small limits and sifted colimits for which the functor taking sifted colimits is continuous. They conject...
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.
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.
Turner, Natalie; Wong, Hui-Li; Templeton, Arnoud; Tripathy, Sagarika; Whiti Rogers, Te; Croxford, Matthew; Jones, Ian; Sinnathamby, Mathuranthakan; Desai, Jayesh; Tie, Jeanne; Bae, Susie; Christie, Michael; Gibbs, Peter; Tran, Ben
2016-02-01
In Stage II colon cancer, multiple independent studies have shown that a dense intratumoural immune infiltrate (local inflammation) is associated with improved outcomes, while systemic inflammation, measured by various markers, has been associated with poorer outcomes. However, previous studies have not considered the interaction between local and systemic inflammation, nor have they assessed the type of inflammatory response compared with standard clinicopathologic criteria. In order to evaluate the potential clinical utility of inflammatory markers in Stage II colon cancer, we examined local and systemic inflammation in a consecutive series of patients with resected Stage II colon cancer between 2000 and 2010 who were identified from a prospective clinical database. Increased intratumoural chronic inflammatory cell (CIC) density, as assessed by pathologist review of hematoxylin and eosin stained slides, was used to represent local inflammation. Neutrophil-to-lymphocyte ratio (NLR) >5, as calculated from pre-operative full blood counts, was used to represent systemic inflammation. In 396 eligible patients identified, there was a non-significant inverse relationship between local and systemic inflammation. Increased CIC density was significantly associated with improved overall (HR 0.45, p = 0.001) and recurrence-free survival (HR 0.37, p = 0.003). High NLR was significantly associated with poorer overall survival (HR 2.56, p < 0.001). The combination of these markers further stratified prognosis independent of standard high-risk criteria, with a dominant systemic inflammatory response (low CIC/high NLR) associated with the worst outcome (5-year overall survival 55.8%). With further validation this simple, inexpensive combined inflammatory biomarker might assist in patient selection for adjuvant chemotherapy in Stage II colon cancer. © 2015 UICC.
Algebras with actions and automata
Directory of Open Access Journals (Sweden)
W. Kühnel
1982-01-01
Full Text Available In the present paper we want to give a common structure theory of left action, group operations, R-modules and automata of different types defined over various kinds of carrier objects: sets, graphs, presheaves, sheaves, topological spaces (in particular: compactly generated Hausdorff spaces. The first section gives an axiomatic approach to algebraic structures relative to a base category B, slightly more powerful than that of monadic (tripleable functors. In section 2 we generalize Lawveres functorial semantics to many-sorted algebras over cartesian closed categories. In section 3 we treat the structures mentioned in the beginning as many-sorted algebras with fixed scalar or input object and show that they still have an algebraic (or monadic forgetful functor (theorem 3.3 and hence the general theory of algebraic structures applies. These structures were usually treated as one-sorted in the Lawvere-setting, the action being expressed by a family of unary operations indexed over the scalars. But this approach cannot, as the one developed here, describe continuity of the action (more general: the action to be a B-morphism, which is essential for the structures mentioned above, e.g. modules for a sheaf of rings or topological automata. Finally we discuss consequences of theorem 3.3 for the structure theory of various types of automata. The particular case of algebras with fixed natural numbers object has been studied by the authors in [23].
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.
Egodawatte, Gunawardena; Stoilescu, Dorian
2015-01-01
The purpose of this mixed-method study was to investigate grade 11 university/college stream mathematics students' difficulties in applying conceptual knowledge, procedural skills, strategic competence, and algebraic thinking in solving routine (instructional) algebraic problems. A standardized algebra test was administered to thirty randomly…
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...
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...
Free probability on Hecke algebras and certain group C^{*}-algebras induced by Hecke algebras
Directory of Open Access Journals (Sweden)
Ilwoo Cho
2016-01-01
Full Text Available In this paper, by establishing free-probabilistic models on the Hecke algebras \\(\\mathcal{H}\\left(GL_{2}(\\mathbb{Q}_{p}\\right\\ induced by \\(p\\-adic number fields \\(\\mathbb{Q}_{p}\\, we construct free probability spaces for all primes \\(p\\. Hilbert-space representations are induced by such free-probabilistic structures. We study \\(C^{*}\\-algebras induced by certain partial isometries realized under the representations.
κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
Directory of Open Access Journals (Sweden)
Andrzej Borowiec
2010-10-01
Full Text Available Some classes of Deformed Special Relativity (DSR theories are reconsidered within the Hopf algebraic formulation. For this purpose we shall explore a minimal framework of deformed Weyl-Heisenberg algebras provided by a smash product construction of DSR algebra. It is proved that this DSR algebra, which uniquely unifies κ-Minkowski spacetime coordinates with Poincaré generators, can be obtained by nonlinear change of generators from undeformed one. Its various realizations in terms of the standard (undeformed Weyl-Heisenberg algebra opens the way for quantum mechanical interpretation of DSR theories in terms of relativistic (Stückelberg version Quantum Mechanics. On this basis we review some recent results concerning twist realization of κ-Minkowski spacetime described as a quantum covariant algebra determining a deformation quantization of the corresponding linear Poisson structure. Formal and conceptual issues concerning quantum κ-Poincaré and κ-Minkowski algebras as well as DSR theories are discussed. Particularly, the so-called ''q-analog'' version of DSR algebra is introduced. Is deformed special relativity quantization of doubly special relativity remains an open question. Finally, possible physical applications of DSR algebra to description of some aspects of Planck scale physics are shortly recalled.
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
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
Non-local matrix generalizations of W-algebras
International Nuclear Information System (INIS)
Bilal, A.
1995-01-01
There is a standard way to define two symplectic (hamiltonian) structures, the first and second Gelfand-Dikii brackets, on the space of ordinary m th -order linear differential operators L=-d m +U 1 d m-1 +U 2 d m-2 +..+U m . In this paper, I consider in detail the case where the U k are nxn-matrix-valued functions, with particular emphasis on the (more interesting) second Gelfand-Dikii bracket. Of particular interest is the reduction to the symplectic submanifold U 1 =0. This reduction gives rise to matrix generalizations of (the classical version of) the non-linear W m -algebras, called V n,m -algebras. The non-commutativity of the matrices leads to non-local terms in these V n,m -algebras. I show that these algebras contain a conformal Virasoro subalgebra and that combinations W k of the U k can be formed that are nxn-matrices of conformally primary fields of spin k, in analogy with the scalar case n=1. In general however, the V m,n -algebras have a much richer structure than the W m -algebras as can be seen on the examples of the non-linear and non-local Poisson brackets {(U 2 ) ab (σ),(U 2 ) cd (σ')}, {(U 2 ) ab (σ),(W 3 ) cd (σ')} and {(W 3 ) ab (σ),(W 3 ) cd (σ')} which I work out explicitly for all m and n. A matrix Miura transformation is derived, mapping these complicated (second Gelfand-Dikii) brackets of the U k to a set of much simpler Poisson brackets, providing the analogue of the free-field representation of the W m -algebras. (orig.)
Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories
Alazzawi, Sabina; Lechner, Gandalf
2017-09-01
We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary number of massive particles transforming under an arbitrary compact global gauge group is allowed, thereby generalizing previous constructions of scalar theories. The two-particle S-matrix S is assumed to be an analytic solution of the Yang-Baxter equation with standard properties, including unitarity, TCP invariance, and crossing symmetry. Using methods from operator algebras and complex analysis, we identify sufficient criteria on S that imply the solution of the inverse scattering problem. These conditions are shown to be satisfied in particular by so-called diagonal S-matrices, but presumably also in other cases such as the O( N)-invariant nonlinear {σ}-models.
Finite-dimensional division algebras over fields
Jacobson, Nathan
2009-01-01
Finite-Dimensional Division Algebras over fields determine, by the Wedderburn Theorem, the semi-simple finite-dimensional algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brauer-Severi varieties. The book concentrates on those algebras that have an involution. Algebras with involution appear in many contexts; they arose first in the study of the so-called 'multiplication algebras of Riemann matrices'. The largest part of the book is the fifth chapter, dealing with involutorial simple algebras of finite dimension over a field. Of parti
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,
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....
Coillard, Christine; Vachon, Valerie; Circo, Alin B; Beauséjour, Marie; Rivard, Charles H
2007-06-01
The purpose of this prospective observational study was to evaluate the effectiveness of the Dynamic SpineCor brace for adolescent idiopathic scoliosis in accordance with the standardized criteria proposed by the Scoliosis Research Society Committee on Bracing and Nonoperative Management. They proposed these guidelines to make the comparison among studies more valid and reliable. From 1993 to 2006, 493 patients were treated using the SpineCor brace. Two hundred forty-nine patients met the criteria for inclusion, and 79 patients were still actively being treated. Overall, 170 patients have a definitive outcome. All girls were premenarchal or less than 1 year postmenarchal. Assessment of brace effectiveness included (1) percentage of patients who have 5 degrees or less curve progression, and percentage of patients who have 6 degrees or more progression; (2) percentage of patients who have been recommended/undergone surgery before skeletal maturity; (3) percentage of patients with curves exceeding 45 degrees at maturity (end of treatment); and (4) Two-year follow-up beyond maturity to determine the percentage of patients who subsequently underwent surgery. Successful treatment (correction, >5 degrees, or stabilization, +/-5 degrees) was achieved in 101 (59.4%) of the 170 patients from the time of the fitting of the SpineCor brace to the point in which it was discontinued. Thirty-nine immature patients (22.9%) required surgical fusion while receiving treatment. Two (1.2%) of 170 patients had curves exceeding 45 degrees at maturity. One mature patient (2.1%) required surgery within 2 years of follow-up beyond skeletal maturity. The conclusion drawn from these findings is that the SpineCor brace is effective for the treatment of adolescent idiopathic scoliosis. Moreover, positive outcomes are maintained after 2 years because 45 (95.7%) of 47 patients stabilized or corrected their end of bracing Cobb angle up to 2 years after bracing. Therapeutic study-investigating the
Cosmological applications of algebraic quantum field theory in curved spacetimes
Hack, Thomas-Paul
2016-01-01
This book provides a largely self-contained and broadly accessible exposition on two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology; and a fundamental study of the perturbations in inflation. The two central sections of the book dealing with these applications are preceded by sections providing a pedagogical introduction to the subject. Introductory material on the construction of linear QFTs on general curved spacetimes with and without gauge symmetry in the algebraic approach, physically meaningful quantum states on general curved spacetimes, and the backreaction of quantum fields in curved spacetimes via the semiclassical Einstein equation is also given. The reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but no background in QFT on curved spacetimes or the algebraic approach to QFT is required.
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
International Nuclear Information System (INIS)
Pigford, T.H.
1999-01-01
The proposed geologic repositories being designed in the US and in other countries that have nuclear power plants need well-defined goals and criteria to protect public health. The criteria must be stringent enough to build confidence in the adequacy of public health protection in the face of legal and political challenges. Yet, there are emerging pressures for relaxation of traditional approaches to protect public health when applied to buried radioactive waste. To build acceptance by the scientific community and the public, both the benefits and consequences of proposed relaxed standards must be dealt with openly and understandably. Arguments over safety standards center on six key issues. (1) For how long must public health protection be assured? Should protection be based on calculated radiation doses to people living for many tens of thousands of years in the future, until peak values of calculated radiation have appeared, or should the protection period be limited to a few thousand years? (2) Whom to protect? Should protection be based on protecting the critical group of future people who unknowingly eat food and drink water contaminated by released radioactivity or should it be based on limiting the average exposure, averaged over all persons projected to live within 'the vicinity' of the repository site? (3) How much radiation exposure should be allowed? Should future people be protected to the same level of radiation exposure as now required for licensed nuclear facilities, or should greater exposures be allowed because future people might be better protected by medical breakthroughs or by their taking remedial action to detect and clean up radioactivity that reaches the environment? (4) Can future people be excluded from using contaminated water drawn from near the site? Should protection of future people be based on doses calculated for ground water extracted from present farming wells, where distance and dilution resulted in lower calculated contaminant
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 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.)
Logarithmic exotic conformal Galilean algebras
Energy Technology Data Exchange (ETDEWEB)
Henkel, Malte, E-mail: Malte.henkel@univ-lorraine.fr [Groupe de Physique Statistique, Institut Jean Lamour (CNRS UMR 7198), Université de Lorraine Nancy, B.P. 70239, F-54506 Vandoeuvre-lès-Nancy Cedex (France); Hosseiny, Ali, E-mail: al_hosseiny@sbu.ac.ir [Department of Physics, Shahid Beheshti University, G.C. Evin, Tehran 19839 (Iran, Islamic Republic of); School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Rouhani, Shahin, E-mail: rouhani@ipm.ir [Department of Physics, Sharif University of Technology, P.O. Box 11165-9161, Tehran (Iran, Islamic Republic of); School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)
2014-02-15
Logarithmic representations of the conformal Galilean algebra (CGA) and the Exotic Conformal Galilean algebra (ECGA) are constructed. This can be achieved by non-decomposable representations of the scaling dimensions or the rapidity indices, specific to conformal Galilean algebras. Logarithmic representations of the non-exotic CGA lead to the expected constraints on scaling dimensions and rapidities and also on the logarithmic contributions in the co-variant two-point functions. On the other hand, the ECGA admits several distinct situations which are distinguished by different sets of constraints and distinct scaling forms of the two-point functions. Two distinct realisations for the spatial rotations are identified as well. This is the first concrete example of a reducible, but non-decomposable representation, without logarithmic terms. Such cases had been anticipated before.
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...
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
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)
ON THE BINARY DIGITS OF ALGEBRAIC NUMBERS
KANEKO, HAJIME
2010-01-01
Borel conjectured that all algebraic irrational numbers are normal in base 2. However, very little is known about this problem. We improve the lower bounds for the number of digit changes in the binary expansions of algebraic irrational numbers.
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.)
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.)
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.
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
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.
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.
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
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
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
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.
Entropic Forms and Related Algebras
Directory of Open Access Journals (Sweden)
Antonio Maria Scarfone
2013-02-01
Full Text Available Starting from a very general trace-form entropy, we introduce a pair of algebraic structures endowed by a generalized sum and a generalized product. These algebras form, respectively, two Abelian fields in the realm of the complex numbers isomorphic each other. We specify our results to several entropic forms related to distributions recurrently observed in social, economical, biological and physical systems including the stretched exponential, the power-law and the interpolating Bosons-Fermions distributions. Some potential applications in the study of complex systems are advanced.
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
The planar algebra associated to a Kac algebra
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
and not just the plane). ..... We will need the following facts from [L], which we state as a proposition for conve- nience of reference. PROPOSITION 3.3. Suppose P (L; R) is an exchange relation planar algebra. Then,. (i) dimPn(L; R) < ∞ ∀n;.
AT-algebras and extensions of AT-algebras
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 120; Issue 2. A T -Algebras and Extensions of A T ... School of Science, Nanjing University of Science and Technology, Nanjing 210014, People's Republic of China; Department of Mathematics, Tongji University, Shanghai 200092, People's Republic of China ...
Parts of the Whole: An Algebra Lesson
Directory of Open Access Journals (Sweden)
Dorothy Wallace
2011-07-01
Full Text Available This column draws on research of Eon Harper to demonstrate how an understanding of his proposed stages of algebra acquisition would inform a systemic overhaul of algebra education. Harper's stages also explain why students may pass a series of algebra courses yet still be unable to make sense of calculus, as well as offering insight on what aspects of algebra support quantitative literacy.
Discrimination in a General Algebraic Setting
Directory of Open Access Journals (Sweden)
Benjamin Fine
2015-01-01
Full Text Available Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras.
Discrimination in a General Algebraic Setting.
Fine, Benjamin; Gaglione, Anthony; Lipschutz, Seymour; Spellman, Dennis
2015-01-01
Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras.
Post-Lie algebras and factorization theorems
Ebrahimi-Fard, Kurusch; Mencattini, Igor; Munthe-Kaas, Hans
2017-09-01
In this note we further explore the properties of universal enveloping algebras associated to a post-Lie algebra. Emphasizing the role of the Magnus expansion, we analyze the properties of group like-elements belonging to (suitable completions of) those Hopf algebras. Of particular interest is the case of post-Lie algebras defined in terms of solutions of modified classical Yang-Baxter equations. In this setting we will study factorization properties of the aforementioned group-like elements.
Quantized Matrix Algebras and Quantum Seeds
DEFF Research Database (Denmark)
Jakobsen, Hans Plesner; Pagani, Chiara
2015-01-01
We determine explicitly quantum seeds for classes of quantized matrix algebras. Furthermore, we obtain results on centres and block diagonal forms of these algebras. In the case where is an arbitrary root of unity, this further determines the degrees.......We determine explicitly quantum seeds for classes of quantized matrix algebras. Furthermore, we obtain results on centres and block diagonal forms of these algebras. In the case where is an arbitrary root of unity, this further determines the degrees....
Simple Lie algebras and Dynkin diagrams
International Nuclear Information System (INIS)
Buccella, F.
1983-01-01
The following theorem is studied: in a simple Lie algebra of rank p there are p positive roots such that all the other n-3p/2 positive roots are linear combinations of them with integer non negative coefficients. Dykin diagrams are built by representing the simple roots with circles and drawing a junction between the roots. Five exceptional algebras are studied, focusing on triple junction algebra, angular momentum algebra, weights of the representation, antisymmetric tensors, and subalgebras
The large N=4 superconformal W∞ algebra
International Nuclear Information System (INIS)
Beccaria, Matteo; Candu, Constantin; Gaberdiel, Matthias R.
2014-01-01
The most general large N=4 superconformal W ∞ algebra, containing in addition to the superconformal algebra one supermultiplet for each integer spin, is analysed in detail. It is found that the W ∞ algebra is uniquely determined by the levels of the two su(2) algebras, a conclusion that holds both for the linear and the non-linear case. We also perform various cross-checks of our analysis, and exhibit two different types of truncations in some detail.
Algebra success in 20 minutes a day
LearningExpress, LLC
2014-01-01
Stripped of unnecessary math jargon but bursting with algebra essentials, this handy guide covers vital algebra skills that apply to real-world scenarios. Whether you're new to algebra or just looking for a refresher, Algebra Success in 20 Minutes a Day offers a lesson plan that provides quick and thorough instruction in practical, critical skills. All lessons can be completed in just 20 minutes a day, for a manageable and non-intimidating learning experience.
Integrable N dimensional systems on the Hopf algebra and q deformations
International Nuclear Information System (INIS)
Lisitsyn, Ya.V.; Shapovalov, A.V.
2000-01-01
The class of integrable classic and quantum systems on the Hopf algebra, describing the n of interacting particles, is plotted. The general structure of the integrable Hamiltonian system for the Hopf algebra A(g) of the Lee simple algebra g is obtained, wherefrom it follows, that motion integrals depend on the linear combinations k of the phase space coordinates. The q-deformation standard procedure is carried out and the corresponding integrable system is obtained. The general scheme is illustrated by the examples of the sl(2), sl(3) and o(3, 1) algebras. The exact solution is achieved for the N-dimensional Hamiltonian system quantum analog on the Hopf algebra A (sl(2)) through the method of noncommutative integration of linear differential equations [ru
Chomology of Heisenberg Hom-Lie algebras
Nejib, Saadaoui
2017-01-01
In this paper, we define the Heisenberg Hom-Lie algebra. We determine the minimal dimension of faithful representation for Heisenberg Hom-Lie algebra.We study the adjoint representation, the trivial representation and the faithful representation of Heisenberg Hom-Lie algebra.
Quantum groups and double quiver algebras
International Nuclear Information System (INIS)
Huang Hualin; Yang Shilin
2004-07-01
For a finite dimensional sernisimple Lie algebra g and a root q of unity in a field k we associate to these data a double quiver Q-bar. It is shown that a restricted version of the quantized enveloping algebras U q (g) is a quotient of the double quiver algebra kQ-bar. (author)
Algebra in Dutch education, 1600-2000
Krüger, Jenneke
2015-01-01
Algebra became part of mathematics education in the Netherlands in course of the seventeenth century. At first in the form of cossic algebra, but by the end of the century, the influence of the notation of Descartes was noticeable. In the eighteenth century, algebra was part of the basic curriculum
Feature-Oriented Programming with Object Algebras
B.C.d.S. Oliveira (Bruno); T. van der Storm (Tijs); A. Loh; W.R. Cook
2013-01-01
htmlabstractObject algebras are a new programming technique that enables a simple solution to basic extensibility and modularity issues in programming languages. While object algebras excel at deﬁning modular features, the composition mechanisms for object algebras (and features) are still
Classifying bicrossed products of two Taft algebras
Agore, A. L.
2016-01-01
We classify all Hopf algebras which factorize through two Taft algebras $\\mathbb{T}_{n^{2}}(\\bar{q})$ and respectively $T_{m^{2}}(q)$. To start with, all possible matched pairs between the two Taft algebras are described: if $\\bar{q} \
Fractional superLie algebras and groups
Energy Technology Data Exchange (ETDEWEB)
Ahmedov, H. [Feza Gursey Institute, Cengelkoy, Istanbul (Turkey)]. E-mail: hagi@gursey.gov.tr; Yildiz, A. [ Feza Gursey Institute, Cengelkoy, Istanbul (Turkey); Ucan, Y. [Yildiz Technical University, Department of Mathematics, Besiktas, Istanbul (Turkey)
2001-08-24
The nth root of a Lie algebra and its dual (that is the fractional supergroup) based on the permutation group S{sub n} invariant forms is formulated in the Hopf algebra formalism. Detailed discussion of S{sub 3}-graded sl(2) algebras is performed. (author)
Directory of Open Access Journals (Sweden)
Fu-Gui Shi
2010-01-01
Full Text Available The notion of (L,M-fuzzy σ-algebras is introduced in the lattice value fuzzy set theory. It is a generalization of Klement's fuzzy σ-algebras. In our definition of (L,M-fuzzy σ-algebras, each L-fuzzy subset can be regarded as an L-measurable set to some degree.
Teaching Strategies to Improve Algebra Learning
Zbiek, Rose Mary; Larson, Matthew R.
2015-01-01
Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…
Geometry of Spin: Clifford Algebraic Approach
Indian Academy of Sciences (India)
of Pauli matrices follow from the underlying algebra. Clif- ford algebraic approach provides a geometrical and hence intuitive way to understand quantum theory of spin, and is a natural formalism to study spin. Clifford algebraic formal- ism has lot of applications in every field where spin plays an important role. Introduction.
New family of Maxwell like algebras
Energy Technology Data Exchange (ETDEWEB)
Concha, P.K., E-mail: patillusion@gmail.com [Departamento de Ciencias, Facultad de Artes y Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Casilla 567, Valdivia (Chile); Durka, R., E-mail: remigiuszdurka@gmail.com [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Merino, N., E-mail: nemerino@gmail.com [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Rodríguez, E.K., E-mail: everodriguezd@gmail.com [Departamento de Ciencias, Facultad de Artes y Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Casilla 567, Valdivia (Chile)
2016-08-10
We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the S-expansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement.
Coherent state quantization of paragrassmann algebras
Energy Technology Data Exchange (ETDEWEB)
El Baz, M; Hassouni, Y [Laboratoire de Physique Theorique, LPT-URAC 13, Faculte des Sciences, Universite Mohamed V, Av.Ibn Battouta, BP 1014 Agdal Rabat (Morocco); Fresneda, R [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo (Brazil); Gazeau, J P, E-mail: elbaz@fsr.ac.m, E-mail: fresneda@gmail.co, E-mail: gazeau@apc.univ-paris7.f, E-mail: y-hassou@fsr.ac.m [Laboratoire APC, Universite Paris Diderot (Paris 7), 10, rue A Domon et L Duquet 75205 Paris Cedex 13 (France)
2010-09-24
By using a coherent state quantization of paragrassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the paragrassmann algebra. This algebra of finite matrices realizes a deformed Weyl-Heisenberg algebra. The study of mean values in coherent states of some of these operators leads to interesting conclusions.
A Balancing Act: Making Sense of Algebra
Gavin, M. Katherine; Sheffield, Linda Jensen
2015-01-01
For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…
New family of Maxwell like algebras
International Nuclear Information System (INIS)
Concha, P.K.; Durka, R.; Merino, N.; Rodríguez, E.K.
2016-01-01
We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the S-expansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement.
Banana Algebra: Compositional Syntactic Language Extension
DEFF Research Database (Denmark)
Andersen, Jacob; Brabrand, Claus; Christiansen, David Raymond
2013-01-01
algebra as presented in the paper is implemented as the Banana Algebra Tool which may be used to syntactically extend languages in an incremental and modular fashion via algebraic composition of previously defined languages and transformations. We demonstrate and evaluate the tool via several kinds...
Build an Early Foundation for Algebra Success
Knuth, Eric; Stephens, Ana; Blanton, Maria; Gardiner, Angela
2016-01-01
Research tells us that success in algebra is a factor in many other important student outcomes. Emerging research also suggests that students who are started on an algebra curriculum in the earlier grades may have greater success in the subject in secondary school. What's needed is a consistent, algebra-infused mathematics curriculum all…
Teacher Actions to Facilitate Early Algebraic Reasoning
Hunter, Jodie
2015-01-01
In recent years there has been an increased emphasis on integrating the teaching of arithmetic and algebra in primary school classrooms. This requires teachers to develop links between arithmetic and algebra and use pedagogical actions that facilitate algebraic reasoning. Drawing on findings from a classroom-based study, this paper provides an…
On Elementary and Algebraic Cellular Automata
Gulak, Yuriy
In this paper we study elementary cellular automata from an algebraic viewpoint. The goal is to relate the emergent complex behavior observed in such systems with the properties of corresponding algebraic structures. We introduce algebraic cellular automata as a natural generalization of elementary ones and discuss their applications as generic models of complex systems.
Role of associativity in Ramsey algebras
Indian Academy of Sciences (India)
Andrew Rajah
2017-11-02
Nov 2, 2017 ... to understand the role associativity plays in a binary system being a Ramsey algebra. Specifically, we show that the nonassociative Moufang loop of octonions is not a Ramsey algebra. Keywords. Binary systems; Ramsey algebras; octonions; semigroups; associativity; nonassociative Moufang loops ...
Yang-Mills and some related algebras
Connes, Alain; Dubois-Violette, Michel
2004-01-01
15 pages. Contribution to the Proceedings of Rigorous Quantum Field Theory in the honour of Jacques Bros.; International audience; After a short introduction on the theory of homogeneous algebras we describe the application of this theory to the analysis of the cubic Yang-Mills algebra, the quadratic self-duality algebras, their \\"super\\" versions as well as to some generalization.
Computations in finite-dimensional Lie algebras
Cohen, A.M.; Graaf, W.A. de; Rónyai, L.
1997-01-01
This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System), within the computer algebra package GAP. A first sketch of the packagecan be found in Cohen and de Graaf[1]. Since then, in a collaborative
Algebraic treatment of three-body problems
International Nuclear Information System (INIS)
Bijker, R.; Leviatan, A.
1998-01-01
We discuss an algebraic treatment of three-body systems in terms of a U(7) spectrum-generating algebra. In particular, we develop the formalism for nonilnear configurations and present an algebraic description of vibrational and rotational excitations of, symmetric (X 3 ) and asymmetric tops (XY 2 and XYZ). The relevant point-group symmetry is incorporated exactly. (author)
Algebraic scattering theory and heavy ion scattering
International Nuclear Information System (INIS)
Allen, L.J.; Amos, K.; Berge, L.; Fiedeldey, H.
1993-01-01
Algebraic scattering theory is used to analyze elastic scattering cross-sections from heavy ion collisions. Collisions epitomized by strong absorption lead to algebraic potentials that can be described by simple exponential forms. But for collisions that are 'transparent', while asymptotically the algebraic potentials are exponential, their actual form (for low 1-values) is quite complex. 7 refs., 4 figs
Chern-Simons and Born-Infeld gravity theories and Maxwell algebras type
International Nuclear Information System (INIS)
Concha, P.K.; Penafiel, D.M.; Rodriguez, E.K.; Salgado, P.
2014-01-01
Recently it was shown that standard odd- and even-dimensional general relativity can be obtained from a (2n + 1)-dimensional Chern-Simons Lagrangian invariant under the B 2n+1 algebra and from a (2n)-dimensional Born-Infeld Lagrangian invariant under a subalgebra L B 2n+1 , respectively. Very recently, it was shown that the generalized Inoenue-Wigner contraction of the generalized AdS-Maxwell algebras provides Maxwell algebras of types M m which correspond to the so-called B m Lie algebras. In this article we report on a simple model that suggests a mechanism by which standard odd-dimensional general relativity may emerge as the weak coupling constant limit of a (2p + 1)-dimensional Chern-Simons Lagrangian invariant under the Maxwell algebra type M 2m+1 , if and only if m ≥ p. Similarly, we show that standard even-dimensional general relativity emerges as the weak coupling constant limit of a (2p)-dimensional Born-Infeld type Lagrangian invariant under a subalgebra L M 2m of theMaxwell algebra type, if and only if m ≥ p. It is shown that when m 2m+1 and for a (2p)-dimensional Born-Infeld type Lagrangian invariant under the L M 2m algebra. (orig.)
EPA develops water quality criteria based on the latest scientific knowledge to protect human health and aquatic life. This information serves as guidance to states and tribes in adopting water quality standards.
In Defence of Geometrical Algebra
Blasjo, V.N.E.
The geometrical algebra hypothesis was once the received interpretation of Greek mathematics. In recent decades, however, it has become anathema to many. I give a critical review of all arguments against it and offer a consistent rebuttal case against the modern consensus. Consequently, I find that
Algebraic Methods in Plane Geometry
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 10. Algebraic Methods in Plane Geometry - The Use of Conic Sections. Shailesh A Shirali. General Article Volume 13 Issue 10 October 2008 pp 916-928. Fulltext. Click here to view fulltext PDF. Permanent link:
Max Algebraic Complementary Basic Matrices
Czech Academy of Sciences Publication Activity Database
Fiedler, Miroslav; Hall, F.J.
2014-01-01
Roč. 457, 15 September (2014), s. 287-292 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : CB-matrix * Max algebra * Max permanent * Max eigenvalues Subject RIV: BA - General Mathematics Impact factor: 0.939, year: 2014
An introduction to abstract algebra
Robinson, Derek JS
2003-01-01
This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems and error correcting codes are described. Another feature of the book is that group theory and ring theory are carried further than is often done at this level. There is ample material here for a two semester course in abstract algebra. The importance of proof is stressed and rigorous proofs of almost all results are given. But care has been taken to lead the reader through the proofs by gentle stages. There are nearly 400 problems, of varying degrees of difficulty, to test the reader''s skill and progress. The book should be suitable for students ...
Adventures in Flipping College Algebra
Van Sickle, Jenna
2015-01-01
This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses…
Weaving Geometry and Algebra Together
Cetner, Michelle
2015-01-01
When thinking about student reasoning and sense making, teachers must consider the nature of tasks given to students along with how to plan to use the tasks in the classroom. Students should be presented with tasks in a way that encourages them to draw connections between algebraic and geometric concepts. This article focuses on the idea that it…
Gleason parts of bidual algebras
Kosiek, Marek; Rudol, Krzysztof
2017-01-01
It is shown that the embeding of any Gleason part of a uniform algebra into the spectrum of its second dual is an entire Gleason part. This result is based on the equality of weak-star and norm topologies on the Bear-Gleason part.
Inequalities, Assessment and Computer Algebra
Sangwin, Christopher J.
2015-01-01
The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary…
Algebraic Methods in Plane Geometry
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 10. Algebraic Methods in ... General Article Volume 13 Issue 10 October 2008 pp 916-928 ... Keywords. Conics; family of curves; Pascal's theorem; homogeneous coordinates; Butterfly theorem; abelian group; associativity of addition; group law.
Elementary Algebra Connections to Precalculus
Lopez-Boada, Roberto; Daire, Sandra Arguelles
2013-01-01
This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…
Hamiltonian operators in differential algebras
Zharinov, V. V.
2017-12-01
We develop a previously proposed algebraic technique for a Hamiltonian approach to evolution systems of partial differential equations including constrained systems and propose a defining system of equations ( suitable for computer calculations) characterizing the Hamiltonian operators of a given form. We demonstrate the technique with a simple example.
Inference Optimization using Relational Algebra
Evers, S.; Fokkinga, M.M.; Apers, Peter M.G.
Exact inference procedures in Bayesian networks can be expressed using relational algebra; this provides a common ground for optimizations from the AI and database communities. Specifically, the ability to accomodate sparse representations of probability distributions opens up the way to optimize
Directory of Open Access Journals (Sweden)
Arsham Borumand Saeid
2009-01-01
Full Text Available In this note, by using the concept of vague sets, the notion of vague \\(BCK/BCI\\-algebra is introduced. And the notions of \\(\\alpha\\-cut and vague-cut are introduced and the relationships between these notions and crisp subalgebras are studied.
Rationality problem for algebraic tori
Hoshi, Akinari
2017-01-01
The authors give the complete stably rational classification of algebraic tori of dimensions 4 and 5 over a field k. In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank 4 and 5 is given. The authors show that there exist exactly 487 (resp. 7, resp. 216) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension 4, and there exist exactly 3051 (resp. 25, resp. 3003) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension 5. The authors make a procedure to compute a flabby resolution of a G-lattice effectively by using the computer algebra system GAP. Some algorithms may determine whether the flabby class of a G-lattice is invertible (resp. zero) or not. Using the algorithms, the suthors determine all the flabby and coflabby G-lattices of rank up to 6 and verify that they are stably permutation. The authors also show that the Krull-Schmidt theorem for G-...
The Gap between the Beginning and the End of Algebraic Thinking Transition Period
Directory of Open Access Journals (Sweden)
Dian Permatasari
2018-02-01
Full Text Available Algebraic thinking is an important element in mathematics thinking and reasoning. All students experience a transition to algebraic thinking. It happens from elementary school grade V until junior high school grade VII. This study aims to describe the differences in algebraic thinking ability from the beginning of transition period, elementary school grade V, until the end of the transition period, junior high school grade VII. This research was a cross-sectional research using mixed method approach. The results showed that students' algebraic thinking ability at the beginning of the transition period and at the end of the transition period was in moderate criteria. The average score in algebraic thinking test at the end of the transition period, junior high school grade VII, was higher than the students in junior high school grade V, but the algebraic thinking ability of students in elementary school grade V did not have much different with the students of junior high school grade VII, that was in the moderate criteria.
Explicit field realizations of W algebras
International Nuclear Information System (INIS)
Wei Shaowen; Liu Yuxiao; Ren Jirong; Zhang Lijie
2009-01-01
The fact that certain nonlinear W 2,s algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize W 2,s algebras from linear W 1,2,s algebras. In this paper, we first construct the explicit field realizations of linear W 1,2,s algebras with double scalar and double spinor, respectively. Then, after a change of basis, the realizations of W 2,s algebras are presented. The results show that all these realizations are Romans-type realizations.
Characterizations of locally C*-algebras
International Nuclear Information System (INIS)
Mohammad, N.; Somasundaram, S.
1991-08-01
We seek the generalization of the Gelfand-Naimark theorems for locally C*-algebras. Precisely, if A is a unital commutative locally C*-algebra, then it is shown that A is *-isomorphic (topologically and algebraically) to C(Δ). Further, if A is any locally C*-algebra, then it is realized as a closed *-subalgebra of some L(H) up to a topological algebraic *-isomorphism. Also, a brief exposition of the Gelfand-Naimark-Segal construction is given and some of its consequences are discussed. (author). 16 refs
CLASSIFICATION OF 4-DIMENSIONAL GRADED ALGEBRAS
Armour, Aaron; Chen, Hui-Xiang; ZHANG, Yinhuo
2009-01-01
Let k be an algebraically closed field. The algebraic and geometric classification of finite dimensional algebras over k with ch(k) not equal 2 was initiated by Gabriel in [6], where a complete list of nonisomorphic 4-dimensional k-algebras was given and the number of irreducible components of the variety Alg(4) was discovered to be 5. The classification of 5-dimensional k-algebras was done by Mazzola in [10]. The number of irreducible components of the variety Alg(5) is 10. With the dimensio...
A master identity for homotopy Gerstenhaber algebras
Energy Technology Data Exchange (ETDEWEB)
Akman, F. [Coastal Carolina Univ., Conway, SC (United States). Dept. of Math.
2000-01-01
We produce a master identity {l_brace}m{r_brace}{l_brace}m,m,..{r_brace}=0 for a certain type of homotopy Gerstenhaber algebras, in particular suitable for the prototype, namely the Hochschild complex of an associative algebra. This algebraic master identity was inspired by the work of Getzler-Jones and Kimura-Voronov-Zuckerman in the context of topological conformal field theories. To this end, we introduce the notion of a ''partitioned multilinear map'' and explain the mechanics of composing such maps. In addition, many new examples of pre-Lie algebras and homotopy Gerstenhaber algebras are given. (orig.)
A master identity for homotopy Gerstenhaber algebras
International Nuclear Information System (INIS)
Akman, F.
2000-01-01
We produce a master identity {m}{m,m,..}=0 for a certain type of homotopy Gerstenhaber algebras, in particular suitable for the prototype, namely the Hochschild complex of an associative algebra. This algebraic master identity was inspired by the work of Getzler-Jones and Kimura-Voronov-Zuckerman in the context of topological conformal field theories. To this end, we introduce the notion of a ''partitioned multilinear map'' and explain the mechanics of composing such maps. In addition, many new examples of pre-Lie algebras and homotopy Gerstenhaber algebras are given. (orig.)
Spin-zero mesons and current algebras
International Nuclear Information System (INIS)
Wellner, M.
1977-01-01
Large chiral algebras, using the f and d coefficients of SU(3) can be constructed with spin-1/2 baryons. Such algebras have been found useful in some previous investigations. This article examines under what conditions similar or identical current algebras may be realized with spin-0 mesons. A curious lack of analogy emerges between meson and baryon currents. Second-class currents, made of mesons, are required in some algebras. If meson and baryon currents are to satisfy the same extended SU(3) algebra, four meson nonets are needed, in terms of which we give an explicit construction for the currents
International Nuclear Information System (INIS)
Schmidke, W.B.; Wess, J.; Muenchen Univ.; Zumino, B.; Lawrence Berkeley Lab., CA
1991-01-01
We derive a q-deformed version of the Lorentz algebra by deformating the algebra SL(2, C). The method is based on linear representations of the algebra on the complex quantum spinor space. We find that the generators usually identified with SL q (2, C) generate SU q (2) only. Four additional generators are added which generate Lorentz boosts. The full algebra of all seven generators and their coproduct is presented. We show that in the limit q→1 the generators are those of the classical Lorentz algebra plus an additional U(1). Thus we have a deformation of SL(2, C)xU(1). (orig.)
Operator theory, operator algebras and applications
Lebre, Amarino; Samko, Stefan; Spitkovsky, Ilya
2014-01-01
This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i) operator theory and harmonic analysis (singular integral operators with shifts; pseudodifferential operators, factorization of almost periodic matrix functions; inequalities; Cauchy type integrals; maximal and singular operators on generalized Orlicz-Morrey spaces; the Riesz potential operator; modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras; inner endomorphisms of some semi group, crossed products; C*-algebras generated by mappings which have finite orbits; Folner sequences in operator algebras; arithmetic aspect of C*_r SL(2); C*-algebras of singular integral operators; algebras of operator sequences) and (iii) mathematical physics (operator approach to diffraction from polygonal-conical screens; Poisson geo...
Mukkamala, Sambasiva Rao
2018-01-01
This book presents a unified course in BE-algebras with a comprehensive introduction, general theoretical basis and several examples. It introduces the general theoretical basis of BE-algebras, adopting a credible style to offer students a conceptual understanding of the subject. BE-algebras are important tools for certain investigations in algebraic logic, because they can be considered as fragments of any propositional logic containing a logical connective implication and the constant "1", which is considered as the logical value “true”. Primarily aimed at graduate and postgraduate students of mathematics, it also helps researchers and mathematicians to build a strong foundation in applied abstract algebra. Presenting insights into some of the abstract thinking that constitutes modern abstract algebra, it provides a transition from elementary topics to advanced topics in BE-algebras. With abundant examples and exercises arranged after each section, it offers readers a comprehensive, easy-to-follow int...
Additive derivations on algebras of measurable operators
International Nuclear Information System (INIS)
Ayupov, Sh.A.; Kudaybergenov, K.K.
2009-08-01
Given a von Neumann algebra M we introduce the so-called central extension mix(M) of M. We show that mix(M) is a *-subalgebra in the algebra LS(M) of all locally measurable operators with respect to M, and this algebra coincides with LS(M) if and only if M does not admit type II direct summands. We prove that if M is a properly infinite von Neumann algebra then every additive derivation on the algebra mix(M) is inner. This implies that on the algebra LS(M), where M is a type I ∞ or a type III von Neumann algebra, all additive derivations are inner derivations. (author)
Atomic effect algebras with compression bases
International Nuclear Information System (INIS)
Caragheorgheopol, Dan; Tkadlec, Josef
2011-01-01
Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.
Filiform Lie algebras of order 3
International Nuclear Information System (INIS)
Navarro, R. M.
2014-01-01
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases
Filiform Lie algebras of order 3
Navarro, R. M.
2014-04-01
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, "Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes," Bull. Soc. Math. France 98, 81-116 (1970)]. Also we give the dimension, using an adaptation of the {sl}(2,{C})-module Method, and a basis of such infinitesimal deformations in some generic cases.
Classical algebra its nature, origins, and uses
Cooke, Roger L
2008-01-01
This insightful book combines the history, pedagogy, and popularization of algebra to present a unified discussion of the subject. Classical Algebra provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today. With a focus on prominent areas such as the numerical solutions of equations, the systematic study of equations, and Galois theory, this book facilitates a thorough understanding of algebra and illustrates how the concepts of modern algebra originally developed from classical algebraic precursors. This book successfully ties together the disconnect between classical and modern algebraand provides readers with answers to many fascinating questions that typically go unexamined, including: What is algebra about? How did it arise? What uses does it have? How did it develop? What problems and issues have occurred in its history? How were these problems and issues resolved? The author answers these questions and more,...
Powell, Sarah R.; Fuchs, Lynn S.
2014-01-01
According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 second-grade students, we administered: (1) measures of calculations and…
Equivalency of two-dimensional algebras
International Nuclear Information System (INIS)
Santos, Gildemar Carneiro dos; Pomponet Filho, Balbino Jose S.
2011-01-01
Full text: Let us consider a vector z = xi + yj over the field of real numbers, whose basis (i,j) satisfy a given algebra. Any property of this algebra will be reflected in any function of z, so we can state that the knowledge of the properties of an algebra leads to more general conclusions than the knowledge of the properties of a function. However structural properties of an algebra do not change when this algebra suffers a linear transformation, though the structural constants defining this algebra do change. We say that two algebras are equivalent to each other whenever they are related by a linear transformation. In this case, we have found that some relations between the structural constants are sufficient to recognize whether or not an algebra is equivalent to another. In spite that the basis transform linearly, the structural constants change like a third order tensor, but some combinations of these tensors result in a linear transformation, allowing to write the entries of the transformation matrix as function of the structural constants. Eventually, a systematic way to find the transformation matrix between these equivalent algebras is obtained. In this sense, we have performed the thorough classification of associative commutative two-dimensional algebras, and find that even non-division algebra may be helpful in solving non-linear dynamic systems. The Mandelbrot set was used to have a pictorial view of each algebra, since equivalent algebras result in the same pattern. Presently we have succeeded in classifying some non-associative two-dimensional algebras, a task more difficult than for associative one. (author)
Scaling algebras and renormalization group in algebraic quantum field theory
International Nuclear Information System (INIS)
Buchholz, D.; Verch, R.
1995-01-01
For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary spacetime manifolds and provides a framework for the systematic analysis of the short distance properties of local quantum field theories. It is shown that every theory has a (possibly non-unique) scaling limit which can be classified according to its classical or quantum nature. Dilation invariant theories are stable under the action of the renormalization group. Within this framework the problem of wedge (Bisognano-Wichmann) duality in the scaling limit is discussed and some of its physical implications are outlined. (orig.)
Algebraic complexities and algebraic curves over finite fields.
Chudnovsky, D V; Chudnovsky, G V
1987-04-01
We consider the problem of minimal (multiplicative) complexity of polynomial multiplication and multiplication in finite extensions of fields. For infinite fields minimal complexities are known [Winograd, S. (1977) Math. Syst. Theory 10, 169-180]. We prove lower and upper bounds on minimal complexities over finite fields, both linear in the number of inputs, using the relationship with linear coding theory and algebraic curves over finite fields.