Detecting Change-Point via Saddlepoint Approximations

Institute of Scientific and Technical Information of China (English)

Zhaoyuan LI; Maozai TIAN

2017-01-01

It's well-known that change-point problem is an important part of model statistical analysis.Most of the existing methods are not robust to criteria of the evaluation of change-point problem.In this article,we consider "mean-shift" problem in change-point studies.A quantile test of single quantile is proposed based on saddlepoint approximation method.In order to utilize the information at different quantile of the sequence,we further construct a "composite quantile test" to calculate the probability of every location of the sequence to be a change-point.The location of change-point can be pinpointed rather than estimated within a interval.The proposed tests make no assumptions about the functional forms of the sequence distribution and work sensitively on both large and small size samples,the case of change-point in the tails,and multiple change-points situation.The good performances of the tests are confirmed by simulations and real data analysis.The saddlepoint approximation based distribution of the test statistic that is developed in the paper is of independent interest and appealing.This finding may be of independent interest to the readers in this research area.

Fault detection and diagnosis in nonlinear systems a differential and algebraic viewpoint

CERN Document Server

Martinez-Guerra, Rafael

2014-01-01

The high reliability required in industrial processes has created the necessity of detecting abnormal conditions, called faults, while processes are operating. The term fault generically refers to any type of process degradation, or degradation in equipment performance because of changes in the process's physical characteristics, process inputs or environmental conditions. This book is about the fundamentals of fault detection and diagnosis in a variety of nonlinear systems which are represented by ordinary differential equations. The fault detection problem is approached from a differential algebraic viewpoint, using residual generators based upon high-gain nonlinear auxiliary systems (‘observers’). A prominent role is played by the type of mathematical tools that will be used, requiring knowledge of differential algebra and differential equations. Specific theorems tailored to the needs of the problem-solving procedures are developed and proved. Applications to real-world problems, both with constant an...

Change-Point Detection Method for Clinical Decision Support System Rule Monitoring.

Science.gov (United States)

Liu, Siqi; Wright, Adam; Hauskrecht, Milos

2017-06-01

A clinical decision support system (CDSS) and its components can malfunction due to various reasons. Monitoring the system and detecting its malfunctions can help one to avoid any potential mistakes and associated costs. In this paper, we investigate the problem of detecting changes in the CDSS operation, in particular its monitoring and alerting subsystem, by monitoring its rule firing counts. The detection should be performed online, that is whenever a new datum arrives, we want to have a score indicating how likely there is a change in the system. We develop a new method based on Seasonal-Trend decomposition and likelihood ratio statistics to detect the changes. Experiments on real and simulated data show that our method has a lower delay in detection compared with existing change-point detection methods.

A travel time forecasting model based on change-point detection method

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LI, Shupeng; GUANG, Xiaoping; QIAN, Yongsheng; ZENG, Junwei

2017-06-01

Travel time parameters obtained from road traffic sensors data play an important role in traffic management practice. A travel time forecasting model is proposed for urban road traffic sensors data based on the method of change-point detection in this paper. The first-order differential operation is used for preprocessing over the actual loop data; a change-point detection algorithm is designed to classify the sequence of large number of travel time data items into several patterns; then a travel time forecasting model is established based on autoregressive integrated moving average (ARIMA) model. By computer simulation, different control parameters are chosen for adaptive change point search for travel time series, which is divided into several sections of similar state.Then linear weight function is used to fit travel time sequence and to forecast travel time. The results show that the model has high accuracy in travel time forecasting.

Quantum W-algebras and elliptic algebras

International Nuclear Information System (INIS)

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

1996-01-01

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

VEHICLE LOCALIZATION BY LIDAR POINT CORRELATION IMPROVED BY CHANGE DETECTION

Directory of Open Access Journals (Sweden)

A. Schlichting

2016-06-01

Full Text Available LiDAR sensors are proven sensors for accurate vehicle localization. Instead of detecting and matching features in the LiDAR data, we want to use the entire information provided by the scanners. As dynamic objects, like cars, pedestrians or even construction sites could lead to wrong localization results, we use a change detection algorithm to detect these objects in the reference data. If an object occurs in a certain number of measurements at the same position, we mark it and every containing point as static. In the next step, we merge the data of the single measurement epochs to one reference dataset, whereby we only use static points. Further, we also use a classification algorithm to detect trees. For the online localization of the vehicle, we use simulated data of a vertical aligned automotive LiDAR sensor. As we only want to use static objects in this case as well, we use a random forest classifier to detect dynamic scan points online. Since the automotive data is derived from the LiDAR Mobile Mapping System, we are able to use the labelled objects from the reference data generation step to create the training data and further to detect dynamic objects online. The localization then can be done by a point to image correlation method using only static objects. We achieved a localization standard deviation of about 5 cm (position and 0.06° (heading, and were able to successfully localize the vehicle in about 93 % of the cases along a trajectory of 13 km in Hannover, Germany.

Vehicle Localization by LIDAR Point Correlation Improved by Change Detection

Science.gov (United States)

Schlichting, A.; Brenner, C.

2016-06-01

LiDAR sensors are proven sensors for accurate vehicle localization. Instead of detecting and matching features in the LiDAR data, we want to use the entire information provided by the scanners. As dynamic objects, like cars, pedestrians or even construction sites could lead to wrong localization results, we use a change detection algorithm to detect these objects in the reference data. If an object occurs in a certain number of measurements at the same position, we mark it and every containing point as static. In the next step, we merge the data of the single measurement epochs to one reference dataset, whereby we only use static points. Further, we also use a classification algorithm to detect trees. For the online localization of the vehicle, we use simulated data of a vertical aligned automotive LiDAR sensor. As we only want to use static objects in this case as well, we use a random forest classifier to detect dynamic scan points online. Since the automotive data is derived from the LiDAR Mobile Mapping System, we are able to use the labelled objects from the reference data generation step to create the training data and further to detect dynamic objects online. The localization then can be done by a point to image correlation method using only static objects. We achieved a localization standard deviation of about 5 cm (position) and 0.06° (heading), and were able to successfully localize the vehicle in about 93 % of the cases along a trajectory of 13 km in Hannover, Germany.

Statistical methods for change-point detection in surface temperature records

Science.gov (United States)

Pintar, A. L.; Possolo, A.; Zhang, N. F.

2013-09-01

We describe several statistical methods to detect possible change-points in a time series of values of surface temperature measured at a meteorological station, and to assess the statistical significance of such changes, taking into account the natural variability of the measured values, and the autocorrelations between them. These methods serve to determine whether the record may suffer from biases unrelated to the climate signal, hence whether there may be a need for adjustments as considered by M. J. Menne and C. N. Williams (2009) "Homogenization of Temperature Series via Pairwise Comparisons", Journal of Climate 22 (7), 1700-1717. We also review methods to characterize patterns of seasonality (seasonal decomposition using monthly medians or robust local regression), and explain the role they play in the imputation of missing values, and in enabling robust decompositions of the measured values into a seasonal component, a possible climate signal, and a station-specific remainder. The methods for change-point detection that we describe include statistical process control, wavelet multi-resolution analysis, adaptive weights smoothing, and a Bayesian procedure, all of which are applicable to single station records.

Detecting change points in VIX and S&P 500: A new approach to dynamic asset allocation

DEFF Research Database (Denmark)

Nystrup, Peter; Hansen, Bo William; Madsen, Henrik

2016-01-01

to DAA that is based on detection of change points without fitting a model with a fixed number of regimes to the data, without estimating any parameters and without assuming a specific distribution of the data. It is examined whether DAA is most profitable when based on changes in the Chicago Board...... Options Exchange Volatility Index or change points detected in daily returns of the S&P 500 index. In an asset universe consisting of the S&P 500 index and cash, it is shown that a dynamic strategy based on detected change points significantly improves the Sharpe ratio and reduces the drawdown risk when...

Building Change Detection from Bi-Temporal Dense-Matching Point Clouds and Aerial Images.

Science.gov (United States)

Pang, Shiyan; Hu, Xiangyun; Cai, Zhongliang; Gong, Jinqi; Zhang, Mi

2018-03-24

In this work, a novel building change detection method from bi-temporal dense-matching point clouds and aerial images is proposed to address two major problems, namely, the robust acquisition of the changed objects above ground and the automatic classification of changed objects into buildings or non-buildings. For the acquisition of changed objects above ground, the change detection problem is converted into a binary classification, in which the changed area above ground is regarded as the foreground and the other area as the background. For the gridded points of each period, the graph cuts algorithm is adopted to classify the points into foreground and background, followed by the region-growing algorithm to form candidate changed building objects. A novel structural feature that was extracted from aerial images is constructed to classify the candidate changed building objects into buildings and non-buildings. The changed building objects are further classified as "newly built", "taller", "demolished", and "lower" by combining the classification and the digital surface models of two periods. Finally, three typical areas from a large dataset are used to validate the proposed method. Numerous experiments demonstrate the effectiveness of the proposed algorithm.

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

International Nuclear Information System (INIS)

Gebert, R.W.

1993-09-01

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

Extended Virasoro algebra and algebra of area preserving diffeomorphisms

International Nuclear Information System (INIS)

Arakelyan, T.A.

1990-01-01

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

Detection and localization of change points in temporal networks with the aid of stochastic block models

Science.gov (United States)

De Ridder, Simon; Vandermarliere, Benjamin; Ryckebusch, Jan

2016-11-01

A framework based on generalized hierarchical random graphs (GHRGs) for the detection of change points in the structure of temporal networks has recently been developed by Peel and Clauset (2015 Proc. 29th AAAI Conf. on Artificial Intelligence). We build on this methodology and extend it to also include the versatile stochastic block models (SBMs) as a parametric family for reconstructing the empirical networks. We use five different techniques for change point detection on prototypical temporal networks, including empirical and synthetic ones. We find that none of the considered methods can consistently outperform the others when it comes to detecting and locating the expected change points in empirical temporal networks. With respect to the precision and the recall of the results of the change points, we find that the method based on a degree-corrected SBM has better recall properties than other dedicated methods, especially for sparse networks and smaller sliding time window widths.

An algebraic approach to finding the Fermat-Torricelli point

Science.gov (United States)

Palacios-Vélez, Óscar Luis; Pedraza-Oropeza, Felipe J. A.; Escobar-Villagran, Bernardo Samuel

2015-11-01

Using a calculus and an algebraic approach, the Cartesian coordinates of the Fermat-Torricelli point are deduced for triangles with no internal angle greater than 120°. Although in theory, the deduction of these coordinates could be made 'by hand', in practice it is very laborious to obtain them without the aid of mathematical computer software, but with human guidance, since there are mathematical artifices not yet incorporated into the software. It is also shown that these coordinates can be conveniently expressed in terms of the side lengths and the area of the triangle. These coordinates are contrasted with the coordinates of a similar point: one whose sum of the squares of the distances to the vertices of an arbitrary triangle is a minimum.

3D change detection at street level using mobile laser scanning point clouds and terrestrial images

Science.gov (United States)

Qin, Rongjun; Gruen, Armin

2014-04-01

Automatic change detection and geo-database updating in the urban environment are difficult tasks. There has been much research on detecting changes with satellite and aerial images, but studies have rarely been performed at the street level, which is complex in its 3D geometry. Contemporary geo-databases include 3D street-level objects, which demand frequent data updating. Terrestrial images provides rich texture information for change detection, but the change detection with terrestrial images from different epochs sometimes faces problems with illumination changes, perspective distortions and unreliable 3D geometry caused by the lack of performance of automatic image matchers, while mobile laser scanning (MLS) data acquired from different epochs provides accurate 3D geometry for change detection, but is very expensive for periodical acquisition. This paper proposes a new method for change detection at street level by using combination of MLS point clouds and terrestrial images: the accurate but expensive MLS data acquired from an early epoch serves as the reference, and terrestrial images or photogrammetric images captured from an image-based mobile mapping system (MMS) at a later epoch are used to detect the geometrical changes between different epochs. The method will automatically mark the possible changes in each view, which provides a cost-efficient method for frequent data updating. The methodology is divided into several steps. In the first step, the point clouds are recorded by the MLS system and processed, with data cleaned and classified by semi-automatic means. In the second step, terrestrial images or mobile mapping images at a later epoch are taken and registered to the point cloud, and then point clouds are projected on each image by a weighted window based z-buffering method for view dependent 2D triangulation. In the next step, stereo pairs of the terrestrial images are rectified and re-projected between each other to check the geometrical

Logic, algebra and topology: investigations into canonical extensions, duality theory and point-free topology

NARCIS (Netherlands)

Vosmaer, J.

2010-01-01

In this dissertation we discuss three subjects: canonical extensions of lattice-based algebras, Stone duality for distributive lattices with operators, and a generalization of the point-free Vietoris powerlocale construction.

Three-dimensional quantum algebras: a Cartan-like point of view

International Nuclear Information System (INIS)

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

2004-01-01

A perturbative quantization procedure for Lie bialgebras is introduced. The relevance of the choice of a completely symmetrized basis of the quantum universal enveloping algebra is stressed. Sets of elements of the quantum algebra that play a role similar to generators in the case of Lie algebras are considered and a Cartan-like procedure applied to find a representative for each class of quantum algebras. The method is used to construct and classify all three-dimensional complex quantum algebras that are compatible with a given type of coproduct. The quantization of all Lie algebras that, in the classical limit, belong to the most relevant sector in the classification for three-dimensional Lie bialgebras is thus performed. New quantizations of solvable algebras, whose simplicity makes them suitable for possible physical applications, are obtained and already known related quantum algebras recovered

Trend analysis and change point detection of annual and seasonal temperature series in Peninsular Malaysia

Science.gov (United States)

Suhaila, Jamaludin; Yusop, Zulkifli

2017-06-01

Most of the trend analysis that has been conducted has not considered the existence of a change point in the time series analysis. If these occurred, then the trend analysis will not be able to detect an obvious increasing or decreasing trend over certain parts of the time series. Furthermore, the lack of discussion on the possible factors that influenced either the decreasing or the increasing trend in the series needs to be addressed in any trend analysis. Hence, this study proposes to investigate the trends, and change point detection of mean, maximum and minimum temperature series, both annually and seasonally in Peninsular Malaysia and determine the possible factors that could contribute to the significance trends. In this study, Pettitt and sequential Mann-Kendall (SQ-MK) tests were used to examine the occurrence of any abrupt climate changes in the independent series. The analyses of the abrupt changes in temperature series suggested that most of the change points in Peninsular Malaysia were detected during the years 1996, 1997 and 1998. These detection points captured by Pettitt and SQ-MK tests are possibly related to climatic factors, such as El Niño and La Niña events. The findings also showed that the majority of the significant change points that exist in the series are related to the significant trend of the stations. Significant increasing trends of annual and seasonal mean, maximum and minimum temperatures in Peninsular Malaysia were found with a range of 2-5 °C/100 years during the last 32 years. It was observed that the magnitudes of the increasing trend in minimum temperatures were larger than the maximum temperatures for most of the studied stations, particularly at the urban stations. These increases are suspected to be linked with the effect of urban heat island other than El Niño event.

The Casimir Effect from the Point of View of Algebraic Quantum Field Theory

Energy Technology Data Exchange (ETDEWEB)

Dappiaggi, Claudio, E-mail: claudio.dappiaggi@unipv.it; Nosari, Gabriele [Università degli Studi di Pavia, Dipartimento di Fisica (Italy); Pinamonti, Nicola [Università di Genova, Dipartimento di Matematica (Italy)

2016-06-15

We consider a region of Minkowski spacetime bounded either by one or by two parallel, infinitely extended plates orthogonal to a spatial direction and a real Klein-Gordon field satisfying Dirichlet boundary conditions. We quantize these two systems within the algebraic approach to quantum field theory using the so-called functional formalism. As a first step we construct a suitable unital ∗-algebra of observables whose generating functionals are characterized by a labelling space which is at the same time optimal and separating and fulfils the F-locality property. Subsequently we give a definition for these systems of Hadamard states and we investigate explicit examples. In the case of a single plate, it turns out that one can build algebraic states via a pull-back of those on the whole Minkowski spacetime, moreover inheriting from them the Hadamard property. When we consider instead two plates, algebraic states can be put in correspondence with those on flat spacetime via the so-called method of images, which we translate to the algebraic setting. For a massless scalar field we show that this procedure works perfectly for a large class of quasi-free states including the Poincaré vacuum and KMS states. Eventually Wick polynomials are introduced. Contrary to the Minkowski case, the extended algebras, built in globally hyperbolic subregions can be collected in a global counterpart only after a suitable deformation which is expressed locally in terms of a *-isomorphism. As a last step, we construct explicitly the two-point function and the regularized energy density, showing, moreover, that the outcome is consistent with the standard results of the Casimir effect.

Fast and Robust Segmentation and Classification for Change Detection in Urban Point Clouds

Science.gov (United States)

Roynard, X.; Deschaud, J.-E.; Goulette, F.

2016-06-01

Change detection is an important issue in city monitoring to analyse street furniture, road works, car parking, etc. For example, parking surveys are needed but are currently a laborious task involving sending operators in the streets to identify the changes in car locations. In this paper, we propose a method that performs a fast and robust segmentation and classification of urban point clouds, that can be used for change detection. We apply this method to detect the cars, as a particular object class, in order to perform parking surveys automatically. A recently proposed method already addresses the need for fast segmentation and classification of urban point clouds, using elevation images. The interest to work on images is that processing is much faster, proven and robust. However there may be a loss of information in complex 3D cases: for example when objects are one above the other, typically a car under a tree or a pedestrian under a balcony. In this paper we propose a method that retain the three-dimensional information while preserving fast computation times and improving segmentation and classification accuracy. It is based on fast region-growing using an octree, for the segmentation, and specific descriptors with Random-Forest for the classification. Experiments have been performed on large urban point clouds acquired by Mobile Laser Scanning. They show that the method is as fast as the state of the art, and that it gives more robust results in the complex 3D cases.

Effects of Using Problem of the Week in Teaching on Teacher Learning and Change in Algebraic Thinking and Algebra

Science.gov (United States)

Wu, Zhonghe

2017-01-01

The study investigated the effects of using the problem of the week in teaching (POWT) on teachers' learning and changes in knowledge and teaching skills, in algebraic thinking and algebra tasks, in the setting of a university mathematics education graduate program. The graduate students participated in learning POWT weekly in a mathematics…

q-Derivatives, quantization methods and q-algebras

International Nuclear Information System (INIS)

Twarock, Reidun

1998-01-01

Using the example of Borel quantization on S 1 , we discuss the relation between quantization methods and q-algebras. In particular, it is shown that a q-deformation of the Witt algebra with generators labeled by Z is realized by q-difference operators. This leads to a discrete quantum mechanics. Because of Z, the discretization is equidistant. As an approach to a non-equidistant discretization of quantum mechanics one can change the Witt algebra using not the number field Z as labels but a quadratic extension of Z characterized by an irrational number τ. This extension is denoted as quasi-crystal Lie algebra, because this is a relation to one-dimensional quasicrystals. The q-deformation of this quasicrystal Lie algebra is discussed. It is pointed out that quasicrystal Lie algebras can be considered also as a 'deformed' Witt algebra with a 'deformation' of the labeling number field. Their application to the theory is discussed

Linearizing W-algebras

International Nuclear Information System (INIS)

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

1994-06-01

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

FAST AND ROBUST SEGMENTATION AND CLASSIFICATION FOR CHANGE DETECTION IN URBAN POINT CLOUDS

Directory of Open Access Journals (Sweden)

X. Roynard

2016-06-01

Full Text Available Change detection is an important issue in city monitoring to analyse street furniture, road works, car parking, etc. For example, parking surveys are needed but are currently a laborious task involving sending operators in the streets to identify the changes in car locations. In this paper, we propose a method that performs a fast and robust segmentation and classification of urban point clouds, that can be used for change detection. We apply this method to detect the cars, as a particular object class, in order to perform parking surveys automatically. A recently proposed method already addresses the need for fast segmentation and classification of urban point clouds, using elevation images. The interest to work on images is that processing is much faster, proven and robust. However there may be a loss of information in complex 3D cases: for example when objects are one above the other, typically a car under a tree or a pedestrian under a balcony. In this paper we propose a method that retain the three-dimensional information while preserving fast computation times and improving segmentation and classification accuracy. It is based on fast region-growing using an octree, for the segmentation, and specific descriptors with Random-Forest for the classification. Experiments have been performed on large urban point clouds acquired by Mobile Laser Scanning. They show that the method is as fast as the state of the art, and that it gives more robust results in the complex 3D cases.

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

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Dinh Trung Hoa

2013-01-01

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

Brauer algebras of type B

NARCIS (Netherlands)

Cohen, A.M.; Liu, S.

2011-01-01

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

Current algebras, measures quasi-invariant under diffeomorphism groups, and infinite quantum systems with accumulation points

Science.gov (United States)

Sakuraba, Takao

The approach to quantum physics via current algebra and unitary representations of the diffeomorphism group is established. This thesis studies possible infinite Bose gas systems using this approach. Systems of locally finite configurations and systems of configurations with accumulation points are considered, with the main emphasis on the latter. In Chapter 2, canonical quantization, quantization via current algebra and unitary representations of the diffeomorphism group are reviewed. In Chapter 3, a new definition of the space of configurations is proposed and an axiom for general configuration spaces is abstracted. Various subsets of the configuration space, including those specifying the number of points in a Borel set and those specifying the number of accumulation points in a Borel set are proved to be measurable using this axiom. In Chapter 4, known results on the space of locally finite configurations and Poisson measure are reviewed in the light of the approach developed in Chapter 3, including the approach to current algebra in the Poisson space by Albeverio, Kondratiev, and Rockner. Goldin and Moschella considered unitary representations of the group of diffeomorphisms of the line based on self-similar random processes, which may describe infinite quantum gas systems with clusters. In Chapter 5, the Goldin-Moschella theory is developed further. Their construction of measures quasi-invariant under diffeomorphisms is reviewed, and a rigorous proof of their conjectures is given. It is proved that their measures with distinct correlation parameters are mutually singular. A quasi-invariant measure constructed by Ismagilov on the space of configurations with accumulation points on the circle is proved to be singular with respect to the Goldin-Moschella measures. Finally a generalization of the Goldin-Moschella measures to the higher-dimensional case is studied, where the notion of covariance matrix and the notion of condition number play important roles. A

The change points of HbA(1C) for detection of retinopathy in Chinese type 2 diabetic patients.

Science.gov (United States)

Hou, Jia-Ning; Bi, Yu-Fang; Xu, Min; Huang, Yun; Li, Xiao-Ying; Wang, Wei-Qing; Chen, Yu-Hong; Ning, Guang

2011-03-01

To investigate the change points of HbA(1C) for detection of retinopathy in Chinese type 2 diabetic patients. This cross-sectional investigation included 992 diagnosed type 2 diabetic patients, who received non-mydriatic digital fundus photography examination. Joinpoint regression software was adopted to identify the change points of HbA(1C) in association with retinopathy prevalence. The mean age of all patients was 59.1 ± 8.4 years and the duration of diabetes was 5.5 (95% CI: 5.2-5.9) years. The prevalence of retinopathy was 10.3% in total, and 4.1%, 7.4% and 19.6% in patients with different diabetes duration of ≤ 5 years, 5-10 years and >10 years, respectively. The change point of HbA(1C) was 6.5% (95%CI 5.8-7.5%), at which retinopathy prevalence began to rise sharply. Furthermore, in subjects with diabetes duration ≤ 5 years, 5-10 years and >10 years, the change points of HbA(1C) were 8.1% (95%CI 7.9-8.3%), 6.1% (95%CI 5.7-6.8%), 5.6% (95%CI 5.1-8.1%) for detection of retinopathy, respectively. The steepest increase in retinopathy prevalence occurred when HbA(1C) reached 6.5%. However, the duration of diabetes should be taken into concern, when using the change points of HbA(1C) for detection of retinopathy in diabetic patients. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.

JB*-Algebras of Topological Stable Rank 1

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Akhlaq A. Siddiqui

2007-01-01

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

MODIS 250m burned area mapping based on an algorithm using change point detection and Markov random fields.

Science.gov (United States)

Mota, Bernardo; Pereira, Jose; Campagnolo, Manuel; Killick, Rebeca

2013-04-01

Area burned in tropical savannas of Brazil was mapped using MODIS-AQUA daily 250m resolution imagery by adapting one of the European Space Agency fire_CCI project burned area algorithms, based on change point detection and Markov random fields. The study area covers 1,44 Mkm2 and was performed with data from 2005. The daily 1000 m image quality layer was used for cloud and cloud shadow screening. The algorithm addresses each pixel as a time series and detects changes in the statistical properties of NIR reflectance values, to identify potential burning dates. The first step of the algorithm is robust filtering, to exclude outlier observations, followed by application of the Pruned Exact Linear Time (PELT) change point detection technique. Near-infrared (NIR) spectral reflectance changes between time segments, and post change NIR reflectance values are combined into a fire likelihood score. Change points corresponding to an increase in reflectance are dismissed as potential burn events, as are those occurring outside of a pre-defined fire season. In the last step of the algorithm, monthly burned area probability maps and detection date maps are converted to dichotomous (burned-unburned maps) using Markov random fields, which take into account both spatial and temporal relations in the potential burned area maps. A preliminary assessment of our results is performed by comparison with data from the MODIS 1km active fires and the 500m burned area products, taking into account differences in spatial resolution between the two sensors.

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)

On compact multipliers of topological algebras

International Nuclear Information System (INIS)

Mohammad, N.

1994-08-01

It is shown that if the maximal ideal space Δ(A) of a semisimple commutative complete metrizable locally convex algebra contains no isolated points, then every compact multiplier is trivial. Particularly, compact multipliers on semisimple commutative Frechet algebras whose maximal ideal space has no isolated points are identically zero. (author). 5 refs

Interest point detection for hyperspectral imagery

Science.gov (United States)

Dorado-Muñoz, Leidy P.; Vélez-Reyes, Miguel; Roysam, Badrinath; Mukherjee, Amit

2009-05-01

This paper presents an algorithm for automated extraction of interest points (IPs)in multispectral and hyperspectral images. Interest points are features of the image that capture information from its neighbours and they are distinctive and stable under transformations such as translation and rotation. Interest-point operators for monochromatic images were proposed more than a decade ago and have since been studied extensively. IPs have been applied to diverse problems in computer vision, including image matching, recognition, registration, 3D reconstruction, change detection, and content-based image retrieval. Interest points are helpful in data reduction, and reduce the computational burden of various algorithms (like registration, object detection, 3D reconstruction etc) by replacing an exhaustive search over the entire image domain by a probe into a concise set of highly informative points. An interest operator seeks out points in an image that are structurally distinct, invariant to imaging conditions, stable under geometric transformation, and interpretable which are good candidates for interest points. Our approach extends ideas from Lowe's keypoint operator that uses local extrema of Difference of Gaussian (DoG) operator at multiple scales to detect interest point in gray level images. The proposed approach extends Lowe's method by direct conversion of scalar operations such as scale-space generation, and extreme point detection into operations that take the vector nature of the image into consideration. Experimental results with RGB and hyperspectral images which demonstrate the potential of the method for this application and the potential improvements of a fully vectorial approach over band-by-band approaches described in the literature.

Quantitative Algebraic Reasoning

DEFF Research Database (Denmark)

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

2016-01-01

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

Orbifold Riemann surfaces: Teichmueller spaces and algebras of geodesic functions

Energy Technology Data Exchange (ETDEWEB)

Mazzocco, Marta [Loughborough University, Loughborough (United Kingdom); Chekhov, Leonid O [Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow (Russian Federation)

2009-12-31

A fat graph description is given for Teichmueller spaces of Riemann surfaces with holes and with Z{sub 2}- and Z{sub 3}-orbifold points (conical singularities) in the Poincare uniformization. The corresponding mapping class group transformations are presented, geodesic functions are constructed, and the Poisson structure is introduced. The resulting Poisson algebras are then quantized. In the particular cases of surfaces with n Z{sub 2}-orbifold points and with one and two holes, the respective algebras A{sub n} and D{sub n} of geodesic functions (classical and quantum) are obtained. The infinite-dimensional Poisson algebra D{sub n}, which is the semiclassical limit of the twisted q-Yangian algebra Y'{sub q}(o{sub n}) for the orthogonal Lie algebra o{sub n}, is associated with the algebra of geodesic functions on an annulus with n Z{sub 2}-orbifold points, and the braid group action on this algebra is found. From this result the braid group actions are constructed on the finite-dimensional reductions of this algebra: the p-level reduction and the algebra D{sub n}. The central elements for these reductions are found. Also, the algebra D{sub n} is interpreted as the Poisson algebra of monodromy data of a Frobenius manifold in the vicinity of a non-semisimple point. Bibliography: 36 titles.

AN APPROACH TO ALLEVIATE THE FALSE ALARM IN BUILDING CHANGE DETECTION FROM URBAN VHR IMAGE

Directory of Open Access Journals (Sweden)

J. Chen

2016-06-01

Full Text Available Building change detection from very-high-resolution (VHR urban remote sensing image frequently encounter the challenge of serious false alarm caused by different illumination or viewing angles in bi-temporal images. An approach to alleviate the false alarm in urban building change detection is proposed in this paper. Firstly, as shadows casted by urban buildings are of distinct spectral and shape feature, it adopts a supervised object-based classification technique to extract them in this paper. Secondly, on the opposite direction of sunlight illumination, a straight line is drawn along the principal orientation of building in every extracted shadow region. Starting from the straight line and moving toward the sunlight direction, a rectangular area is constructed to cover partial shadow and rooftop of each building. Thirdly, an algebra and geometry invariant based method is used to abstract the spatial topological relationship of the potential unchanged buildings from all central points of the rectangular area. Finally, based on an oriented texture curvature descriptor, an index is established to determine the actual false alarm in building change detection result. The experiment results validate that the proposed method can be used as an effective framework to alleviate the false alarm in building change detection from urban VHR image.

Affine Kac-Moody algebras and their representations

International Nuclear Information System (INIS)

Slansky, R.

1988-01-01

Highest weight representation theory of finite dimensional and affine Kac-Moody algebras is summarized from a unified point of view. Lattices of discrete additive quantum numbers and the presentation of Lie algebras on Cartan matrices are the central points of departure for the analysis. (author)

Algebraic computing

International Nuclear Information System (INIS)

MacCallum, M.A.H.

1990-01-01

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

Chiral algebras of class S

CERN Document Server

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

2015-01-01

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

Algebraic Methods in Plane Geometry

Indian Academy of Sciences (India)

Srimath

rally, a1 ;a2 ;a3 ;a4 m ust not all be 0.) If w e m ultiply all th e ai's by a non-zero constant w e get the sam e cubic. .... B ut a sm all m odi¯cation of the operation changes the ..... Robert Bix, Conics and Cubics: A Concrete Introduction to Algebraic ... Joseph H Silverman and John Torrence Tate, Rational Points on Elliptic.

Application of change-point problem to the detection of plant patches.

Science.gov (United States)

López, I; Gámez, M; Garay, J; Standovár, T; Varga, Z

2010-03-01

In ecology, if the considered area or space is large, the spatial distribution of individuals of a given plant species is never homogeneous; plants form different patches. The homogeneity change in space or in time (in particular, the related change-point problem) is an important research subject in mathematical statistics. In the paper, for a given data system along a straight line, two areas are considered, where the data of each area come from different discrete distributions, with unknown parameters. In the paper a method is presented for the estimation of the distribution change-point between both areas and an estimate is given for the distributions separated by the obtained change-point. The solution of this problem will be based on the maximum likelihood method. Furthermore, based on an adaptation of the well-known bootstrap resampling, a method for the estimation of the so-called change-interval is also given. The latter approach is very general, since it not only applies in the case of the maximum-likelihood estimation of the change-point, but it can be also used starting from any other change-point estimation known in the ecological literature. The proposed model is validated against typical ecological situations, providing at the same time a verification of the applied algorithms.

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.)

An introduction to Clifford algebras and spinors

CERN Document Server

Vaz, Jayme

2016-01-01

This text explores how Clifford algebras and spinors have been sparking a collaboration and bridging a gap between Physics and Mathematics. This collaboration has been the consequence of a growing awareness of the importance of algebraic and geometric properties in many physical phenomena, and of the discovery of common ground through various touch points: relating Clifford algebras and the arising geometry to so-called spinors, and to their three definitions (both from the mathematical and physical viewpoint). The main point of contact are the representations of Clifford algebras and the periodicity theorems. Clifford algebras also constitute a highly intuitive formalism, having an intimate relationship to quantum field theory. The text strives to seamlessly combine these various viewpoints and is devoted to a wider audience of both physicists and mathematicians. Among the existing approaches to Clifford algebras and spinors this book is unique in that it provides a didactical presentation of the topic and i...

P-commutative topological *-algebras

International Nuclear Information System (INIS)

Mohammad, N.; Thaheem, A.B.

1991-07-01

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

Connections between algebra, combinatorics, and geometry

CERN Document Server

Sather-Wagstaff, Sean

2014-01-01

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

Change Analysis in Structural Laser Scanning Point Clouds: The Baseline Method.

Science.gov (United States)

Shen, Yueqian; Lindenbergh, Roderik; Wang, Jinhu

2016-12-24

A method is introduced for detecting changes from point clouds that avoids registration. For many applications, changes are detected between two scans of the same scene obtained at different times. Traditionally, these scans are aligned to a common coordinate system having the disadvantage that this registration step introduces additional errors. In addition, registration requires stable targets or features. To avoid these issues, we propose a change detection method based on so-called baselines. Baselines connect feature points within one scan. To analyze changes, baselines connecting corresponding points in two scans are compared. As feature points either targets or virtual points corresponding to some reconstructable feature in the scene are used. The new method is implemented on two scans sampling a masonry laboratory building before and after seismic testing, that resulted in damages in the order of several centimeters. The centres of the bricks of the laboratory building are automatically extracted to serve as virtual points. Baselines connecting virtual points and/or target points are extracted and compared with respect to a suitable structural coordinate system. Changes detected from the baseline analysis are compared to a traditional cloud to cloud change analysis demonstrating the potential of the new method for structural analysis.

Change Analysis in Structural Laser Scanning Point Clouds: The Baseline Method

Directory of Open Access Journals (Sweden)

Yueqian Shen

2016-12-01

Full Text Available A method is introduced for detecting changes from point clouds that avoids registration. For many applications, changes are detected between two scans of the same scene obtained at different times. Traditionally, these scans are aligned to a common coordinate system having the disadvantage that this registration step introduces additional errors. In addition, registration requires stable targets or features. To avoid these issues, we propose a change detection method based on so-called baselines. Baselines connect feature points within one scan. To analyze changes, baselines connecting corresponding points in two scans are compared. As feature points either targets or virtual points corresponding to some reconstructable feature in the scene are used. The new method is implemented on two scans sampling a masonry laboratory building before and after seismic testing, that resulted in damages in the order of several centimeters. The centres of the bricks of the laboratory building are automatically extracted to serve as virtual points. Baselines connecting virtual points and/or target points are extracted and compared with respect to a suitable structural coordinate system. Changes detected from the baseline analysis are compared to a traditional cloud to cloud change analysis demonstrating the potential of the new method for structural analysis.

Adaptive 4d Psi-Based Change Detection

Science.gov (United States)

Yang, Chia-Hsiang; Soergel, Uwe

2018-04-01

In a previous work, we proposed a PSI-based 4D change detection to detect disappearing and emerging PS points (3D) along with their occurrence dates (1D). Such change points are usually caused by anthropic events, e.g., building constructions in cities. This method first divides an entire SAR image stack into several subsets by a set of break dates. The PS points, which are selected based on their temporal coherences before or after a break date, are regarded as change candidates. Change points are then extracted from these candidates according to their change indices, which are modelled from their temporal coherences of divided image subsets. Finally, we check the evolution of the change indices for each change point to detect the break date that this change occurred. The experiment validated both feasibility and applicability of our method. However, two questions still remain. First, selection of temporal coherence threshold associates with a trade-off between quality and quantity of PS points. This selection is also crucial for the amount of change points in a more complex way. Second, heuristic selection of change index thresholds brings vulnerability and causes loss of change points. In this study, we adapt our approach to identify change points based on statistical characteristics of change indices rather than thresholding. The experiment validates this adaptive approach and shows increase of change points compared with the old version. In addition, we also explore and discuss optimal selection of temporal coherence threshold.

Paragrassmann analysis and covariant quantum algebras

International Nuclear Information System (INIS)

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

1993-01-01

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

Algebraic curves and cryptography

CERN Document Server

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

Algebraic topology a primer

CERN Document Server

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...

Normed algebras and the geometric series test

Directory of Open Access Journals (Sweden)

Robert Kantrowitz

2017-11-01

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

Introductory modern algebra a historical approach

CERN Document Server

Stahl, Saul

2013-01-01

Praise for the First Edition ""Stahl offers the solvability of equations from the historical point of view...one of the best books available to support a one-semester introduction to abstract algebra.""-CHOICE Introductory Modern Algebra: A Historical Approach, Second Edition presents the evolution of algebra and provides readers with the opportunity to view modern algebra as a consistent movement from concrete problems to abstract principles. With a few pertinent excerpts from the writings of some of the greatest mathematicians, the Second Edition uniquely facilitates the understanding of pi

Vertex algebras and algebraic curves

CERN Document Server

Frenkel, Edward

2004-01-01

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

Algebraic partial Boolean algebras

International Nuclear Information System (INIS)

Smith, Derek

2003-01-01

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

Detecting corner points from digital curves

International Nuclear Information System (INIS)

Sarfraz, M.

2011-01-01

Corners in digital images give important clues for shape representation, recognition, and analysis. Since dominant information regarding shape is usually available at the corners, they provide important features for various real life applications in the disciplines like computer vision, pattern recognition, computer graphics. Corners are the robust features in the sense that they provide important information regarding objects under translation, rotation and scale change. They are also important from the view point of understanding human perception of objects. They play crucial role in decomposing or describing the digital curves. They are also used in scale space theory, image representation, stereo vision, motion tracking, image matching, building mosaics and font designing systems. If the corner points are identified properly, a shape can be represented in an efficient and compact way with sufficient accuracy. Corner detection schemes, based on their applications, can be broadly divided into two categories: binary (suitable for binary images) and gray level (suitable for gray level images). Corner detection approaches for binary images usually involve segmenting the image into regions and extracting boundaries from those regions that contain them. The techniques for gray level images can be categorized into two classes: (a) Template based and (b) gradient based. The template based techniques utilize correlation between a sub-image and a template of a given angle. A corner point is selected by finding the maximum of the correlation output. Gradient based techniques require computing curvature of an edge that passes through a neighborhood in a gray level image. Many corner detection algorithms have been proposed in the literature which can be broadly divided into two parts. One is to detect corner points from grayscale images and other relates to boundary based corner detection. This contribution mainly deals with techniques adopted for later approach

Detection of uterine MMG contractions using a multiple change point estimator and the K-means cluster algorithm.

Science.gov (United States)

La Rosa, Patricio S; Nehorai, Arye; Eswaran, Hari; Lowery, Curtis L; Preissl, Hubert

2008-02-01

We propose a single channel two-stage time-segment discriminator of uterine magnetomyogram (MMG) contractions during pregnancy. We assume that the preprocessed signals are piecewise stationary having distribution in a common family with a fixed number of parameters. Therefore, at the first stage, we propose a model-based segmentation procedure, which detects multiple change-points in the parameters of a piecewise constant time-varying autoregressive model using a robust formulation of the Schwarz information criterion (SIC) and a binary search approach. In particular, we propose a test statistic that depends on the SIC, derive its asymptotic distribution, and obtain closed-form optimal detection thresholds in the sense of the Neyman-Pearson criterion; therefore, we control the probability of false alarm and maximize the probability of change-point detection in each stage of the binary search algorithm. We compute and evaluate the relative energy variation [root mean squares (RMS)] and the dominant frequency component [first order zero crossing (FOZC)] in discriminating between time segments with and without contractions. The former consistently detects a time segment with contractions. Thus, at the second stage, we apply a nonsupervised K-means cluster algorithm to classify the detected time segments using the RMS values. We apply our detection algorithm to real MMG records obtained from ten patients admitted to the hospital for contractions with gestational ages between 31 and 40 weeks. We evaluate the performance of our detection algorithm in computing the detection and false alarm rate, respectively, using as a reference the patients' feedback. We also analyze the fusion of the decision signals from all the sensors as in the parallel distributed detection approach.

Exact Identification of a Quantum Change Point

Science.gov (United States)

Sentís, Gael; Calsamiglia, John; Muñoz-Tapia, Ramon

2017-10-01

The detection of change points is a pivotal task in statistical analysis. In the quantum realm, it is a new primitive where one aims at identifying the point where a source that supposedly prepares a sequence of particles in identical quantum states starts preparing a mutated one. We obtain the optimal procedure to identify the change point with certainty—naturally at the price of having a certain probability of getting an inconclusive answer. We obtain the analytical form of the optimal probability of successful identification for any length of the particle sequence. We show that the conditional success probabilities of identifying each possible change point show an unexpected oscillatory behavior. We also discuss local (online) protocols and compare them with the optimal procedure.

Algebraic and analyticity properties of the n-point function in quantum field theory

International Nuclear Information System (INIS)

Bros, Jacques

1970-01-01

The general theory of quantized fields (axiomatic approach) is investigated. A systematic study of the algebraic properties of all the Green functions of a local field, which generalize the ordinary retarded and advanced functions, is presented. The notion emerges of a primitive analyticity domain of the n-point function, and of the existence of auxiliary analytic functions into which the various Green functions can be decomposed. Certain processes of analytic completion are described, and then applied to enlarging the primitive domain, particularly for the case n = 4; among the results the crossing property for all scattering amplitudes which involve two incoming and two outgoing particles is proved. (author) [fr

Algebraic number theory

CERN Document Server

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

Hecke algebraic properties of dynamical R-matrices. Application to related quantum matrix algebras

International Nuclear Information System (INIS)

Khadzhiivanov, L.K.; Todorov, I.T.; Isaev, A.P.; Pyatov, P.N.; Ogievetskij, O.V.

1998-01-01

The quantum dynamical Yang-Baxter (or Gervais-Neveu-Felder) equation defines an R-matrix R cap (p), where p stands for a set of mutually commuting variables. A family of SL (n)-type solutions of this equation provides a new realization of the Hecke algebra. We define quantum antisymmetrizers, introduce the notion of quantum determinant and compute the inverse quantum matrix for matrix algebras of the type R cap (p) a 1 a 2 = a 1 a 2 R cap. It is pointed out that such a quantum matrix algebra arises in the operator realization of the chiral zero modes of the WZNW model

Linear Algebra and Smarandache Linear Algebra

OpenAIRE

Vasantha, Kandasamy

2003-01-01

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

The $K$-theory of real graph $C*$-algebras

OpenAIRE

Boersema, Jeffrey L.

2014-01-01

In this paper, we will introduce real graph algebras and develop the theory to the point of being able to calculate the $K$-theory of such algebras. The $K$-theory situation is significantly more complicated than in the case for complex graph algebras. To develop the long exact sequence to compute the $K$-theory of a real graph algebra, we need to develop a generalized theory of crossed products for real C*-algebras for groups with involution. We also need to deal with the additional algebrai...

The N=2 super-W3 algebra

International Nuclear Information System (INIS)

Romans, L.J.

1992-01-01

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

Higher regulators, algebraic

CERN Document Server

Bloch, Spencer J

2000-01-01

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

Filtrated K-theory for real rank zero C*-algebras

DEFF Research Database (Denmark)

Arklint, Sara Esther; Restorff, Gunnar; Ruiz, Efren

2012-01-01

The smallest primitive ideal spaces for which there exist counterexamples to the classification of non-simple, purely infinite, nuclear, separable C*-algebras using filtrated K-theory, are four-point spaces. In this article, we therefore restrict to real rank zero C*-algebras with four-point prim...

Point Cloud Based Change Detection - an Automated Approach for Cloud-based Services

Science.gov (United States)

Collins, Patrick; Bahr, Thomas

2016-04-01

The fusion of stereo photogrammetric point clouds with LiDAR data or terrain information derived from SAR interferometry has a significant potential for 3D topographic change detection. In the present case study latest point cloud generation and analysis capabilities are used to examine a landslide that occurred in the village of Malin in Maharashtra, India, on 30 July 2014, and affected an area of ca. 44.000 m2. It focuses on Pléiades high resolution satellite imagery and the Airbus DS WorldDEMTM as a product of the TanDEM-X mission. This case study was performed using the COTS software package ENVI 5.3. Integration of custom processes and automation is supported by IDL (Interactive Data Language). Thus, ENVI analytics is running via the object-oriented and IDL-based ENVITask API. The pre-event topography is represented by the WorldDEMTM product, delivered with a raster of 12 m x 12 m and based on the EGM2008 geoid (called pre-DEM). For the post-event situation a Pléiades 1B stereo image pair of the AOI affected was obtained. The ENVITask "GeneratePointCloudsByDenseImageMatching" was implemented to extract passive point clouds in LAS format from the panchromatic stereo datasets: • A dense image-matching algorithm is used to identify corresponding points in the two images. • A block adjustment is applied to refine the 3D coordinates that describe the scene geometry. • Additionally, the WorldDEMTM was input to constrain the range of heights in the matching area, and subsequently the length of the epipolar line. The "PointCloudFeatureExtraction" task was executed to generate the post-event digital surface model from the photogrammetric point clouds (called post-DEM). Post-processing consisted of the following steps: • Adding the geoid component (EGM 2008) to the post-DEM. • Pre-DEM reprojection to the UTM Zone 43N (WGS-84) coordinate system and resizing. • Subtraction of the pre-DEM from the post-DEM. • Filtering and threshold based classification of

Alternative algebraic approaches in quantum chemistry

International Nuclear Information System (INIS)

Mezey, Paul G.

2015-01-01

Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies of molecular conformational and reaction processes. Two relevant theorems will be discussed

Alternative algebraic approaches in quantum chemistry

Energy Technology Data Exchange (ETDEWEB)

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

2015-01-22

Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies of molecular conformational and reaction processes. Two relevant theorems will be discussed.

Change Detection Based on Persistent Scatterer Interferometry - a New Method of Monitoring Building Changes

Science.gov (United States)

Yang, C. H.; Kenduiywo, B. K.; Soergel, U.

2016-06-01

Persistent Scatterer Interferometry (PSI) is a technique to detect a network of extracted persistent scatterer (PS) points which feature temporal phase stability and strong radar signal throughout time-series of SAR images. The small surface deformations on such PS points are estimated. PSI particularly works well in monitoring human settlements because regular substructures of man-made objects give rise to large number of PS points. If such structures and/or substructures substantially alter or even vanish due to big change like construction, their PS points are discarded without additional explorations during standard PSI procedure. Such rejected points are called big change (BC) points. On the other hand, incoherent change detection (ICD) relies on local comparison of multi-temporal images (e.g. image difference, image ratio) to highlight scene modifications of larger size rather than detail level. However, image noise inevitably degrades ICD accuracy. We propose a change detection approach based on PSI to synergize benefits of PSI and ICD. PS points are extracted by PSI procedure. A local change index is introduced to quantify probability of a big change for each point. We propose an automatic thresholding method adopting change index to extract BC points along with a clue of the period they emerge. In the end, PS ad BC points are integrated into a change detection image. Our method is tested at a site located around north of Berlin main station where steady, demolished, and erected building substructures are successfully detected. The results are consistent with ground truth derived from time-series of aerial images provided by Google Earth. In addition, we apply our technique for traffic infrastructure, business district, and sports playground monitoring.

Turning points in the history of mathematics

CERN Document Server

Grant, Hardy

2015-01-01

This book explores some of the major turning points in the history of mathematics, ranging from ancient Greece to the present, demonstrating the drama that has often been a part of its evolution. Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, can help illuminate the importance of the history of mathematics for its teaching, learning, and appreciation. Some of the turning points considered are the rise of the axiomatic method (most famously in Euclid), and the subsequent major changes in it (for example, by David Hilbert); the “wedding,” via analytic geometry, of algebra and geometry; the “taming” of the infinitely small and the infinitely large; the passages from algebra to algebras, from geometry to geometries, and from arithmetic to arithmetics; and the revolutions in the late nineteenth and early twentieth centuries that resulted from Georg Cantor’s creation of transfinite set theory. The origin of each turning point is discussed, along with...

Recoupling Lie algebra and universal ω-algebra

International Nuclear Information System (INIS)

Joyce, William P.

2004-01-01

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

A note on derivations of Murray–von Neumann algebras

Science.gov (United States)

Kadison, Richard V.; Liu, Zhe

2014-01-01

A Murray–von Neumann algebra is the algebra of operators affiliated with a finite von Neumann algebra. In this article, we first present a brief introduction to the theory of derivations of operator algebras from both the physical and mathematical points of view. We then describe our recent work on derivations of Murray–von Neumann algebras. We show that the “extended derivations” of a Murray–von Neumann algebra, those that map the associated finite von Neumann algebra into itself, are inner. In particular, we prove that the only derivation that maps a Murray–von Neumann algebra associated with a factor of type II1 into that factor is 0. Those results are extensions of Singer’s seminal result answering a question of Kaplansky, as applied to von Neumann algebras: The algebra may be noncommutative and may even contain unbounded elements. PMID:24469831

A note on derivations of Murray-von Neumann algebras.

Science.gov (United States)

Kadison, Richard V; Liu, Zhe

2014-02-11

A Murray-von Neumann algebra is the algebra of operators affiliated with a finite von Neumann algebra. In this article, we first present a brief introduction to the theory of derivations of operator algebras from both the physical and mathematical points of view. We then describe our recent work on derivations of Murray-von Neumann algebras. We show that the "extended derivations" of a Murray-von Neumann algebra, those that map the associated finite von Neumann algebra into itself, are inner. In particular, we prove that the only derivation that maps a Murray-von Neumann algebra associated with a factor of type II1 into that factor is 0. Those results are extensions of Singer's seminal result answering a question of Kaplansky, as applied to von Neumann algebras: The algebra may be noncommutative and may even contain unbounded elements.

Jump point detection for real estate investment success

Science.gov (United States)

Hui, Eddie C. M.; Yu, Carisa K. W.; Ip, Wai-Cheung

2010-03-01

In the literature, studies on real estate market were mainly concentrating on the relation between property price and some key factors. The trend of the real estate market is a major concern. It is believed that changes in trend are signified by some jump points in the property price series. Identifying such jump points reveals important findings that enable policy-makers to look forward. However, not all jump points are observable from the plot of the series. This paper looks into the trend and introduces a new approach to the framework for real estate investment success. The main purpose of this paper is to detect jump points in the time series of some housing price indices and stock price index in Hong Kong by applying the wavelet analysis. The detected jump points reflect to some significant political issues and economic collapse. Moreover, the relations among properties of different classes and between stocks and properties are examined. It can be shown from the empirical result that a lead-lag effect happened between the prices of large-size property and those of small/medium-size property. However, there is no apparent relation or consistent lead in terms of change point measure between property price and stock price. This may be due to the fact that globalization effect has more impact on the stock price than the property price.

Multi-lane detection based on multiple vanishing points detection

Science.gov (United States)

Li, Chuanxiang; Nie, Yiming; Dai, Bin; Wu, Tao

2015-03-01

Lane detection plays a significant role in Advanced Driver Assistance Systems (ADAS) for intelligent vehicles. In this paper we present a multi-lane detection method based on multiple vanishing points detection. A new multi-lane model assumes that a single lane, which has two approximately parallel boundaries, may not parallel to others on road plane. Non-parallel lanes associate with different vanishing points. A biological plausibility model is used to detect multiple vanishing points and fit lane model. Experimental results show that the proposed method can detect both parallel lanes and non-parallel lanes.

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

NARCIS (Netherlands)

N.W. van den Hijligenberg; R. Martini

1995-01-01

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

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

CERN Document Server

Cox, David A; O'Shea, Donal

2015-01-01

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

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

OpenAIRE

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

2010-01-01

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

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

Explicit field realizations of W algebras

OpenAIRE

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

2009-01-01

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

Explicit field realizations of W algebras

International Nuclear Information System (INIS)

Wei Shaowen; Liu Yuxiao; Ren Jirong; Zhang Lijie

2009-01-01

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

Automorphic Lie algebras with dihedral symmetry

International Nuclear Information System (INIS)

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

2014-01-01

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

CHANGE DETECTION BASED ON PERSISTENT SCATTERER INTERFEROMETRY – A NEW METHOD OF MONITORING BUILDING CHANGES

Directory of Open Access Journals (Sweden)

C. H. Yang

2016-06-01

Full Text Available Persistent Scatterer Interferometry (PSI is a technique to detect a network of extracted persistent scatterer (PS points which feature temporal phase stability and strong radar signal throughout time-series of SAR images. The small surface deformations on such PS points are estimated. PSI particularly works well in monitoring human settlements because regular substructures of man-made objects give rise to large number of PS points. If such structures and/or substructures substantially alter or even vanish due to big change like construction, their PS points are discarded without additional explorations during standard PSI procedure. Such rejected points are called big change (BC points. On the other hand, incoherent change detection (ICD relies on local comparison of multi-temporal images (e.g. image difference, image ratio to highlight scene modifications of larger size rather than detail level. However, image noise inevitably degrades ICD accuracy. We propose a change detection approach based on PSI to synergize benefits of PSI and ICD. PS points are extracted by PSI procedure. A local change index is introduced to quantify probability of a big change for each point. We propose an automatic thresholding method adopting change index to extract BC points along with a clue of the period they emerge. In the end, PS ad BC points are integrated into a change detection image. Our method is tested at a site located around north of Berlin main station where steady, demolished, and erected building substructures are successfully detected. The results are consistent with ground truth derived from time-series of aerial images provided by Google Earth. In addition, we apply our technique for traffic infrastructure, business district, and sports playground monitoring.

Lattice and algebra homomorphisms on C (X) in Zermelo-Fraenkel ...

African Journals Online (AJOL)

Let C (X) denote the lattice-ordered algebra of all real-valued continuous functions on a topological space X. This paper discusses in Zermelo-Fraenkel Set Theory the equivalence on C (X) between algebra homomorphisms, lattice homo- morphisms, and point evaluations. Keywords: Algebra homomorphism, lattice ...

Critical points in an algebra of elementary embeddings

OpenAIRE

Dougherty, Randall

1992-01-01

Given two elementary embeddings from the collection of sets of rank less than $\\lambda$ to itself, one can combine them to obtain another such embedding in two ways: by composition, and by applying one to (initial segments of) the other. Hence, a single such nontrivial embedding $j$ generates an algebra of embeddings via these two operations, which satisfies certain laws (for example, application distributes over both composition and application). Laver has shown, among other things, that thi...

Note on Studying Change Point of LRD Traffic Based on Li's Detection of DDoS Flood Attacking

Directory of Open Access Journals (Sweden)

Zhengmin Xia

2010-01-01

Full Text Available Distributed denial-of-service (DDoS flood attacks remain great threats to the Internet. To ensure network usability and reliability, accurate detection of these attacks is critical. Based on Li's work on DDoS flood attack detection, we propose a DDoS detection method by monitoring the Hurst variation of long-range dependant traffic. Specifically, we use an autoregressive system to estimate the Hurst parameter of normal traffic. If the actual Hurst parameter varies significantly from the estimation, we assume that DDoS attack happens. Meanwhile, we propose two methods to determine the change point of Hurst parameter that indicates the occurrence of DDoS attacks. The detection rate associated with one method and false alarm rate for the other method are also derived. The test results on DARPA intrusion detection evaluation data show that the proposed approaches can achieve better detection performance than some well-known self-similarity-based detection methods.

A Geometric Algebra Co-Processor for Color Edge Detection

Directory of Open Access Journals (Sweden)

Biswajit Mishra

2015-01-01

Full Text Available This paper describes advancement in color edge detection, using a dedicated Geometric Algebra (GA co-processor implemented on an Application Specific Integrated Circuit (ASIC. GA provides a rich set of geometric operations, giving the advantage that many signal and image processing operations become straightforward and the algorithms intuitive to design. The use of GA allows images to be represented with the three R, G, B color channels defined as a single entity, rather than separate quantities. A novel custom ASIC is proposed and fabricated that directly targets GA operations and results in significant performance improvement for color edge detection. Use of the hardware described in this paper also shows that the convolution operation with the rotor masks within GA belongs to a class of linear vector filters and can be applied to image or speech signals. The contribution of the proposed approach has been demonstrated by implementing three different types of edge detection schemes on the proposed hardware. The overall performance gains using the proposed GA Co-Processor over existing software approaches are more than 3.2× faster than GAIGEN and more than 2800× faster than GABLE. The performance of the fabricated GA co-processor is approximately an order of magnitude faster than previously published results for hardware implementations.

Cylindric-like algebras and algebraic logic

CERN Document Server

Ferenczi, Miklós; Németi, István

2013-01-01

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

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

NARCIS (Netherlands)

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

1995-01-01

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

Current algebras and many-body physics

International Nuclear Information System (INIS)

Albertin, U.K.

1989-01-01

Several applications of current algebras in many body physics are examined. The first is the interacting Bose gas in three dimensions. Theories for phonons, vortices and rotons are all described within the current algebra formalism. Next the one dimensional electron gas is examined within the approximation of linear dispersion so that relativistic current algebra techniques may be used. The relation with Thirring strings and compactified boson models is examined, and points of enhanced symmetry in the compactified boson models are shown to lie on phase transition lines for the electron gas. Finally, mathematical aspects of the current algebra are studied. The theory of induced representations of the diffeomorphism group are used to describe the Aharanov-Bohm effect, the thermodynamics of the Bose gas, and the Bose gas in the presence of vortex filaments

Introduction to relation algebras relation algebras

CERN Document Server

Givant, Steven

2017-01-01

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

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.

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.

Classical theory of algebraic numbers

CERN Document Server

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...

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

Twisted boundary states and representation of generalized fusion algebra

International Nuclear Information System (INIS)

Ishikawa, Hiroshi; Tani, Taro

2006-01-01

The mutual consistency of boundary conditions twisted by an automorphism group G of the chiral algebra is studied for general modular invariants of rational conformal field theories. We show that a consistent set of twisted boundary states associated with any modular invariant realizes a non-negative integer matrix representation (NIM-rep) of the generalized fusion algebra, an extension of the fusion algebra by representations of the twisted chiral algebra associated with the automorphism group G. We check this result for several concrete cases. In particular, we find that two NIM-reps of the fusion algebra for su(3) k (k=3,5) are organized into a NIM-rep of the generalized fusion algebra for the charge-conjugation automorphism of su(3) k . We point out that the generalized fusion algebra is non-commutative if G is non-Abelian and provide some examples for G-bar S 3 . Finally, we give an argument that the graph fusion algebra associated with simple current extensions coincides with the generalized fusion algebra for the extended chiral algebra, and thereby explain that the graph fusion algebra contains the fusion algebra of the extended theory as a subalgebra

Parametric change point estimation, testing and confidence interval ...

African Journals Online (AJOL)

In many applications like finance, industry and medicine, it is important to consider that the model parameters may undergo changes at unknown moment in time. This paper deals with estimation, testing and confidence interval of a change point for a univariate variable which is assumed to be normally distributed. To detect ...

The Euclidean distance degree of an algebraic variety

NARCIS (Netherlands)

Draisma, J.; Horobet, E.; Ottaviani, G.; Sturmfels, B.; Thomas, R.R.

2013-01-01

The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Theorem states that this map is given by the singular value decomposition. This article develops a theory of such nearest

The Euclidean distance degree of an algebraic variety

NARCIS (Netherlands)

Draisma, J.; Horobet, E.; Ottaviani, G.; Sturmfels, B.; Thomas, R.R.

The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low-rank matrices, the Eckart–Young Theorem states that this map is given by the singular value decomposition. This article develops a theory of such nearest

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

International Nuclear Information System (INIS)

Marquette, Ian

2013-01-01

We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently

Generating loop graphs via Hopf algebra in quantum field theory

International Nuclear Information System (INIS)

Mestre, Angela; Oeckl, Robert

2006-01-01

We use the Hopf algebra structure of the time-ordered algebra of field operators to generate all connected weighted Feynman graphs in a recursive and efficient manner. The algebraic representation of the graphs is such that they can be evaluated directly as contributions to the connected n-point functions. The recursion proceeds by loop order and vertex number

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 ...

AIRBORNE LIGHT DETECTION AND RANGING (LIDAR DERIVED DEFORMATION FROM THE MW 6.0 24 AUGUST, 2014 SOUTH NAPA EARTHQUAKE ESTIMATED BY TWO AND THREE DIMENSIONAL POINT CLOUD CHANGE DETECTION TECHNIQUES

Directory of Open Access Journals (Sweden)

A. W. Lyda

2016-06-01

Full Text Available Remote sensing via LiDAR (Light Detection And Ranging has proven extremely useful in both Earth science and hazard related studies. Surveys taken before and after an earthquake for example, can provide decimeter-level, 3D near-field estimates of land deformation that offer better spatial coverage of the near field rupture zone than other geodetic methods (e.g., InSAR, GNSS, or alignment array. In this study, we compare and contrast estimates of deformation obtained from different pre and post-event airborne laser scanning (ALS data sets of the 2014 South Napa Earthquake using two change detection algorithms, Iterative Control Point (ICP and Particle Image Velocimetry (PIV. The ICP algorithm is a closest point based registration algorithm that can iteratively acquire three dimensional deformations from airborne LiDAR data sets. By employing a newly proposed partition scheme, “moving window,” to handle the large spatial scale point cloud over the earthquake rupture area, the ICP process applies a rigid registration of data sets within an overlapped window to enhance the change detection results of the local, spatially varying surface deformation near-fault. The other algorithm, PIV, is a well-established, two dimensional image co-registration and correlation technique developed in fluid mechanics research and later applied to geotechnical studies. Adapted here for an earthquake with little vertical movement, the 3D point cloud is interpolated into a 2D DTM image and horizontal deformation is determined by assessing the cross-correlation of interrogation areas within the images to find the most likely deformation between two areas. Both the PIV process and the ICP algorithm are further benefited by a presented, novel use of urban geodetic markers. Analogous to the persistent scatterer technique employed with differential radar observations, this new LiDAR application exploits a classified point cloud dataset to assist the change detection

Regularisation in multi- and hyperspectral remote sensing change detection

DEFF Research Database (Denmark)

Nielsen, Allan Aasbjerg

2005-01-01

Change detection methods for multi- and hypervariate data look for differences in data acquired over the same area at different points in time. These differences may be due to noise or differences in (atmospheric etc.) conditions at the two acquisition time points. To prevent a change detection m...

Quantum cluster algebras and quantum nilpotent algebras

Science.gov (United States)

Goodearl, Kenneth R.; Yakimov, Milen T.

2014-01-01

A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197

An introduction to algebraic geometry and algebraic groups

CERN Document Server

Geck, Meinolf

2003-01-01

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

Gauss Elimination: Workhorse of Linear Algebra.

Science.gov (United States)

1995-08-05

linear algebra computation for solving systems, computing determinants and determining the rank of matrix. All of these are discussed in varying contexts. These include different arithmetic or algebraic setting such as integer arithmetic or polynomial rings as well as conventional real (floating-point) arithmetic. These have effects on both accuracy and complexity analyses of the algorithm. These, too, are covered here. The impact of modern parallel computer architecture on GE is also

Fuzzy commutative algebra and its application in mechanical engineering

International Nuclear Information System (INIS)

Han, J.; Song, H.

1996-01-01

Based on literature data, this paper discusses the whole mathematical structure about point-fuzzy number set F(R). By introducing some new operations about addition, subtraction, multiplication, division and scalar multiplication, we prove that F(R) can form fuzzy linear space, fuzzy commutative ring, fuzzy commutative algebra in order. Furthermore, we get that A is fuzzy commutative algebra for any fuzzy subset. At last, we give an application of point-fuzzy number to mechanical engineering

Discrete event systems in dioid algebra and conventional algebra

CERN Document Server

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

Conformal algebras of two-dimensional disordered systems

International Nuclear Information System (INIS)

Gurarie, Victor; Ludwig, Andreas W.W.

2002-01-01

We discuss the structure of two-dimensional conformal field theories at a central charge c=0 describing critical disordered systems, polymers and percolation. We construct a novel extension of the c=0 Virasoro algebra, characterized by a number b measuring the effective number of massless degrees of freedom, and by a logarithmic partner of the stress tensor. It is argued to be present at a generic random critical point, lacking super Kac-Moody, or other higher symmetries, and is a tool to describe and classify such theories. Interestingly, this algebra is not only consistent with, but indeed naturally accommodates in general an underlying global supersymmetry. Polymers and percolation realize this algebra. Unexpectedly, we find that the c=0 Kac table of the degenerate fields contains two distinct theories with b=5/6 and b=-5/8 which we conjecture to correspond to percolation and polymers, respectively. A given Kac-table field can be degenerate only in one of them. Remarkably, we also find this algebra, and thereby an ensuing hidden supersymmetry, realized at general replica-averaged critical points, for which we derive an explicit formula for b. (author). Letter-to-the-editor

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

NARCIS (Netherlands)

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

1995-01-01

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

The relation between quantum W algebras and Lie algebras

International Nuclear Information System (INIS)

Boer, J. de; Tjin, T.

1994-01-01

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

Tracing a planar algebraic curve

International Nuclear Information System (INIS)

Chen Falai; Kozak, J.

1994-09-01

In this paper, an algorithm that determines a real algebraic curve is outlined. Its basic step is to divide the plane into subdomains that include only simple branches of the algebraic curve without singular points. Each of the branches is then stably and efficiently traced in the particular subdomain. Except for the tracing, the algorithm requires only a couple of simple operations on polynomials that can be carried out exactly if the coefficients are rational, and the determination of zeros of several polynomials of one variable. (author). 5 refs, 4 figs

Fusion algebra and fusing matrices

International Nuclear Information System (INIS)

Gao Yihong; Li Miao; Yu Ming.

1989-09-01

We show that the Wilson line operators in topological field theories form a fusion algebra. In general, the fusion algebra is a relation among the fusing (F) matrices. In the case of the SU(2) WZW model, some special F matrix elements are found in this way, and the remaining F matrix elements are then determined up to a sign. In addition, the S(j) modular transformation of the one point blocks on the torus is worked out. Our results are found to agree with those obtained from the quantum group method. (author). 24 refs

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

International Nuclear Information System (INIS)

Ayupov, Shavkat; Kudaybergenov, Karimbergen

2016-01-01

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

LAND COVER CHANGE DETECTION BASED ON GENETICALLY FEATURE AELECTION AND IMAGE ALGEBRA USING HYPERION HYPERSPECTRAL IMAGERY

Directory of Open Access Journals (Sweden)

S. T. Seydi

2015-12-01

Full Text Available The Earth has always been under the influence of population growth and human activities. This process causes the changes in land use. Thus, for optimal management of the use of resources, it is necessary to be aware of these changes. Satellite remote sensing has several advantages for monitoring land use/cover resources, especially for large geographic areas. Change detection and attribution of cultivation area over time present additional challenges for correctly analyzing remote sensing imagery. In this regards, for better identifying change in multi temporal images we use hyperspectral images. Hyperspectral images due to high spectral resolution created special placed in many of field. Nevertheless, selecting suitable and adequate features/bands from this data is crucial for any analysis and especially for the change detection algorithms. This research aims to automatically feature selection for detect land use changes are introduced. In this study, the optimal band images using hyperspectral sensor using Hyperion hyperspectral images by using genetic algorithms and Ratio bands, we select the optimal band. In addition, the results reveal the superiority of the implemented method to extract change map with overall accuracy by a margin of nearly 79% using multi temporal hyperspectral imagery.

Nonassociativity, Malcev algebras and string theory

International Nuclear Information System (INIS)

Guenaydin, M.; Minic, D.

2013-01-01

Nonassociative structures have appeared in the study of D-branes in curved backgrounds. In recent work, string theory backgrounds involving three-form fluxes, where such structures show up, have been studied in more detail. We point out that under certain assumptions these nonassociative structures coincide with nonassociative Malcev algebras which had appeared in the quantum mechanics of systems with non-vanishing three-cocycles, such as a point particle moving in the field of a magnetic charge. We generalize the corresponding Malcev algebras to include electric as well as magnetic charges. These structures find their classical counterpart in the theory of Poisson-Malcev algebras and their generalizations. We also study their connection to Stueckelberg's generalized Poisson brackets that do not obey the Jacobi identity and point out that nonassociative string theory with a fundamental length corresponds to a realization of his goal to find a non-linear extension of quantum mechanics with a fundamental length. Similar nonassociative structures are also known to appear in the cubic formulation of closed string field theory in terms of open string fields, leading us to conjecture a natural string-field theoretic generalization of the AdS/CFT-like (holographic) duality. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Quantum cluster algebra structures on quantum nilpotent algebras

CERN Document Server

Goodearl, K R

2017-01-01

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

Detecting determinism from point processes.

Science.gov (United States)

Andrzejak, Ralph G; Mormann, Florian; Kreuz, Thomas

2014-12-01

The detection of a nonrandom structure from experimental data can be crucial for the classification, understanding, and interpretation of the generating process. We here introduce a rank-based nonlinear predictability score to detect determinism from point process data. Thanks to its modular nature, this approach can be adapted to whatever signature in the data one considers indicative of deterministic structure. After validating our approach using point process signals from deterministic and stochastic model dynamics, we show an application to neuronal spike trains recorded in the brain of an epilepsy patient. While we illustrate our approach in the context of temporal point processes, it can be readily applied to spatial point processes as well.

Exchange algebra and exotic supersymmetry in the Chiral Potts model

International Nuclear Information System (INIS)

Bernard, D.; Pasquier, V.

1989-01-01

We obtain an exchange algebra for the Chiral Potts model, the elements of which are linear in the parameters defining the rapidity curve. This enables us to connect the Chiral Potts model to a U q (GL(2)) algebra. On the other hand, looking at the model from the S-matrix point of view relates it to a Z N generalisation of the supersymmetric algebra

On the topology of real algebraic plane curves

DEFF Research Database (Denmark)

Cheng, Jinsan; Lazard, Sylvain; Peñaranda, Luis

2010-01-01

We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and critical points, is also relevant. A challenge is to compute efficiently this information for the given...... and isolation with rational univariate representations. This has the advantage of avoiding computations with polynomials with algebraic coefficients, even in non-generic positions. Our algorithm isolates critical points in boxes and computes a decomposition of the plane by rectangular boxes. This decomposition...

Unitary W-algebras and three-dimensional higher spin gravities with spin one symmetry

International Nuclear Information System (INIS)

Afshar, Hamid; Creutzig, Thomas; Grumiller, Daniel; Hikida, Yasuaki; Rønne, Peter B.

2014-01-01

We investigate whether there are unitary families of W-algebras with spin one fields in the natural example of the Feigin-Semikhatov W_n"("2")-algebra. This algebra is conjecturally a quantum Hamiltonian reduction corresponding to a non-principal nilpotent element. We conjecture that this algebra admits a unitary real form for even n. Our main result is that this conjecture is consistent with the known part of the operator product algebra, and especially it is true for n=2 and n=4. Moreover, we find certain ranges of allowed levels where a positive definite inner product is possible. We also find a unitary conformal field theory for every even n at the special level k+n=(n+1)/(n−1). At these points, the W_n"("2")-algebra is nothing but a compactified free boson. This family of W-algebras admits an ’t Hooft limit. Further, in the case of n=4, we reproduce the algebra from the higher spin gravity point of view. In general, gravity computations allow us to reproduce some leading coefficients of the operator product.

Quadratic algebras

CERN Document Server

Polishchuk, Alexander

2005-01-01

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

Regularity of C*-algebras and central sequence algebras

DEFF Research Database (Denmark)

Christensen, Martin S.

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

Real division algebras and other algebras motivated by physics

International Nuclear Information System (INIS)

Benkart, G.; Osborn, J.M.

1981-01-01

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

Donaldson invariants in algebraic geometry

International Nuclear Information System (INIS)

Goettsche, L.

2000-01-01

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

Ghost imaging with bucket detection and point detection

Science.gov (United States)

Zhang, De-Jian; Yin, Rao; Wang, Tong-Biao; Liao, Qing-Hua; Li, Hong-Guo; Liao, Qinghong; Liu, Jiang-Tao

2018-04-01

We experimentally investigate ghost imaging with bucket detection and point detection in which three types of illuminating sources are applied: (a) pseudo-thermal light source; (b) amplitude modulated true thermal light source; (c) amplitude modulated laser source. Experimental results show that the quality of ghost images reconstructed with true thermal light or laser beam is insensitive to the usage of bucket or point detector, however, the quality of ghost images reconstructed with pseudo-thermal light in bucket detector case is better than that in point detector case. Our theoretical analysis shows that the reason for this is due to the first order transverse coherence of the illuminating source.

Laser desorption mass spectrometry for point mutation detection

Energy Technology Data Exchange (ETDEWEB)

Taranenko, N.I.; Chung, C.N.; Zhu, Y.F. [Oak Ridge National Lab., TN (United States)] [and others

1996-12-31

A point mutation can be associated with the pathogenesis of inherited or acquired diseases. Laser desorption mass spectrometry coupled with allele specific polymerase chain reaction (PCR) was first used for point mutation detection. G551D is one of several mutations of the cystic fibrosis transmembrane conductance regulator (CFTR) gene present in 1-3% of the mutant CFTR alleles in most European populations. In this work, two different approaches were pursued to detect G551D point mutation in the cystic fibrosis gene. The strategy is to amplify the desired region of DNA template by PCR using two primers that overlap one base at the site of the point mutation and which vary in size. If the two primers based on the normal sequence match the target DNA sequence, a normal PCR product will be produced. However, if the alternately sized primers that match the mutant sequence recognize the target DNA, an abnormal PCR product will be produced. Thus, the mass spectrometer can be used to identify patients that are homozygous normal, heterozygous for a mutation or homozygous abnormal at a mutation site. Another approach to identify similar mutations is the use of sequence specific restriction enzymes which respond to changes in the DNA sequence. Mass spectrometry is used to detect the length of the restriction fragments by digestion of a PCR generated target fragment. 21 refs., 10 figs., 2 tabs.

A note on the algebraic evaluation of correlators in local chiral conformal field theory

International Nuclear Information System (INIS)

Honecker, A.

1992-09-01

We comment on a program designed for the study of local chiral algebras and their representations in 2D conformal field theory. Based on the algebraic approach described by W. Nahm, this program efficiently calculates arbitrary n-point functions of these algebras. The program is designed such that calculations involving e.g. current algebras, W-algebras and N-Superconformal algebras can be performed. As a non-trivial application we construct an extension of the Virasoro algebra by two fields with spin four and six using the N=1-Super-Virasoro algebra. (orig.)

Hom-Novikov algebras

International Nuclear Information System (INIS)

Yau, Donald

2011-01-01

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

On the q-deformation of certain infinite dimensional Lie algebras

International Nuclear Information System (INIS)

El Kinani, E.H.; Zakkari, M.

1995-07-01

A representation of the q-deformed centreless Virasoro algebra in terms of the Gauss derivatives D x and D y on the quantum plane C q [x,y] is given. Moreover, we obtain the deformed version of the algebra of the area-preserving diffeomorphisms of the torus T 2 . In the end, the correspondence between Psd(q,p,r) and the a-bar ∞ algebra is pointed out. (author). 11 refs

Model-based decoding, information estimation, and change-point detection techniques for multineuron spike trains.

Science.gov (United States)

Pillow, Jonathan W; Ahmadian, Yashar; Paninski, Liam

2011-01-01

One of the central problems in systems neuroscience is to understand how neural spike trains convey sensory information. Decoding methods, which provide an explicit means for reading out the information contained in neural spike responses, offer a powerful set of tools for studying the neural coding problem. Here we develop several decoding methods based on point-process neural encoding models, or forward models that predict spike responses to stimuli. These models have concave log-likelihood functions, which allow efficient maximum-likelihood model fitting and stimulus decoding. We present several applications of the encoding model framework to the problem of decoding stimulus information from population spike responses: (1) a tractable algorithm for computing the maximum a posteriori (MAP) estimate of the stimulus, the most probable stimulus to have generated an observed single- or multiple-neuron spike train response, given some prior distribution over the stimulus; (2) a gaussian approximation to the posterior stimulus distribution that can be used to quantify the fidelity with which various stimulus features are encoded; (3) an efficient method for estimating the mutual information between the stimulus and the spike trains emitted by a neural population; and (4) a framework for the detection of change-point times (the time at which the stimulus undergoes a change in mean or variance) by marginalizing over the posterior stimulus distribution. We provide several examples illustrating the performance of these estimators with simulated and real neural data.

Linear algebra meets Lie algebra: the Kostant-Wallach theory

OpenAIRE

Shomron, Noam; Parlett, Beresford N.

2008-01-01

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

Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems

International Nuclear Information System (INIS)

Marquette, Ian

2011-01-01

There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.

Riemann surfaces, Clifford algebras and infinite dimensional groups

International Nuclear Information System (INIS)

Carey, A.L.; Eastwood, M.G.; Hannabuss, K.C.

1990-01-01

We introduce of class of Riemann surfaces which possess a fixed point free involution and line bundles over these surfaces with which we can associate an infinite dimensional Clifford algebra. Acting by automorphisms of this algebra is a 'gauge' group of meromorphic functions on the Riemann surface. There is a natural Fock representation of the Clifford algebra and an associated projective representation of this group of meromorphic functions in close analogy with the construction of the basic representation of Kac-Moody algebras via a Fock representation of the Fermion algebra. In the genus one case we find a form of vertex operator construction which allows us to prove a version of the Boson-Fermion correspondence. These results are motivated by the analysis of soliton solutions of the Landau-Lifshitz equation and are rather distinct from recent developments in quantum field theory on Riemann surfaces. (orig.)

International Conference on Semigroups, Algebras and Operator Theory

CERN Document Server

Meakin, John; Rajan, A

2015-01-01

This book discusses recent developments in semigroup theory and its applications in areas such as operator algebras, operator approximations and category theory. All contributing authors are eminent researchers in their respective fields, from across the world. Their papers, presented at the 2014 International Conference on Semigroups, Algebras and Operator Theory in Cochin, India, focus on recent developments in semigroup theory and operator algebras. They highlight current research activities on the structure theory of semigroups as well as the role of semigroup theoretic approaches to other areas such as rings and algebras. The deliberations and discussions at the conference point to future research directions in these areas. This book presents 16 unpublished, high-quality and peer-reviewed research papers on areas such as structure theory of semigroups, decidability vs. undecidability of word problems, regular von Neumann algebras, operator theory and operator approximations. Interested researchers will f...

Computational algebraic geometry of epidemic models

Science.gov (United States)

Rodríguez Vega, Martín.

2014-06-01

Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.

Contraction-based classification of supersymmetric extensions of kinematical lie algebras

International Nuclear Information System (INIS)

Campoamor-Stursberg, R.; Rausch de Traubenberg, M.

2010-01-01

We study supersymmetric extensions of classical kinematical algebras from the point of view of contraction theory. It is shown that contracting the supersymmetric extension of the anti-de Sitter algebra leads to a hierarchy similar in structure to the classical Bacry-Levy-Leblond classification.

Some homological properties of skew PBW extensions arising in non-commutative algebraic geometry

Directory of Open Access Journals (Sweden)

Lezama Oswaldo

2017-06-01

Full Text Available In this short paper we study for the skew PBW (Poincar-Birkhoff-Witt extensions some homological properties arising in non-commutative algebraic geometry, namely, Auslander-Gorenstein regularity, Cohen-Macaulayness and strongly noetherianity. Skew PBW extensions include a considerable number of non-commutative rings of polynomial type such that classical PBW extensions, quantum polynomial rings, multiplicative analogue of the Weyl algebra, some Sklyanin algebras, operator algebras, diffusion algebras, quadratic algebras in 3 variables, among many others. Parametrization of the point modules of some examples is also presented.

Beltrami parametrization and gauging of Virasoro and w-infinity algebras

International Nuclear Information System (INIS)

Tatar, L.

1992-07-01

The gauging of the Virasoro and w-infinity algebras are discussed from the point of view of BRST symmetry. Both algebras are realised as ''Russian formulas'' for the curvatures built from the generators of the Lie algebras and the corresponding gauge fields. The generalized curvatures are used to determine the gauge invariant Lagrangians as well as the anomaly structures of the conformal two dimensional theory and the w-gravity. (author). 21 refs

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

International Nuclear Information System (INIS)

Foot, R.; Joshi, G.C.

1992-01-01

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

Interactions Between Representation Ttheory, Algebraic Topology and Commutative Algebra

CERN Document Server

Pitsch, Wolfgang; Zarzuela, Santiago

2016-01-01

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

Clifford Algebras and magnetic monopoles

International Nuclear Information System (INIS)

Recami, E.

1987-01-01

It is known that the introduction of magnetic monopolies in electromagnetism does still present formal problems from the point of view of classical field theory. The author attempts to overcome at least some of them by making recourse to the Clifford Algebra formalism. In fact, while the events of a two-dimensional Minkowski space-time M(1,1) are sufficiently well represented by ordinary Complex Numbers, when dealing with the events of the four-dimensional Minkowski space M(1,3)identical to M/sub 4/ one has of course to look for hypercomplex numbers or, more generally, for the elements of a Clifford Algebra. The author uses the Clifford Algebras in terms of ''multivectors'', and in particular by Hestenes' language, which suits space-time quite well. He recalls that the Clifford product chiγ is the sum of the internal product chi . γ and of the wedge product chiΛγ

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

Science.gov (United States)

Verburgt, Lukas M

2016-01-01

This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s.

Monomial algebras

CERN Document Server

Villarreal, Rafael

2015-01-01

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

Algebra

CERN Document Server

Tabak, John

2004-01-01

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

Iwahori-Hecke algebras and Schur algebras of the symmetric group

CERN Document Server

Mathas, Andrew

1999-01-01

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

Algebra of pseudo-differential operators over C*-algebra

International Nuclear Information System (INIS)

Mohammad, N.

1982-08-01

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

Commutative algebra with a view toward algebraic geometry

CERN Document Server

Eisenbud, David

1995-01-01

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

Laser desorption mass spectrometry for point mutation detection

Energy Technology Data Exchange (ETDEWEB)

Taranenko, N.I.; Chung, C.N.; Zhu, Y.F. [Oak Ridge National Lab., TN (United States)] [and others

1996-10-01

A point mutation can be associated with the pathogenesis of inherited or acquired diseases. Laser desorption mass spectrometry coupled with allele specific polymerase chain reaction (PCR) was first used for point mutation detection. G551D is one of several mutations of the cystic fibrosis transmembrane conductance regulator (CFTR) gene present in 1-3% of the mutant CFTR alleles in most European populations. In this work, two different approaches were pursued to detect G551D point mutation in the cystic fibrosis gene. The strategy is to amplify the desired region of DNA template by PCR using two primers that overlap one base at the site of the point mutation and which vary in size. If the two primers based on the normal sequence match the target DNA sequence, a normal PCR product will be produced. However, if the alternately sized primers that match the mutant sequence recognize the target DNA, an abnormal PCR product will be produced. Thus, the mass spectrometer can be used to identify patients that are homozygous normal, heterozygous for a mutation or homozygous abnormal at a mutation site. Another approach to identify similar mutations is the use of sequence specific restriction enzymes which respond to changes in the DNA sequence. Mass spectrometry is used to detect the length of the restriction fragments generated by digestion of a PCR generated target fragment. 21 refs., 10 figs., 2 tabs.

Ratio-based estimators for a change point in persistence.

Science.gov (United States)

Halunga, Andreea G; Osborn, Denise R

2012-11-01

We study estimation of the date of change in persistence, from [Formula: see text] to [Formula: see text] or vice versa. Contrary to statements in the original papers, our analytical results establish that the ratio-based break point estimators of Kim [Kim, J.Y., 2000. Detection of change in persistence of a linear time series. Journal of Econometrics 95, 97-116], Kim et al. [Kim, J.Y., Belaire-Franch, J., Badillo Amador, R., 2002. Corringendum to "Detection of change in persistence of a linear time series". Journal of Econometrics 109, 389-392] and Busetti and Taylor [Busetti, F., Taylor, A.M.R., 2004. Tests of stationarity against a change in persistence. Journal of Econometrics 123, 33-66] are inconsistent when a mean (or other deterministic component) is estimated for the process. In such cases, the estimators converge to random variables with upper bound given by the true break date when persistence changes from [Formula: see text] to [Formula: see text]. A Monte Carlo study confirms the large sample downward bias and also finds substantial biases in moderate sized samples, partly due to properties at the end points of the search interval.

Jordan algebras versus C*- algebras

International Nuclear Information System (INIS)

Stormer, E.

1976-01-01

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

Some Applications of Algebraic System Solving

Science.gov (United States)

Roanes-Lozano, Eugenio

2011-01-01

Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact…

Implicative Algebras

African Journals Online (AJOL)

Tadesse

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

Exact WKB analysis and cluster algebras

International Nuclear Information System (INIS)

Iwaki, Kohei; Nakanishi, Tomoki

2014-01-01

We develop the mutation theory in the exact WKB analysis using the framework of cluster algebras. Under a continuous deformation of the potential of the Schrödinger equation on a compact Riemann surface, the Stokes graph may change the topology. We call this phenomenon the mutation of Stokes graphs. Along the mutation of Stokes graphs, the Voros symbols, which are monodromy data of the equation, also mutate due to the Stokes phenomenon. We show that the Voros symbols mutate as variables of a cluster algebra with surface realization. As an application, we obtain the identities of Stokes automorphisms associated with periods of cluster algebras. The paper also includes an extensive introduction of the exact WKB analysis and the surface realization of cluster algebras for nonexperts. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’. (paper)

Detecting Brain State Changes via Fiber-Centered Functional Connectivity Analysis

Science.gov (United States)

Li, Xiang; Lim, Chulwoo; Li, Kaiming; Guo, Lei; Liu, Tianming

2013-01-01

Diffusion tensor imaging (DTI) and functional magnetic resonance imaging (fMRI) have been widely used to study structural and functional brain connectivity in recent years. A common assumption used in many previous functional brain connectivity studies is the temporal stationarity. However, accumulating literature evidence has suggested that functional brain connectivity is under temporal dynamic changes in different time scales. In this paper, a novel and intuitive approach is proposed to model and detect dynamic changes of functional brain states based on multimodal fMRI/DTI data. The basic idea is that functional connectivity patterns of all fiber-connected cortical voxels are concatenated into a descriptive functional feature vector to represent the brain’s state, and the temporal change points of brain states are decided by detecting the abrupt changes of the functional vector patterns via the sliding window approach. Our extensive experimental results have shown that meaningful brain state change points can be detected in task-based fMRI/DTI, resting state fMRI/DTI, and natural stimulus fMRI/DTI data sets. Particularly, the detected change points of functional brain states in task-based fMRI corresponded well to the external stimulus paradigm administered to the participating subjects, thus partially validating the proposed brain state change detection approach. The work in this paper provides novel perspective on the dynamic behaviors of functional brain connectivity and offers a starting point for future elucidation of the complex patterns of functional brain interactions and dynamics. PMID:22941508

Open algebraic surfaces

CERN Document Server

Miyanishi, Masayoshi

2000-01-01

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

Separable algebras

CERN Document Server

Ford, Timothy J

2017-01-01

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

Loop homotopy algebras in closed string field theory

International Nuclear Information System (INIS)

Markl, M.

2001-01-01

Barton Zwiebach (1993) constructed ''string products'' on the Hilbert space of a combined conformal field theory of matter and ghosts, satisfying the ''main identity''. It has been well known that the ''tree level'' of the theory gives an example of a strongly homotopy Lie algebra (though, as we will see later, this is not the whole truth). Strongly homotopy Lie algebras are now well-understood objects. On the one hand, strongly homotopy Lie algebra is given by a square zero coderivation on the cofree cocommutative connected coalgebra on the other hand, strongly homotopy Lie algebras are algebras over the cobar dual of the operad Com for commutative algebras. No such characterization of the structure of string products for arbitrary genera has been available, though there are two series of papers directly pointing towards the requisite characterization. As far as the characterization in terms of (co)derivations is concerned, we need the concept of higher order (co)derivations. For our characterization we need to understand the behavior of these higher (co)derivations on (co)free (co)algebras. The necessary machinery for the operadic approach is that of modular operads. We also indicate how to adapt the loop homotopy structure to the case of open string field theory. (orig.)

Basic linear algebra

CERN Document Server

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:...

Equivalent D = 3 supergravity amplitudes from double copies of three-algebra and two-algebra gauge theories.

Science.gov (United States)

Huang, Yu-tin; Johansson, Henrik

2013-04-26

We show that three-dimensional supergravity amplitudes can be obtained as double copies of either three-algebra super-Chern-Simons matter theory or two-algebra super-Yang-Mills theory when either theory is organized to display the color-kinematics duality. We prove that only helicity-conserving four-dimensional gravity amplitudes have nonvanishing descendants when reduced to three dimensions, implying the vanishing of odd-multiplicity S-matrix elements, in agreement with Chern-Simons matter theory. We explicitly verify the double-copy correspondence at four and six points for N = 12,10,8 supergravity theories and discuss its validity for all multiplicity.

New WZW D-branes from the algebra of Wilson loop operators

International Nuclear Information System (INIS)

Monnier, Samuel

2009-01-01

We investigate the algebra generated by the topological Wilson loop operators in WZW models. Wilson loops describe the nontrivial fixed points of the boundary renormalization group flows triggered by Kondo perturbations. Their enveloping algebra therefore encodes all the fixed points which can be reached by sequences of Kondo flows. This algebra is easily described in the case of SU(2), but displays a very rich structure for higher rank groups. In the latter case, its action on known D-branes creates a profusion of new and generically non-rational D-branes. We describe their symmetries and the geometry of their worldvolumes. We briefly explain how to extend these results to coset models.

Generalized EMV-Effect Algebras

Science.gov (United States)

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

2018-04-01

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

Variational linear algebraic equations method

International Nuclear Information System (INIS)

Moiseiwitsch, B.L.

1982-01-01

A modification of the linear algebraic equations method is described which ensures a variational bound on the phaseshifts for potentials having a definite sign at all points. The method is illustrated by the elastic scattering of s-wave electrons by the static field of atomic hydrogen. (author)

Induced Temporal Signatures for Point-Source Detection

International Nuclear Information System (INIS)

Stephens, Daniel L.; Runkle, Robert C.; Carlson, Deborah K.; Peurrung, Anthony J.; Seifert, Allen; Wyatt, Cory R.

2005-01-01

Detection of radioactive point-sized sources is inherently divided into two regimes encompassing stationary and moving detectors. The two cases differ in their treatment of background radiation and its influence on detection sensitivity. In the stationary detector case the statistical fluctuation of the background determines the minimum detectable quantity. In the moving detector case the detector may be subjected to widely and irregularly varying background radiation, as a result of geographical and environmental variation. This significant systematic variation, in conjunction with the statistical variation of the background, requires a conservative threshold to be selected to yield the same false-positive rate as the stationary detection case. This results in lost detection sensitivity for real sources. This work focuses on a simple and practical modification of the detector geometry that increase point-source recognition via a distinctive temporal signature. A key part of this effort is the integrated development of both detector geometries that induce a highly distinctive signature for point sources and the development of statistical algorithms able to optimize detection of this signature amidst varying background. The identification of temporal signatures for point sources has been demonstrated and compared with the canonical method showing good results. This work demonstrates that temporal signatures are efficient at increasing point-source discrimination in a moving detector system

Special set linear algebra and special set fuzzy linear algebra

OpenAIRE

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

2009-01-01

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

Banach Synaptic Algebras

Science.gov (United States)

Foulis, David J.; Pulmannov, Sylvia

2018-04-01

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

An invitation to general algebra and universal constructions

CERN Document Server

Bergman, George M

2015-01-01

Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.

Grassmann algebras

International Nuclear Information System (INIS)

Garcia, R.L.

1983-11-01

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

Algebraic geometry

CERN Document Server

Lefschetz, Solomon

2005-01-01

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

Converting nested algebra expressions into flat algebra expressions

NARCIS (Netherlands)

Paredaens, J.; Van Gucht, D.

1992-01-01

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

Fibered F-Algebra

OpenAIRE

Kleyn, Aleks

2007-01-01

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

Explicit behavioral detection of visual changes develops without their implicit neurophysiological detectability

Directory of Open Access Journals (Sweden)

Pessi eLyyra

2012-03-01

Full Text Available Change blindness is a failure of explicitly detecting changes between consecutively presented images when separated, e.g., by a brief blank screen. There is a growing body of evidence of implicit detection of even explicitly undetectable changes, pointing to the possibility of the implicit change detection as a prerequisite for its explicit counterpart. We recorded event-related potentials (ERPs of the electroencephalography in adults during an oddball-variant of change blindness flicker paradigm. In this variant, rare pictures with a change were interspersed with frequent pictures with no change. In separate stimulus blocks, the blank screen between the change and no-change picture was either of 100 ms or 500 ms in duration. In both stimulus conditions the participants eventually explicitly detect the changed pictures, the blank screen of the longer duration only requiring in average 10 % longer exposure to the picture series until the ability emerged. However, during the change blindness, ERPs were displaced towards negative polarity at 200–260 ms after the stimulus onset (visual mismatch negativity only with the blank screens of the shorter ISI. Our finding of ‘implicit change blindness’ for pictorial material that, nevertheless, successfully prepares the visual system for explicit change detection suggests that implicit change detection may not be a necessary condition for explicit change detection and that they may recruit at least partially distinct memory mechanisms.

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

International Nuclear Information System (INIS)

Grimm, Uwe; Martin, Paul P

2003-01-01

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

Developing early algebraic reasoning in a mathematical community of inquiry

OpenAIRE

Hunter, Jodie Margaret Roberta

2013-01-01

This study explores the development of early algebraic reasoning in mathematical communities of inquiry. Under consideration is the different pathways teachers take as they develop their own understanding of early algebra and then enact changes in their classroom to facilitate algebraic reasoning opportunities. Teachers participated in a professional development intervention which focused on understanding of early algebraic concepts, task development, modification, and enactment, and clas...

Robust Spacecraft Component Detection in Point Clouds

Directory of Open Access Journals (Sweden)

Quanmao Wei

2018-03-01

Full Text Available Automatic component detection of spacecraft can assist in on-orbit operation and space situational awareness. Spacecraft are generally composed of solar panels and cuboidal or cylindrical modules. These components can be simply represented by geometric primitives like plane, cuboid and cylinder. Based on this prior, we propose a robust automatic detection scheme to automatically detect such basic components of spacecraft in three-dimensional (3D point clouds. In the proposed scheme, cylinders are first detected in the iteration of the energy-based geometric model fitting and cylinder parameter estimation. Then, planes are detected by Hough transform and further described as bounded patches with their minimum bounding rectangles. Finally, the cuboids are detected with pair-wise geometry relations from the detected patches. After successive detection of cylinders, planar patches and cuboids, a mid-level geometry representation of the spacecraft can be delivered. We tested the proposed component detection scheme on spacecraft 3D point clouds synthesized by computer-aided design (CAD models and those recovered by image-based reconstruction, respectively. Experimental results illustrate that the proposed scheme can detect the basic geometric components effectively and has fine robustness against noise and point distribution density.

Robust Spacecraft Component Detection in Point Clouds.

Science.gov (United States)

Wei, Quanmao; Jiang, Zhiguo; Zhang, Haopeng

2018-03-21

Automatic component detection of spacecraft can assist in on-orbit operation and space situational awareness. Spacecraft are generally composed of solar panels and cuboidal or cylindrical modules. These components can be simply represented by geometric primitives like plane, cuboid and cylinder. Based on this prior, we propose a robust automatic detection scheme to automatically detect such basic components of spacecraft in three-dimensional (3D) point clouds. In the proposed scheme, cylinders are first detected in the iteration of the energy-based geometric model fitting and cylinder parameter estimation. Then, planes are detected by Hough transform and further described as bounded patches with their minimum bounding rectangles. Finally, the cuboids are detected with pair-wise geometry relations from the detected patches. After successive detection of cylinders, planar patches and cuboids, a mid-level geometry representation of the spacecraft can be delivered. We tested the proposed component detection scheme on spacecraft 3D point clouds synthesized by computer-aided design (CAD) models and those recovered by image-based reconstruction, respectively. Experimental results illustrate that the proposed scheme can detect the basic geometric components effectively and has fine robustness against noise and point distribution density.

Algebraic monoids, group embeddings, and algebraic combinatorics

CERN Document Server

Li, Zhenheng; Steinberg, Benjamin; Wang, Qiang

2014-01-01

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

Leavitt path algebras

CERN Document Server

Abrams, Gene; Siles Molina, Mercedes

2017-01-01

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

Multi parametric deformed Heisenberg algebras: a route to complexity

International Nuclear Information System (INIS)

Curado, E.M.F.; Rego-Monteiro, M.A.

2000-09-01

We introduce a generalized of the Heisenberg which is written in terms of a functional of one generator of the algebra, f(J 0 ), that can be any analytical function. When f is linear with slope θ, we show that the algebra in this case corresponds to q-oscillators for q 2 = tan θ. The case where f is polynomial of order n in J 0 corresponds to a n-parameter Heisenberg algebra. The representations of the algebra, when f is any analytical function, are shown to be obtained through the study of the stability of the fixed points of f and their composed functions. The case when f is a quadratic polynomial in J 0 , the simplest non-linear scheme which is able to create chaotic behavior, is analyzed in detail and special regions in the parameter space give representations that ca not be continuously deformed to representations of Heisenberg algebra. (author)

Changes in Pre-Service Teachers' Algebraic Misconceptions by Using Computer-Assisted Instruction

Science.gov (United States)

Lin, ByCheng-Yao; Ko, Yi-Yin; Kuo, Yu-Chun

2014-01-01

In order to carry out current reforms regarding algebra and technology in elementary school mathematics successfully, pre-service elementary mathematics teachers must be equipped with adequate understandings of algebraic concepts and self-confidence in using computers for their future teaching. This paper examines the differences in preservice…

Approximation of complex algebraic numbers by algebraic numbers of bounded degree

OpenAIRE

Bugeaud, Yann; Evertse, Jan-Hendrik

2007-01-01

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

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

International Nuclear Information System (INIS)

Huang Yizhi

1994-01-01

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

Determinant formula for the topological N = 2 superconformal algebra

International Nuclear Information System (INIS)

Doerrzapf, Matthias; Gato-Rivera, Beatriz

1999-01-01

The Kac determinant for the topological N = 2 superconformal algebra is presented as well as a detailed analysis of the singular vectors detected by the roots of the determinants. In addition we identify the standard Verma modules containing 'no-label' singular vectors (which are not detected directly by the roots of the determinants). We show that in standard Verma modules there are (at least) four different types of submodules, regarding size and shape. We also review the chiral determinant formula, for chiral Verma modules, adding new insights. Finally we transfer the results obtained to the Verma modules and singular vectors of the Ramond N = 2 algebra, which have been very poorly studied so far. This work clarifies several misconceptions and confusing claims appeared in the literature about the singular vectors, Verma modules and submodules of the topological N = 2 superconformal algebra

A ROBUST REGISTRATION ALGORITHM FOR POINT CLOUDS FROM UAV IMAGES FOR CHANGE DETECTION

Directory of Open Access Journals (Sweden)

A. Al-Rawabdeh

2016-06-01

in two epochs over the period of one year (i.e., May 2014 and May 2015. Note that due to the coarse accuracy of the on-board GPS receiver (e.g., +/- 5-10 m the geo-tagged positions of the images were only used as initial values in the bundle block adjustment. Normal distances, signifying detected changes, varying from 20 cm to 4 m were identified between the two epochs. The accuracy of the co-registered surfaces was estimated by comparing non-active patches within the monitored area of interest. Since these non-active sub-areas are stationary, the computed normal distances should theoretically be close to zero. The quality control of the registration results showed that the average normal distance was approximately 4 cm, which is within the noise level of the reconstructed surfaces.

a Robust Registration Algorithm for Point Clouds from Uav Images for Change Detection

Science.gov (United States)

Al-Rawabdeh, A.; Al-Gurrani, H.; Al-Durgham, K.; Detchev, I.; He, F.; El-Sheimy, N.; Habib, A.

2016-06-01

over the period of one year (i.e., May 2014 and May 2015). Note that due to the coarse accuracy of the on-board GPS receiver (e.g., +/- 5-10 m) the geo-tagged positions of the images were only used as initial values in the bundle block adjustment. Normal distances, signifying detected changes, varying from 20 cm to 4 m were identified between the two epochs. The accuracy of the co-registered surfaces was estimated by comparing non-active patches within the monitored area of interest. Since these non-active sub-areas are stationary, the computed normal distances should theoretically be close to zero. The quality control of the registration results showed that the average normal distance was approximately 4 cm, which is within the noise level of the reconstructed surfaces.

Wn(2) algebras

International Nuclear Information System (INIS)

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

2004-01-01

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

Algebraic topology a first course

CERN Document Server

Fulton, William

1995-01-01

To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re­ lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ­ ential topology, etc.), we concentrate our attention on concrete prob­ lems in low dimensions, introducing only as much algebraic machin­ ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol­ ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel­ opment of the subject. What would we like a student to know after a first course in to­ pology (assuming we reject the answer: ...

Examining Heterogeneity in the Effect of Taking Algebra in Eighth Grade

Science.gov (United States)

Rickles, Jordan H.

2013-01-01

Increased access to algebra was a focal point of the National Mathematics Advisory Panel's 2008 report on improving mathematics learning in the United States. Past research found positive effects for early access to algebra, but the focus on average effects may mask important variation across student subgroups. The author addresses whether these…

3rd International Algebra Conference

CERN Document Server

Fong, Yuen; Zelmanov, Efim

2003-01-01

This volume contains one invited lecture which was presented by the 1994 Fields Medal­ ist Professor E. Zelmanov and twelve other papers which were presented at the Third International Conference on Algebra and Their Related Topics at Chang Jung Christian University, Tainan, Republic of China, during the period June 26-July 1, 200l. All papers in this volume have been refereed by an international referee board and we would like to express our deepest thanks to all the referees who were so helpful and punctual in submitting their reports. Thanks are also due to the Promotion and Research Center of National Science Council of Republic of China and the Chang Jung Christian University for their generous financial support of this conference. The spirit of this conference is a continuation of the last two International Tainan­ Moscow Algebra Workshop on Algebras and Their Related Topics which were held in the mid-90's of the last century. The purpose of this very conference was to give a clear picture of the rece...

The vacuum preserving Lie algebra of a classical W-algebra

International Nuclear Information System (INIS)

Feher, L.; Tsutsui, I.

1993-07-01

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

Cluster algebras in scattering amplitudes with special 2D kinematics

Energy Technology Data Exchange (ETDEWEB)

Torres, Marcus A.C. [Institut de Physique Theorique, CEA-Saclay, Gif-sur-Yvette Cedex (France)

2014-02-15

We study the cluster algebra of the kinematic configuration space Conf{sub n}(P{sup 3}P3) of an n-particle scattering amplitude restricted to the special 2D kinematics. We found that the n-point two-loop MHVremainder function in special 2D kinematics depends on a selection of the X-coordinates that are part of a special structure of the cluster algebra related to snake triangulations of polygons. This structure forms a necklace of hypercube beads in the corresponding Stasheff polytope. Furthermore at n = 12, the cluster algebra and the selection of theX-coordinates in special2Dkinematics replicates the cluster algebra and the selection of X-coordinates of the n = 6 two-loop MHV amplitude in 4D kinematics. (orig.)

Asymptotic identity in min-plus algebra: a report on CPNS.

Science.gov (United States)

Li, Ming; Zhao, Wei

2012-01-01

Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Though min-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions.

Nonflexible Lie-admissible algebras

International Nuclear Information System (INIS)

Myung, H.C.

1978-01-01

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

On 2-Banach algebras

International Nuclear Information System (INIS)

Mohammad, N.; Siddiqui, A.H.

1987-11-01

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

Quasi-Linear Algebras and Integrability (the Heisenberg Picture

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Alexei Zhedanov

2008-02-01

Full Text Available We study Poisson and operator algebras with the ''quasi-linear property'' from the Heisenberg picture point of view. This means that there exists a set of one-parameter groups yielding an explicit expression of dynamical variables (operators as functions of ''time'' t. We show that many algebras with nonlinear commutation relations such as the Askey-Wilson, q-Dolan-Grady and others satisfy this property. This provides one more (explicit Heisenberg evolution interpretation of the corresponding integrable systems.

Algebra

CERN Document Server

Flanders, Harley

1975-01-01

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

Optimizing Probability of Detection Point Estimate Demonstration

Science.gov (United States)

Koshti, Ajay M.

2017-01-01

Probability of detection (POD) analysis is used in assessing reliably detectable flaw size in nondestructive evaluation (NDE). MIL-HDBK-18231and associated mh18232POD software gives most common methods of POD analysis. Real flaws such as cracks and crack-like flaws are desired to be detected using these NDE methods. A reliably detectable crack size is required for safe life analysis of fracture critical parts. The paper provides discussion on optimizing probability of detection (POD) demonstration experiments using Point Estimate Method. POD Point estimate method is used by NASA for qualifying special NDE procedures. The point estimate method uses binomial distribution for probability density. Normally, a set of 29 flaws of same size within some tolerance are used in the demonstration. The optimization is performed to provide acceptable value for probability of passing demonstration (PPD) and achieving acceptable value for probability of false (POF) calls while keeping the flaw sizes in the set as small as possible.

Algebra a teaching and source book

CERN Document Server

Shult, Ernest

2015-01-01

This book presents a graduate-level course on modern algebra. It can be used as a teaching book – owing to the copious exercises – and as a source book for those who wish to use the major theorems of algebra. The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan–Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic courses on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products. Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results reside in the exercises, for example, the proof that ideals in a Dedekind domain are generated by at most two elements. The emphasis throughout is on real understanding as opposed to memorizing a catech...

Lukasiewicz-Moisil algebras

CERN Document Server

Boicescu, V; Georgescu, G; Rudeanu, S

1991-01-01

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

Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

Science.gov (United States)

Wasserman, Nicholas H.

2016-01-01

This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

Traditional vectors as an introduction to geometric algebra

International Nuclear Information System (INIS)

Carroll, J E

2003-01-01

The 2002 Oersted Medal Lecture by David Hestenes concerns the many advantages for education in physics if geometric algebra were to replace standard vector algebra. However, such a change has difficulties for those who have been taught traditionally. A new way of introducing geometric algebra is presented here using a four-element array composed of traditional vector and scalar products. This leads to an explicit 4 x 4 matrix representation which contains key requirements for three-dimensional geometric algebra. The work can be extended to include Maxwell's equations where it is found that curl and divergence appear naturally together. However, to obtain an explicit representation of space-time algebra with the correct behaviour under Lorentz transformations, an 8 x 8 matrix representation has to be formed. This leads to a Dirac representation of Maxwell's equations showing that space-time algebra has hidden within its formalism the symmetry of 'parity, charge conjugation and time reversal'

Analytical solution using computer algebra of a biosensor for detecting toxic substances in water

Science.gov (United States)

Rúa Taborda, María. Isabel

2014-05-01

In a relatively recent paper an electrochemical biosensor for water toxicity detection based on a bio-chip as a whole cell was proposed and numerically solved and analyzed. In such paper the kinetic processes in a miniaturized electrochemical biosensor system was described using the equations for specific enzymatic reaction and the diffusion equation. The numerical solution shown excellent agreement with the measured data but such numerical solution is not enough to design efficiently the corresponding bio-chip. For this reason an analytical solution is demanded. The object of the present work is to provide such analytical solution and then to give algebraic guides to design the bio-sensor. The analytical solution is obtained using computer algebra software, specifically Maple. The method of solution is the Laplace transform, with Bromwich integral and residue theorem. The final solution is given as a series of Bessel functions and the effective time for the bio-sensor is computed. It is claimed that the analytical solutions that were obtained will be very useful to predict further current variations in similar systems with different geometries, materials and biological components. Beside of this the analytical solution that we provide is very useful to investigate the relationship between different chamber parameters such as cell radius and height; and electrode radius.

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.

Wavelets and quantum algebras

International Nuclear Information System (INIS)

Ludu, A.; Greiner, M.

1995-09-01

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

Novikov-Jordan algebras

OpenAIRE

Dzhumadil'daev, A. S.

2002-01-01

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

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

Science.gov (United States)

Gonzalez-Vega, Laureano

1999-01-01

Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)

Enhancing Engagement in Algebra: Didactical Strategies Implemented and Discussed by Teachers

Science.gov (United States)

Nyman, Rimma; Kilhamn, Cecilia

2015-01-01

The aim of this study is to investigate student engagement from the point of view of the teacher, by focusing on teacher's didactical strategies used to engage students during algebra introduction. Eight teachers in grade 6 and 7 participated in a focus-group interview study. The findings are based on episodes of student engagement in algebra and…

(Quasi-)Poisson enveloping algebras

OpenAIRE

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

2010-01-01

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

Iterated Leavitt Path Algebras

International Nuclear Information System (INIS)

Hazrat, R.

2009-11-01

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

Smooth random change point models.

Science.gov (United States)

van den Hout, Ardo; Muniz-Terrera, Graciela; Matthews, Fiona E

2011-03-15

Change point models are used to describe processes over time that show a change in direction. An example of such a process is cognitive ability, where a decline a few years before death is sometimes observed. A broken-stick model consists of two linear parts and a breakpoint where the two lines intersect. Alternatively, models can be formulated that imply a smooth change between the two linear parts. Change point models can be extended by adding random effects to account for variability between subjects. A new smooth change point model is introduced and examples are presented that show how change point models can be estimated using functions in R for mixed-effects models. The Bayesian inference using WinBUGS is also discussed. The methods are illustrated using data from a population-based longitudinal study of ageing, the Cambridge City over 75 Cohort Study. The aim is to identify how many years before death individuals experience a change in the rate of decline of their cognitive ability. Copyright © 2010 John Wiley & Sons, Ltd.

Asymptotic Identity in Min-Plus Algebra: A Report on CPNS

Science.gov (United States)

Li, Ming; Zhao, Wei

2012-01-01

Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Though min-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions. PMID:21822446

Algebraic topological entropy

International Nuclear Information System (INIS)

Hudetz, T.

1989-01-01

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

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

International Nuclear Information System (INIS)

Kobayashi, Tatsuo

1993-01-01

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

Reductive Lie-admissible algebras applied to H-spaces and connections

International Nuclear Information System (INIS)

Sagle, A.A.

1982-01-01

An algebra A with multiplication xy is Lie-admissible if the vector space A with new multiplication [x,y] = xy-yx is a Lie algebra; we denote this Lie algebra by A - . Thus, an associative algebra is Lie-admissible but a Cayley algebra is not Lie-admissible. In this paper we show how Lie-admissible algebras arise from Lie groups and their application to differential geometry on Lie groups via the following theorem. Let A be an n-dimensional Lie-admissible algebra over the reals. Let G be a Lie group with multiplication function μ and with Lie algebra g which is isomorphic to A - . Then there exiss a corrdinate system at the identify e in G which represents μ by a function F:gxg→g defined locally at the origin, such that the second derivative, F 2 , at the origin defines on the vector space g the structure of a nonassociative algebra (g, F 2 ). Furthermore this algebra is isomorphic to A and (g, F 2 ) - is isomorphic to A - . Thus roughly, any Lie-admissible algebra is isomorphic to an algebra obtained from a Lie algebra via a change of coordinates in the Lie group. Lie algebras arise by using canonical coordinates and the Campbell-Hausdorff formula. Applications of this show that any G-invariant psuedo-Riemannian connection on G is completely determined by a suitable Lie-admissible algebra. These results extend to H-spaces, reductive Lie-admissible algebras and connections on homogeneous H-spaces. Thus, alternative and other non-Lie-admissible algebras can be utilized

Linear algebraic groups

CERN Document Server

Springer, T A

1998-01-01

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

Extended conformal algebras

International Nuclear Information System (INIS)

Goddard, Peter

1990-01-01

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

STRUCTURE LINE DETECTION FROM LIDAR POINT CLOUDS USING TOPOLOGICAL ELEVATION ANALYSIS

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C. Y. Lo

2012-07-01

Full Text Available Airborne LIDAR point clouds, which have considerable points on object surfaces, are essential to building modeling. In the last two decades, studies have developed different approaches to identify structure lines using two main approaches, data-driven and modeldriven. These studies have shown that automatic modeling processes depend on certain considerations, such as used thresholds, initial value, designed formulas, and predefined cues. Following the development of laser scanning systems, scanning rates have increased and can provide point clouds with higher point density. Therefore, this study proposes using topological elevation analysis (TEA to detect structure lines instead of threshold-dependent concepts and predefined constraints. This analysis contains two parts: data pre-processing and structure line detection. To preserve the original elevation information, a pseudo-grid for generating digital surface models is produced during the first part. The highest point in each grid is set as the elevation value, and its original threedimensional position is preserved. In the second part, using TEA, the structure lines are identified based on the topology of local elevation changes in two directions. Because structure lines can contain certain geometric properties, their locations have small relieves in the radial direction and steep elevation changes in the circular direction. Following the proposed approach, TEA can be used to determine 3D line information without selecting thresholds. For validation, the TEA results are compared with those of the region growing approach. The results indicate that the proposed method can produce structure lines using dense point clouds.

Generalized symmetry algebras

International Nuclear Information System (INIS)

Dragon, N.

1979-01-01

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

Rota-Baxter algebras and the Hopf algebra of renormalization

Energy Technology Data Exchange (ETDEWEB)

Ebrahimi-Fard, K.

2006-06-15

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

Rota-Baxter algebras and the Hopf algebra of renormalization

International Nuclear Information System (INIS)

Ebrahimi-Fard, K.

2006-06-01

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

Central extensions and semi-infinite wedge representations of Krichever-Novikov algebras for more than two points

International Nuclear Information System (INIS)

Schlichenmaier, M.

1990-01-01

For the generalized Krichever-Novikov algebras of meromorphic vector fields and their induced modules of weight λ a different basis is given. With respect to this basis the module structure is generalized graded. 'Local' central extensions of these algebras and their representations on the space of semi-infinite wedge product of forms of weight λ are studied. In this generalization, one again obtains c = -2(6λ 2 -6λ+1) as the value for the central charge. (orig.)

Galilean contractions of W-algebras

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Jørgen Rasmussen

2017-09-01

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

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

International Nuclear Information System (INIS)

Frenkel, E.; Reshetikhin, N.

1996-01-01

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

Algebraic entropy for algebraic maps

International Nuclear Information System (INIS)

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

2016-01-01

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

On hyper BCC-algebras

OpenAIRE

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

2006-01-01

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

Perturbative quantum field theory via vertex algebras

International Nuclear Information System (INIS)

Hollands, Stefan; Olbermann, Heiner

2009-01-01

In this paper, we explain how perturbative quantum field theory can be formulated in terms of (a version of) vertex algebras. Our starting point is the Wilson-Zimmermann operator product expansion (OPE). Following ideas of a previous paper (S. Hollands, e-print arXiv:0802.2198), we consider a consistency (essentially associativity) condition satisfied by the coefficients in this expansion. We observe that the information in the OPE coefficients can be repackaged straightforwardly into 'vertex operators' and that the consistency condition then has essentially the same form as the key condition in the theory of vertex algebras. We develop a general theory of perturbations of the algebras that we encounter, similar in nature to the Hochschild cohomology describing the deformation theory of ordinary algebras. The main part of the paper is devoted to the question how one can calculate the perturbations corresponding to a given interaction Lagrangian (such as λφ 4 ) in practice, using the consistency condition and the corresponding nonlinear field equation. We derive graphical rules, which display the vertex operators (i.e., OPE coefficients) in terms of certain multiple series of hypergeometric type.

A Continuous Formulation for Logical Decisions in Differential Algebraic Systems using Mathematical Programs with Complementarity Constraints

Directory of Open Access Journals (Sweden)

Kody M. Powell

2016-03-01

Full Text Available This work presents a methodology to represent logical decisions in differential algebraic equation simulation and constrained optimization problems using a set of continuous algebraic equations. The formulations may be used when state variables trigger a change in process dynamics, and introduces a pseudo-binary decision variable, which is continuous, but should only have valid solutions at values of either zero or one within a finite time horizon. This formulation enables dynamic optimization problems with logical disjunctions to be solved by simultaneous solution methods without using methods such as mixed integer programming. Several case studies are given to illustrate the value of this methodology including nonlinear model predictive control of a chemical reactor using a surge tank with overflow to buffer disturbances in feed flow rate. Although this work contains novel methodologies for solving dynamic algebraic equation (DAE constrained problems where the system may experience an abrupt change in dynamics that may otherwise require a conditional statement, there remain substantial limitations to this methodology, including a limited domain where problems may converge and the possibility for ill-conditioning. Although the problems presented use only continuous algebraic equations, the formulation has inherent non-smoothness. Hence, these problems must be solved with care and only in select circumstances, such as in simulation or situations when the solution is expected to be near the solver’s initial point.

On hyper BCC-algebras

Directory of Open Access Journals (Sweden)

R. A. Borzooei

2006-01-01

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

Algebraic theory of numbers

CERN Document Server

Samuel, Pierre

2008-01-01

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

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

The BRS algebra of a free differential algebra

International Nuclear Information System (INIS)

Boukraa, S.

1987-04-01

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

Realization Of Algebraic Processor For XML Documents Processing

International Nuclear Information System (INIS)

Georgiev, Bozhidar; Georgieva, Adriana

2010-01-01

In this paper, are presented some possibilities concerning the implementation of an algebraic method for XML hierarchical data processing which makes faster the XML search mechanism. Here is offered a different point of view for creation of advanced algebraic processor (with all necessary software tools and programming modules respectively). Therefore, this nontraditional approach for fast XML navigation with the presented algebraic processor may help to build an easier user-friendly interface provided XML transformations, which can avoid the difficulties in the complicated language constructions of XSL, XSLT and XPath. This approach allows comparatively simple search of XML hierarchical data by means of the following types of functions: specification functions and so named build-in functions. The choice of programming language Java may appear strange at first, but it isn't when you consider that the applications can run on different kinds of computers. The specific search mechanism based on the linear algebra theory is faster in comparison with MSXML parsers (on the basis of the developed examples with about 30%). Actually, there exists the possibility for creating new software tools based on the linear algebra theory, which cover the whole navigation and search techniques characterizing XSLT/XPath. The proposed method is able to replace more complicated operations in other SOA components.

Pseudo-Riemannian Novikov algebras

Energy Technology Data Exchange (ETDEWEB)

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

2008-08-08

Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. Pseudo-Riemannian Novikov algebras denote Novikov algebras with non-degenerate invariant symmetric bilinear forms. In this paper, we find that there is a remarkable geometry on pseudo-Riemannian Novikov algebras, and give a special class of pseudo-Riemannian Novikov algebras.

On the PR-algebras

International Nuclear Information System (INIS)

Lebedenko, V.M.

1978-01-01

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

Introduction to W-algebras

International Nuclear Information System (INIS)

Takao, Masaru

1989-01-01

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

(Modular Effect Algebras are Equivalent to (Frobenius Antispecial Algebras

Directory of Open Access Journals (Sweden)

Dusko Pavlovic

2017-01-01

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

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

NARCIS (Netherlands)

Horobeţ, E.

2016-01-01

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

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

International Nuclear Information System (INIS)

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

1999-04-01

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

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

Directory of Open Access Journals (Sweden)

Zdenka Riečanová

2013-01-01

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

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

International Nuclear Information System (INIS)

Kanakoglou, K; Daskaloyannis, C

2008-01-01

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

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

OpenAIRE

Vasselli, Ezio

2004-01-01

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

Bicovariant quantum algebras and quantum Lie algebras

International Nuclear Information System (INIS)

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

1993-01-01

A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(G q ) to U q g, given by elements of the pure braid group. These operators - the 'reflection matrix' Y= triple bond L + SL - being a special case - generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N). (orig.)

Simple relation algebras

CERN Document Server

Givant, Steven

2017-01-01

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

Linear algebra and group theory for physicists

CERN Document Server

Rao, K N Srinivasa

2006-01-01

Professor Srinivasa Rao's text on Linear Algebra and Group Theory is directed to undergraduate and graduate students who wish to acquire a solid theoretical foundation in these mathematical topics which find extensive use in physics. Based on courses delivered during Professor Srinivasa Rao's long career at the University of Mysore, this text is remarkable for its clear exposition of the subject. Advanced students will find a range of topics such as the Representation theory of Linear Associative Algebras, a complete analysis of Dirac and Kemmer algebras, Representations of the Symmetric group via Young Tableaux, a systematic derivation of the Crystallographic point groups, a comprehensive and unified discussion of the Rotation and Lorentz groups and their representations, and an introduction to Dynkin diagrams in the classification of Lie groups. In addition, the first few chapters on Elementary Group Theory and Vector Spaces also provide useful instructional material even at an introductory level. An author...

Magnetic charge and non-associative algebras

International Nuclear Information System (INIS)

Guenaydin, M.; Zumino, B.

1985-02-01

We consider the possibility that the quantum mechanics of a nonrelativistic electron in the magnetic field of a magnetic charge distribution can be described in terms of a non-associative algebra of observables. It appears that the case of a point monopole is excluded, while that of a constant charge distribution is acceptable. 21 references

Boolean algebra

CERN Document Server

Goodstein, R L

2007-01-01

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

Combinatorial commutative algebra

CERN Document Server

Miller, Ezra

2005-01-01

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

Topological أ-algebras with Cأ-enveloping algebras II

Indian Academy of Sciences (India)

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

Towards a Process Algebra for Shared Processors

DEFF Research Database (Denmark)

Buchholtz, Mikael; Andersen, Jacob; Løvengreen, Hans Henrik

2002-01-01

We present initial work on a timed process algebra that models sharing of processor resources allowing preemption at arbitrary points in time. This enables us to model both the functional and the timely behaviour of concurrent processes executed on a single processor. We give a refinement relation...

C*-algebras by example

CERN Document Server

Davidson, Kenneth R

1996-01-01

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

Spin structures on algebraic curves and their applications in string theories

International Nuclear Information System (INIS)

Ferrari, F.

1990-01-01

The free fields on a Riemann surface carrying spin structures live on an unramified r-covering of the surface itself. When the surface is represented as an algebraic curve related to the vanishing of the Weierstrass polynomial, its r-coverings are algebraic curves as well. We construct explicitly the Weierstrass polynomial associated to the r-coverings of an algebraic curve. Using standard techniques of algebraic geometry it is then possible to solve the inverse Jacobi problem for the odd spin structures. As an application we derive the partition functions of bosonic string theories in many examples, including two general curves of genus three and four. The partition functions are explicitly expressed in terms of branch points apart from a factor which is essentially a theta constant. 53 refs., 4 figs. (Author)

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

International Nuclear Information System (INIS)

Blumenhagen, R.

1994-07-01

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

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

Boolean algebra essentials

CERN Document Server

Solomon, Alan D

2012-01-01

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

Parametric statistical change point analysis

CERN Document Server

Chen, Jie

2000-01-01

This work is an in-depth study of the change point problem from a general point of view and a further examination of change point analysis of the most commonly used statistical models Change point problems are encountered in such disciplines as economics, finance, medicine, psychology, signal processing, and geology, to mention only several The exposition is clear and systematic, with a great deal of introductory material included Different models are presented in each chapter, including gamma and exponential models, rarely examined thus far in the literature Other models covered in detail are the multivariate normal, univariate normal, regression, and discrete models Extensive examples throughout the text emphasize key concepts and different methodologies are used, namely the likelihood ratio criterion, and the Bayesian and information criterion approaches A comprehensive bibliography and two indices complete the study

q-deformed Poincare algebra

International Nuclear Information System (INIS)

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

1992-01-01

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

Stability of Linear Equations--Algebraic Approach

Science.gov (United States)

Cherif, Chokri; Goldstein, Avraham; Prado, Lucio M. G.

2012-01-01

This article could be of interest to teachers of applied mathematics as well as to people who are interested in applications of linear algebra. We give a comprehensive study of linear systems from an application point of view. Specifically, we give an overview of linear systems and problems that can occur with the computed solution when the…

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

Science.gov (United States)

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

2018-03-01

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

Introduction to quantum algebras

International Nuclear Information System (INIS)

Kibler, M.R.

1992-09-01

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

Degree of a isolated real point or a singular complex point on a plane curve defined over Q

DEFF Research Database (Denmark)

Hansen, Johan Peder

2010-01-01

Let $X$ be a curve in the affine plane defined by a reduced polynomial of degree $d$ with rational coefficients. Assume that $P$ is an isolated real point or a singular complex point on the curve $X$. The coordinates of $P$ are algebraic numbers over the rationals of degree at most $d^2$. The res......Let $X$ be a curve in the affine plane defined by a reduced polynomial of degree $d$ with rational coefficients. Assume that $P$ is an isolated real point or a singular complex point on the curve $X$. The coordinates of $P$ are algebraic numbers over the rationals of degree at most $d^2...

Street-side vehicle detection, classification and change detection using mobile laser scanning data

Science.gov (United States)

Xiao, Wen; Vallet, Bruno; Schindler, Konrad; Paparoditis, Nicolas

2016-04-01

Statistics on street-side car parks, e.g. occupancy rates, parked vehicle types, parking durations, are of great importance for urban planning and policy making. Related studies, e.g. vehicle detection and classification, mostly focus on static images or video. Whereas mobile laser scanning (MLS) systems are increasingly utilized for urban street environment perception due to their direct 3D information acquisition, high accuracy and movability. In this paper, we design a complete system for car park monitoring, including vehicle recognition, localization, classification and change detection, from laser scanning point clouds. The experimental data are acquired by an MLS system using high frequency laser scanner which scans the streets vertically along the system's moving trajectory. The point clouds are firstly classified as ground, building façade, and street objects which are then segmented using state-of-the-art methods. Each segment is treated as an object hypothesis, and its geometric features are extracted. Moreover, a deformable vehicle model is fitted to each object. By fitting an explicit model to the vehicle points, detailed information, such as precise position and orientation, can be obtained. The model parameters are also treated as vehicle features. Together with the geometric features, they are applied to a supervised learning procedure for vehicle or non-vehicle recognition. The classes of detected vehicles are also investigated. Whether vehicles have changed across two datasets acquired at different times is detected to estimate the durations. Here, vehicles are trained pair-wisely. Two same or different vehicles are paired up as training samples. As a result, the vehicle recognition, classification and change detection accuracies are 95.9%, 86.0% and 98.7%, respectively. Vehicle modelling improves not only the recognition rate, but also the localization precision compared to bounding boxes.

Genetic algorithms in teaching artificial intelligence (automated generation of specific algebras)

Science.gov (United States)

Habiballa, Hashim; Jendryscik, Radek

2017-11-01

The problem of teaching essential Artificial Intelligence (AI) methods is an important task for an educator in the branch of soft-computing. The key focus is often given to proper understanding of the principle of AI methods in two essential points - why we use soft-computing methods at all and how we apply these methods to generate reasonable results in sensible time. We present one interesting problem solved in the non-educational research concerning automated generation of specific algebras in the huge search space. We emphasize above mentioned points as an educational case study of an interesting problem in automated generation of specific algebras.

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

Parallel Element Agglomeration Algebraic Multigrid and Upscaling Library

Energy Technology Data Exchange (ETDEWEB)

2017-10-24

ParELAG is a parallel C++ library for numerical upscaling of finite element discretizations and element-based algebraic multigrid solvers. It provides optimal complexity algorithms to build multilevel hierarchies and solvers that can be used for solving a wide class of partial differential equations (elliptic, hyperbolic, saddle point problems) on general unstructured meshes. Additionally, a novel multilevel solver for saddle point problems with divergence constraint is implemented.

Lectures on algebraic statistics

CERN Document Server

Drton, Mathias; Sullivant, Seth

2009-01-01

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

Quiver W-algebras

Science.gov (United States)

Kimura, Taro; Pestun, Vasily

2018-06-01

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

Tensor models, Kronecker coefficients and permutation centralizer algebras

Science.gov (United States)

Geloun, Joseph Ben; Ramgoolam, Sanjaye

2017-11-01

We show that the counting of observables and correlators for a 3-index tensor model are organized by the structure of a family of permutation centralizer algebras. These algebras are shown to be semi-simple and their Wedderburn-Artin decompositions into matrix blocks are given in terms of Clebsch-Gordan coefficients of symmetric groups. The matrix basis for the algebras also gives an orthogonal basis for the tensor observables which diagonalizes the Gaussian two-point functions. The centres of the algebras are associated with correlators which are expressible in terms of Kronecker coefficients (Clebsch-Gordan multiplicities of symmetric groups). The color-exchange symmetry present in the Gaussian model, as well as a large class of interacting models, is used to refine the description of the permutation centralizer algebras. This discussion is extended to a general number of colors d: it is used to prove the integrality of an infinite family of number sequences related to color-symmetrizations of colored graphs, and expressible in terms of symmetric group representation theory data. Generalizing a connection between matrix models and Belyi maps, correlators in Gaussian tensor models are interpreted in terms of covers of singular 2-complexes. There is an intriguing difference, between matrix and higher rank tensor models, in the computational complexity of superficially comparable correlators of observables parametrized by Young diagrams.

Abstract algebra

CERN Document Server

Garrett, Paul B

2007-01-01

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

College algebra

CERN Document Server

Kolman, Bernard

1985-01-01

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

Spherical Hecke algebra in the Nekrasov-Shatashvili limit

Energy Technology Data Exchange (ETDEWEB)

Bourgine, Jean-Emile [Asia Pacific Center for Theoretical Physics (APCTP),Pohang, Gyeongbuk 790-784 (Korea, Republic of)

2015-01-21

The Spherical Hecke central (SHc) algebra has been shown to act on the Nekrasov instanton partition functions of N=2 gauge theories. Its presence accounts for both integrability and AGT correspondence. On the other hand, a specific limit of the Omega background, introduced by Nekrasov and Shatashvili (NS), leads to the appearance of TBA and Bethe like equations. To unify these two points of view, we study the NS limit of the SHc algebra. We provide an expression of the instanton partition function in terms of Bethe roots, and define a set of operators that generates infinitesimal variations of the roots. These operators obey the commutation relations defining the SHc algebra at first order in the equivariant parameter ϵ{sub 2}. Furthermore, their action on the bifundamental contributions reproduces the Kanno-Matsuo-Zhang transformation. We also discuss the connections with the Mayer cluster expansion approach that leads to TBA-like equations.

Twisted classical Poincare algebras

International Nuclear Information System (INIS)

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

1993-11-01

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

Pre-Algebra Essentials For Dummies

CERN Document Server

Zegarelli, Mark

2010-01-01

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

Change-Point and Trend Analysis on Annual Maximum Discharge in Continental United States

Science.gov (United States)

Serinaldi, F.; Villarini, G.; Smith, J. A.; Krajewski, W. F.

2008-12-01

Annual maximum discharge records from 36 stations representing different hydro-climatic regimes in the continental United States with at least 100 years of records are used to investigate the presence of temporal trends and abrupt changes in mean and variance. Change point analysis is performed by means of two non- parametric (Pettitt and CUSUM), one semi-parametric (Guan), and two parametric (Rodionov and Bayesian Change Point) tests. Two non-parametric (Mann-Kendall and Spearman) and one parametric (Pearson) tests are applied to detect the presence of temporal trends. Generalized Additive Model for Location Scale and Shape (GAMLSS) models are also used to parametrically model the streamflow data exploiting their flexibility to account for changes and temporal trends in the parameters of distribution functions. Additionally, serial correlation is assessed in advance by computing the autocorrelation function (ACF), and the Hurst parameter is estimated using two estimators (aggregated variance and differenced variance methods) to investigate the presence of long range dependence. The results of this study indicate lack of long range dependence in the maximum streamflow series. At some stations the authors found a statistically significant change point in the mean and/or variance, while in general they detected no statistically significant temporal trends.

Fixed Points of α-Admissible Mappings in Cone Metric Spaces with Banach Algebra

Directory of Open Access Journals (Sweden)

S.K. Malhotra

2015-11-01

Full Text Available In this paper, we introduce the $\\alpha$-admissible mappings in the setting of cone metric spaces equipped with Banach algebra and solid cones. Our results generalize and extend several known results of metric and cone metric spaces. An example is presented which illustrates and shows the significance of results proved herein.

Physical Holonomy, Thomas Precession, and Clifford Algebra

International Nuclear Information System (INIS)

Urbantke, H.

1988-01-01

After a general discussion of the physical significance of holonomy group transformations, a relation between the transports of Fermi-Walker and Levi-Civita in Special Relativity is pointed out. A well-known example -the Thomas-Wigner angle - is rederived in a completely frame-independent manner using Clifford algebra. 14 refs. (Author)

Representations of quantum bicrossproduct algebras

International Nuclear Information System (INIS)

Arratia, Oscar; Olmo, Mariano A del

2002-01-01

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

Krichever correspondence for algebraic varieties

International Nuclear Information System (INIS)

Osipov, D V

2001-01-01

We construct new acyclic resolutions of quasicoherent sheaves. These resolutions are connected with multidimensional local fields. The resolutions obtained are applied to construct a generalization of the Krichever map to algebraic varieties of any dimension. This map canonically produces two k-subspaces B contained in k((z 1 ))...((z n )) and W contained in k((z 1 ))...((z n )) o+r from the following data: an arbitrary algebraic n-dimensional Cohen-Macaulay projective integral scheme X over a field k, a flag of closed integral subschemes X=Y 0 contains Y 1 contains ... contains Y n such that Y i is an ample Cartier divisor on Y i-1 and Y n is a smooth point on all Y i , formal local parameters of this flag at the point Y n , a rank r vector bundle F on X, and a trivialization of F in the formal neighbourhood of the point Y n where the n-dimensional local field B contained in k((z 1 ))...((z n )) is associated with the flag Y 0 contains Y 1 contains ... contains Y n . In addition, the map constructed is injective, that is, one can uniquely reconstruct all the original geometric data. Moreover, given the subspace B, we can explicitly write down a complex which calculates the cohomology of the sheaf O X on X and, given the subspace W, we can explicitly write down a complex which calculates the cohomology of F on X

Schematic limits of rank 4 Azumaya bundles are the locally-Witt algebras

International Nuclear Information System (INIS)

Venkata Balaji, T.E.

2002-07-01

It is shown that the schematic image of the scheme of Azumaya algebra structures on a vector bundle of rank 4 over any base scheme is separated, of finite type, smooth of relative dimension 13 and geometrically irreducible over that base and that this construction base-changes well. This generalises the main theorem of Part I of an earlier work and clarifies it by showing that the algebraic operation of forming the even Clifford algebra (=Witt algebra) of a rank 3 quadratic module essentially translates to performing the geometric operation of taking the schematic image of the scheme of Azumaya algebra structures. (author)

Algorithms in Algebraic Geometry

CERN Document Server

Dickenstein, Alicia; Sommese, Andrew J

2008-01-01

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

Computer algebra and operators

Science.gov (United States)

Fateman, Richard; Grossman, Robert

1989-01-01

The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.

Abstract Algebra to Secondary School Algebra: Building Bridges

Science.gov (United States)

Christy, Donna; Sparks, Rebecca

2015-01-01

The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

Infinite dimension algebra and conformal symmetry

International Nuclear Information System (INIS)

Ragoucy-Aubezon, E.

1991-04-01

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

Lisa's Lemonade Stand: Exploring Algebraic Ideas.

Science.gov (United States)

Billings, Esther M. H.; Lakatos, Tracy

2003-01-01

Presents an activity, "Lisa's Lemonade Stand," that actively engages students in algebraic thinking as they analyze change by investigating relationships between variables and gain experience describing and representing these relationships graphically. (YDS)

Hypothesis testing of a change point during cognitive decline among Alzheimer's disease patients.

Science.gov (United States)

Ji, Ming; Xiong, Chengjie; Grundman, Michael

2003-10-01

In this paper, we present a statistical hypothesis test for detecting a change point over the course of cognitive decline among Alzheimer's disease patients. The model under the null hypothesis assumes a constant rate of cognitive decline over time and the model under the alternative hypothesis is a general bilinear model with an unknown change point. When the change point is unknown, however, the null distribution of the test statistics is not analytically tractable and has to be simulated by parametric bootstrap. When the alternative hypothesis that a change point exists is accepted, we propose an estimate of its location based on the Akaike's Information Criterion. We applied our method to a data set from the Neuropsychological Database Initiative by implementing our hypothesis testing method to analyze Mini Mental Status Exam scores based on a random-slope and random-intercept model with a bilinear fixed effect. Our result shows that despite large amount of missing data, accelerated decline did occur for MMSE among AD patients. Our finding supports the clinical belief of the existence of a change point during cognitive decline among AD patients and suggests the use of change point models for the longitudinal modeling of cognitive decline in AD research.

Thinking Visually about Algebra

Science.gov (United States)

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,…

Without derivatives or limits: from visual and geometrical points of view to algebraic methods for identifying tangent lines

Science.gov (United States)

Vivier, L.

2013-07-01

Usually, the tangent line is considered to be a calculus notion. However, it is also a graphical and an algebraic notion. The graphical frame, where our primary conceptions are conceived, could give rise to algebraic methods to obtain the tangent line to a curve. In this pre-calculus perspective, two methods are described and discussed according to their potential for secondary students and teacher training.

Eighth Grade Algebra Course Placement and Student Motivation for Mathematics

Science.gov (United States)

Simzar, Rahila M.; Domina, Thurston; Tran, Cathy

2016-01-01

This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics. PMID:26942210

Eighth Grade Algebra Course Placement and Student Motivation for Mathematics.

Science.gov (United States)

Simzar, Rahila M; Domina, Thurston; Tran, Cathy

2016-01-01

This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics.

Axis Problem of Rough 3-Valued Algebras

Institute of Scientific and Technical Information of China (English)

Jianhua Dai; Weidong Chen; Yunhe Pan

2006-01-01

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

Spatio-temporal change detection from multidimensional arrays: Detecting deforestation from MODIS time series

Science.gov (United States)

Lu, Meng; Pebesma, Edzer; Sanchez, Alber; Verbesselt, Jan

2016-07-01

Growing availability of long-term satellite imagery enables change modeling with advanced spatio-temporal statistical methods. Multidimensional arrays naturally match the structure of spatio-temporal satellite data and can provide a clean modeling process for complex spatio-temporal analysis over large datasets. Our study case illustrates the detection of breakpoints in MODIS imagery time series for land cover change in the Brazilian Amazon using the BFAST (Breaks For Additive Season and Trend) change detection framework. BFAST includes an Empirical Fluctuation Process (EFP) to alarm the change and a change point time locating process. We extend the EFP to account for the spatial autocorrelation between spatial neighbors and assess the effects of spatial correlation when applying BFAST on satellite image time series. In addition, we evaluate how sensitive EFP is to the assumption that its time series residuals are temporally uncorrelated, by modeling it as an autoregressive process. We use arrays as a unified data structure for the modeling process, R to execute the analysis, and an array database management system to scale computation. Our results point to BFAST as a robust approach against mild temporal and spatial correlation, to the use of arrays to ease the modeling process of spatio-temporal change, and towards communicable and scalable analysis.

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.

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

Indian Academy of Sciences (India)

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

Colour-kinematics duality and the Drinfeld double of the Lie algebra of diffeomorphisms

Energy Technology Data Exchange (ETDEWEB)

Fu, Chih-Hao; Krasnov, Kirill [School of Mathematical Sciences, The University of Nottingham,University Park, Nottingham NG7 2RD (United Kingdom)

2017-01-17

Colour-kinematics duality suggests that Yang-Mills (YM) theory possesses some hidden Lie algebraic structure. So far this structure has resisted understanding, apart from some progress in the self-dual sector. We show that there is indeed a Lie algebra behind the YM Feynman rules. The Lie algebra we uncover is the Drinfeld double of the Lie algebra of vector fields. More specifically, we show that the kinematic numerators following from the YM Feynman rules satisfy a version of the Jacobi identity, in that the Jacobiator of the bracket defined by the YM cubic vertex is cancelled by the contribution of the YM quartic vertex. We then show that this Jacobi-like identity is in fact the Jacobi identity of the Drinfeld double. All our considerations are off-shell. Our construction explains why numerators computed using the Feynman rules satisfy the colour-kinematics at four but not at higher numbers of points. It also suggests a way of modifying the Feynman rules so that the duality can continue to hold for an arbitrary number of gluons. Our construction stops short of producing explicit higher point numerators because of an absence of a certain property at four points. We comment on possible ways of correcting this, but leave the next word in the story to future work.

Hecke algebras with unequal parameters

CERN Document Server

Lusztig, G

2003-01-01

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

Applications of multiscale change point detections to monthly stream flow and rainfall in Xijiang River in southern China, part I: correlation and variance

Science.gov (United States)

Zhu, Yuxiang; Jiang, Jianmin; Huang, Changxing; Chen, Yongqin David; Zhang, Qiang

2018-04-01

This article, as part I, introduces three algorithms and applies them to both series of the monthly stream flow and rainfall in Xijiang River, southern China. The three algorithms include (1) normalization of probability distribution, (2) scanning U test for change points in correlation between two time series, and (3) scanning F-test for change points in variances. The normalization algorithm adopts the quantile method to normalize data from a non-normal into the normal probability distribution. The scanning U test and F-test have three common features: grafting the classical statistics onto the wavelet algorithm, adding corrections for independence into each statistic criteria at given confidence respectively, and being almost objective and automatic detection on multiscale time scales. In addition, the coherency analyses between two series are also carried out for changes in variance. The application results show that the changes of the monthly discharge are still controlled by natural precipitation variations in Xijiang's fluvial system. Human activities disturbed the ecological balance perhaps in certain content and in shorter spells but did not violate the natural relationships of correlation and variance changes so far.

Categories and Commutative Algebra

CERN Document Server

Salmon, P

2011-01-01

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

Particle-like structure of Lie algebras

Science.gov (United States)

Vinogradov, A. M.

2017-07-01

If a Lie algebra structure 𝔤 on a vector space is the sum of a family of mutually compatible Lie algebra structures 𝔤i's, we say that 𝔤 is simply assembled from the 𝔤i's. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the 𝔤i's, one obtains a Lie algebra assembled in two steps from 𝔤i's, and so on. We describe the process of modular disassembling of a Lie algebra into a unimodular and a non-unimodular part. We then study two inverse questions: which Lie algebras can be assembled from a given family of Lie algebras, and from which Lie algebras can a given Lie algebra be assembled. We develop some basic assembling and disassembling techniques that constitute the elements of a new approach to the general theory of Lie algebras. The main result of our theory is that any finite-dimensional Lie algebra over an algebraically closed field of characteristic zero or over R can be assembled in a finite number of steps from two elementary constituents, which we call dyons and triadons. Up to an abelian summand, a dyon is a Lie algebra structure isomorphic to the non-abelian 2-dimensional Lie algebra, while a triadon is isomorphic to the 3-dimensional Heisenberg Lie algebra. As an example, we describe constructions of classical Lie algebras from triadons.

Mapping the order and pattern of brain structural MRI changes using change-point analysis in premanifest Huntington's disease.

Science.gov (United States)

Wu, Dan; Faria, Andreia V; Younes, Laurent; Mori, Susumu; Brown, Timothy; Johnson, Hans; Paulsen, Jane S; Ross, Christopher A; Miller, Michael I

2017-10-01

Huntington's disease (HD) is an autosomal dominant neurodegenerative disorder that progressively affects motor, cognitive, and emotional functions. Structural MRI studies have demonstrated brain atrophy beginning many years prior to clinical onset ("premanifest" period), but the order and pattern of brain structural changes have not been fully characterized. In this study, we investigated brain regional volumes and diffusion tensor imaging (DTI) measurements in premanifest HD, and we aim to determine (1) the extent of MRI changes in a large number of structures across the brain by atlas-based analysis, and (2) the initiation points of structural MRI changes in these brain regions. We adopted a novel multivariate linear regression model to detect the inflection points at which the MRI changes begin (namely, "change-points"), with respect to the CAG-age product (CAP, an indicator of extent of exposure to the effects of CAG repeat expansion). We used approximately 300 T1-weighted and DTI data from premanifest HD and control subjects in the PREDICT-HD study, with atlas-based whole brain segmentation and change-point analysis. The results indicated a distinct topology of structural MRI changes: the change-points of the volumetric measurements suggested a central-to-peripheral pattern of atrophy from the striatum to the deep white matter; and the change points of DTI measurements indicated the earliest changes in mean diffusivity in the deep white matter and posterior white matter. While interpretation needs to be cautious given the cross-sectional nature of the data, these findings suggest a spatial and temporal pattern of spread of structural changes within the HD brain. Hum Brain Mapp 38:5035-5050, 2017. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Dynamical entropy of C* algebras and Von Neumann algebras

International Nuclear Information System (INIS)

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

1986-01-01

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

Gradings on simple Lie algebras

CERN Document Server

Elduque, Alberto

2013-01-01

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

A Simple and Practical Linear Algebra Library Interface with Static Size Checking

Directory of Open Access Journals (Sweden)

Akinori Abe

2015-12-01

Full Text Available Linear algebra is a major field of numerical computation and is widely applied. Most linear algebra libraries (in most programming languages do not statically guarantee consistency of the dimensions of vectors and matrices, causing runtime errors. While advanced type systems—specifically, dependent types on natural numbers—can ensure consistency among the sizes of collections such as lists and arrays, such type systems generally require non-trivial changes to existing languages and application programs, or tricky type-level programming. We have developed a linear algebra library interface that verifies the consistency (with respect to dimensions of matrix operations by means of generative phantom types, implemented via fairly standard ML types and module system. To evaluate its usability, we ported to it a practical machine learning library from a traditional linear algebra library. We found that most of the changes required for the porting could be made mechanically, and changes that needed human thought are minor.

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

International Nuclear Information System (INIS)

Fujikawa, Kazuo; Suzuki, Hiroshi.

1991-03-01

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

Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras

Directory of Open Access Journals (Sweden)

Madjid Eshaghi Gordji

2012-01-01

Full Text Available Let n>1 be an integer, let A be an algebra, and X be an A-module. A quadratic function D:A→X is called a quadratic n-derivation if D(∏i=1nai=D(a1a22⋯an2+a12D(a2a32⋯an2+⋯+a12a22⋯an−12D(an for all a1,...,an∈A. We investigate the Hyers-Ulam stability of quadratic n-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.

The Minnesota notes on Jordan algebras and their applications

CERN Document Server

Walcher, Sebastian

1999-01-01

This volume contains a re-edition of Max Koecher's famous Minnesota Notes. The main objects are homogeneous, but not necessarily convex, cones. They are described in terms of Jordan algebras. The central point is a correspondence between semisimple real Jordan algebras and so-called omega-domains. This leads to a construction of half-spaces which give an essential part of all bounded symmetric domains. The theory is presented in a concise manner, with only elementary prerequisites. The editors have added notes on each chapter containing an account of the relevant developments of the theory since these notes were first written.

Algebraic K-theory

CERN Document Server

Srinivas, V

1996-01-01

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

Head First Algebra A Learner's Guide to Algebra I

CERN Document Server

Pilone, Tracey

2008-01-01

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

Detecting changes in real-time data: a user's guide to optimal detection.

Science.gov (United States)

Johnson, P; Moriarty, J; Peskir, G

2017-08-13

The real-time detection of changes in a noisily observed signal is an important problem in applied science and engineering. The study of parametric optimal detection theory began in the 1930s, motivated by applications in production and defence. Today this theory, which aims to minimize a given measure of detection delay under accuracy constraints, finds applications in domains including radar, sonar, seismic activity, global positioning, psychological testing, quality control, communications and power systems engineering. This paper reviews developments in optimal detection theory and sequential analysis, including sequential hypothesis testing and change-point detection, in both Bayesian and classical (non-Bayesian) settings. For clarity of exposition, we work in discrete time and provide a brief discussion of the continuous time setting, including recent developments using stochastic calculus. Different measures of detection delay are presented, together with the corresponding optimal solutions. We emphasize the important role of the signal-to-noise ratio and discuss both the underlying assumptions and some typical applications for each formulation.This article is part of the themed issue 'Energy management: flexibility, risk and optimization'. © 2017 The Author(s).

Novikov algebras with associative bilinear forms

Energy Technology Data Exchange (ETDEWEB)

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

2007-11-23

Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. The goal of this paper is to study Novikov algebras with non-degenerate associative symmetric bilinear forms, which we call quadratic Novikov algebras. Based on the classification of solvable quadratic Lie algebras of dimension not greater than 4 and Novikov algebras in dimension 3, we show that quadratic Novikov algebras up to dimension 4 are commutative. Furthermore, we obtain the classification of transitive quadratic Novikov algebras in dimension 4. But we find that not every quadratic Novikov algebra is commutative and give a non-commutative quadratic Novikov algebra in dimension 6.

Test-retest reliability and minimal detectable change of two simplified 3-point balance measures in patients with stroke.

Science.gov (United States)

Chen, Yi-Miau; Huang, Yi-Jing; Huang, Chien-Yu; Lin, Gong-Hong; Liaw, Lih-Jiun; Lee, Shih-Chieh; Hsieh, Ching-Lin

2017-10-01

The 3-point Berg Balance Scale (BBS-3P) and 3-point Postural Assessment Scale for Stroke Patients (PASS-3P) were simplified from the BBS and PASS to overcome the complex scoring systems. The BBS-3P and PASS-3P were more feasible in busy clinical practice and showed similarly sound validity and responsiveness to the original measures. However, the reliability of the BBS-3P and PASS-3P is unknown limiting their utility and the interpretability of scores. We aimed to examine the test-retest reliability and minimal detectable change (MDC) of the BBS-3P and PASS-3P in patients with stroke. Cross-sectional study. The rehabilitation departments of a medical center and a community hospital. A total of 51 chronic stroke patients (64.7% male). Both balance measures were administered twice 7 days apart. The test-retest reliability of both the BBS-3P and PASS-3P were examined by intraclass correlation coefficients (ICC). The MDC and its percentage over the total score (MDC%) of each measure was calculated for examining the random measurement errors. The ICC values of the BBS-3P and PASS-3P were 0.99 and 0.97, respectively. The MDC% (MDC) of the BBS-3P and PASS-3P were 9.1% (5.1 points) and 8.4% (3.0 points), respectively, indicating that both measures had small and acceptable random measurement errors. Our results showed that both the BBS-3P and the PASS-3P had good test-retest reliability, with small and acceptable random measurement error. These two simplified 3-level balance measures can provide reliable results over time. Our findings support the repeated administration of the BBS-3P and PASS-3P to monitor the balance of patients with stroke. The MDC values can help clinicians and researchers interpret the change scores more precisely.

Lie algebra in quantum physics by means of computer algebra

OpenAIRE

Kikuchi, Ichio; Kikuchi, Akihito

2017-01-01

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

Tensor spaces and exterior algebra

CERN Document Server

Yokonuma, Takeo

1992-01-01

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

Profinite algebras and affine boundedness

OpenAIRE

Schneider, Friedrich Martin; Zumbrägel, Jens

2015-01-01

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

Superconformal algebras and mock theta functions

International Nuclear Information System (INIS)

Eguchi, Tohru; Hikami, Kazuhiro

2009-01-01

It is known that characters of BPS representations of extended superconformal algebras do not have good modular properties due to extra singular vectors coming from the BPS condition. In order to improve their modular properties we apply the method of Zwegers which has recently been developed to analyze modular properties of mock theta functions. We consider the case of the N=4 superconformal algebra at general levels and obtain the decomposition of characters of BPS representations into a sum of simple Jacobi forms and an infinite series of non-BPS representations. We apply our method to study elliptic genera of hyper-Kaehler manifolds in higher dimensions. In particular, we determine the elliptic genera in the case of complex four dimensions of the Hilbert scheme of points on K3 surfaces K [2] and complex tori A [[3

Superconformal algebras and mock theta functions

Energy Technology Data Exchange (ETDEWEB)

Eguchi, Tohru [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Hikami, Kazuhiro [Department of Mathematics, Naruto University of Education, Tokushima 772-8502 (Japan)], E-mail: eguchi@yukawa.kyoto-u.ac.jp, E-mail: hikami@naruto-u.ac.jp

2009-07-31

It is known that characters of BPS representations of extended superconformal algebras do not have good modular properties due to extra singular vectors coming from the BPS condition. In order to improve their modular properties we apply the method of Zwegers which has recently been developed to analyze modular properties of mock theta functions. We consider the case of the N=4 superconformal algebra at general levels and obtain the decomposition of characters of BPS representations into a sum of simple Jacobi forms and an infinite series of non-BPS representations. We apply our method to study elliptic genera of hyper-Kaehler manifolds in higher dimensions. In particular, we determine the elliptic genera in the case of complex four dimensions of the Hilbert scheme of points on K3 surfaces K{sup [2]} and complex tori A{sup [[3

Double-partition Quantum Cluster Algebras

DEFF Research Database (Denmark)

Jakobsen, Hans Plesner; Zhang, Hechun

2012-01-01

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

Algebra II workbook for dummies

CERN Document Server

Sterling, Mary Jane

2014-01-01

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

Very true operators on MTL-algebras

Directory of Open Access Journals (Sweden)

Wang Jun Tao

2016-01-01

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

Towards a Framework for Change Detection in Data Sets

Science.gov (United States)

Böttcher, Mirko; Nauck, Detlef; Ruta, Dymitr; Spott, Martin

Since the world with its markets, innovations and customers is changing faster than ever before, the key to survival for businesses is the ability to detect, assess and respond to changing conditions rapidly and intelligently. Discovering changes and reacting to or acting upon them before others do has therefore become a strategical issue for many companies. However, existing data analysis techniques are insufflent for this task since they typically assume that the domain under consideration is stable over time. This paper presents a framework that detects changes within a data set at virtually any level of granularity. The underlying idea is to derive a rule-based description of the data set at different points in time and to subsequently analyse how these rules change. Nevertheless, further techniques are required to assist the data analyst in interpreting and assessing their changes. Therefore the framework also contains methods to discard rules that are non-drivers for change and to assess the interestingness of detected changes.

Quantum algebra structure of certain Jackson integrals

International Nuclear Information System (INIS)

Matsuo, Atsushi

1993-01-01

The q-difference system satisfied by Jackson integrals with a configuration of A-type root system is studied. We explicitly construct some linear combination of Jackson integrals, which satisfies the quantum Knizhnik-Zamolodchikov equation for the 2-point correlation function of q-vertex operators, introduced by Frenkel and Reshetik hin, for the quantum affine algebra U q (sl 2 ). The expression of integrands for the n-point case is conjectured, and a set of linear relations for the corresponding Jackson integrals is proved. (orig.)

Hopf algebras in noncommutative geometry

International Nuclear Information System (INIS)

Varilly, Joseph C.

2001-10-01

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

Algebraic K-theory of crystallographic groups the three-dimensional splitting case

CERN Document Server

Farley, Daniel Scott

2014-01-01

The Farrell-Jones isomorphism conjecture in algebraic K-theory offers a description of the algebraic K-theory of a group using a generalized homology theory. In cases where the conjecture is known to be a theorem, it gives a powerful method for computing the lower algebraic K-theory of a group. This book contains a computation of the lower algebraic K-theory of the split three-dimensional crystallographic groups, a geometrically important class of three-dimensional crystallographic group, representing a third of the total number. The book leads the reader through all aspects of the calculation. The first chapters describe the split crystallographic groups and their classifying spaces. Later chapters assemble the techniques that are needed to apply the isomorphism theorem. The result is a useful starting point for researchers who are interested in the computational side of the Farrell-Jones isomorphism conjecture, and a contribution to the growing literature in the field.

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

International Nuclear Information System (INIS)

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

1996-05-01

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

Extended Kac-Moody algebras and applications

International Nuclear Information System (INIS)

Ragoucy, E.; Sorba, P.

1991-04-01

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

Symbolic Algebra Development for Higher-Order Electron Propagator Formulation and Implementation.

Science.gov (United States)

Tamayo-Mendoza, Teresa; Flores-Moreno, Roberto

2014-06-10

Through the use of symbolic algebra, implemented in a program, the algebraic expression of the elements of the self-energy matrix for the electron propagator to different orders were obtained. In addition, a module for the software package Lowdin was automatically generated. Second- and third-order electron propagator results have been calculated to test the correct operation of the program. It was found that the Fortran 90 modules obtained automatically with our algorithm succeeded in calculating ionization energies with the second- and third-order electron propagator in the diagonal approximation. The strategy for the development of this symbolic algebra program is described in detail. This represents a solid starting point for the automatic derivation and implementation of higher-order electron propagator methods.

Lie algebras and applications

CERN Document Server

Iachello, Francesco

2015-01-01

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

(Fuzzy) Ideals of BN-Algebras

Science.gov (United States)

Walendziak, Andrzej

2015-01-01

The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained. PMID:26125050

Fast Erasure and Error decoding of Algebraic Geometry Codes up to the Feng-Rao Bound

DEFF Research Database (Denmark)

Jensen, Helge Elbrønd; Sakata, S.; Leonard, D.

1996-01-01

This paper gives an errata(that is erasure-and error-) decoding algorithm of one-point algebraic geometry codes up to the Feng-Rao designed minimum distance using Sakata's multidimensional generalization of the Berlekamp-massey algorithm and the votin procedure of Feng and Rao.......This paper gives an errata(that is erasure-and error-) decoding algorithm of one-point algebraic geometry codes up to the Feng-Rao designed minimum distance using Sakata's multidimensional generalization of the Berlekamp-massey algorithm and the votin procedure of Feng and Rao....

Lectures on Hilbert schemes of points on surfaces

CERN Document Server

Nakajima, Hiraku

1999-01-01

This beautifully written book deals with one shining example: the Hilbert schemes of points on algebraic surfaces ... The topics are carefully and tastefully chosen ... The young person will profit from reading this book. --Mathematical Reviews The Hilbert scheme of a surface X describes collections of n (not necessarily distinct) points on X. More precisely, it is the moduli space for 0-dimensional subschemes of X of length n. Recently it was realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory--even theoretical physics. The discussion in the book reflects this feature of Hilbert schemes. One example of the modern, broader interest in the subject is a construction of the representation of the infinite-dimensional Heisenberg algebra, i.e., Fock space. This representation has been studied extensively in the literature in connection with affine Lie algebras, conformal field...

Algebraic Properties of First Integrals for Scalar Linear Third-Order ODEs of Maximal Symmetry

Directory of Open Access Journals (Sweden)

K. S. Mahomed

2013-01-01

Full Text Available By use of the Lie symmetry group methods we analyze the relationship between the first integrals of the simplest linear third-order ordinary differential equations (ODEs and their point symmetries. It is well known that there are three classes of linear third-order ODEs for maximal cases of point symmetries which are 4, 5, and 7. The simplest scalar linear third-order equation has seven-point symmetries. We obtain the classifying relation between the symmetry and the first integral for the simplest equation. It is shown that the maximal Lie algebra of a first integral for the simplest equation y′′′=0 is unique and four-dimensional. Moreover, we show that the Lie algebra of the simplest linear third-order equation is generated by the symmetries of the two basic integrals. We also obtain counting theorems of the symmetry properties of the first integrals for such linear third-order ODEs. Furthermore, we provide insights into the manner in which one can generate the full Lie algebra of higher-order ODEs of maximal symmetry from two of their basic integrals.

Non-relativistic Bondi-Metzner-Sachs algebra

Science.gov (United States)

Batlle, Carles; Delmastro, Diego; Gomis, Joaquim

2017-09-01

We construct two possible candidates for non-relativistic bms4 algebra in four space-time dimensions by contracting the original relativistic bms4 algebra. bms4 algebra is infinite-dimensional and it contains the generators of the Poincaré algebra, together with the so-called super-translations. Similarly, the proposed nrbms4 algebras can be regarded as two infinite-dimensional extensions of the Bargmann algebra. We also study a canonical realization of one of these algebras in terms of the Fourier modes of a free Schrödinger field, mimicking the canonical realization of relativistic bms4 algebra using a free Klein-Gordon field.

A 3D clustering approach for point clouds to detect and quantify changes at a rock glacier front

Science.gov (United States)

Micheletti, Natan; Tonini, Marj; Lane, Stuart N.

2016-04-01

Terrestrial Laser Scanners (TLS) are extensively used in geomorphology to remotely-sense landforms and surfaces of any type and to derive digital elevation models (DEMs). Modern devices are able to collect many millions of points, so that working on the resulting dataset is often troublesome in terms of computational efforts. Indeed, it is not unusual that raw point clouds are filtered prior to DEM creation, so that only a subset of points is retained and the interpolation process becomes less of a burden. Whilst this procedure is in many cases necessary, it implicates a considerable loss of valuable information. First, and even without eliminating points, the common interpolation of points to a regular grid causes a loss of potentially useful detail. Second, it inevitably causes the transition from 3D information to only 2.5D data where each (x,y) pair must have a unique z-value. Vector-based DEMs (e.g. triangulated irregular networks) partially mitigate these issues, but still require a set of parameters to be set and a considerable burden in terms of calculation and storage. Because of the reasons above, being able to perform geomorphological research directly on point clouds would be profitable. Here, we propose an approach to identify erosion and deposition patterns on a very active rock glacier front in the Swiss Alps to monitor sediment dynamics. The general aim is to set up a semiautomatic method to isolate mass movements using 3D-feature identification directly from LiDAR data. An ultra-long range LiDAR RIEGL VZ-6000 scanner was employed to acquire point clouds during three consecutive summers. In order to isolate single clusters of erosion and deposition we applied the Density-Based Scan Algorithm with Noise (DBSCAN), previously successfully employed by Tonini and Abellan (2014) in a similar case for rockfall detection. DBSCAN requires two input parameters, strongly influencing the number, shape and size of the detected clusters: the minimum number of

Inverse Modelling Problems in Linear Algebra Undergraduate Courses

Science.gov (United States)

Martinez-Luaces, Victor E.

2013-01-01

This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

The Unitality of Quantum B-algebras

Science.gov (United States)

Han, Shengwei; Xu, Xiaoting; Qin, Feng

2018-02-01

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

On Weak-BCC-Algebras

Science.gov (United States)

Thomys, Janus; Zhang, Xiaohong

2013-01-01

We describe weak-BCC-algebras (also called BZ-algebras) in which the condition (x∗y)∗z = (x∗z)∗y is satisfied only in the case when elements x, y belong to the same branch. We also characterize ideals, nilradicals, and nilpotent elements of such algebras. PMID:24311983

G-identities of non-associative algebras

International Nuclear Information System (INIS)

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

1999-01-01

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

Landsat change detection can aid in water quality monitoring

Science.gov (United States)

Macdonald, H. C.; Steele, K. F.; Waite, W. P.; Shinn, M. R.

1977-01-01

Comparison between Landsat-1 and -2 imagery of Arkansas provided evidence of significant land use changes during the 1972-75 time period. Analysis of Arkansas historical water quality information has shown conclusively that whereas point source pollution generally can be detected by use of water quality data collected by state and federal agencies, sampling methodologies for nonpoint source contamination attributable to surface runoff are totally inadequate. The expensive undertaking of monitoring all nonpoint sources for numerous watersheds can be lessened by implementing Landsat change detection analyses.

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

Energy Technology Data Exchange (ETDEWEB)

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

1996-05-01

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

On Dunkl angular momenta algebra

Energy Technology Data Exchange (ETDEWEB)

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

2015-11-17

We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl(N) version of the subalgebra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.

The fate of object memory traces under change detection and change blindness.

Science.gov (United States)

Busch, Niko A

2013-07-03

Observers often fail to detect substantial changes in a visual scene. This so-called change blindness is often taken as evidence that visual representations are sparse and volatile. This notion rests on the assumption that the failure to detect a change implies that representations of the changing objects are lost all together. However, recent evidence suggests that under change blindness, object memory representations may be formed and stored, but not retrieved. This study investigated the fate of object memory representations when changes go unnoticed. Participants were presented with scenes consisting of real world objects, one of which changed on each trial, while recording event-related potentials (ERPs). Participants were first asked to localize where the change had occurred. In an additional recognition task, participants then discriminated old objects, either from the pre-change or the post-change scene, from entirely new objects. Neural traces of object memories were studied by comparing ERPs for old and novel objects. Participants performed poorly in the detection task and often failed to recognize objects from the scene, especially pre-change objects. However, a robust old/novel effect was observed in the ERP, even when participants were change blind and did not recognize the old object. This implicit memory trace was found both for pre-change and post-change objects. These findings suggest that object memories are stored even under change blindness. Thus, visual representations may not be as sparse and volatile as previously thought. Rather, change blindness may point to a failure to retrieve and use these representations for change detection. Copyright © 2013 Elsevier B.V. All rights reserved.

Abstract algebra for physicists

International Nuclear Information System (INIS)

Zeman, J.

1975-06-01

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

Basic notions of algebra

CERN Document Server

Shafarevich, Igor Rostislavovich

2005-01-01

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

Characterizations of locally C*-algebras

International Nuclear Information System (INIS)

Mohammad, N.; Somasundaram, S.

1991-08-01

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

Galois Theory of Differential Equations, Algebraic Groups and Lie Algebras

NARCIS (Netherlands)

Put, Marius van der

1999-01-01

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

Algebra, Home Mortgages, and Recessions

Science.gov (United States)

Mariner, Jean A. Miller; Miller, Richard A.

2009-01-01

The current financial crisis and recession in the United States present an opportunity to discuss relevant applications of some topics in typical first-and second-year algebra and precalculus courses. Real-world applications of percent change, exponential functions, and sums of finite geometric sequences can help students understand the problems…

Video change detection for fixed wing UAVs

Science.gov (United States)

Bartelsen, Jan; Müller, Thomas; Ring, Jochen; Mück, Klaus; Brüstle, Stefan; Erdnüß, Bastian; Lutz, Bastian; Herbst, Theresa

2017-10-01

In this paper we proceed the work of Bartelsen et al.1 We present the draft of a process chain for an image based change detection which is designed for videos acquired by fixed wing unmanned aerial vehicles (UAVs). From our point of view, automatic video change detection for aerial images can be useful to recognize functional activities which are typically caused by the deployment of improvised explosive devices (IEDs), e.g. excavations, skid marks, footprints, left-behind tooling equipment, and marker stones. Furthermore, in case of natural disasters, like flooding, imminent danger can be recognized quickly. Due to the necessary flight range, we concentrate on fixed wing UAVs. Automatic change detection can be reduced to a comparatively simple photogrammetric problem when the perspective change between the "before" and "after" image sets is kept as small as possible. Therefore, the aerial image acquisition demands a mission planning with a clear purpose including flight path and sensor configuration. While the latter can be enabled simply by a fixed and meaningful adjustment of the camera, ensuring a small perspective change for "before" and "after" videos acquired by fixed wing UAVs is a challenging problem. Concerning this matter, we have performed tests with an advanced commercial off the shelf (COTS) system which comprises a differential GPS and autopilot system estimating the repetition accuracy of its trajectory. Although several similar approaches have been presented,23 as far as we are able to judge, the limits for this important issue are not estimated so far. Furthermore, we design a process chain to enable the practical utilization of video change detection. It consists of a front-end of a database to handle large amounts of video data, an image processing and change detection implementation, and the visualization of the results. We apply our process chain on the real video data acquired by the advanced COTS fixed wing UAV and synthetic data. For the

Current algebra and bosonization in three dimensions

International Nuclear Information System (INIS)

Le Guillou, J.C.; Schaposnik, F.A.

1996-01-01

We consider the fermion-boson mapping in three dimensional space-time, in the Abelian case, from the current algebra point of view. We show that in a path-integral framework one can derive a general bosonization recipe leading, in the bosonic language, to the correct equal-time current commutators of the original free fermionic theory. Copyright copyright 1996 Academic Press, Inc

A course in BE-algebras

CERN Document Server

Mukkamala, Sambasiva Rao

2018-01-01

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

Linear-algebraic approach to electron-molecule collisions: General formulation

International Nuclear Information System (INIS)

Collins, L.A.; Schneider, B.I.

1981-01-01

We present a linear-algebraic approach to electron-molecule collisions based on an integral equations form with either logarithmic or asymptotic boundary conditions. The introduction of exchange effects does not alter the basic form or order of the linear-algebraic equations for a local potential. In addition to the standard procedure of directly evaluating the exchange integrals by numerical quadrature, we also incorporate exchange effects through a separable-potential approximation. Efficient schemes are developed for reducing the number of points and channels that must be included. The method is applied at the static-exchange level to a number of molecular systems including H 2 , N 2 , LiH, and CO 2

On Associative Conformal Algebras of Linear Growth

OpenAIRE

Retakh, Alexander

2000-01-01

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

Representations of quantum algebras and combinatorics of Young tableaux

CERN Document Server

Ariki, Susumu

2002-01-01

Among several tools used in studying representations of quantum groups (or quantum algebras) are the notions of Kashiwara's crystal bases and Lusztig's canonical bases. Mixing both approaches allows us to use a combinatorial approach to representations of quantum groups and to apply the theory to representations of Hecke algebras. The primary goal of this book is to introduce the representation theory of quantum groups using quantum groups of type A_{r-1}^{(1)} as a main example. The corresponding combinatorics, developed by Misra and Miwa, turns out to be the combinatorics of Young tableaux. The second goal of this book is to explain the proof of the (generalized) Leclerc-Lascoux-Thibon conjecture. This conjecture, which is now a theorem, is an important breakthrough in the modular representation theory of the Hecke algebras of classical type. The book contains most of the nonstandard material necessary to get acquainted with this new rapidly developing area. It can be used as a good entry point into the stu...

DETECTION OF SLOPE MOVEMENT BY COMPARING POINT CLOUDS CREATED BY SFM SOFTWARE

Directory of Open Access Journals (Sweden)

K. Oda

2016-06-01

Full Text Available This paper proposes movement detection method between point clouds created by SFM software, without setting any onsite georeferenced points. SfM software, like Smart3DCaputure, PhotoScan, and Pix4D, are convenient for non-professional operator of photogrammetry, because these systems require simply specification of sequence of photos and output point clouds with colour index which corresponds to the colour of original image pixel where the point is projected. SfM software can execute aerial triangulation and create dense point clouds fully automatically. This is useful when monitoring motion of unstable slopes, or loos rocks in slopes along roads or railroads. Most of existing method, however, uses mesh-based DSM for comparing point clouds before/after movement and it cannot be applied in such cases that part of slopes forms overhangs. And in some cases movement is smaller than precision of ground control points and registering two point clouds with GCP is not appropriate. Change detection method in this paper adopts CCICP (Classification and Combined ICP algorithm for registering point clouds before / after movement. The CCICP algorithm is a type of ICP (Iterative Closest Points which minimizes point-to-plane, and point-to-point distances, simultaneously, and also reject incorrect correspondences based on point classification by PCA (Principle Component Analysis. Precision test shows that CCICP method can register two point clouds up to the 1 pixel size order in original images. Ground control points set in site are useful for initial setting of two point clouds. If there are no GCPs in site of slopes, initial setting is achieved by measuring feature points as ground control points in the point clouds before movement, and creating point clouds after movement with these ground control points. When the motion is rigid transformation, in case that a loose Rock is moving in slope, motion including rotation can be analysed by executing CCICP for a

Lie algebra lattices and strings on T-folds

Energy Technology Data Exchange (ETDEWEB)

Satoh, Yuji [Institute of Physics, University of Tsukuba,Ibaraki 305-8571 (Japan); Sugawara, Yuji [Department of Physical Sciences, College of Science and Engineering, Ritsumeikan University,Shiga 525-8577 (Japan)

2017-02-06

We study the world-sheet conformal field theories for T-folds systematically based on the Lie algebra lattices representing the momenta of strings. The fixed point condition required for the T-duality twist restricts the possible Lie algebras. When the T-duality acts as a simple chiral reflection, one is left with the four cases, A{sub 1},D{sub 2r},E{sub 7},E{sub 8}, among the simple simply-laced algebras. From the corresponding Englert-Neveu lattices, we construct the modular invariant partition functions for the T-fold CFTs in bosonic string theory. Similar construction is possible also by using Euclidean even self-dual lattices. We then apply our formulation to the T-folds in the E{sub 8}×E{sub 8} heterotic string theory. Incorporating non-trivial phases for the T-duality twist, we obtain, as simple examples, a class of modular invariant partition functions parametrized by three integers. Our construction includes the cases which are not reduced to the free fermion construction.

Non-commutative multiple-valued logic algebras

CERN Document Server

Ciungu, Lavinia Corina

2014-01-01

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

Certain number-theoretic episodes in algebra

CERN Document Server

Sivaramakrishnan, R

2006-01-01

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

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.)

Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor

International Nuclear Information System (INIS)

Senovilla, Jose M M

2010-01-01

The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved. (fast track communication)

Computations in finite-dimensional Lie algebras

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A. M. Cohen

1997-12-01

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

Coset realization of unifying W-algebras

International Nuclear Information System (INIS)

Blumenhagen, R.; Huebel, R.

1994-06-01

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

Two dissimilar approaches to dynamical systems on hyper MV -algebras and their information entropy

Science.gov (United States)

Mehrpooya, Adel; Ebrahimi, Mohammad; Davvaz, Bijan

2017-09-01

Measuring the flow of information that is related to the evolution of a system which is modeled by applying a mathematical structure is of capital significance for science and usually for mathematics itself. Regarding this fact, a major issue in concern with hyperstructures is their dynamics and the complexity of the varied possible dynamics that exist over them. Notably, the dynamics and uncertainty of hyper MV -algebras which are hyperstructures and extensions of a central tool in infinite-valued Lukasiewicz propositional calculus that models many valued logics are of primary concern. Tackling this problem, in this paper we focus on the subject of dynamical systems on hyper MV -algebras and their entropy. In this respect, we adopt two varied approaches. One is the set-based approach in which hyper MV -algebra dynamical systems are developed by employing set functions and set partitions. By the other method that is based on points and point partitions, we establish the concept of hyper injective dynamical systems on hyper MV -algebras. Next, we study the notion of entropy for both kinds of systems. Furthermore, we consider essential ergodic characteristics of those systems and their entropy. In particular, we introduce the concept of isomorphic hyper injective and hyper MV -algebra dynamical systems, and we demonstrate that isomorphic systems have the same entropy. We present a couple of theorems in order to help calculate entropy. In particular, we prove a contemporary version of addition and Kolmogorov-Sinai Theorems. Furthermore, we provide a comparison between the indispensable properties of hyper injective and semi-independent dynamical systems. Specifically, we present and prove theorems that draw comparisons between the entropies of such systems. Lastly, we discuss some possible relationships between the theories of hyper MV -algebra and MV -algebra dynamical systems.

Algebra

CERN Document Server

Sepanski, Mark R

2010-01-01

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

Identities and derivations for Jacobian algebras

International Nuclear Information System (INIS)

Dzhumadil'daev, A.S.

2001-09-01

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

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

Science.gov (United States)

Sialaros, Michalis; Christianidis, Jean

2016-06-01

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

Cohomology of Effect Algebras

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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.

Topology general & algebraic

CERN Document Server

Chatterjee, D

2007-01-01

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

Graded associative conformal algebras of finite type

OpenAIRE

Kolesnikov, Pavel

2011-01-01

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

Algebra for All: California's Eighth-Grade Algebra Initiative as Constrained Curricula.

Science.gov (United States)

Domina, Thurston; Penner, Andrew M; Penner, Emily K; Conley, Annemarie

2014-08-01

Across the United States, secondary school curricula are intensifying as a growing proportion of students enroll in high-level academic math courses. In many districts, this intensification process occurs as early as eighth grade, where schools are effectively constraining their mathematics curricula by restricting course offerings and placing more students into Algebra I. This paper provides a quantitative single-case research study of policy-driven curricular intensification in one California school district. (1a) What effect did 8th eighth grade curricular intensification have on mathematics course enrollment patterns in Towering Pines Unified schools? (2b) How did the distribution of prior achievement in Towering Pines math classrooms change as the district constrained the curriculum by universalizing 8th eighth grade Algebra? (3c) Did 8th eighth grade curricular intensification improve students' mathematics achievement? Towering Pines is an immigrant enclave in the inner-ring suburbs of a major metropolitan area. The district's 10 middle schools together enroll approximately 4,000 eighth graders each year. The districts' students are ethnically diverse and largely economically disadvantaged. The study draws upon administrative data describing 8th eighth graders in the district in the 2004-20-05 through 2007-20-08 school years. During the study period, Towering Pines dramatically intensified middle school students' math curricula: In the 2004-20-05 school year 32% of the district's 8th eighth graders enrolled in Algebra or a higher- level mathematics course; by the 2007-20-08 school year that proportion had increased to 84%. We use an interrupted time-series design, comparing students' 8th eighth grade math course enrollments, 10th grade math course enrollments, and 10th grade math test scores across the four cohorts, controlling for demographics and prior achievement. We find that students' odds of taking higher level mathematics courses increased as this

Principles of linear algebra with Mathematica

CERN Document Server

Shiskowski, Kenneth M

2013-01-01

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

Analytic real algebras.

Science.gov (United States)

Seo, Young Joo; Kim, Young Hee

2016-01-01

In this paper we construct some real algebras by using elementary functions, and discuss some relations between several axioms and its related conditions for such functions. We obtain some conditions for real-valued functions to be a (edge) d -algebra.

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

OpenAIRE

Tang, Xiaomin

2016-01-01

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

Green's functions through so(2,1) lie algebra in nonrelativistic quantum mechanics

International Nuclear Information System (INIS)

Boschi-Filho, H.; Vaidya, A.N.

1991-01-01

The authors discuss an algebraic technique to construct the Green's function for systems described by the noncompact so(2,1) Lie algebra. They show that this technique solves the one-dimensional linear oscillator and Coulomb potentials and also generates particular solutions for other one-dimensional potentials. Then they construct explicitly the Green's function for the three-dimensional oscillator and the three-dimensional Coulomb potential, which are generalizations of the one-dimensional cases, and the Coulomb plus an Aharanov-Bohm, potential. They discuss the dynamical algebra involved in each case and also find their wave functions and bound state spectra. Finally they introduce in each case and also find their wave functions and bound state spectra. Finally they introduce a point canonical transformation in the generators of so(2,10) Lie algebra, show that this procedure permits us to solve the one-dimensional Morse potential in addition to the previous cases, and construct its Green's function and find its energy spectrum and wave functions

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)

Robust Algorithms for Detecting a Change in a Stochastic Process with Infinite Memory

Science.gov (United States)

1988-03-01

breakdown point and the additional assumption of 0-mixing on the nominal meas- influence function . The structure of the optimal algorithm ures. Then Huber’s...are i.i.d. sequences of Gaus- For the breakdown point and the influence function sian random variables, with identical variance o2 . Let we will use...algebraic sign for i=0,1. Here z will be chosen such = f nthat it leads to worst case or earliest breakdown. i (14) Next, the influence function measures

Adaptive Ridge Point Refinement for Seeds Detection in X-Ray Coronary Angiogram

Directory of Open Access Journals (Sweden)

Ruoxiu Xiao

2015-01-01

Full Text Available Seed point is prerequired condition for tracking based method for extracting centerline or vascular structures from the angiogram. In this paper, a novel seed point detection method for coronary artery segmentation is proposed. Vessels on the image are first enhanced according to the distribution of Hessian eigenvalue in multiscale space; consequently, centerlines of tubular vessels are also enhanced. Ridge point is extracted as candidate seed point, which is then refined according to its mathematical definition. The theoretical feasibility of this method is also proven. Finally, all the detected ridge points are checked using a self-adaptive threshold to improve the robustness of results. Clinical angiograms are used to evaluate the performance of the proposed algorithm, and the results show that the proposed algorithm can detect a large set of true seed points located on most branches of vessels. Compared with traditional seed point detection algorithms, the proposed method can detect a larger number of seed points with higher precision. Considering that the proposed method can achieve accurate seed detection without any human interaction, it can be utilized for several clinical applications, such as vessel segmentation, centerline extraction, and topological identification.

Classical algebraic chromodynamics

International Nuclear Information System (INIS)

Adler, S.L.

1978-01-01

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

On the classification of quantum W-algebras

International Nuclear Information System (INIS)

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

1992-01-01

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

Lie-Algebras. Pt. 1

International Nuclear Information System (INIS)

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

1990-01-01

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

Semiprojectivity of universal -algebras generated by algebraic elements

DEFF Research Database (Denmark)

Shulman, Tatiana

2012-01-01

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

On numerical characteristics of subvarieties for three varieties of Lie algebras

International Nuclear Information System (INIS)

Petrogradskii, V M

1999-01-01

Let V be a variety of Lie algebras. For each n we consider the dimension of the space of multilinear elements in n distinct letters of a free algebra of this variety. This gives rise to the codimension sequence c n (V). To study the exponential growth one defines the exponent of the variety. The variety of Lie algebras with nilpotent derived subalgebra N s A is known to have Exp(N s A)=s. Over a field of characteristic zero the exponent of every subvariety V subset of N s A is known to be an integer. We shall prove that this is true over any field. Unlike associative algebras, for varieties of Lie algebras it is typical to have superexponential growth for the codimension sequence. Earlier the author introduced a scale for measuring this growth. The following extreme property is established for two varieties AN 2 and A 3 . Any subvariety in each of them cannot be 'just slightly smaller' in terms of this scale. That is, either a subvariety lies at the same point of the scale as the variety itself, or it is situated substantially lower on the scale. These results are also established over an arbitrary field and without using the representation theory of symmetric groups

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

African Journals Online (AJOL)

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

Macdonald index and chiral algebra

Science.gov (United States)

Song, Jaewon

2017-08-01

For any 4d N = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. We conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type ( A 1 , A 2 n ) and ( A 1 , D 2 n+1) where the chiral algebras are given by Virasoro and \\widehat{su}(2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.

Vertex algebras and mirror symmetry

International Nuclear Information System (INIS)

Borisov, L.A.

2001-01-01

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

Advanced modern algebra part 2

CERN Document Server

Rotman, Joseph J

2017-01-01

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

A q-deformed Lorentz algebra

International Nuclear Information System (INIS)

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

1991-01-01

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

Introduction to algebraic quantum field theory

International Nuclear Information System (INIS)

Horuzhy, S.S.

1990-01-01

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

Comments on N=4 superconformal algebras

International Nuclear Information System (INIS)

Rasmussen, J.

2001-01-01

We present a new and asymmetric N=4 superconformal algebra for arbitrary central charge, thus completing our recent work on its classical analogue with vanishing central charge. Besides the Virasoro generator and 4 supercurrents, the algebra consists of an internal SU(2)xU(1) Kac-Moody algebra in addition to two spin 1/2 fermions and a bosonic scalar. The algebra is shown to be invariant under a linear twist of the generators, except for a unique value of the continuous twist parameter. At this value, the invariance is broken and the algebra collapses to the small N=4 superconformal algebra. The asymmetric N=4 superconformal algebra may be seen as induced by an affine SL(2 vertical bar 2) current superalgebra. Replacing SL(2 vertical bar 2) with the coset SL(2 vertical bar 2)/U(1), results directly in the small N=4 superconformal algebra

The theory of algebraic numbers

CERN Document Server

Pollard, Harry

1998-01-01

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

Quantum Heisenberg groups and Sklyanin algebras

International Nuclear Information System (INIS)

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

1993-05-01

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

Classification of simple flexible Lie-admissible algebras

International Nuclear Information System (INIS)

Okubo, S.; Myung, H.C.

1979-01-01

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

Anyons, deformed oscillator algebras and projectors

International Nuclear Information System (INIS)

Engquist, Johan

2009-01-01

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

On graded algebras of global dimension 3

International Nuclear Information System (INIS)

Piontkovskii, D I

2001-01-01

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

Unipotent and nilpotent classes in simple algebraic groups and lie algebras

CERN Document Server

Liebeck, Martin W

2012-01-01

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

Matrix algebra and sampling theory : The case of the Horvitz-Thompson estimator

NARCIS (Netherlands)

Dol, W.; Steerneman, A.G.M.; Wansbeek, T.J.

Matrix algebra is a tool not commonly employed in sampling theory. The intention of this paper is to help change this situation by showing, in the context of the Horvitz-Thompson (HT) estimator, the convenience of the use of a number of matrix-algebra results. Sufficient conditions for the

Elements of mathematics algebra

CERN Document Server

Bourbaki, Nicolas

2003-01-01

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

A Clifford algebra approach to chiral symmetry breaking and fermion mass hierarchies

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