On discretization of tori of compact simple Lie groups: II
International Nuclear Information System (INIS)
Hrivnák, Jiří; Motlochová, Lenka; Patera, Jiří
2012-01-01
The discrete orthogonality of special function families, called C- and S-functions, which are derived from the characters of compact simple Lie groups, is described in Hrivnák and Patera (2009 J. Phys. A: Math. Theor. 42 385208). Here, the results of Hrivnák and Patera are extended to two additional recently discovered families of special functions, called S s - and S l -functions. The main result is an explicit description of their pairwise discrete orthogonality within each family, when the functions are sampled on finite fragments F s M and F l M of a lattice in any dimension n ⩾ 2 and of any density controlled by M, and of the symmetry of the weight lattice of any compact simple Lie group with two different lengths of roots. (paper)
A representation independent propagator. Pt. 1. Compact Lie groups
International Nuclear Information System (INIS)
Tome, W.A.
1995-01-01
Conventional path integral expressions for propagators are representation dependent. Rather than having to adapt each propagator to the representation in question, it is shown that for compact Lie groups it is possible to introduce a propagator that is representation independent. For a given set of kinematical variables this propagator is a single function independent of any particular choice of fiducial vector, which monetheless, correctly propagates each element of the coherent state representation associated with these kinematical variables. Although the configuration space is in general curved, nevertheless the lattice phase-space path integral for the representation independent propagator has the form appropriate to flat space. To illustrate the general theory a representation independent propagator is explicitly constructed for the Lie group SU(2). (orig.)
Chevalley, Claude
2018-01-01
The standard text on the subject for many years, this introductory treatment covers classical linear groups, topological groups, manifolds, analytic groups, differential calculus of Cartan, and compact Lie groups and their representations. 1946 edition.
A very strong difference property for semisimple compact connected lie groups
Shtern, A. I.
2011-06-01
Let G be a topological group. For a function f: G → ℝ and h ∈ G, the difference function Δ h f is defined by the rule Δ h f( x) = f( xh) - f( x) ( x ∈ G). A function H: G → ℝ is said to be additive if it satisfies the Cauchy functional equation H( x + y) = H( x) + H( y) for every x, y ∈ G. A class F of real-valued functions defined on G is said to have the difference property if, for every function f: G → ℝ satisfying Δ h f ∈ F for each h ∈ G, there is an additive function H such that f - H ∈ F. Erdős' conjecture claiming that the class of continuous functions on ℝ has the difference property was proved by N. G. de Bruijn; later on, F. W. Carroll and F. S. Koehl obtained a similar result for compact Abelian groups and, under the additional assumption that the other one-sided difference function ∇ h f defined by ∇ h f( x) = f( xh) - f( x) ( x ∈ G, h ∈ G) is measurable for any h ∈ G, also for noncommutative compact metric groups. In the present paper, we consider a narrower class of groups, namely, the family of semisimple compact connected Lie groups. It turns out that these groups admit a significantly stronger difference property. Namely, if a function f: G → ℝ on a semisimple compact connected Lie group has continuous difference functions Δ h f for any h ∈ G (without the additional assumption concerning the measurability of the functions of the form ∇ h f), then f is automatically continuous, and no nontrivial additive function of the form H is needed. Some applications are indicated, including difference theorems for homogeneous spaces of compact connected Lie groups.
An isomorphism for algebra of distributions with compact support on Lie groups
International Nuclear Information System (INIS)
El-Hussein, K.
1991-08-01
Let (H, H 0 ,...,H L L is an element of IN) be a finite sequence of abelian connected Lie Groups, G L = H, G 1 G i+1 χ ρi+1 H i+1 (0 ≤ i ≤ L - 1) and G = G 0 χ ρo H 0 the Lie groups which are the semi-direct product of G i by H-i (0 ≤ i ≤ L), where ρ i : H i → Aut(G i ) is a group homomorphism (0 ≤ i ≤ L). Let G-tilde = H x H L x...xH 0 be the Lie group of the direct product of H, H L ,..., and H 0 and let ε'(G-tilde) the Topological vector space of all distributions with compact support on G-tilde. In this paper, we prove that there is a structure of algebra on ε'(G-tilde) such that the algebra (convolution) of all distributions with compact support on G is isomorphic onto ε'(G-tilde). (author). 7 refs
Invariant differential operators for non-compact Lie groups: an introduction
International Nuclear Information System (INIS)
Dobrev, V.K.
2015-01-01
In the present paper we review the progress of the project of classification and construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we called earlier 'conformal Lie algebras' (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this we introduced recently the new notion of parabolic relation between two non-compact semisimple Lie algebras G and G' that have the same complexification and possess maximal parabolic subalgebras with the same complexification. In the present paper we consider in detail the orthogonal algebras so(p,q) all of which are parabolically related to the conformal algebra so(n,2) with p+q=n+2, the parabolic subalgebras including the Lorentz subalgebra so(n-1,1) and its analogs so(p-1,q-1)
Hsiang, Wu-Yi
2017-01-01
This volume consists of nine lectures on selected topics of Lie group theory. We provide the readers a concise introduction as well as a comprehensive 'tour of revisiting' the remarkable achievements of S Lie, W Killing, É Cartan and H Weyl on structural and classification theory of semi-simple Lie groups, Lie algebras and their representations; and also the wonderful duet of Cartans' theory on Lie groups and symmetric spaces.With the benefit of retrospective hindsight, mainly inspired by the outstanding contribution of H Weyl in the special case of compact connected Lie groups, we develop the above theory via a route quite different from the original methods engaged by most other books.We begin our revisiting with the compact theory which is much simpler than that of the general semi-simple Lie theory; mainly due to the well fittings between the Frobenius-Schur character theory and the maximal tori theorem of É Cartan together with Weyl's reduction (cf. Lectures 1-4). It is a wonderful reality of the Lie t...
A comparison between star products on regular orbits of compact Lie groups
International Nuclear Information System (INIS)
Fioresi, R.; Lledo, M.A.
2002-01-01
In this paper, an algebraic and a differential star product defined on a regular coadjoint orbit of a compact semisimple group are compared. It has been proved that there is an injective algebra homomorphism between the algebra of polynomials with the algebraic star product and the algebra of differential functions with the differential star product structure. (author)
Invariant differential operators for non-compact Lie groups: the SO* (12) case
Dobrev, V. K.
2015-04-01
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra so* (12). We give the main multiplets of indecomposable elementary representations. Due to the recently established parabolic relations the multiplet classification results are valid also for the algebra so(6, 6) with suitably chosen maximal parabolic subalgebra.
International Nuclear Information System (INIS)
Alvarez, O.; Liu Chienhao
1996-01-01
It has been suggested that a possible classical remnant of the phenomenon of target-space duality (T-duality) would be the equivalence of the classical string Hamiltonian systems. Given a simple compact Lie group G with a bi-invariant metric and a generating function Γ suggested in the physics literature, we follow the above line of thought and work out the canonical transformation Φ generated by Γ together with an Ad-invariant metric and a B-field on the associated Lie algebra g of G so that G and g form a string target-space dual pair at the classical level under the Hamiltonian formalism. In this article, some general features of this Hamiltonian setting are discussed. We study properties of the canonical transformation Φ including a careful analysis of its domain and image. The geometry of the T-dual structure on g is lightly touched. We leave the task of tracing back the Hamiltonian formalism at the quantum level to the sequel of this paper. (orig.). With 4 figs
Lie groups and Lie algebras for physicists
Das, Ashok
2015-01-01
The book is intended for graduate students of theoretical physics (with a background in quantum mechanics) as well as researchers interested in applications of Lie group theory and Lie algebras in physics. The emphasis is on the inter-relations of representation theories of Lie groups and the corresponding Lie algebras.
Quasi-Lie algebras and Lie groups
International Nuclear Information System (INIS)
Momo Bangoura
2006-07-01
In this work, we define the quasi-Poisson Lie quasigroups, dual objects to the quasi-Poisson Lie groups and we establish the correspondence between the local quasi-Poisson Lie quasigoups and quasi-Lie bialgebras (up to isomorphism). (author) [fr
On E-discretization of tori of compact simple Lie groups. II
Hrivnák, Jiří; Juránek, Michal
2017-10-01
Ten types of discrete Fourier transforms of Weyl orbit functions are developed. Generalizing one-dimensional cosine, sine, and exponential, each type of the Weyl orbit function represents an exponential symmetrized with respect to a subgroup of the Weyl group. Fundamental domains of even affine and dual even affine Weyl groups, governing the argument and label symmetries of the even orbit functions, are determined. The discrete orthogonality relations are formulated on finite sets of points from the refinements of the dual weight lattices. Explicit counting formulas for the number of points of the discrete transforms are deduced. Real-valued Hartley orbit functions are introduced, and all ten types of the corresponding discrete Hartley transforms are detailed.
MINAMI, Haruo
2016-01-01
For a compact simple Lie group $G$, we show that the element $[G, \\mathcal{L}] \\in \\pi^S_*(S^0)$ represented by the pair $(G, \\mathcal{L})$ is zero, where $\\mathcal{L}$ denotes the left invariant framing of $G$. The proof relies on the method of E. Ossa [Topology, 21 (1982), 315–323].
String Topology for Lie Groups
DEFF Research Database (Denmark)
A. Hepworth, Richard
2010-01-01
In 1999 Chas and Sullivan showed that the homology of the free loop space of an oriented manifold admits the structure of a Batalin-Vilkovisky algebra. In this paper we give a direct description of this Batalin-Vilkovisky algebra in the case that the manifold is a compact Lie group G. Our answer ...
Styrt, O. G.
2016-01-01
The problem in question is whether the quotient space of a compact linear group is a topological manifold and whether it is a homological manifold. In the paper, the case of an infinite group with commutative connected component is considered.
Lie groups and algebraic groups
Indian Academy of Sciences (India)
We give an exposition of certain topics in Lie groups and algebraic groups. This is not a complete ... of a polynomial equation is equivalent to the solva- bility of the equation ..... to a subgroup of the group of roots of unity in k (in particular, it is a ...
Lipkin, Harry J
2002-01-01
According to the author of this concise, high-level study, physicists often shy away from group theory, perhaps because they are unsure which parts of the subject belong to the physicist and which belong to the mathematician. However, it is possible for physicists to understand and use many techniques which have a group theoretical basis without necessarily understanding all of group theory. This book is designed to familiarize physicists with those techniques. Specifically, the author aims to show how the well-known methods of angular momentum algebra can be extended to treat other Lie group
International Nuclear Information System (INIS)
Guenaydin, M.; Saclioglu, C.
1981-06-01
We give a construction of the Lie algebras of the non-compact groups appearing in four dimensional supergravity theories in terms of boson operators. Our construction parallels very closely their emergence in supergravity and is an extension of the well-known construction of the Lie algebras of the non-compact groups Sp(2n,IR) and SO(2n) from boson operators transforming like a fundamental representation of their maximal compact subgroup U(n). However this extension is non-trivial only for n >= 4 and stops at n = 8 leading to the Lie algebras of SU(4) x SU(1,1), SU(5,1), SO(12) and Esub(7(7)). We then give a general construction of an infinite class of unitary irreducible representations of the respective non-compact groups (except for Esub(7(7)) and SO(12) obtained from the extended construction). We illustrate our construction with the examples of SU(5,1) and SO(12). (orig.)
Energy Technology Data Exchange (ETDEWEB)
Salam, A. [Imperial College of Science and Technology, London (United Kingdom)
1963-01-15
Throughout the history of quantum theory, a battle has raged between the amateurs and professional group theorists. The amateurs have maintained that everything one needs in the theory of groups can be discovered by the light of nature provided one knows how to multiply two matrices. In support of this claim, they of course, justifiably, point to the successes of that prince of amateurs in this field, Dirac, particularly with the spinor representations of the Lorentz group. As an amateur myself, I strongly believe in the truth of the non-professionalist creed. I think perhaps there is not much one has to learn in the way of methodology from the group theorists except caution. But this does not mean one should not be aware of the riches which have been amassed over the course of years particularly in that most highly developed of all mathematical disciplines - the theory of Lie groups. My lectures then are an amateur's attempt to gather some of the fascinating results for compact simple Lie groups which are likely to be of physical interest. I shall state theorems; and with a physicist's typical unconcern rarely, if ever, shall I prove these. Throughout, the emphasis will be to show the close similarity of these general groups with that most familiar of all groups, the group of rotations in three dimensions.
The representations of Lie groups and geometric quantizations
International Nuclear Information System (INIS)
Zhao Qiang
1998-01-01
In this paper we discuss the relation between representations of Lie groups and geometric quantizations. A series of representations of Lie groups are constructed by geometric quantization of coadjoint orbits. Particularly, all representations of compact Lie groups, holomorphic discrete series of representations and spherical representations of reductive Lie groups are constructed by geometric quantizations of elliptic and hyperbolic coadjoint orbits. (orig.)
International Nuclear Information System (INIS)
El Naschie, M.S.
2008-01-01
The maximal number of elementary particles which could be expected to be found within a modestly extended energy scale of the standard model was found using various methods to be N = 69. In particular using E-infinity theory the present Author found the exact transfinite expectation value to be =α-bar o /2≅69 where α-bar o =137.082039325 is the exact inverse fine structure constant. In the present work we show among other things how to derive the exact integer value 69 from the exceptional Lie symmetry groups hierarchy. It is found that the relevant number is given by dim H = 69 where H is the maximal compact subspace of E 7(-5) so that N = dim H = 69 while dim E 7 = 133
International Nuclear Information System (INIS)
Prakash, M.
1985-01-01
The theory of supergravity has attracted increasing attention in the recent years as a unified theory of elementary particle interactions. The superspace formulation of the theory is highly suggestive of an underlying geometrical structure of superspace. It also incorporates the beautifully geometrical general theory of relativity. It leads us to believe that a better understanding of its geometry would result in a better understanding of the theory itself, and furthermore, that the geometry of superspace would also have physical consequences. As a first step towards that goal, we develop here a theory of super Lie groups. These are groups that have the same relation to a super Lie algebra as Lie groups have to a Lie algebra. More precisely, a super Lie group is a super-manifold and a group such that the group operations are super-analytic. The super Lie algebra of a super Lie group is related to the local properties of the group near the identity. This work develops the algebraic and super-analytical tools necessary for our theory, including proofs of a set of existence and uniqueness theorems for a class of super-differential equations
Pro-Lie Groups: A Survey with Open Problems
Directory of Open Access Journals (Sweden)
Karl H. Hofmann
2015-07-01
Full Text Available A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and forms a complete category. It includes each finite-dimensional Lie group, each locally-compact group that has a compact quotient group modulo its identity component and, thus, in particular, each compact and each connected locally-compact group; it also includes all locally-compact Abelian groups. This paper provides an overview of the structure theory and the Lie theory of pro-Lie groups, including results more recent than those in the authors’ reference book on pro-Lie groups. Significantly, it also includes a review of the recent insight that weakly-complete unital algebras provide a natural habitat for both pro-Lie algebras and pro-Lie groups, indeed for the exponential function that links the two. (A topological vector space is weakly complete if it is isomorphic to a power RX of an arbitrary set of copies of R. This class of real vector spaces is at the basis of the Lie theory of pro-Lie groups. The article also lists 12 open questions connected to pro-Lie groups.
Lie groups, lie algebras, and representations an elementary introduction
Hall, Brian
2015-01-01
This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compac...
Transformation groups and Lie algebras
Ibragimov, Nail H
2013-01-01
This book is based on the extensive experience of teaching for mathematics, physics and engineering students in Russia, USA, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics. The methods of local Lie groups discussed in the book provide universal and effective method for solving nonlinear differential equations analytically. Introduction to approximate transformation groups also contained in the book helps to develop skills in constructing approximate solutions for differential equations with a small parameter.
Lie groups, Lie algebras, and some of their applications
Gilmore, Robert
1974-01-01
Lie group theory plays an increasingly important role in modern physical theories. Many of its calculations remain fundamentally unchanged from one field of physics to another, altering only in terms of symbols and the language. Using the theory of Lie groups as a unifying vehicle, concepts and results from several fields of physics can be expressed in an extremely economical way. With rigor and clarity, this text introduces upper-level undergraduate students to Lie group theory and its physical applications.An opening discussion of introductory concepts leads to explorations of the classical
Simple Lie groups without the approximation property
DEFF Research Database (Denmark)
Haagerup, Uffe; de Laat, Tim
2013-01-01
For a locally compact group G, let A(G) denote its Fourier algebra, and let M0A(G) denote the space of completely bounded Fourier multipliers on G. The group G is said to have the Approximation Property (AP) if the constant function 1 can be approximated by a net in A(G) in the weak-∗ topology...... on the space M0A(G). Recently, Lafforgue and de la Salle proved that SL(3,R) does not have the AP, implying the first example of an exact discrete group without it, namely, SL(3,Z). In this paper we prove that Sp(2,R) does not have the AP. It follows that all connected simple Lie groups with finite center...
Riesz transforms and Lie groups of polynomial growth
Elst, ter A.F.M.; Robinson, D.W.; Sikora, A.
1999-01-01
Let G be a Lie group of polynomial growth. We prove that the second-order Riesz transforms onL2(G; dg) are bounded if, and only if, the group is a direct product of a compact group and a nilpotent group, in which case the transforms of all orders are bounded.
Physically detached 'compact groups'
Hernquist, Lars; Katz, Neal; Weinberg, David H.
1995-01-01
A small fraction of galaxies appear to reside in dense compact groups, whose inferred crossing times are much shorter than a Hubble time. These short crossing times have led to considerable disagreement among researchers attempting to deduce the dynamical state of these systems. In this paper, we suggest that many of the observed groups are not physically bound but are chance projections of galaxies well separated along the line of sight. Unlike earlier similar proposals, ours does not require that the galaxies in the compact group be members of a more diffuse, but physically bound entity. The probability of physically separated galaxies projecting into an apparent compact group is nonnegligible if most galaxies are distributed in thin filaments. We illustrate this general point with a specific example: a simulation of a cold dark matter universe, in which hydrodynamic effects are included to identify galaxies. The simulated galaxy distribution is filamentary and end-on views of these filaments produce apparent galaxy associations that have sizes and velocity dispersions similar to those of observed compact groups. The frequency of such projections is sufficient, in principle, to explain the observed space density of groups in the Hickson catalog. We discuss the implications of our proposal for the formation and evolution of groups and elliptical galaxies. The proposal can be tested by using redshift-independent distance estimators to measure the line-of-sight spatial extent of nearby compact groups.
On squares of representations of compact Lie algebras
Energy Technology Data Exchange (ETDEWEB)
Zeier, Robert, E-mail: robert.zeier@ch.tum.de [Department Chemie, Technische Universität München, Lichtenbergstrasse 4, 85747 Garching (Germany); Zimborás, Zoltán, E-mail: zimboras@gmail.com [Department of Computer Science, University College London, Gower St., London WC1E 6BT (United Kingdom)
2015-08-15
We study how tensor products of representations decompose when restricted from a compact Lie algebra to one of its subalgebras. In particular, we are interested in tensor squares which are tensor products of a representation with itself. We show in a classification-free manner that the sum of multiplicities and the sum of squares of multiplicities in the corresponding decomposition of a tensor square into irreducible representations has to strictly grow when restricted from a compact semisimple Lie algebra to a proper subalgebra. For this purpose, relevant details on tensor products of representations are compiled from the literature. Since the sum of squares of multiplicities is equal to the dimension of the commutant of the tensor-square representation, it can be determined by linear-algebra computations in a scenario where an a priori unknown Lie algebra is given by a set of generators which might not be a linear basis. Hence, our results offer a test to decide if a subalgebra of a compact semisimple Lie algebra is a proper one without calculating the relevant Lie closures, which can be naturally applied in the field of controlled quantum systems.
On squares of representations of compact Lie algebras
International Nuclear Information System (INIS)
Zeier, Robert; Zimborás, Zoltán
2015-01-01
We study how tensor products of representations decompose when restricted from a compact Lie algebra to one of its subalgebras. In particular, we are interested in tensor squares which are tensor products of a representation with itself. We show in a classification-free manner that the sum of multiplicities and the sum of squares of multiplicities in the corresponding decomposition of a tensor square into irreducible representations has to strictly grow when restricted from a compact semisimple Lie algebra to a proper subalgebra. For this purpose, relevant details on tensor products of representations are compiled from the literature. Since the sum of squares of multiplicities is equal to the dimension of the commutant of the tensor-square representation, it can be determined by linear-algebra computations in a scenario where an a priori unknown Lie algebra is given by a set of generators which might not be a linear basis. Hence, our results offer a test to decide if a subalgebra of a compact semisimple Lie algebra is a proper one without calculating the relevant Lie closures, which can be naturally applied in the field of controlled quantum systems
The structure of complex Lie groups
Lee, Dong Hoon
2001-01-01
Complex Lie groups have often been used as auxiliaries in the study of real Lie groups in areas such as differential geometry and representation theory. To date, however, no book has fully explored and developed their structural aspects.The Structure of Complex Lie Groups addresses this need. Self-contained, it begins with general concepts introduced via an almost complex structure on a real Lie group. It then moves to the theory of representative functions of Lie groups- used as a primary tool in subsequent chapters-and discusses the extension problem of representations that is essential for studying the structure of complex Lie groups. This is followed by a discourse on complex analytic groups that carry the structure of affine algebraic groups compatible with their analytic group structure. The author then uses the results of his earlier discussions to determine the observability of subgroups of complex Lie groups.The differences between complex algebraic groups and complex Lie groups are sometimes subtle ...
Elementary construction of graded lie groups
International Nuclear Information System (INIS)
Scheunert, M.; Rittenberg, V.
1977-06-01
We show how the definitions of the classical Lie groups have to be modified in the case where Grassmann variables are present. In particular, we construct the general linear, the special linear and the orthosymplectic graded Lie groups. Special attention is paid to the question of how to formulate an adequate 'unitarity condition'. (orig.) [de
On approximation of Lie groups by discrete subgroups
Indian Academy of Sciences (India)
1Department of Mathematics, Faculty of Sciences at Sfax, University of Sfax,. Route Soukra ... Let S (G) denote the space of discrete co-compact subgroup of a Lie group G. We ..... For example, it suffices to apply the following fact: The mapping.
Introduction to the theory of Lie groups
Godement, Roger
2017-01-01
This textbook covers the general theory of Lie groups. By first considering the case of linear groups (following von Neumann's method) before proceeding to the general case, the reader is naturally introduced to Lie theory. Written by a master of the subject and influential member of the Bourbaki group, the French edition of this textbook has been used by several generations of students. This translation preserves the distinctive style and lively exposition of the original. Requiring only basics of topology and algebra, this book offers an engaging introduction to Lie groups for graduate students and a valuable resource for researchers.
The BRST complex and the cohomology of compact lie algebras
International Nuclear Information System (INIS)
Holten, J.W. van
1990-02-01
The authors construct the BRST and anti-BRST operator for a compact Lie algebra which is a direct sum of abelian and simple ideals. Two different inner products are defined on the ghost space and the hermiticity propeties of the ghost and BRST operators with respect to these inner products are discussed. A decomposition theorem for ghost states is derived and the cohomology of the BRST complex is shown to reduce to the standard Lie-algebra cohomology. The authors show that the cohomology classes of the Lie algebra are given by all invariant anti-symmetric tensors and explain how thse can be obtained as zero-modes of an invariant operator in the representation space of the ghosts. Explicit examples are given. (author) 24 refs
Lie groups and grand unified theories
International Nuclear Information System (INIS)
Gubitoso, M.D.
1987-01-01
This work presents some concepts in group theory and Lie algebras and, at same time, shows a method to study and work with semisimple Lie groups, based on Dynkin diagrams. The aproach taken is not completely formal, but it presents the main points of the elaboration of the method, so its mathematical basis is designed with the purpose of making the reading not so cumbersome to those who are interested only in a general picture of the method and its usefulness. At the end it is shown a brief review of gauge theories and two grand-unification models based on SO(13) and E 7 gauge groups. (author) [pt
van der Noort, V.
2009-01-01
This thesis is written in the subfield of mathematics known as representation theory of real reductive Lie groups. Let G be a Lie group in the Harish-Chandra class with maximal compact subgroup K and Lie algebra g. Let Omega be a connected complex manifold. By a family of G-representations
The classification of p-compact groups for p odd
DEFF Research Database (Denmark)
Andersen, Kasper K. S.; Grodal, Jesper Kragh; Møller, Jesper Michael
2008-01-01
A p-compact group, as defined by Dwyer and Wilkerson, is a purely homotopically defined p-local analog of a compact Lie group. It has long been the hope, and later the conjecture, that these objects should have a classification similar to the classification of compact Lie groups. In this paper we...... groups are uniquely determined as p-compact groups by their Weyl groups seen as finite reflection groups over the p-adic integers. Our approach in fact gives a largely self-contained proof of the entire classification theorem for p odd....
Differential calculus on quantized simple Lie groups
International Nuclear Information System (INIS)
Jurco, B.
1991-01-01
Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU q (2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q ε R are also discussed. (orig.)
Harmonic analysis on exponential solvable Lie groups
Fujiwara, Hidenori
2015-01-01
This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated alge...
Differential calculus on quantized simple Lie groups
Energy Technology Data Exchange (ETDEWEB)
Jurco, B. (Dept. of Optics, Palacky Univ., Olomouc (Czechoslovakia))
1991-07-01
Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU{sub q}(2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q {epsilon} R are also discussed. (orig.).
$C^1$ actions on manifolds by lattices in Lie groups with sufficiently high rank
Damjanovic, Danijela; Zhang, Zhiyuan
2018-01-01
In this paper we study Zimmer's conjecture for $C^1$ actions of higher-rank lattices of a connected, semisimple Lie group with finite center on compact manifolds. We show that if the Lie group has no compact factor, and all of whose non-compact factors are of ranks in some sense sufficiently large with respect to the dimension of the manifold, then every $C^1$ action of an irreducible, co-compact lattice has a finite image. As a corollary of our results, for every (uniform or non-uniform) lat...
Analytic factorization of Lie group representations
DEFF Research Database (Denmark)
Gimperlein, Heiko; Krötz, Bernhard; Lienau, Christoph
2012-01-01
For every moderate growth representation (p,E)(p,E) of a real Lie group G on a Fréchet space, we prove a factorization theorem of Dixmier–Malliavin type for the space of analytic vectors E¿E¿. There exists a natural algebra of superexponentially decreasing analytic functions A(G)A(G), such that E......¿=¿(A(G))E¿E¿=¿(A(G))E¿. As a corollary we obtain that E¿E¿ coincides with the space of analytic vectors for the Laplace–Beltrami operator on G....
Introduction to quantized LIE groups and algebras
International Nuclear Information System (INIS)
Tjin, T.
1992-01-01
In this paper, the authors give a self-contained introduction to the theory of quantum groups according to Drinfeld, highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras, Poisson structures and deformation quantization are also provided. After defining Poisson Lie groups the authors study their relation to Lie bialgebras and the classical Yang-Baxter equation. Then the authors explain in detail the concept of quantization for them. As an example the quantization of sl 2 is explicitly carried out. Next, the authors show how quantum groups are related to the Yang-Baxter equation and how they can be used to solve it. Using the quantum double construction, the authors explicitly construct the universal R matrix for the quantum sl 2 algebra. In the last section, the authors deduce all finite-dimensional irreducible representations for q a root of unity. The authors also give their tensor product decomposition (fusion rules), which is relevant to conformal field theory
Construction of Difference Equations Using Lie Groups
International Nuclear Information System (INIS)
Axford, R.A.
1998-01-01
The theory of prolongations of the generators of groups of point transformations to the grid point values of dependent variables and grid spacings is developed and applied to the construction of group invariant numerical algorithms. The concepts of invariant difference operators and generalized discrete sources are introduced for the discretization of systems of inhomogeneous differential equations and shown to produce exact difference equations. Invariant numerical flux functions are constructed from the general solutions of first order partial differential equations that come out of the evaluation of the Lie derivatives of conservation forms of difference schemes. It is demonstrated that invariant numerical flux functions with invariant flux or slope limiters can be determined to yield high resolution difference schemes. The introduction of an invariant flux or slope limiter can be done so as not to break the symmetry properties of a numerical flux-function
Lie group structures on automorphism groups of real-analytic CR manifolds
ZAITSEV, DMITRI
2008-01-01
PUBLISHED Given any real-analytic CR manifold M, we provide general conditions on M guar- anteeing that the group of all its global real-analytic CR automorphisms AutCR(M) is a Lie group (in an appropriate topology). In particular, we obtain a Lie group structure for AutCR(M) when M is an arbitrary compact real-analytic hypersurface embedded in some Stein manifold. The first author was supported by the Austrian Science Fund FWF, Project P17111 and Project P19667. The second ...
Energy Technology Data Exchange (ETDEWEB)
Larouche, M [Departement de Mathematiques et Statistique, Universite de Montreal, 2920 chemin de la Tour, Montreal, Quebec H3T 1J4 (Canada); Lemire, F W [Department of Mathematics, University of Windsor, Windsor, Ontario (Canada); Patera, J, E-mail: larouche@dms.umontreal.ca, E-mail: lemire@uwindsor.ca, E-mail: patera@crm.umontreal.ca [Centre de Recherches Mathematiques, Universite de Montreal, CP 6128-Centre ville, Montreal, Quebec H3C 3J7 (Canada)
2011-10-14
In this paper, we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a continuous group of rank 1, or a product, not necessarily direct, of a continuous group of rank 1 with a finite cyclic group. Explicit formulas for the action of such centralizers on irreducible representations of the simple Lie algebras are given. (paper)
Essays in the history of Lie groups and algebraic groups
Borel, Armand
2001-01-01
Lie groups and algebraic groups are important in many major areas of mathematics and mathematical physics. We find them in diverse roles, notably as groups of automorphisms of geometric structures, as symmetries of differential systems, or as basic tools in the theory of automorphic forms. The author looks at their development, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. Starting from Lie's theory of local analytic transformation groups and early work on Lie algebras, he follows the process of globalization in its two main frameworks: differential geometry and topology on one hand, algebraic geometry on the other. Chapters II to IV are devoted to the former, Chapters V to VIII, to the latter. The essays in the first part of the book survey various proofs of the full reducibility of linear representations of \\mathbf{SL}_2{(\\mathbb{C})}, the contributions of H. Weyl to representations and invariant theory for semisimple Lie groups, and con...
Renormalization group flows and continual Lie algebras
International Nuclear Information System (INIS)
Bakas, Ioannis
2003-01-01
We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by (d/dt;1), with anti-symmetric Cartan kernel K(t,t') = δ'(t-t'); as such, it coincides with the Cartan matrix of the superalgebra sl(N vertical bar N+1) in the large-N limit. The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time, t. We provide the general solution of the renormalization group flows in terms of free fields, via Baecklund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Z n to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra (d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown. (author)
Theory of the unitary representations of compact groups
International Nuclear Information System (INIS)
Burzynski, A.; Burzynska, M.
1979-01-01
An introduction contains some basic notions used in group theory, Lie group, Lie algebras and unitary representations. Then we are dealing with compact groups. For these groups we show the problem of reduction of unitary representation of Wigner's projection operators, Clebsch-Gordan coefficients and Wigner-Eckart theorem. We show (this is a new approach) the representations reduction formalism by using superoperators in Hilbert-Schmidt space. (author)
Uncertainty Principles on Two Step Nilpotent Lie Groups
Indian Academy of Sciences (India)
Abstract. We extend an uncertainty principle due to Cowling and Price to two step nilpotent Lie groups, which generalizes a classical theorem of Hardy. We also prove an analogue of Heisenberg inequality on two step nilpotent Lie groups.
Non-commutative representation for quantum systems on Lie groups
Energy Technology Data Exchange (ETDEWEB)
Raasakka, Matti Tapio
2014-01-27
space path integral with the help of the non-commutative dual variables. In studying the classical limit of the path integral, we show that we recover the correct classical equations of motion for the particle, if we account for the deformation of the phase space in the variational calculus. The non-commutative variables correspond in this limit to the classical momentum variables, further verifying their physical interpretation. We conclude that the non-commutative harmonic analysis facilitates a convenient study of the classical limit of quantum dynamics on a Lie group even if the group is compact, in which case variational calculus cannot easily be applied. As the second physics application, we repeat our above considerations for the case of Ponzano-Regge spin foam model for 3-dimensional quantum gravity. The non-commutative dual variables correspond in this case to discrete metric variables, thus illuminating the geometrical interpretation of the model. Again, we find that a convenient study of the classical limit is made possible through the non-commutative phase space path integral.
Non-commutative representation for quantum systems on Lie groups
International Nuclear Information System (INIS)
Raasakka, Matti Tapio
2014-01-01
integral with the help of the non-commutative dual variables. In studying the classical limit of the path integral, we show that we recover the correct classical equations of motion for the particle, if we account for the deformation of the phase space in the variational calculus. The non-commutative variables correspond in this limit to the classical momentum variables, further verifying their physical interpretation. We conclude that the non-commutative harmonic analysis facilitates a convenient study of the classical limit of quantum dynamics on a Lie group even if the group is compact, in which case variational calculus cannot easily be applied. As the second physics application, we repeat our above considerations for the case of Ponzano-Regge spin foam model for 3-dimensional quantum gravity. The non-commutative dual variables correspond in this case to discrete metric variables, thus illuminating the geometrical interpretation of the model. Again, we find that a convenient study of the classical limit is made possible through the non-commutative phase space path integral.
Automorphisms of p-compact groups and their root data
DEFF Research Database (Denmark)
Andersen, Kasper K. S.; Grodal, Jesper Kragh
2008-01-01
We construct a model for the space of automorphisms of a connected p–compact group in terms of the space of automorphisms of its maximal torus normalizer and its root datum. As a consequence we show that any homomorphism to the outer automorphism group of a p–compact group can be lifted to a group...... action, analogous to a classical theorem of de Siebenthal for compact Lie groups. The model of this paper is used in a crucial way in our paper `The classification of 2-compact groups' [arXiv:math.AT/0611437], where we prove the conjectured classification of 2–compact groups and determine...... their automorphism spaces....
Lie symmetries and differential galois groups of linear equations
Oudshoorn, W.R.; Put, M. van der
2002-01-01
For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In
Enveloping algebras of Lie groups with descrete series
International Nuclear Information System (INIS)
Nguyen huu Anh; Vuong manh Son
1990-09-01
In this article we shall prove that the enveloping algebra of the Lie algebra of some unimodular Lie group having discrete series, when localized at some element of the center, is isomorphic to the tensor product of a Weyl algebra over the ring of Laurent polynomials of one variable and the enveloping algebra of some reductive Lie algebra. In particular, it will be proved that the Lie algebra of a unimodular solvable Lie group having discrete series satisfies the Gelfand-Kirillov conjecture. (author). 6 refs
Basic gerbe over non simply connected compact groups
Gawedzki, Krzysztof; Reis, Nuno
2003-01-01
We present an explicit construction of the basic bundle gerbes with connection over all connected compact simple Lie groups. These are geometric objects that appear naturally in the Lagrangian approach to the WZW conformal field theories. Our work extends the recent construction of E. Meinrenken \\cite{Meinr} restricted to the case of simply connected groups.
On approximation of Lie groups by discrete subgroups
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... The notion of approximation of Lie groups by discrete subgroups was introduced by Tôyama in Kodai Math. Sem. Rep. 1 (1949) 36–37 and investigated in detail by Kuranishi in Nagoya Math. J. 2 (1951) 63–71. It is known as a theorem of Tôyama that any connected Lie group approximated by discrete ...
Invariant subsets under compact quantum group actions
Huang, Huichi
2012-01-01
We investigate compact quantum group actions on unital $C^*$-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact metrizable spaces with infinitely many points are not quantum homogeneous spaces.
Real representations of Lie groups and a theorem of H. Pittie
International Nuclear Information System (INIS)
Freitas, R.
1992-01-01
In this paper, we prove a structure theorem of the real representation ring RO(T) as a module over the real representation ring RO(G), where G is a compact, connected and simply connected Lie group and T is a maximal torus of G. This provides a real version to a theorem of H. Pittie. (author). 24 refs
Property A and Coarse Embedding for Locally Compact Groups
DEFF Research Database (Denmark)
Li, Kang
property A. In a joint work with Knudby, we characterize the connected simple Lie groups with the discrete topology that have different approximation properties (see Article B). Moreover, we give a contractive Schur multiplier characterization of locally compact groups coarsely embeddable into Hilbert......In the study of the Novikov conjecture, property A and coarse embedding of metric spaces were introduced by Yu and Gromov, respectively. The main topic of the thesis is property A and coarse embedding for locally compact second countable groups. We prove that many of the results that are known...... to hold in the discrete setting, hold also in the locally compact setting.In a joint work with Deprez, we show that property A is equivalent to amenability at infinity and the strong Novikov conjecture is true for every locally compact group that embeds coarsely into a Hilbert space (see Article A...
S7 without any construction of Lie group
International Nuclear Information System (INIS)
Zhou Jian; Xu Senlin.
1988-12-01
It was proved that the sphere S n is a parallelizable manifold if and only if n = 1,3 or 7, and that S n is an H-space if and only if n = 0,1,3 or 7. Because a Lie group must necessarily be a parallelizable manifold and also an H-space, naturally one asks that S n is a Lie group for n = 0, 1,3 or 7? In this paper we prove that S 7 is not a Lie group, and it is not even a topological group. Therefore, S n is a Lie group (or a topological group) if and only if n = 0,1,3. (author). 11 refs
Statistics on Lie groups: A need to go beyond the pseudo-Riemannian framework
Miolane, Nina; Pennec, Xavier
2015-01-01
Lie groups appear in many fields from Medical Imaging to Robotics. In Medical Imaging and particularly in Computational Anatomy, an organ's shape is often modeled as the deformation of a reference shape, in other words: as an element of a Lie group. In this framework, if one wants to model the variability of the human anatomy, e.g. in order to help diagnosis of diseases, one needs to perform statistics on Lie groups. A Lie group G is a manifold that carries an additional group structure. Statistics on Riemannian manifolds have been well studied with the pioneer work of Fréchet, Karcher and Kendall [1, 2, 3, 4] followed by others [5, 6, 7, 8, 9]. In order to use such a Riemannian structure for statistics on Lie groups, one needs to define a Riemannian metric that is compatible with the group structure, i.e a bi-invariant metric. However, it is well known that general Lie groups which cannot be decomposed into the direct product of compact and abelian groups do not admit a bi-invariant metric. One may wonder if removing the positivity of the metric, thus asking only for a bi-invariant pseudo-Riemannian metric, would be sufficient for most of the groups used in Computational Anatomy. In this paper, we provide an algorithmic procedure that constructs bi-invariant pseudo-metrics on a given Lie group G. The procedure relies on a classification theorem of Medina and Revoy. However in doing so, we prove that most Lie groups do not admit any bi-invariant (pseudo-) metric. We conclude that the (pseudo-) Riemannian setting is not the richest setting if one wants to perform statistics on Lie groups. One may have to rely on another framework, such as affine connection space.
Quantum algebras as quantizations of dual Poisson–Lie groups
International Nuclear Information System (INIS)
Ballesteros, Ángel; Musso, Fabio
2013-01-01
A systematic computational approach for the explicit construction of any quantum Hopf algebra (U z (g), Δ z ) starting from the Lie bialgebra (g, δ) that gives the first-order deformation of the coproduct map Δ z is presented. The procedure is based on the well-known ‘quantum duality principle’, namely the fact that any quantum algebra can be viewed as the quantization of the unique Poisson–Lie structure (G*, Λ g ) on the dual group G*, which is obtained by exponentiating the Lie algebra g* defined by the dual map δ*. From this perspective, the coproduct for U z (g) is just the pull-back of the group law for G*, and the Poisson analogues of the quantum commutation rules for U z (g) are given by the unique Poisson–Lie structure Λ g on G* whose linearization is the Poisson analogue of the initial Lie algebra g. This approach is shown to be a very useful technical tool in order to solve the Lie bialgebra quantization problem explicitly since, once a Lie bialgebra (g, δ) is given, the full dual Poisson–Lie group (G*, Λ) can be obtained either by applying standard Poisson–Lie group techniques or by implementing the algorithm presented here with the aid of symbolic manipulation programs. As a consequence, the quantization of (G*, Λ) will give rise to the full U z (g) quantum algebra, provided that ordering problems are appropriately fixed through the choice of certain local coordinates on G* whose coproduct fulfils a precise ‘quantum symmetry’ property. The applicability of this approach is explicitly demonstrated by reviewing the construction of several instances of quantum deformations of physically relevant Lie algebras such as sl(2,R), the (2+1) anti-de Sitter algebra so(2, 2) and the Poincaré algebra in (3+1) dimensions. (paper)
Reflection Positive Stochastic Processes Indexed by Lie Groups
Jorgensen, Palle E. T.; Neeb, Karl-Hermann; Ólafsson, Gestur
2016-06-01
Reflection positivity originates from one of the Osterwalder-Schrader axioms for constructive quantum field theory. It serves as a bridge between euclidean and relativistic quantum field theory. In mathematics, more specifically, in representation theory, it is related to the Cartan duality of symmetric Lie groups (Lie groups with an involution) and results in a transformation of a unitary representation of a symmetric Lie group to a unitary representation of its Cartan dual. In this article we continue our investigation of representation theoretic aspects of reflection positivity by discussing reflection positive Markov processes indexed by Lie groups, measures on path spaces, and invariant gaussian measures in spaces of distribution vectors. This provides new constructions of reflection positive unitary representations.
Lie Algebras Associated with Group U(n)
International Nuclear Information System (INIS)
Zhang Yufeng; Dong Huanghe; Honwah Tam
2007-01-01
Starting from the subgroups of the group U(n), the corresponding Lie algebras of the Lie algebra A 1 are presented, from which two well-known simple equivalent matrix Lie algebras are given. It follows that a few expanding Lie algebras are obtained by enlarging matrices. Some of them can be devoted to producing double integrable couplings of the soliton hierarchies of nonlinear evolution equations. Others can be used to generate integrable couplings involving more potential functions. The above Lie algebras are classified into two types. Only one type can generate the integrable couplings, whose Hamiltonian structure could be obtained by use of the quadratic-form identity. In addition, one condition on searching for integrable couplings is improved such that more useful Lie algebras are enlightened to engender. Then two explicit examples are shown to illustrate the applications of the Lie algebras. Finally, with the help of closed cycling operation relations, another way of producing higher-dimensional Lie algebras is given.
The classification of 2-compact groups
DEFF Research Database (Denmark)
K. S. Andersen, Kasper; Grodal, Jesper
2009-01-01
with Moeller and Viruel for p odd, this establishes the full classification of p-compact groups, stating that, up to isomorphism, there is a one-to-one correspondence between connected p-compact groups and root data over the p-adic integers. As a consequence we prove the maximal torus conjecture, giving a one...
Co-compact Gabor Systems on Locally Compact Abelian Groups
DEFF Research Database (Denmark)
Jakobsen, Mads Sielemann; Lemvig, Jakob
2016-01-01
In this work we extend classical structure and duality results in Gabor analysis on the euclidean space to the setting of second countable locally compact abelian (LCA) groups. We formulate the concept of rationally oversampling of Gabor systems in an LCA group and prove corresponding characteriz...
Anti-Kählerian Geometry on Lie Groups
Fernández-Culma, Edison Alberto; Godoy, Yamile
2018-03-01
Let G be a Lie group of even dimension and let ( g, J) be a left invariant anti-Kähler structure on G. In this article we study anti-Kähler structures considering the distinguished cases where the complex structure J is abelian or bi-invariant. We find that if G admits a left invariant anti-Kähler structure ( g, J) where J is abelian then the Lie algebra of G is unimodular and ( G, g) is a flat pseudo-Riemannian manifold. For the second case, we see that for any left invariant metric g for which J is an anti-isometry we obtain that the triple ( G, g, J) is an anti-Kähler manifold. Besides, given a left invariant anti-Hermitian structure on G we associate a covariant 3-tensor 𝜃 on its Lie algebra and prove that such structure is anti-Kähler if and only if 𝜃 is a skew-symmetric and pure tensor. From this tensor we classify the real 4-dimensional Lie algebras for which the corresponding Lie group has a left invariant anti-Kähler structure and study the moduli spaces of such structures (up to group isomorphisms that preserve the anti-Kähler structures).
Application of Lie group analysis in geophysical fluid dynamics
Ibragimov, Ranis
2011-01-01
This is the first monograph dealing with the applications of the Lie group analysis to the modeling equations governing internal wave propagation in the deep ocean. A new approach to describe the nonlinear interactions of internal waves in the ocean is presented. While the central idea of the book is to investigate oceanic internal waves through the prism of Lie group analysis, it is also shown for the first time that internal wave beams, representing exact solutions to the equation of motion of stratified fluid, can be found by solving the given model as invariant solutions of nonlinear equat
Controllability of linear vector fields on Lie groups
International Nuclear Information System (INIS)
Ayala, V.; Tirao, J.
1994-11-01
In this paper, we shall deal with a linear control system Σ defined on a Lie group G with Lie algebra g. The dynamic of Σ is determined by the drift vector field which is an element in the normalizer of g in the Lie algebra of all smooth vector field on G and by the control vectors which are elements in g considered as left-invariant vector fields. We characterize the normalizer of g identifying vector fields on G with C ∞ -functions defined on G into g. For this class of control systems we study algebraic conditions for the controllability problem. Indeed, we prove that if the drift vector field has a singularity then the Lie algebra rank condition is necessary for the controllability property, but in general this condition does not determine this property. On the other hand, we show that the rank (ad-rank) condition is sufficient for the controllability of Σ. In particular, we extend the fundamental Kalman's theorem when G is an Abelian connected Lie group. Our work is related with a paper of L. Markus and we also improve his results. (author). 7 refs
Galois Theory of Differential Equations, Algebraic Groups and Lie Algebras
Put, Marius van der
1999-01-01
The Galois theory of linear differential equations is presented, including full proofs. The connection with algebraic groups and their Lie algebras is given. As an application the inverse problem of differential Galois theory is discussed. There are many exercises in the text.
Cluster X-varieties, amalgamation, and Poisson-Lie groups
DEFF Research Database (Denmark)
Fock, V. V.; Goncharov, A. B.
2006-01-01
In this paper, starting from a split semisimple real Lie group G with trivial center, we define a family of varieties with additional structures. We describe them as cluster χ-varieties, as defined in [FG2]. In particular they are Poisson varieties. We define canonical Poisson maps of these varie...
Exceptional Lie groups, E-infinity theory and Higgs Boson
International Nuclear Information System (INIS)
El-Okaby, Ayman A.
2008-01-01
In this paper we study the correlation between El-Naschie's exceptional Lie groups hierarchies and his transfinite E-infinity space-time theory. Subsequently this correlation is used to calculate the number of elementary particles in the standard model, mass of the Higgs Bosons and some coupling constants
Observability of linear control systems on Lie groups
International Nuclear Information System (INIS)
Ayala, V.; Hacibekiroglu, A.K.
1995-01-01
In this paper, we study the observability problem for a linear control system Σ on a Lie group G. The drift vector field of Σ is an infinitesimal automorphism of G and the control vectors are elements in the Lie algebra of G. We establish algebraic conditions to characterize locally and globally observability for Σ. As in the linear case on R n , these conditions are independent of the control vector. We give an algorithm on the co-tangent bundle of G to calculate the equivalence class of the neutral element. (author). 6 refs
Observational properties of compact groups of galaxies
International Nuclear Information System (INIS)
Hickson, P.
1990-01-01
Compact groups are small, relatively isolated, systems of galaxies with projected separations comparable to the diameters of the galaxies themselves. Two well-known examples are Stephan's Quintet (Stephan, 1877) and Seyfert's Sextet (Seyfert 1948a,b). In groups such as these, the apparent space density of galaxies approaches 10(exp 6) Mpc(sub -3), denser even than the cores of rich clusters. The apparent unlikeliness of the chance occurrence of such tight groupings lead Ambartsumyan (1958, 1975) to conclude that compact groups must be physically dense systems. This view is supported by clear signs of galaxy interactions that are seen in many groups. Spectroscopic observations reveal that typical relative velocities of galaxies in the groups are comparable to their internal stellar velocities. This should be conducive to strong gravitational interactions - more so than in rich clusters, where galaxy velocities are typically much higher. This suggests that compact groups could be excellent laboratories in which to study galaxy interactions and their effects. Compact groups often contain one or more galaxies whose redshift differs greatly from those of the other group members. If these galaxies are at the same distance as the other members, either entire galaxies are being ejected at high velocities from these groups, or some new physical phenomena must be occurring. If their redshifts are cosmological, we must explain why so many discordant galaxies are found in compact groups. In recent years much progress has been made in addressing these questions. Here, the author discusses the current observational data on compact groups and their implications
Expansion in finite simple groups of Lie type
Tao, Terence
2015-01-01
Expander graphs are an important tool in theoretical computer science, geometric group theory, probability, and number theory. Furthermore, the techniques used to rigorously establish the expansion property of a graph draw from such diverse areas of mathematics as representation theory, algebraic geometry, and arithmetic combinatorics. This text focuses on the latter topic in the important case of Cayley graphs on finite groups of Lie type, developing tools such as Kazhdan's property (T), quasirandomness, product estimates, escape from subvarieties, and the Balog-Szemerédi-Gowers lemma. Applications to the affine sieve of Bourgain, Gamburd, and Sarnak are also given. The material is largely self-contained, with additional sections on the general theory of expanders, spectral theory, Lie theory, and the Lang-Weil bound, as well as numerous exercises and other optional material.
Explaining compact groups as change alignments
International Nuclear Information System (INIS)
Mamon, G.A.
1990-01-01
The physical nature of the apparently densest groups of galaxies, known as compact groups is a topic of some recent controversy, despite the detailed observations of a well-defined catalog of 100 isolated compact groups compiled by Hickson (1982). Whereas many authors have espoused the view that compact groups are bound systems, typically as dense as they appear in projection on the sky (e.g., Williams ampersand Rood 1987; Sulentic 1987; Hickson ampersand Rood 1988), others see them as the result of chance configurations within larger systems, either in 1D (chance alignments: Mamon 1986; Walke ampersand Mamon 1989), or in 3D (transient cores: Rose 1979). As outlined in the companion review to this contribution (Mamon, in these proceedings), the implication of Hickson's compact groups (HCGs) being dense bound systems is that they would then constitute the densest isolated systems of galaxies in the Universe and the privileged site for galaxy interactions. In a previous paper (Mamon 1986), the author reviewed the arguments given for the different theories of compact groups. Since then, a dozen papers have been published on the subject, including a thorough and perceptive review by White (1990), thus more than doubling the amount written on the subject. Here, the author first enumerates the arguments that he brought up in 1986 substantiating the chance alignment hypothesis, then he reviews the current status of the numerous recent arguments arguing against chance alignments and/or for the bound dense group hypothesis (both for the majority of HCGs but not all of them), and finally he reconsiders each one of these anti-chance alignment arguments and shows that, rather than being discredited, the chance alignment hypothesis remains a fully consistent explanation for the nature of compact groups
Trust and compactness in social network groups.
De Meo, Pasquale; Ferrara, Emilio; Rosaci, Domenico; Sarné, Giuseppe M L
2015-02-01
Understanding the dynamics behind group formation and evolution in social networks is considered an instrumental milestone to better describe how individuals gather and form communities, how they enjoy and share the platform contents, how they are driven by their preferences/tastes, and how their behaviors are influenced by peers. In this context, the notion of compactness of a social group is particularly relevant. While the literature usually refers to compactness as a measure to merely determine how much members of a group are similar among each other, we argue that the mutual trustworthiness between the members should be considered as an important factor in defining such a term. In fact, trust has profound effects on the dynamics of group formation and their evolution: individuals are more likely to join with and stay in a group if they can trust other group members. In this paper, we propose a quantitative measure of group compactness that takes into account both the similarity and the trustworthiness among users, and we present an algorithm to optimize such a measure. We provide empirical results, obtained from the real social networks EPINIONS and CIAO, that compare our notion of compactness versus the traditional notion of user similarity, clearly proving the advantages of our approach.
Coherent states for quantum compact groups
International Nuclear Information System (INIS)
Jurco, B.; Stovicek, P.; CTU, Prague
1996-01-01
Coherent states are introduced and their properties are discussed for simple quantum compact groups A l , B l , C l and D l . The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested. (orig.)
Coherent states for quantum compact groups
Energy Technology Data Exchange (ETDEWEB)
Jurco, B. [European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.; Stovicek, P. [Ceske Vysoke Uceni Technicke, Prague (Czech Republic). Dept. of Mathematics]|[CTU, Prague (Czech Republic). Doppler Inst.
1996-12-01
Coherent states are introduced and their properties are discussed for simple quantum compact groups A{sub l}, B{sub l}, C{sub l} and D{sub l}. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested. (orig.)
Coherent states for quantum compact groups
Jurco, B
1996-01-01
Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit and interpret the coherent state as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R--matrix formulation (generalizing this way the q--deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel--Weil construction) are described using the concept of coherent state. The relation between representation theory and non--commutative differential geometry is suggested.}
International Nuclear Information System (INIS)
El-Hussein, K.
1991-08-01
Let V be a real finite dimensional vector space and let K be a connected compact Lie group, which acts on V by means of a continuous linear representation ρ. Let G=V x p K be the motion group which is the semi-direct product of V by K and let P be an invariant differential operator on G. In this paper we give a necessary and sufficient condition for the global solvability of P on G. Now let G be a connected semi-simple Lie group with finite centre and let P be an invariant differential operator on G. We give also a necessary and sufficient condition for the global solvability of P on G. (author). 8 refs
International Workshop "Groups, Rings, Lie and Hopf Algebras"
2003-01-01
The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.
Lie groups, differential equations, and geometry advances and surveys
2017-01-01
This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. As such, it is suitable for students in doctoral courses, and will also benefit researchers who want to expand their field of interest.
ROSAT: X ray survey of compact groups
van Gorkom, Jacqueline
1993-01-01
This is the final technical report on grant NAG5-1954, which was awarded under the NASA ROSAT Guest Investigator Program to Columbia University. This grant was awarded for a number of projects on two rather different topics: (1) an x-ray survey of compact groups of galaxies; and (2) the fate of gas
An introduction to Lie group integrators – basics, new developments and applications
International Nuclear Information System (INIS)
Celledoni, Elena; Marthinsen, Håkon; Owren, Brynjulf
2014-01-01
We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of symplectic integrators on cotangent bundles of Lie groups is presented and the notion of discrete gradient methods is generalised to Lie groups
Topological entropy of continuous actions of compactly generated groups
Schneider, Friedrich Martin
2015-01-01
We introduce a notion of topological entropy for continuous actions of compactly generated topological groups on compact Hausdorff spaces. It is shown that any continuous action of a compactly generated topological group on a compact Hausdorff space with vanishing topological entropy is amenable. Given an arbitrary compactly generated locally compact Hausdorff topological group $G$, we consider the canonical action of $G$ on the closed unit ball of $L^{1}(G)' \\cong L^{\\infty}(G)$ endowed with...
Quantization and harmonic analysis on nilpotent Lie groups
International Nuclear Information System (INIS)
Wildberger, N.J.
1983-01-01
Weyl Quantization is a procedure for associating a function on which the canonical commutation relations are realized. If G is a simply-connected, connected nilpotent Lie group with Lie algebra g and dual g/sup */, it is shown how to inductively construct symplectic isomorphisms between every co-adjoint orbit O and the bundle in Hilbert Space for some m. Weyl Quantization can then be used to associate to each orbit O a unitary representation rho 0 of G, recovering the classification of the unitary dual by Kirillov. It is used to define a geometric Fourier transform, F : L 1 (G) → functions on g/sup */, and it is shown that the usual operator-valued Fourier transform can be recovered from F, characters are inverse Fourier transforms of invariant measures on orbits, and matrix coefficients are inverse Fourier transforms of non-invariant measures supported on orbits. Realizations of the representations rho 0 in subspaces of L 2 (O) are obtained.. Finally, the kernel function is computed for the upper triangular unipotent group and one other example
Koszul information geometry and Souriau Lie group thermodynamics
Energy Technology Data Exchange (ETDEWEB)
Barbaresco, Frédéric, E-mail: frederic.barbaresco@thalesgroup.com
2015-01-13
The François Massieu 1869 idea to derive some mechanical and thermal properties of physical systems from 'Characteristic Functions', was developed by Gibbs and Duhem in thermodynamics with the concept of potentials, and introduced by Poincaré in probability. This paper deals with generalization of this Characteristic Function concept by Jean-Louis Koszul in Mathematics and by Jean-Marie Souriau in Statistical Physics. The Koszul-Vinberg Characteristic Function (KVCF) on convex cones will be presented as cornerstone of 'Information Geometry' theory, defining Koszul Entropy as Legendre transform of minus the logarithm of KVCF, and Fisher Information Metrics as hessian of these dual functions, invariant by their automorphisms. In parallel, Souriau has extended the Characteristic Function in Statistical Physics looking for other kinds of invariances through co-adjoint action of a group on its momentum space, defining physical observables like energy, heat and momentum as pure geometrical objects. In covariant Souriau model, Gibbs equilibriums states are indexed by a geometric parameter, the Geometric (Planck) Temperature, with values in the Lie algebra of the dynamical Galileo/Poincaré groups, interpreted as a space-time vector, giving to the metric tensor a null Lie derivative. Fisher Information metric appears as the opposite of the derivative of Mean 'Moment map' by geometric temperature, equivalent to a Geometric Capacity or Specific Heat. These elements has been developed by author in [10][11].
Topological Poisson Sigma models on Poisson-Lie groups
International Nuclear Information System (INIS)
Calvo, Ivan; Falceto, Fernando; Garcia-Alvarez, David
2003-01-01
We solve the topological Poisson Sigma model for a Poisson-Lie group G and its dual G*. We show that the gauge symmetry for each model is given by its dual group that acts by dressing transformations on the target. The resolution of both models in the open geometry reveals that there exists a map from the reduced phase of each model (P and P*) to the main symplectic leaf of the Heisenberg double (D 0 ) such that the symplectic forms on P, P* are obtained as the pull-back by those maps of the symplectic structure on D 0 . This uncovers a duality between P and P* under the exchange of bulk degrees of freedom of one model with boundary degrees of freedom of the other one. We finally solve the Poisson Sigma model for the Poisson structure on G given by a pair of r-matrices that generalizes the Poisson-Lie case. The Hamiltonian analysis of the theory requires the introduction of a deformation of the Heisenberg double. (author)
Group formalism of Lie transformations to time-fractional partial ...
Indian Academy of Sciences (India)
Lie symmetry analysis; Fractional partial differential equation; Riemann–Liouville fractional derivative ... science and engineering. It is known that while ... differential equations occurring in different areas of applied science [11,14]. The Lie ...
Quantum dressing orbits on compact groups
Energy Technology Data Exchange (ETDEWEB)
Jurco, B. (Technische Univ. Clausthal, Clausthal-Zellerfeld (Germany). Sommerfeld Inst.); Stovicek, P. (Prague Univ. (Czechoslovakia). Dept. of Mathematics)
1993-02-01
The quantum double is shown to imply the dressing transformation on quantum compact groups and the quantum Iwasawa decomposition in the general case. Quantum dressing orbits are describing explicitly as *-algebras. The dual coalgebras consisting of differential operators are related to the quantum Weyl elements. Besides, the differential geometry on a quantum leaf allows a remarkably simple construction of irreducible *-representations of the algebras of quantum functions. Representation spaces then consist of analytic functions on classical phase spaces. These representations are also interpreted in the framework of quantization in the spirit of Berezin applied to symplectic leaves on classical compact groups. Convenient 'coherent states' are introduced and a correspondence between classical and quantum observables is given. (orig.).
Quantum dressing orbits on compact groups
International Nuclear Information System (INIS)
Jurco, B.; Stovicek, P.
1993-01-01
The quantum double is shown to imply the dressing transformation on quantum compact groups and the quantum Iwasawa decomposition in the general case. Quantum dressing orbits are describing explicitly as *-algebras. The dual coalgebras consisting of differential operators are related to the quantum Weyl elements. Besides, the differential geometry on a quantum leaf allows a remarkably simple construction of irreducible *-representations of the algebras of quantum functions. Representation spaces then consist of analytic functions on classical phase spaces. These representations are also interpreted in the framework of quantization in the spirit of Berezin applied to symplectic leaves on classical compact groups. Convenient 'coherent states' are introduced and a correspondence between classical and quantum observables is given. (orig.)
The Higgs mass derived from the U(3) Lie group
DEFF Research Database (Denmark)
Trinhammer, Ole; Bohr, Henrik; Jensen, Mogens O Stibius
2015-01-01
The Higgs mass value is derived from a Hamiltonian on the Lie group U(3) where we relate strong and electroweak energy scales. The baryon states of nucleon and delta resonances originate in specific Bloch wave degrees of freedom coupled to a Higgs mechanism which also gives rise to the usual gauge...... boson masses. The derived Higgs mass is around 125 GeV. From the same Hamiltonian, we derive the relative neutron to proton mass ratio and the N and Delta mass spectra. All compare rather well with the experimental values. We predict scarce neutral flavor baryon singlets that should be visible...... in scattering cross-sections for negative pions on protons, in photoproduction on neutrons, in neutron diffraction dissociation experiments and in invariant mass spectra of protons and negative pions in B-decays. The fundamental predictions are based on just one length scale and the fine structure constant...
Dual Solutions for Nonlinear Flow Using Lie Group Analysis.
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Muhammad Awais
Full Text Available `The aim of this analysis is to investigate the existence of the dual solutions for magnetohydrodynamic (MHD flow of an upper-convected Maxwell (UCM fluid over a porous shrinking wall. We have employed the Lie group analysis for the simplification of the nonlinear differential system and computed the absolute invariants explicitly. An efficient numerical technique namely the shooting method has been employed for the constructions of solutions. Dual solutions are computed for velocity profile of an upper-convected Maxwell (UCM fluid flow. Plots reflecting the impact of dual solutions for the variations of Deborah number, Hartman number, wall mass transfer are presented and analyzed. Streamlines are also plotted for the wall mass transfer effects when suction and blowing situations are considered.
Nature of compact groups of galaxies
International Nuclear Information System (INIS)
Hickson, P.; Rood, H.J.
1988-01-01
Monte Carlo numerical simulation is used to calculate the probability for the chance occurrence of four galaxies projected on the sky satisfying the Hickson isolation criterion within a loose group of eight members. For the models which match most closely the size and galaxy multiplicity function of observed groups, this chance occurrence is found to be smaller by a factor of about 100 than the value obtained previously by Mamom from numerical simulations of dynamical models of groups. This and other direct independent observational results from the literature constitute strong evidence that nearly all of the Hickson compact groups are real physical systems. It is concluded that the tendency for the spiral fraction of a compact group to be larger than the value inferred from the galaxy morphology-group density relation of rich clusters and loose groups is a real physical effect indicating that galaxy morphology depends strongly on a second parameter which, it is suggested, is the velocity dispersion of a system. 21 references
The structure of compact groups a primer for the student, a handbook for the expert
Hofmann, Karl H
2013-01-01
Dealing with subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics, this book - now in its third revised and augmented edition - has been conceived with the dual purpose of providing a text book for upper level graduate courses or seminars, and of serving as a source book for research specialists who need to apply the structure and representation theory of compact groups. After a gentle introduction to compact groups and their representation theory, the book presents self-contained courses on linear Lie groups,
Cartan determinants, LIE algebra extensions, and the exceptional group series
International Nuclear Information System (INIS)
Capps, R.H.
1986-01-01
In this note the author utilizes the determinant of the generalized Cartan matrix for candidate Dynkin systems for two purposes. The first is to provide an uncomplicated criterion for classifying candidate one-root extensions of diagrams for semisimple Lie algebras. The second is to help determine some important properties of related Lie algebras and their representations
Photometric observations of nine Shakhbazian compact groups
International Nuclear Information System (INIS)
Tovmassian, H.M.; Tiersch, H.; Tovmassian, G.H.; Neizvestny, S.
2010-01-01
By observations with the 1.5m telescope at San Pedro Martir (OAN, UNAM, Mexico) the BVR magnitudes are determined for 66 member galaxies in Shakhbazian Compact Galaxy Groups ShCG 40, ShCG 176, ShCG 270, ShCG 278, ShCG 310 and ShCG 342. Three other groups were observed in two or only in one band. Seven galaxies in ShCG 298 were observed in B and R, six galaxies in ShCG 95 were observed in V and 7 galaxies in ShCG 345 were observed in V and R. The distribution of brightness of observed galaxies is determined. Signs of interaction between galaxies are detected in some groups
Lie Group Classifications and Non-differentiable Solutions for Time-Fractional Burgers Equation
International Nuclear Information System (INIS)
Wu Guocheng
2011-01-01
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Free Fermions and the Classical Compact Groups
Cunden, Fabio Deelan; Mezzadri, Francesco; O'Connell, Neil
2018-06-01
There is a close connection between the ground state of non-interacting fermions in a box with classical (absorbing, reflecting, and periodic) boundary conditions and the eigenvalue statistics of the classical compact groups. The associated determinantal point processes can be extended in two natural directions: (i) we consider the full family of admissible quantum boundary conditions (i.e., self-adjoint extensions) for the Laplacian on a bounded interval, and the corresponding projection correlation kernels; (ii) we construct the grand canonical extensions at finite temperature of the projection kernels, interpolating from Poisson to random matrix eigenvalue statistics. The scaling limits in the bulk and at the edges are studied in a unified framework, and the question of universality is addressed. Whether the finite temperature determinantal processes correspond to the eigenvalue statistics of some matrix models is, a priori, not obvious. We complete the picture by constructing a finite temperature extension of the Haar measure on the classical compact groups. The eigenvalue statistics of the resulting grand canonical matrix models (of random size) corresponds exactly to the grand canonical measure of free fermions with classical boundary conditions.
Free Fermions and the Classical Compact Groups
Cunden, Fabio Deelan; Mezzadri, Francesco; O'Connell, Neil
2018-04-01
There is a close connection between the ground state of non-interacting fermions in a box with classical (absorbing, reflecting, and periodic) boundary conditions and the eigenvalue statistics of the classical compact groups. The associated determinantal point processes can be extended in two natural directions: (i) we consider the full family of admissible quantum boundary conditions (i.e., self-adjoint extensions) for the Laplacian on a bounded interval, and the corresponding projection correlation kernels; (ii) we construct the grand canonical extensions at finite temperature of the projection kernels, interpolating from Poisson to random matrix eigenvalue statistics. The scaling limits in the bulk and at the edges are studied in a unified framework, and the question of universality is addressed. Whether the finite temperature determinantal processes correspond to the eigenvalue statistics of some matrix models is, a priori, not obvious. We complete the picture by constructing a finite temperature extension of the Haar measure on the classical compact groups. The eigenvalue statistics of the resulting grand canonical matrix models (of random size) corresponds exactly to the grand canonical measure of free fermions with classical boundary conditions.
Isometric coactions of compact quantum groups on compact ...
Indian Academy of Sciences (India)
a compact quantum metric space in the framework of Rieffel, where the ... This problem can be formulated and studied in various settings. ... The spaces we are interested in this paper are metric spaces, both classical and quantum. ... He has given a definition for a quantum symmetry of a classical ...... by the construction of I.
Dynamical properties of compact groups of galaxies
Hickson, Paul; De Oliveira, Claudia M.; Huchra, John P.; Palumbo, Giorgio G.
1992-01-01
Radial velocities are presented for 457 galaxies in the 100 Hickson compact groups. More than 84 percent of the galaxies measured have velocities within 1000 km/s of the median velocity in the group. Ninety-two groups have at least three accordant members, and 69 groups have at least four. The radial velocities of these groups range from 1380 to 42,731 km/s with a median of 8889 km/s, corresponding to a median distance of 89/h Mpc. The apparent space density of these systems ranges from 300 to as much as 10 exp 8 sq h/sq Mpc, which exceeds the densities in the centers of rich clusters. The median projected separation between galaxies is 39/h kpc, comparable to the sizes of the galaxies themselves. A significant correlation is found between crossing time and the fraction of gas-rich galaxies in the groups, and a weak anticorrelation is found between crossing time and the luminosity contrast of the first-ranked galaxy.
An Lp−Lq version of Hardy's theorem for spherical Fourier transform on semisimple Lie groups
Directory of Open Access Journals (Sweden)
S. Ben Farah
2004-01-01
Full Text Available We consider a real semisimple Lie group G with finite center and K a maximal compact subgroup of G. We prove an Lp−Lq version of Hardy's theorem for the spherical Fourier transform on G. More precisely, let a, b be positive real numbers, 1≤p, q≤∞, and f a K-bi-invariant measurable function on G such that ha−1f∈Lp(G and eb‖λ‖2ℱ(f∈Lq(+* (ha is the heat kernel on G. We establish that if ab≥1/4 and p or q is finite, then f=0 almost everywhere. If ab<1/4, we prove that for all p, q, there are infinitely many nonzero functions f and if ab=1/4 with p=q=∞, we have f=const ha.
Definably compact groups definable in real closed fields. I
Barriga, Eliana
2017-01-01
We study definably compact definably connected groups definable in a sufficiently saturated real closed field $R$. We introduce the notion of group-generic point for $\\bigvee$-definable groups and show the existence of group-generic points for definably compact groups definable in a sufficiently saturated o-minimal expansion of a real closed field. We use this notion along with some properties of generic sets to prove that for every definably compact definably connected group $G$ definable in...
6th Hilbert's problem and S.Lie's infinite groups
International Nuclear Information System (INIS)
Konopleva, N.P.
1999-01-01
The progress in Hilbert's sixth problem solving is demonstrated. That became possible thanks to the gauge field theory in physics and to the geometrical treatment of the gauge fields. It is shown that the fibre bundle spaces geometry is the best basis for solution of the problem being discussed. This talk has been reported at the International Seminar '100 Years after Sophus Lie' (Leipzig, Germany)
't Hooft's solution for arbitrary semisimple Lie group
International Nuclear Information System (INIS)
Leznov, A.N.; Mukhtarov, M.A.
1990-07-01
The generalization of the 't Hooft's A 1 solution for every semisimple Lie algebra is found. The solution depends on r-independent chains of linear self-dual systems (Δ s α ) z = (Δ s+1 α ) y -bar, (Δ s α ) y -bar = -(Δ s+1 α ) z (1 ≤ α ≤ r); the length of α chain is equal to 2ω α + 1, where ω α are the indexes of the semisimple algebra and r is its rank. In the special case the O(4)-invariant solutions with instanton number equal to one arises. (author). 6 refs
The Ultraviolet and Infrared Star Formation Rates of Compact Group Galaxies: An Expanded Sample
Lenkic, Laura; Tzanavaris, Panayiotis; Gallagher, Sarah C.; Desjardins, Tyler D.; Walker, Lisa May; Johnson, Kelsey E.; Fedotov, Konstantin; Charlton, Jane; Cardiff, Ann H.; Durell, Pat R.
2016-01-01
Compact groups of galaxies provide insight into the role of low-mass, dense environments in galaxy evolution because the low velocity dispersions and close proximity of galaxy members result in frequent interactions that take place over extended time-scales. We expand the census of star formation in compact group galaxies by Tzanavaris et al. (2010) and collaborators with Swift UVOT, Spitzer IRAC and MIPS 24 m photometry of a sample of 183 galaxies in 46 compact groups. After correcting luminosities for the contribution from old stellar populations, we estimate the dust-unobscured star formation rate (SFRUV) using the UVOT uvw2 photometry. Similarly, we use the MIPS 24 m photometry to estimate the component of the SFR that is obscured by dust (SFRIR). We find that galaxies which are MIR-active (MIR-red), also have bluer UV colours, higher specific SFRs, and tend to lie in Hi-rich groups, while galaxies that are MIR-inactive (MIR-blue) have redder UV colours, lower specific SFRs, and tend to lie in Hi-poor groups. We find the SFRs to be continuously distributed with a peak at about 1 M yr1, indicating this might be the most common value in compact groups. In contrast, the specific SFR distribution is bimodal, and there is a clear distinction between star-forming and quiescent galaxies. Overall, our results suggest that the specific SFR is the best tracer of gas depletion and galaxy evolution in compact groups.
Sobolev Spaces on Locally Compact Abelian Groups: Compact Embeddings and Local Spaces
Directory of Open Access Journals (Sweden)
Przemysław Górka
2014-01-01
Full Text Available We continue our research on Sobolev spaces on locally compact abelian (LCA groups motivated by our work on equations with infinitely many derivatives of interest for string theory and cosmology. In this paper, we focus on compact embedding results and we prove an analog for LCA groups of the classical Rellich lemma and of the Rellich-Kondrachov compactness theorem. Furthermore, we introduce Sobolev spaces on subsets of LCA groups and study its main properties, including the existence of compact embeddings into Lp-spaces.
Directory of Open Access Journals (Sweden)
Decio Levi
2013-10-01
Full Text Available We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which the “first differential approximation” is invariant under the same Lie group as the original ordinary differential equation.
International Nuclear Information System (INIS)
Dobrev, V.K.
1986-11-01
Let G be a real linear connected semisimple Lie group. We present a canonical construction of the differential operators intertwining elementary (≡ generalized principal series) representations of G. The results are easily extended to real linear reductive Lie groups. (author). 20 refs
An introduction to Lie groups and the geometry of homogeneous spaces
Arvanitoyeorgos, Andreas
2003-01-01
It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. In this way, he avoids the extra detail needed for a thorough discussion of other topics. Lie groups and homogeneous spaces are especially useful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. The book is suitable for advanced undergraduates, graduate students, and research mathematicians interested in differenti...
Algebras of Complete Hörmander Vector Fields, and Lie-Group Construction
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Andrea Bonfiglioli
2014-12-01
Full Text Available The aim of this note is to characterize the Lie algebras g of the analytic vector fields in RN which coincide with the Lie algebras of the (analytic Lie groups defined on RN (with its usual differentiable structure. We show that such a characterization amounts to asking that: (i g is N-dimensional; (ii g admits a set of Lie generators which are complete vector fields; (iii g satisfies Hörmander’s rank condition. These conditions are necessary, sufficient and mutually independent. Our approach is constructive, in that for any such g we show how to construct a Lie group G = (RN, * whose Lie algebra is g. We do not make use of Lie’s Third Theorem, but we only exploit the Campbell-Baker-Hausdorff-Dynkin Theorem for ODE’s.
Where are compact groups in the local Universe?
Díaz-Giménez, Eugenia; Zandivarez, Ariel
2015-06-01
Aims: The purpose of this work is to perform a statistical analysis of the location of compact groups in the Universe from observational and semi-analytical points of view. Methods: We used the velocity-filtered compact group sample extracted from the Two Micron All Sky Survey for our analysis. We also used a new sample of galaxy groups identified in the 2M++ galaxy redshift catalogue as tracers of the large-scale structure. We defined a procedure to search in redshift space for compact groups that can be considered embedded in other overdense systems and applied this criterion to several possible combinations of different compact and galaxy group subsamples. We also performed similar analyses for simulated compact and galaxy groups identified in a 2M++ mock galaxy catalogue constructed from the Millennium Run Simulation I plus a semi-analytical model of galaxy formation. Results: We observed that only ~27% of the compact groups can be considered to be embedded in larger overdense systems, that is, most of the compact groups are more likely to be isolated systems. The embedded compact groups show statistically smaller sizes and brighter surface brightnesses than non-embedded systems. No evidence was found that embedded compact groups are more likely to inhabit galaxy groups with a given virial mass or with a particular dynamical state. We found very similar results when the analysis was performed using mock compact and galaxy groups. Based on the semi-analytical studies, we predict that 70% of the embedded compact groups probably are 3D physically dense systems. Finally, real space information allowed us to reveal the bimodal behaviour of the distribution of 3D minimum distances between compact and galaxy groups. Conclusions: The location of compact groups should be carefully taken into account when comparing properties of galaxies in environments that are a priori different. Appendices are available in electronic form at http://www.aanda.orgFull Tables B.1 and B.2
Global dimensions for Lie groups at level k and their conformally exceptional quantum subgroups
Coquereaux, Robert
2010-01-01
We obtain formulae giving global dimensions for fusion categories defined by Lie groups G at level k and for the associated module-categories obtained via conformal embeddings. The results can be expressed in terms of Lie quantum superfactorials of type G. The later are related, for the type Ar, to the quantum Barnes function.
Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups
DEFF Research Database (Denmark)
Hilgert, Joachim; Kobayashi, Toshiyuki; Möllers, Jan
2012-01-01
For any Hermitian Lie group G of tube type we construct a Fock model of its minimal representation. The Fock space is defined on the minimal nilpotent K_C-orbit X in p_C and the L^2-inner product involves a K-Bessel function as density. Here K is a maximal compact subgroup of G, and g......_C=k_C+p_C is a complexified Cartan decomposition. In this realization the space of k-finite vectors consists of holomorphic polynomials on X. The reproducing kernel of the Fock space is calculated explicitly in terms of an I-Bessel function. We further find an explicit formula of a generalized Segal-Bargmann transform which...... intertwines the Schroedinger and Fock model. Its kernel involves the same I-Bessel function. Using the Segal--Bargmann transform we also determine the integral kernel of the unitary inversion operator in the Schroedinger model which is given by a J-Bessel function....
A decomposition theorem for compact groups with an application to supercompactness
Czech Academy of Sciences Publication Activity Database
Kubiś, Wieslaw; Turek, S.
2011-01-01
Roč. 9, č. 3 (2011), s. 593-602 ISSN 1895-1074 R&D Projects: GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : Simple compact Lie group * Supercompact space Subject RIV: BA - General Mathematics Impact factor: 0.440, year: 2011 http://www.springerlink.com/content/h86v44387542637r/
International Nuclear Information System (INIS)
Zhi Hongyan
2009-01-01
In this paper, based on the symbolic computing system Maple, the direct method for Lie symmetry groups presented by Sen-Yue Lou [J. Phys. A: Math. Gen. 38 (2005) L129] is extended from the continuous differential equations to the differential-difference equations. With the extended method, we study the well-known differential-difference KP equation, KZ equation and (2+1)-dimensional ANNV system, and both the Lie point symmetry groups and the non-Lie symmetry groups are obtained.
The Exceptional Lie symmetry groups hierarchy and the expected number of Higgs bosons
International Nuclear Information System (INIS)
El Naschie, M.S.
2008-01-01
New insights into the structure of various exceptional Lie symmetry groups hierarchies are utilized to shed light on various problems pertinent to the standard model of high energy physics and the Higgs
Smooth vectors and Weyl-Pedersen calculus for representations of nilpotent Lie groups
Beltita, Ingrid; Beltita, Daniel
2009-01-01
We present some recent results on smooth vectors for unitary irreducible representations of nilpotent Lie groups. Applications to the Weyl-Pedersen calculus of pseudo-differential operators with symbols on the coadjoint orbits are also discussed.
On the Chabauty space of locally compact abelian groups
Cornulier, Yves
2010-01-01
This paper contains several results about the Chabauty space of a general locally compact abelian group. Notably, we determine its topological dimension, we characterize when it is totally disconnected or connected; we characterize isolated points.
Fourier-like frames on locally compact abelian groups
DEFF Research Database (Denmark)
Christensen, Ole; Goh, Say Song
2015-01-01
We consider a class of functions, defined on a locally compact abelian group by letting a class of modulation operators act on a countable collection of functions. We derive sufficient conditions for such a class of functions to form a Bessel sequence or a frame and for two such systems to be dual...... frames. Explicit constructions are obtained via various generalizations of the classical B-splines to the setting of locally compact abelian groups. (C) 2014 Elsevier Inc. All rights reserved....
Sweet, Monica A; Heyman, Gail D; Fu, Genyue; Lee, Kang
2010-07-01
This study explored the effects of collectivism on lying to conceal a group transgression. Seven-, 9-, and 11-year-old US and Chinese children (N = 374) were asked to evaluate stories in which protagonists either lied or told the truth about their group's transgression and were then asked about either the protagonist's motivations or justification for their own evaluations. Previous research suggests that children in collectivist societies such as China find lying for one's group to be more acceptable than do children from individualistic societies such as the United States. The current study provides evidence that this is not always the case: Chinese children in this study viewed lies told to conceal a group's transgressions less favourably than did US children. An examination of children's reasoning about protagonists' motivations for lying indicated that children in both countries focused on an impact to self when discussing motivations for protagonists to lie for their group. Overall, results suggest that children living in collectivist societies do not always focus on the needs of the group.
Definably compact groups definable in real closed fields.II
Barriga, Eliana
2017-01-01
We continue the analysis of definably compact groups definable in a real closed field $\\mathcal{R}$. In [3], we proved that for every definably compact definably connected semialgebraic group $G$ over $\\mathcal{R}$ there are a connected $R$-algebraic group $H$, a definable injective map $\\phi$ from a generic definable neighborhood of the identity of $G$ into the group $H\\left(R\\right)$ of $R$-points of $H$ such that $\\phi$ acts as a group homomorphism inside its domain. The above result and o...
Algebras of functions on compact quantum groups, Schubert cells and quantum tori
International Nuclear Information System (INIS)
Levendorskij, S.; Soibelman, Ya.
1991-01-01
The structure of Poisson Lie groups on a simple compact group are parametrized by pairs (a, u), where aelement ofR, uelement ofΛ 2 f R , and f R is a real Cartan subalgebra of complexification of Lie algebra of the group in question. In the present article the description of the symplectic leaves for all pairs (a, u) is given. Also, the corresponding quantized algebras of functions are constructed and their irreducible representations are described. In the course of investigation Schubert cells and quantum tori appear. At the end of the article the quantum analog of the Weyl group is constructed and some of its applications, among them the formula for the universal R-matrix, are given. (orig.)
Lie group classification and exact solutions of the generalized Kompaneets equations
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Oleksii Patsiuk
2015-04-01
Full Text Available We study generalized Kompaneets equations (GKEs with one functional parameter, and using the Lie-Ovsiannikov algorithm, we carried out the group classification. It is shown that the kernel algebra of the full groups of the GKEs is the one-dimensional Lie algebra. Using the direct method, we find the equivalence group. We obtain six non-equivalent (up to transformations from the equivalence group GKEs that allow wider invariance algebras than the kernel one. We find a number of exact solutions of the non-linear GKE which has the maximal symmetry properties.
Non-coboundary Poisson–Lie structures on the book group
International Nuclear Information System (INIS)
Ballesteros, Ángel; Blasco, Alfonso; Musso, Fabio
2012-01-01
All possible Poisson–Lie (PL) structures on the 3D real Lie group generated by a dilation and two commuting translations are obtained. Their classification is fully performed by relating these PL groups to the corresponding Lie bialgebra structures on the corresponding ‘book’ Lie algebra. By construction, all these Poisson structures are quadratic Poisson–Hopf algebras for which the group multiplication is a Poisson map. In contrast to the case of simple Lie groups, it turns out that most of the PL structures on the book group are non-coboundary ones. Moreover, from the viewpoint of Poisson dynamics, the most interesting PL book structures are just some of these non-coboundaries, which are explicitly analysed. In particular, we show that the two different q-deformed Poisson versions of the sl(2, R) algebra appear as two distinguished cases in this classification, as well as the quadratic Poisson structure that underlies the integrability of a large class of 3D Lotka–Volterra equations. Finally, the quantization problem for these PL groups is sketched. (paper)
Continuous bounded cohomology of locally compact groups
2001-01-01
Recent research has repeatedly led to connections between important rigidity questions and bounded cohomology. However, the latter has remained by and large intractable. This monograph introduces the functorial study of the continuous bounded cohomology for topological groups, with coefficients in Banach modules. The powerful techniques of this more general theory have successfully solved a number of the original problems in bounded cohomology. As applications, one obtains, in particular, rigidity results for actions on the circle, for representations on complex hyperbolic spaces and on Teichmüller spaces. A special effort has been made to provide detailed proofs or references in quite some generality.
Limits of commutative triangular systems on locally compact groups
Indian Academy of Sciences (India)
Commutative triangular systems of probability measures on locally compact groups have been studied extensively and ... in [S3,S4], we extend our earlier result to some particular triangular systems on algebraic groups. We also discuss ..... Now G can be embedded as a closed subgroup in. G2 ¼ G1=D and G0. 2 ¼ ًG0 آ ...
Non-Supramenable Groups Acting on Locally Compact Spaces
DEFF Research Database (Denmark)
Kellerhals, Julian; Monod, Nicolas; Rørdam, Mikael
2013-01-01
Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product $C^*$-algebras for non-supramenable groups. In particular, stable Kirchberg algebras in the UCT class are constructed using crossed ...
Invariance Lie algebra and group of the non relativistic hydrogen atom
International Nuclear Information System (INIS)
Decoster, Alain
1970-01-01
The first part of this work contains a general survey of the use of Lie groups and algebras in quantum mechanics, followed by an extensive description of tbe invariance algebra and invariance group of the non-relativistic hydrogen atom; the realization of this group discovered by FOCK is specially examined. The second part is a two-hundred items bibliography on invariance groups and algebras of classical and quantum-mechanical simple systems. (author) [fr
Mapping Spaces, Centralizers, and p-Local Finite Groups of Lie Type
DEFF Research Database (Denmark)
Laude, Isabelle
We study the space of maps from the classifying space of a finite p-group to theBorel construction of a finite group of Lie type G in characteristic p acting on itsbuilding. The first main result is a description of the homology with Fp-coefficients,showing that the mapping space, up to p...... between a finite p-group and theuncompleted classifying space of the p-local finite group coming from a finite groupof Lie type in characteristic p, providing some of the first results in this uncompletedsetting.......-completion, is a disjoint union indexedover the group homomorphism up to conjugation of classifying spaces of centralizersof p-subgroups in the underlying group G. We complement this description bydetermining the actual homotopy groups of the mapping space. These resultstranslate to descriptions of the space of maps...
GLOBAL PROPERTIES OF NEUTRAL HYDROGEN IN COMPACT GROUPS
Energy Technology Data Exchange (ETDEWEB)
Walker, Lisa May [Steward Observatory, University of Arizona, Tucson, AZ 85721 (United States); Johnson, Kelsey E. [Department of Astronomy, University of Virginia, Charlottesville, VA 22904 (United States); Gallagher, Sarah C. [Department of Physics and Astronomy, University of Western Ontario, London, ON (Canada); Privon, George C. [Departamento de Astronomía, Universidad de Concepción, Concepción (Chile); Kepley, Amanda A. [National Radio Astronomy Observatory, Charlottesville, VA 22903 (United States); Whelan, David G. [Physics Department, Austin College, Sherman, TX 75090 (United States); Desjardins, Tyler D. [Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045 (United States); Zabludoff, Ann I. [Department of Astronomy and Steward Observatory, University of Arizona, Tucson, AZ 85721 (United States)
2016-02-15
Compact groups of galaxies provide a unique environment to study the evolution of galaxies amid frequent gravitational encounters. These nearby groups have conditions similar to those in the earlier universe when galaxies were assembled and give us the opportunity to witness hierarchical formation in progress. To understand how the compact group environment affects galaxy evolution, we examine the gas and dust in these groups. We present new single-dish GBT neutral hydrogen (H i) observations of 30 compact groups and define a new way to quantify the group H i content as the H i-to-stellar mass ratio of the group as a whole. We compare the H i content with mid-IR indicators of star formation and optical [g − r] color to search for correlations between group gas content and star formation activity of individual group members. Quiescent galaxies tend to live in H i-poor groups, and galaxies with active star formation are more commonly found in H i-rich groups. Intriguingly, we also find “rogue” galaxies whose star formation does not correlate with group H i content. In particular, we identify three galaxies (NGC 2968 in RSCG 34, KUG 1131+202A in RSCG 42, and NGC 4613 in RSCG 64) whose mid-IR activity is discrepant with the H i. We speculate that this mismatch between mid-IR activity and H i content is a consequence of strong interactions in this environment that can strip H i from galaxies and abruptly affect star formation. Ultimately, characterizing how and on what timescales the gas is processed in compact groups will help us understand the interstellar medium in complex, dense environments similar to the earlier universe.
GLOBAL PROPERTIES OF NEUTRAL HYDROGEN IN COMPACT GROUPS
International Nuclear Information System (INIS)
Walker, Lisa May; Johnson, Kelsey E.; Gallagher, Sarah C.; Privon, George C.; Kepley, Amanda A.; Whelan, David G.; Desjardins, Tyler D.; Zabludoff, Ann I.
2016-01-01
Compact groups of galaxies provide a unique environment to study the evolution of galaxies amid frequent gravitational encounters. These nearby groups have conditions similar to those in the earlier universe when galaxies were assembled and give us the opportunity to witness hierarchical formation in progress. To understand how the compact group environment affects galaxy evolution, we examine the gas and dust in these groups. We present new single-dish GBT neutral hydrogen (H i) observations of 30 compact groups and define a new way to quantify the group H i content as the H i-to-stellar mass ratio of the group as a whole. We compare the H i content with mid-IR indicators of star formation and optical [g − r] color to search for correlations between group gas content and star formation activity of individual group members. Quiescent galaxies tend to live in H i-poor groups, and galaxies with active star formation are more commonly found in H i-rich groups. Intriguingly, we also find “rogue” galaxies whose star formation does not correlate with group H i content. In particular, we identify three galaxies (NGC 2968 in RSCG 34, KUG 1131+202A in RSCG 42, and NGC 4613 in RSCG 64) whose mid-IR activity is discrepant with the H i. We speculate that this mismatch between mid-IR activity and H i content is a consequence of strong interactions in this environment that can strip H i from galaxies and abruptly affect star formation. Ultimately, characterizing how and on what timescales the gas is processed in compact groups will help us understand the interstellar medium in complex, dense environments similar to the earlier universe
Global solvability of the differential operators non-invariants on semi-simple Lie groups
International Nuclear Information System (INIS)
El Hussein, K.
1991-09-01
Let G be a connected semi-simple Lie group with finite centre and let G=KAN be the Iwasawa decomposition of G. Let P be a differential operator on G, which is right invariant by the sub-group AN and left invariant by the sub-group K. In this paper, we give a necessary and sufficient condition for the global solvability of P on G. (author). 5 refs
Bismut's way of the Malliavin calculus for large order generators on a Lie group
Léandre, Rémi
2018-01-01
We adapt Bismut's mechanism of the Malliavin Calculus to right invariant big order generator on a Lie group. We use deeply the symmetry in order to avoid the use of the Malliavin matrix. As an application, we deduce logarithmic estimates in small time of the heat kernel.
A density matrix renormalization group study of low-lying excitations ...
Indian Academy of Sciences (India)
Symmetrized density-matrix-renormalization-group calculations have been carried out, within Pariser-Parr-Pople Hamiltonian, to explore the nature of the ground and low-lying excited states of long polythiophene oligomers. We have exploited 2 symmetry and spin parity of the system to obtain excited states of ...
Control Algorithms Along Relative Equilibria of Underactuated Lagrangian Systems on Lie Groups
DEFF Research Database (Denmark)
Nordkvist, Nikolaj; Bullo, F.
2008-01-01
We present novel algorithms to control underactuated mechanical systems. For a class of invariant systems on Lie groups, we design iterative small-amplitude control forces to accelerate along, decelerate along, and stabilize relative equilibria. The technical approach is based upon a perturbation...
Control algorithms along relative equilibria of underactuated Lagrangian systems on Lie groups
DEFF Research Database (Denmark)
Nordkvist, Nikolaj; Bullo, Francesco
2007-01-01
We present novel algorithms to control underactuated mechanical systems. For a class of invariant systems on Lie groups, we design iterative small-amplitude control forces to accelerate along, decelerate along, and stabilize relative equilibria. The technical approach is based upon a perturbation...
Introduction to compact (matrix) quantum groups and Banica ...
Indian Academy of Sciences (India)
Moritz Weber
2017-11-27
Nov 27, 2017 ... Building on this, we define Banica–Speicher quantum .... four vertices) are ... A compact Hausdorff space X gives rise to a commutative unitalC .... (a) Recall the construction of the group C ..... Having formulated the features of the Haar integration in 'quantum terms', ...... paper: When is the map in [30, Prop.
Modulus of smoothness and theorems concerning approximation on compact groups
Directory of Open Access Journals (Sweden)
H. Vaezi
2003-01-01
Full Text Available We consider the generalized shift operator defined by (Shuf(g=∫Gf(tut−1gdt on a compact group G, and by using this operator, we define spherical modulus of smoothness. So, we prove Stechkin and Jackson-type theorems.
Little strings, quasi-topological sigma model on loop group, and toroidal Lie algebras
Ashwinkumar, Meer; Cao, Jingnan; Luo, Yuan; Tan, Meng-Chwan; Zhao, Qin
2018-03-01
We study the ground states and left-excited states of the Ak-1 N = (2 , 0) little string theory. Via a theorem by Atiyah [1], these sectors can be captured by a supersymmetric nonlinear sigma model on CP1 with target space the based loop group of SU (k). The ground states, described by L2-cohomology classes, form modules over an affine Lie algebra, while the left-excited states, described by chiral differential operators, form modules over a toroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPS sectors of the M5-brane worldvolume theory.
Little strings, quasi-topological sigma model on loop group, and toroidal Lie algebras
Directory of Open Access Journals (Sweden)
Meer Ashwinkumar
2018-03-01
Full Text Available We study the ground states and left-excited states of the Ak−1 N=(2,0 little string theory. Via a theorem by Atiyah [1], these sectors can be captured by a supersymmetric nonlinear sigma model on CP1 with target space the based loop group of SU(k. The ground states, described by L2-cohomology classes, form modules over an affine Lie algebra, while the left-excited states, described by chiral differential operators, form modules over a toroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPS sectors of the M5-brane worldvolume theory.
International Nuclear Information System (INIS)
Ton-That, Tuong
2005-01-01
In a previous paper we gave a generalization of the notion of Casimir invariant differential operators for the infinite-dimensional Lie groups GL ∞ (C) (or equivalently, for its Lie algebra gj ∞ (C)). In this paper we give a generalization of the Casimir invariant differential operators for a class of infinite-dimensional Lie groups (or equivalently, for their Lie algebras) which contains the infinite-dimensional complex classical groups. These infinite-dimensional Lie groups, and their Lie algebras, are inductive limits of finite-dimensional Lie groups, and their Lie algebras, with some additional properties. These groups or their Lie algebras act via the generalized adjoint representations on projective limits of certain chains of vector spaces of universal enveloping algebras. Then the generalized Casimir operators are the invariants of the generalized adjoint representations. In order to be able to explicitly compute the Casimir operators one needs a basis for the universal enveloping algebra of a Lie algebra. The Poincare-Birkhoff-Witt (PBW) theorem gives an explicit construction of such a basis. Thus in the first part of this paper we give a generalization of the PBW theorem for inductive limits of Lie algebras. In the last part of this paper a generalization of the very important theorem in representation theory, namely the Chevalley-Racah theorem, is also discussed
Jacobson, Nathan
1979-01-01
Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses.Chapter I introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Carlan's criterion and its
Bounds on the number of possible Higgs particles using grand unification and exceptional Lie groups
International Nuclear Information System (INIS)
El Naschie, M.S.
2008-01-01
The total sum of dimensions of a magnum exceptional Lie symmetry groups hierarchy is 4α-bar o =(4)(137+k o )≅548. Dividing this value among the various quantum fields leads to the possibility of an eight degrees of freedom Higgs field. However analyzing the same situation using sub groups of the largest exceptional Lie group leads to the conclusion that we are likely to find three Higgs particles only at the energy scale of the standard model. Consequently five of the eight degrees of freedom are unlikely to materialize as particles at this particular energy scale. This conclusion is reinforced by an entirely different approach based on grand unification analysis which excludes any grand unification using 4HD, i.e. four Higgs doublets. This leaves us with one, two and three Higgs doublets. Noting that a super symmetric standard model with two Higgs doublets gives almost perfect grand unification and that the result agrees with our exceptional Lie symmetry groups analysis, we exclude everything else. The final result is that we expect to find at least three more Higgs particles leading to a total of 66 elementary particles while at a somewhat higher energy, the expected number of 69 particles found using E-infinity theory is obtained
Quantum spaces, central extensions of Lie groups and related quantum field theories
Poulain, Timothé; Wallet, Jean-Christophe
2018-02-01
Quantum spaces with su(2) noncommutativity can be modelled by using a family of SO(3)-equivariant differential *-representations. The quantization maps are determined from the combination of the Wigner theorem for SU(2) with the polar decomposition of the quantized plane waves. A tracial star-product, equivalent to the Kontsevich product for the Poisson manifold dual to su(2) is obtained from a subfamily of differential *-representations. Noncommutative (scalar) field theories free from UV/IR mixing and whose commutative limit coincides with the usual ϕ 4 theory on ℛ3 are presented. A generalization of the construction to semi-simple possibly non simply connected Lie groups based on their central extensions by suitable abelian Lie groups is discussed. Based on a talk presented by Poulain T at the XXVth International Conference on Integrable Systems and Quantum symmetries (ISQS-25), Prague, June 6-10 2017.
Path integral quantization of the Symplectic Leaves of the SU(2)*Poisson-Lie Group
International Nuclear Information System (INIS)
Morariu, B.
1997-01-01
The Feynman path integral is used to quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of Uq(su(2)). This is achieved by finding explicit Darboux coordinates and then using a phase space path integral. I discuss the *-structure of SU(2)* and give a detailed description of its leaves using various parameterizations and also compare the results with the path integral quantization of spin
Lie Group Classification of a Generalized Lane-Emden Type System in Two Dimensions
Directory of Open Access Journals (Sweden)
Motlatsi Molati
2012-01-01
Full Text Available The aim of this work is to perform a complete Lie symmetry classification of a generalized Lane-Emden type system in two dimensions which models many physical phenomena in biological and physical sciences. The classical approach of group classification is employed for classification. We show that several cases arise in classifying the arbitrary parameters, the forms of which include amongst others the power law nonlinearity, and exponential and quadratic forms.
Analytic vectors and irreducible representations of nilpotent Lie groups and algebras
International Nuclear Information System (INIS)
Arnal, D.
1978-01-01
Let U be a unitary irreducible locally faithful representation of a nilpotent Lie group G, V the universal enveloping algebra of G, M a simple module on V with kernel ker dU, then there exists an automorphism of V keeping ker dU invariant such that, after transport of structure, M is isomorphic to a submodule of the space of analytic vectors for U. (Auth.)
International Nuclear Information System (INIS)
Berezin, F.A.
1977-01-01
Generalization of the Laplace-Casimir operator theory on the Lie supergroups is considered. The main result is the formula for radial parts of the Laplace operators under some general assumptions about the Lie supergroup. In particular these assumptions are valid for the Lie suppergroups U(p,g) and C (m,n). The first one is the analogue of the unitary group, the second one is the analogue of the linear group of canonical transformations
International Nuclear Information System (INIS)
Bonora, Loriano; Bytsenko, Andrey; Elizalde, Emilio
2012-01-01
This review paper contains a concise introduction to highest weight representations of infinite-dimensional Lie algebras, vertex operator algebras and Hilbert schemes of points, together with their physical applications to elliptic genera of superconformal quantum mechanics and superstring models. The common link of all these concepts and of the many examples considered in this paper is to be found in a very important feature of the theory of infinite-dimensional Lie algebras: the modular properties of the characters (generating functions) of certain representations. The characters of the highest weight modules represent the holomorphic parts of the partition functions on the torus for the corresponding conformal field theories. We discuss the role of the unimodular (and modular) groups and the (Selberg-type) Ruelle spectral functions of hyperbolic geometry in the calculation of elliptic genera and associated q-series. For mathematicians, elliptic genera are commonly associated with new mathematical invariants for spaces, while for physicists elliptic genera are one-loop string partition function. (Therefore, they are applicable, for instance, to topological Casimir effect calculations.) We show that elliptic genera can be conveniently transformed into product expressions, which can then inherit the homology properties of appropriate polygraded Lie algebras. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (review)
Unipotent and nilpotent classes in simple algebraic groups and lie algebras
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...
Symmetry breaking in fluid dynamics: Lie group reducible motions for real fluids
International Nuclear Information System (INIS)
Holm, D.D.
1976-07-01
The physics of fluids is based on certain kinematical invariance principles, which refer to coordinate systems, dimensions, and Galilean reference frames. Other, thermodynamic, symmetry principles are introduced by the material description. In the present work, the interplay between these two kinds of invariance principles is used to solve for classes of one-dimensional non-steady isentropic motions of a fluid whose equation of state is of Mie-Gruneisen type. Also, the change in profile and attenuation of weak shock waves in a dissipative medium is studied at the level of Burgers' approximation from the viewpoint of its underlying symmetry structure. The mathematical method of approach is based on the theory of infinitesimal Lie groups. Fluid motions are characterized according to inequivalent subgroups of the full invariance group of the flow description and exact group reducible solutions are presented
Applications of Lie Group Theory to the Modeling and Control of Multibody Systems
International Nuclear Information System (INIS)
Mladenova, Clementina D.
1999-01-01
This paper reviews our research activities concerning the modeling and control of rigid and elastic joint multibody mechanical systems, including some investigations into nonholonomic systems. Bearing in mind the different parameterizations of the rotation group in three-dimensional space SO(3), and the fact that the properties of the parameterization more or less influence the efficiency of the dynamics model, here the so-called vector parameter is used for parallel considerations of rigid body motion and of rigid and elastic joint multibody mechanical systems. Besides the fundamental role of this study, the vector-parameter approach is efficient in its computational aspect and quite convenient for real time simulation and control. The consideration of the mechanical system on the configuration space of pure vector parameters with a group structure opens the possibilities for the Lie group theory to be applied in problems of dynamics and control
Symmetry breaking in fluid dynamics: Lie group reducible motions for real fluids
Energy Technology Data Exchange (ETDEWEB)
Holm, D.D.
1976-07-01
The physics of fluids is based on certain kinematical invariance principles, which refer to coordinate systems, dimensions, and Galilean reference frames. Other, thermodynamic, symmetry principles are introduced by the material description. In the present work, the interplay between these two kinds of invariance principles is used to solve for classes of one-dimensional non-steady isentropic motions of a fluid whose equation of state is of Mie-Gruneisen type. Also, the change in profile and attenuation of weak shock waves in a dissipative medium is studied at the level of Burgers' approximation from the viewpoint of its underlying symmetry structure. The mathematical method of approach is based on the theory of infinitesimal Lie groups. Fluid motions are characterized according to inequivalent subgroups of the full invariance group of the flow description and exact group reducible solutions are presented.
Directory of Open Access Journals (Sweden)
Kalidas Das
2018-03-01
Full Text Available The temperament of stream characteristic, heat and mass transfer of MHD forced convective flow over a linearly expanding porous medium has been scrutinized in the progress exploration. The germane possessions of the liquid like viscosity along with thermal conductivity are believed to be variable in nature, directly influenced by the temperature of flow. As soon as gaining the system of leading equations of the stream, Lie symmetric group transformations have been employed to come across the fitting parallel conversions to alter the central PDEs into a suit of ODEs. The renovated system of ODE with appropriate boundary conditions is numerically solved with the assistance of illustrative software MAPLE 17. The consequences of the relevant factors of the system have been exemplified through charts and graphs. An analogous qualified survey has been prepared among present inquiry and subsisting reads and achieved an admirable accord between them. The variable viscosity parameter has more significant effect on nanofluid velocity than regular fluid and temporal profile as well as nanoparticle concentration is also influenced with variable viscosity. Keywords: Nanofluid, Stretching sheet, Variable viscosity, Variable thermal conductivity, Lie symmetry group
Tsao, Thomas R.; Tsao, Doris
1997-04-01
In the 1980's, neurobiologist suggested a simple mechanism in primate visual cortex for maintaining a stable and invariant representation of a moving object. The receptive field of visual neurons has real-time transforms in response to motion, to maintain a stable representation. When the visual stimulus is changed due to motion, the geometric transform of the stimulus triggers a dual transform of the receptive field. This dual transform in the receptive fields compensates geometric variation in the stimulus. This process can be modelled using a Lie group method. The massive array of affine parameter sensing circuits will function as a smart sensor tightly coupled to the passive imaging sensor (retina). Neural geometric engine is a neuromorphic computing device simulating our Lie group model of spatial perception of primate's primal visual cortex. We have developed the computer simulation and experimented on realistic and synthetic image data, and performed a preliminary research of using analog VLSI technology for implementation of the neural geometric engine. We have benchmark tested on DMA's terrain data with their result and have built an analog integrated circuit to verify the computational structure of the engine. When fully implemented on ANALOG VLSI chip, we will be able to accurately reconstruct a 3D terrain surface in real-time from stereoscopic imagery.
Knot wormholes and the dimensional invariant of exceptional Lie groups and Stein space hierarchies
International Nuclear Information System (INIS)
Elokaby, Ayman
2009-01-01
The present short note points out a most interesting and quite unexpected connection between the number of distinct knot as a function of their crossing number and exceptional Lie groups and Stein space hierarchies. It is found that the crossing number 7 plays the role of threshold similar to 4 and 5 in E-infinity theory and for the 11 crossing the number of distinct knots is very close to 4α-bar 0 +1=548+1=549, where α-bar 0 =137 is the inverse integer electromagnetic fine structure constant. This is particularly intriguing in view of a similar relation pertinent to the 17 two and three Stein spaces where the total dimension is Σ 1 17 Stein=5α-bar 0 +1=685+1=686, as well as the sum of the eight exceptional Lie symmetry groups Σ i=1 8 |E i |=4α-bar 0 =548. The slight discrepancy of one is explained in both cases by the inclusion of El Naschie's transfinite corrections leading to Σ i=1 8 |E i |=(4)(137+k 0 )=548.328157 and Σ i=1 17 Stein=(5)(137+k 0 )=685.41097, where k o = φ 5 (1 - φ 5 ) and φ=(√(5)-1)/2.
ENHANCED WARM H2 EMISSION IN THE COMPACT GROUP MID-INFRARED ''GREEN VALLEY''
International Nuclear Information System (INIS)
Cluver, M. E.; Ogle, P.; Guillard, P.; Appleton, P. N.; Jarrett, T. H.; Rasmussen, J.; Lisenfeld, U.; Verdes-Montenegro, L.; Antonucci, R.; Bitsakis, T.; Charmandaris, V.; Boulanger, F.; Egami, E.; Xu, C. K.; Yun, M. S.
2013-01-01
We present results from a Spitzer mid-infrared spectroscopy study of a sample of 74 galaxies located in 23 Hickson Compact Groups (HCGs), chosen to be at a dynamically active stage of H I depletion. We find evidence for enhanced warm H 2 emission (i.e., above that associated with UV excitation in star-forming regions) in 14 galaxies (∼20%), with 8 galaxies having extreme values of L(H 2 S(0)-S(3))/L(7.7 μm polycyclic aromatic hydrocarbon), in excess of 0.07. Such emission has been seen previously in the compact group HCG 92 (Stephan's Quintet), and was shown to be associated with the dissipation of mechanical energy associated with a large-scale shock caused when one group member collided, at high velocity, with tidal debris in the intragroup medium. Similarly, shock excitation or turbulent heating is likely responsible for the enhanced H 2 emission in the compact group galaxies, since other sources of heating (UV or X-ray excitation from star formation or active galactic nuclei) are insufficient to account for the observed emission. The group galaxies fall predominantly in a region of mid-infrared color-color space identified by previous studies as being connected to rapid transformations in HCG galaxy evolution. Furthermore, the majority of H 2 -enhanced galaxies lie in the optical ''green valley'' between the blue cloud and red sequence, and are primarily early-type disk systems. We suggest that H 2 -enhanced systems may represent a specific phase in the evolution of galaxies in dense environments and provide new insight into mechanisms which transform galaxies onto the optical red sequence.
On the Lie symmetry group for classical fields in noncommutative space
Energy Technology Data Exchange (ETDEWEB)
Pereira, Ricardo Martinho Lima Santiago [Universidade Federal da Bahia (UFBA), BA (Brazil); Instituto Federal da Bahia (IFBA), BA (Brazil); Ressureicao, Caio G. da [Universidade Federal da Bahia (UFBA), BA (Brazil). Inst. de Fisica; Vianna, Jose David M. [Universidade Federal da Bahia (UFBA), BA (Brazil); Universidade de Brasilia (UnB), DF (Brazil)
2011-07-01
Full text: An alternative way to include effects of noncommutative geometries in field theory is based on the concept of noncommutativity among degrees of freedom of the studied system. In this context it is reasonable to consider that, in the multiparticle noncommutative quantum mechanics (NCQM), the noncommutativity among degrees of freedom to discrete system with N particles is also verified. Further, an analysis of the classical limit of the single particle NCQM leads to a deformed Newtonian mechanics where the Newton's second law is modified in order to include the noncommutative parameter {theta}{sub {iota}j} and, for a one-dimensional discrete system with N particles, the dynamical evolution of each particle is given by this modified Newton's second law. Hence, applying the continuous limit to this multiparticle classical system it is possible to obtain a noncommutative extension of two -dimensional field theory in a noncommutative space. In the present communication we consider a noncommutative extension of the scalar field obtained from this approach and we analyze the Lie symmetries in order to compare the Lie group of this field with the usual scalar field in the commutative space. (author)
Gabor frames on locally compact abelian groups and related topics
DEFF Research Database (Denmark)
Jakobsen, Mads Sielemann
This thesis consists of four papers. The first one introduces generalized translation invariant systems and considers their frame properties, the second and third paper give new results on the theory of Gabor frames, and the fourth is a review paper with proofs and new results on the Feichtinger......- and shearlet-type and for (generalized) shift-invariant systems and their continuous formulations. This thesis advances the theory of both separable and non-separable, discrete, semicontinuous and continuous Gabor systems. In particular, the well established structure theory for separable lattice Gabor frames...... and Gabor Riesz bases. The theory of GTI systems and Gabor frames in this thesis is developed and presented in the setting of locally compact abelian groups, however, even in the euclidean setting the results given here improve the existing theory. Finally, the thesis contains a review paper with proofs...
Hierarchy of kissing numbers for exceptional Lie symmetry groups in high energy physics
International Nuclear Information System (INIS)
El Naschie, M.S.
2008-01-01
We are constructing a hierarchy of kissing numbers representing singular contact points of hyper-spheres in exceptional Lie symmetry groups lattice arrangement embedded in the 26 dimensional bosonic strings spacetime. That way we find a total number of points and dimensions equal to 548. This is 52 more than the order of E 8 E 8 of heterotic string theory and leads to the prediction of 69 elementary particles at an energy scale under 1 T. In other words, our mathematical model predicts nine more particles than what is currently experimentally known to exist in the standard model of high energy physics namely only 60. The result is thus in full agreement with all our previous theoretical findings
Bidirectional composition on lie groups for gradient-based image alignment.
Mégret, Rémi; Authesserre, Jean-Baptiste; Berthoumieu, Yannick
2010-09-01
In this paper, a new formulation based on bidirectional composition on Lie groups (BCL) for parametric gradient-based image alignment is presented. Contrary to the conventional approaches, the BCL method takes advantage of the gradients of both template and current image without combining them a priori. Based on this bidirectional formulation, two methods are proposed and their relationship with state-of-the-art gradient based approaches is fully discussed. The first one, i.e., the BCL method, relies on the compositional framework to provide the minimization of the compensated error with respect to an augmented parameter vector. The second one, the projected BCL (PBCL), corresponds to a close approximation of the BCL approach. A comparative study is carried out dealing with computational complexity, convergence rate and frequence of convergence. Numerical experiments using a conventional benchmark show the performance improvement especially for asymmetric levels of noise, which is also discussed from a theoretical point of view.
A Corresponding Lie Algebra of a Reductive homogeneous Group and Its Applications
International Nuclear Information System (INIS)
Zhang Yu-Feng; Rui Wen-Juan; Wu Li-Xin
2015-01-01
With the help of a Lie algebra of a reductive homogeneous space G/K, where G is a Lie group and K is a resulting isotropy group, we introduce a Lax pair for which an expanding (2+1)-dimensional integrable hierarchy is obtained by applying the binormial-residue representation (BRR) method, whose Hamiltonian structure is derived from the trace identity for deducing (2+1)-dimensional integrable hierarchies, which was proposed by Tu, et al. We further consider some reductions of the expanding integrable hierarchy obtained in the paper. The first reduction is just right the (2+1)-dimensional AKNS hierarchy, the second-type reduction reveals an integrable coupling of the (2+1)-dimensional AKNS equation (also called the Davey-Stewartson hierarchy), a kind of (2+1)-dimensional Schrödinger equation, which was once reobtained by Tu, Feng and Zhang. It is interesting that a new (2+1)-dimensional integrable nonlinear coupled equation is generated from the reduction of the part of the (2+1)-dimensional integrable coupling, which is further reduced to the standard (2+1)-dimensional diffusion equation along with a parameter. In addition, the well-known (1+1)-dimensional AKNS hierarchy, the (1+1)-dimensional nonlinear Schrödinger equation are all special cases of the (2+1)-dimensional expanding integrable hierarchy. Finally, we discuss a few discrete difference equations of the diffusion equation whose stabilities are analyzed by making use of the von Neumann condition and the Fourier method. Some numerical solutions of a special stationary initial value problem of the (2+1)-dimensional diffusion equation are obtained and the resulting convergence and estimation formula are investigated. (paper)
Koszul Information Geometry and Souriau Geometric Temperature/Capacity of Lie Group Thermodynamics
Directory of Open Access Journals (Sweden)
Frédéric Barbaresco
2014-08-01
Full Text Available The François Massieu 1869 idea to derive some mechanical and thermal properties of physical systems from “Characteristic Functions”, was developed by Gibbs and Duhem in thermodynamics with the concept of potentials, and introduced by Poincaré in probability. This paper deals with generalization of this Characteristic Function concept by Jean-Louis Koszul in Mathematics and by Jean-Marie Souriau in Statistical Physics. The Koszul-Vinberg Characteristic Function (KVCF on convex cones will be presented as cornerstone of “Information Geometry” theory, defining Koszul Entropy as Legendre transform of minus the logarithm of KVCF, and Fisher Information Metrics as hessian of these dual functions, invariant by their automorphisms. In parallel, Souriau has extended the Characteristic Function in Statistical Physics looking for other kinds of invariances through co-adjoint action of a group on its momentum space, defining physical observables like energy, heat and momentum as pure geometrical objects. In covariant Souriau model, Gibbs equilibriums states are indexed by a geometric parameter, the Geometric (Planck Temperature, with values in the Lie algebra of the dynamical Galileo/Poincaré groups, interpreted as a space-time vector, giving to the metric tensor a null Lie derivative. Fisher Information metric appears as the opposite of the derivative of Mean “Moment map” by geometric temperature, equivalent to a Geometric Capacity or Specific Heat. We will synthetize the analogies between both Koszul and Souriau models, and will reduce their definitions to the exclusive Cartan “Inner Product”. Interpreting Legendre transform as Fourier transform in (Min,+ algebra, we conclude with a definition of Entropy given by a relation mixing Fourier/Laplace transforms: Entropy = (minus Fourier(Min,+ o Log o Laplace(+,X.
International Nuclear Information System (INIS)
Kashaev, R.M.; Savel'ev, M.V.; Savel'eva, S.A.
1990-01-01
Nonlinear equations associated through a zero curvature type representation with Lie algebras S 0 Diff T 2 and of infinitesimal diffeomorphisms of (S 1 ) 2 , and also with a new infinite-dimensional Lie algebras. In particular, the general solution (in the sense of the Goursat problem) of the heavently equation which describes self-dual Einstein spaces with one rotational Killing symmetry is discussed, as well as the solutions to a generalized equation. The paper is supplied with Appendix containing the definition of the continuum graded Lie algebras and the general construction of the nonlinear equations associated with them. 11 refs
International Nuclear Information System (INIS)
Foroutan, A.
1992-05-01
The essential mathematical challenge in transport theory is based on the nonlinearity of the integro-differential equations governing classical thermodynamic systems on molecular kinetic level. It is the aim of this thesis to gain exact analytical solutions to the model Boltzmann equation suggested by Tjon and Wu. Such solutions afford a deeper insight into the dynamics of rarefied gases. Tjon and Wu have provided a stochastic model of a Boltzmann equation. Its transition probability depends only on the relative speed of the colliding particles. This assumption leads in the case of two translational degrees of freedom to an integro-differential equation of convolution type. According to this convolution structure the integro-differential equation is Laplace transformed. The result is a nonlinear partial differential equation. The investigation of the symmetries of this differential equation by means of Lie groups of transformation enables us to transform the originally nonlinear partial differential equation into ordinary differential equation into ordinary differential equations of Bernoulli type. (author)
Directory of Open Access Journals (Sweden)
Jen-Cheng Wang
Full Text Available Lie group analysis of the photo-induced fluorescence of Drosophila oogenesis with the asymmetrically localized Gurken protein has been performed systematically to assess the roles of ligand-receptor complexes in follicle cells. The (2×2 matrix representations resulting from the polarized tissue spectra were employed to characterize the asymmetrical Gurken distributions. It was found that the fluorescence of the wild-type egg shows the Lie point symmetry X 23 at early stages of oogenesis. However, due to the morphogen regulation by intracellular proteins and extracellular proteins, the fluorescence of the embryogenesis with asymmetrically localized Gurken expansions exhibits specific symmetry features: Lie point symmetry Z 1 and Lie point symmetry X 1. The novel approach developed herein was successfully used to validate that the invariant-theoretical characterizations are consonant with the observed asymmetric fluctuations during early embryological development.
Perturbative expansion of Chern-Simons theory with non-compact gauge group
International Nuclear Information System (INIS)
Bar-Natan, D.; Witten, E.
1991-01-01
Naive imitation of the usual formulas for compact gauge group in quantizing three dimensional Chern-Simons gauge theory with non-compact gauge group leads to formulas that are wrong or unilluminating. In this paper, an appropriate modification is described, which puts the perturbative expansion in a standard manifestly 'unitary' format. The one loop contributions (which differ from naive extrapolation from the case of compact gauge group) are computed, and their topological invariance is verified. (orig.)
Conditionally exponential convex functions on locally compact groups
International Nuclear Information System (INIS)
Okb El-Bab, A.S.
1992-09-01
The main results of the thesis are: 1) The construction of a compact base for the convex cone of all conditionally exponential convex functions. 2) The determination of the extreme parts of this cone. Some supplementary lemmas are proved for this purpose. (author). 8 refs
International Nuclear Information System (INIS)
Burde, G.I.
2002-01-01
A new approach to the use of the Lie group technique for partial and ordinary differential equations dependent on a small parameter is developed. In addition to determining approximate solutions to the perturbed equation, the approach allows constructing integrable equations that have solutions with (partially) prescribed features. Examples of application of the approach to partial differential equations are given
Directory of Open Access Journals (Sweden)
Frédéric Barbaresco
2016-11-01
Full Text Available We introduce the symplectic structure of information geometry based on Souriau’s Lie group thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical observables like energy, heat, and moment as pure geometrical objects. Using geometric Planck temperature of Souriau model and symplectic cocycle notion, the Fisher metric is identified as a Souriau geometric heat capacity. The Souriau model is based on affine representation of Lie group and Lie algebra that we compare with Koszul works on G/K homogeneous space and bijective correspondence between the set of G-invariant flat connections on G/K and the set of affine representations of the Lie algebra of G. In the framework of Lie group thermodynamics, an Euler-Poincaré equation is elaborated with respect to thermodynamic variables, and a new variational principal for thermodynamics is built through an invariant Poincaré-Cartan-Souriau integral. The Souriau-Fisher metric is linked to KKS (Kostant–Kirillov–Souriau 2-form that associates a canonical homogeneous symplectic manifold to the co-adjoint orbits. We apply this model in the framework of information geometry for the action of an affine group for exponential families, and provide some illustrations of use cases for multivariate gaussian densities. Information geometry is presented in the context of the seminal work of Fréchet and his Clairaut-Legendre equation. The Souriau model of statistical physics is validated as compatible with the Balian gauge model of thermodynamics. We recall the precursor work of Casalis on affine group invariance for natural exponential families.
International Nuclear Information System (INIS)
El Naschie, M.S.
2008-01-01
The short note gives a derivation for a new E12 exceptional Lie group corresponding to affine KAC-Moody algebra. We derive the dimension of the group by intersectionally embedding the intrinsic dimension of E8 namely D(E8) = 57 into the 12 spacetime dimensions of F theory and finding that Dim E12 = D(E8) (DF) + 1 = (57)(12) + 1 = 685
BRST-operator for quantum Lie algebra and differential calculus on quantum groups
International Nuclear Information System (INIS)
Isaev, A.P.; Ogievetskij, O.V.
2001-01-01
For A Hopf algebra one determined structure of differential complex in two dual external Hopf algebras: A external expansion and in A* dual algebra external expansion. The Heisenberg double of these two Hopf algebras governs the differential algebra for the Cartan differential calculus on A algebra. The forst differential complex is the analog of the de Rame complex. The second complex coincide with the standard complex. Differential is realized as (anti)commutator with Q BRST-operator. Paper contains recursion relation that determines unequivocally Q operator. For U q (gl(N)) Lie quantum algebra one constructed BRST- and anti-BRST-operators and formulated the theorem of the Hodge expansion [ru
IEA SHC Task 42 / ECES Annex 29 - Working Group B: Applications of Compact Thermal Energy Storage
Helden, W. van; Yamaha, M.; Rathgeber, C.; Hauer, A.; Huaylla, F.; Le Pierrès, N.; Stutz, B.; Mette, B.; Dolado, P.; Lazaro, A.; Mazo, J.; Dannemand, M.; Furbo, S.; Campos-Celador, A.; Diarce, G.; Cuypers, R.; König-Haagen, A.; Höhlein, S.; Brüggemann, D.; Fumey, B.; Weber, R.; Köll, R.; Wagner, W.; Daguenet-Frick, X.; Gantenbein, P.; Kuznik, F.
2016-01-01
The IEA joint Task 42 / Annex 29 is aimed at developing compact thermal energy storage materials and systems. In Working Group B, experts are working on the development of compact thermal energy storage applications, in the areas cooling, domestic heating and hot water and industry. The majority of
A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation
Somma, Rolando D.
2016-06-01
We present a product formula to approximate the exponential of a skew-Hermitian operator that is a sum of generators of a Lie algebra. The number of terms in the product depends on the structure factors. When the generators have large norm with respect to the dimension of the Lie algebra, or when the norm of the effective operator resulting from nested commutators is less than the product of the norms, the number of terms in the product is significantly less than that obtained from well-known results. We apply our results to construct product formulas useful for the quantum simulation of some continuous-variable and bosonic physical systems, including systems whose potential is not quadratic. For many of these systems, we show that the number of terms in the product can be sublinear or even subpolynomial in the dimension of the relevant local Hilbert spaces, where such a dimension is usually determined by the energy scale of the problem. Our results emphasize the power of quantum computers for the simulation of various quantum systems.
Compact groups of positive operators on Banach lattices
Jeu, de M.F.E.; Wortel, M.R.
2014-01-01
In this paper, we study groups of positive operators on Banach lattices. If a certain factorization property holds for the elements of such a group, the group has a homomorphic image in the isometric positive operators which has the same invariant ideals as the original group. If the group is
International Nuclear Information System (INIS)
Srihirun, B; Meleshko, S V; Schulz, E
2006-01-01
The definition of an admitted Lie group of transformations for stochastic differential equations has been already presented for equations with one-dimensional Brownian motion. The transformation of the dependent variables involves time as well, and it has been proven that Brownian motion is transformed to Brownian motion. In this paper, we will discuss this concept for stochastic differential equations involving multi-dimensional Brownian motion and present applications to a variety of stochastic differential equations
International Nuclear Information System (INIS)
Halpern, L.
1981-01-01
Invariant varieties of suitable semisimple groups of transformations can serve as models of the space-time of the universe. The metric is expressible in terms of the basis vectors of the group. The symmetry of the group is broken by introducing a gauge formalism in the space of the basis vectors with the adjoint group as gauge group. The gauge potentials are expressible in terms of the basis vectors for the case of the De Sitter group. The resulting gauge theory is equivalent to De Sitter covariant general relativity. Group covariant generalizations of gravitational theory are discussed. (Auth.)
International Nuclear Information System (INIS)
Steinberg, S.; Wolf, K.B.
1979-01-01
The authors study the construction and action of certain Lie algebras of second- and higher-order differential operators on spaces of solutions of well-known parabolic, hyperbolic and elliptic linear differential equations. The latter include the N-dimensional quadratic quantum Hamiltonian Schroedinger equations, the one-dimensional heat and wave equations and the two-dimensional Helmholtz equation. In one approach, the usual similarity first-order differential operator algebra of the equation is embedded in the larger one, which appears as a quantum-mechanical dynamic algebra. In a second approach, the new algebra is built as the time evolution of a finite-transformation algebra on the initial conditions. In a third approach, the algebra to inhomogeneous similarity algebra is deformed to a noncompact classical one. In every case, we can integrate the algebra to a Lie group of integral transforms acting effectively on the solution space of the differential equation. (author)
International Nuclear Information System (INIS)
Sheftel', M.B.
1997-01-01
The basics of modern group analysis of different equations are presented. The group analysis produces in a natural way the variables, which are most suitable for a problem of question, and also the associated differential-geometric structures, such as pseudo Riemann geometry, connections, Hamiltonian and Lagrangian formalism
On the structure of finite-sheeted coverings of compact connected groups
Grigorian, S. A.; Gumerov, R. N.
2004-01-01
Finite-sheeted covering mappings onto compact connected groups are studied. It is shown that a finite-sheeted covering mapping from a connected Hausdorff topological space onto a compact connected abelian group G must be a homeomorphism provided that the character group of G admits division by the degree of given covering mapping. Using this result, we obtain criteria of triviality for finite coverings of G in terms of its character group and means on G. In order to establish these facts, for...
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)
Lie groups and symmetric spaces in memory of F. I. Karpelevich
Gindikin, S G
2003-01-01
The book contains survey and research articles devoted mainly to geometry and harmonic analysis of symmetric spaces and to corresponding aspects of group representation theory. The volume is dedicated to the memory of Russian mathematician F. I. Karpelevich (1927-2000).
Lie group classification of first-order delay ordinary differential equations
Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel
2018-05-01
A group classification of first-order delay ordinary differential equations (DODEs) accompanied by an equation for the delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs), which consists of linear DODEs and solution-independent delay relations, have infinite-dimensional symmetry algebras—as do nonlinear ones that are linearizable by an invertible transformation of variables. Genuinely nonlinear DODSs have symmetry algebras of dimension n, . It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.
Long, Feng-Shan; Karnbanjong, Adisak; Suriyawichitseranee, Amornrat; Grigoriev, Yurii N.; Meleshko, Sergey V.
2017-07-01
This paper proposes an algorithm for group classification of a nonhomogeneous equation using the group analysis provided for the corresponding homogeneous equation. The approach is illustrated by a partial differential equation, an integro-differential equation, and a delay partial differential equation.
Hyperfunction solutions of the zero rest mass equations and representations of LIE groups
International Nuclear Information System (INIS)
Dunne, E.G.
1984-01-01
Recently, hyperfunctions have arisen in an essential way in separate results in mathematical physics and in representation theory. In the setting of the twistor program, Wells, with others, has extended the Penrose transform to hyperfunction solutions of the zero rest mass equations, showing that the fundamental isomorphisms hold for this larger space. Meanwhile, Schmid has shown the existence of a canonical globalization of a Harish-Chandra module, V, to a representation of the group. This maximal globalization may be realized as the completion of V in a locally convex vector space in the hyperfunction topology. This thesis shows that the former is a particular case of the latter where the globalization can be done by hand. This explicit globalization is then carried out for a more general case of the Radon transform on homogeneous spaces
A diagram approach to character formulae for finite and compact groups
International Nuclear Information System (INIS)
Kibler, M.; Elbaz, E.
1978-06-01
Some basic relations for the representation theory and the Wigner-Racah algebra of a finite or compact continuous group are discussed and transcribed in terms of diagrams. Special emphasis is placed on the case of a simply reducible group and all the diagrams are applicable to SU 2 without any change
EXAMINING THE ROLE OF ENVIRONMENT IN A COMPREHENSIVE SAMPLE OF COMPACT GROUPS
International Nuclear Information System (INIS)
Walker, Lisa May; Johnson, Kelsey E.; Gallagher, Sarah C.; Charlton, Jane C.; Hornschemeier, Ann E.; Hibbard, John E.
2012-01-01
Compact groups, with their high number densities, small velocity dispersions, and an interstellar medium that has not been fully processed, provide a local analog to conditions of galaxy interactions in the earlier universe. The frequent and prolonged gravitational encounters that occur in compact groups affect the evolution of the constituent galaxies in a myriad of ways, for example, gas processing and star formation. Recently, a statistically significant 'gap' has been discovered in the mid-infrared (MIR: 3.6-8 μm) IRAC color space of compact group galaxies. This gap is not seen in field samples and is a new example of how the compact group environment may affect the evolution of member galaxies. In order to investigate the origin and nature of this gap, we have compiled a larger sample of 37 compact groups in addition to the original 12 groups studied by Johnson et al. (yielding 174 individual galaxies with reliable MIR photometry). We find that a statistically significant deficit of galaxies in this gap region of IRAC color space is persistent in the full sample, lending support to the hypothesis that the compact group environment inhibits moderate specific star formation rates. Using this expanded sample, we have more fully characterized the distribution of galaxies in this color space and quantified the low-density region more fully with respect to MIR bluer and MIR redder colors. We note a curvature in the color-space distribution, which is fully consistent with increasing dust temperature as the activity in a galaxy increases. This full sample of 49 compact groups allows us to subdivide the data according to physical properties of the groups. An analysis of these subsamples indicates that neither projected physical diameter nor density shows a trend in color space within the values represented by this sample. We hypothesize that the apparent lack of a trend is due to the relatively small range of properties in this sample, whose groups have already been
Examining the Role of Environment in a Comprehensive Sample of Compact Groups
Walker, Lisa May; Johnson, Kelsey E.; Gallagher, Sarah C.; Charlton, Jane C.; Hornschemeier, Ann E.; Hibbard, John E.
2012-03-01
Compact groups, with their high number densities, small velocity dispersions, and an interstellar medium that has not been fully processed, provide a local analog to conditions of galaxy interactions in the earlier universe. The frequent and prolonged gravitational encounters that occur in compact groups affect the evolution of the constituent galaxies in a myriad of ways, for example, gas processing and star formation. Recently, a statistically significant "gap" has been discovered in the mid-infrared (MIR: 3.6-8 μm) IRAC color space of compact group galaxies. This gap is not seen in field samples and is a new example of how the compact group environment may affect the evolution of member galaxies. In order to investigate the origin and nature of this gap, we have compiled a larger sample of 37 compact groups in addition to the original 12 groups studied by Johnson et al. (yielding 174 individual galaxies with reliable MIR photometry). We find that a statistically significant deficit of galaxies in this gap region of IRAC color space is persistent in the full sample, lending support to the hypothesis that the compact group environment inhibits moderate specific star formation rates. Using this expanded sample, we have more fully characterized the distribution of galaxies in this color space and quantified the low-density region more fully with respect to MIR bluer and MIR redder colors. We note a curvature in the color-space distribution, which is fully consistent with increasing dust temperature as the activity in a galaxy increases. This full sample of 49 compact groups allows us to subdivide the data according to physical properties of the groups. An analysis of these subsamples indicates that neither projected physical diameter nor density shows a trend in color space within the values represented by this sample. We hypothesize that the apparent lack of a trend is due to the relatively small range of properties in this sample, whose groups have already been
Kobayashi, T
2002-01-01
Based on an embedding formula of the CAR algebra into the Cuntz algebra ${\\mathcal O}_{2^p}$, properties of the CAR algebra are studied in detail by restricting those of the Cuntz algebra. Various $\\ast$-endomorphisms of the Cuntz algebra are explicitly constructed, and transcribed into those of the CAR algebra. In particular, a set of $\\ast$-endomorphisms of the CAR algebra into its even subalgebra are constructed. According to branching formulae, which are obtained by composing representations and $\\ast$-endomorphisms, it is shown that a KMS state of the CAR algebra is obtained through the above even-CAR endomorphisms from the Fock representation. A $U(2^p)$ action on ${\\mathcal O}_{2^p}$ induces $\\ast$-automorphisms of the CAR algebra, which are given by nonlinear transformations expressed in terms of polynomials in generators. It is shown that, among such $\\ast$-automorphisms of the CAR algebra, there exists a family of one-parameter groups of $\\ast$-automorphisms describing time evolutions of fermions, i...
Applications of Lie-group methods to the equations of magnetohydrodynamics
International Nuclear Information System (INIS)
Mandrekas, J.
1987-01-01
The invariance properties of various sets of magnetohydrodynamic (MHD) equations are studied using techniques from the theory of differential forms. Equations considered include the ideal MHD equations in different geometries and with different magnetic field configurations, the MHD equations in the presence of gravitational forces due to self-attraction or external fields, and the MHD equations including finite thermal conductivity and magnetic viscosity. The knowledge of the group structure of these equations is then used to introduce similarity variables to these equations. For each choice of similarity variables, the original set of partial differential equations is transformed into a set of ordinary differential equations and the most general form of the initial conditions is determined. Three cases are studied in detail and the corresponding sets of ordinary differential equations are solved numerically: the problem of a blast wave in an inhomogeneous atmosphere, the problem of a piston moving according to a power law in time, and the problem of a piston moving according to an exponential law in time
The low-lying quartet electronic states of group 14 diatomic borides XB (X = C, Si, Ge, Sn, Pb)
Pontes, Marcelo A. P.; de Oliveira, Marcos H.; Fernandes, Gabriel F. S.; Da Motta Neto, Joaquim D.; Ferrão, Luiz F. A.; Machado, Francisco B. C.
2018-04-01
The present work focuses in the characterization of the low-lying quartet electronic and spin-orbit states of diatomic borides XB, in which X is an element of group 14 (C, Si, Ge, Sn, PB). The wavefunction was obtained at the CASSCF/MRCI level with a quintuple-ζ quality basis set. Scalar relativistic effects were also taken into account. A systematic and comparative analysis of the spectroscopic properties for the title molecular series was carried out, showing that the (1)4Π→X4Σ- transition band is expected to be measurable by emission spectroscopy to the GeB, SnB and PbB molecules, as already observed for the lighter CB and SiB species.
Willis, George
2013-01-01
A family of equivalent submultiplicative weights on the to- tally disconnected, locally compact group $G$ is defined in terms of the conjugation action of $G$ on itself. These weights therefore reflect the structure of $G$, and the corresponding weighted convolution algebra is intrinsic to $G$ in the same way that $L^1(G) is.
Papi, Paolo; Advances in Lie Superalgebras
2014-01-01
The volume is the outcome of the conference "Lie superalgebras," which was held at the Istituto Nazionale di Alta Matematica, in 2012. The conference gathered many specialists in the subject, and the talks held provided comprehensive insights into the newest trends in research on Lie superalgebras (and related topics like vertex algebras, representation theory and supergeometry). The book contains contributions of many leading esperts in the field and provides a complete account of the newest trends in research on Lie Superalgebras.
Exact solubility of Chern-Simons theory with compact simple gauge group
International Nuclear Information System (INIS)
Hayashi, Masahito
1993-01-01
We show that vacuum expectation values of Wilson loop operators in (2+1)-dimensional Chern-Simons theory satisfy algebraic equations. Interestingly enough, vacuum expectation values for unknotted Wilson loop operators in any representation of any compact and simple group are exactly computed by solving the equations. So-called 'skein relations', which give us algebraic equations among vacuum expectation values of different Wilson loop operators, are constructed. In our formalism, quantum group symmetry appears naturally. (orig.)
Directory of Open Access Journals (Sweden)
M.J. Uddin
2016-09-01
Full Text Available The two-dimensional unsteady laminar free convective heat and mass transfer fluid flow of a non-Newtonian fluid adjacent to a vertical plate has been analyzed numerically. The two parameters Lie group transformation method that transforms the three independent variables into a single variable is used to transform the continuity, the momentum, the energy and the concentration equations into a set of coupled similarity equations. The transformed equations have been solved by the Runge–Kutta–Fehlberg fourth-fifth order numerical method with shooting technique. Numerical calculations were carried out for the various parameters entering into the problem. The dimensionless velocity, temperature and concentration profiles were shown graphically and the skin friction, heat and mass transfer rates were given in tables. It is found that friction factor and heat transfer (mass transfer rate for methanol are higher (lower than those of hydrogen and water vapor. Friction factor decreases while heat and mass transfer rate increase as the Prandtl number increases. Friction (heat and mass transfer rate factor of Newtonian fluid is higher (lower than the dilatant fluid.
Directory of Open Access Journals (Sweden)
M. M. Rashidi
2014-01-01
Full Text Available The optimal homotopy analysis method (OHAM is employed to investigate the steady laminar incompressible free convective flow of a nanofluid past a chemically reacting upward facing horizontal plate in a porous medium taking into account heat generation/absorption and the thermal slip boundary condition. Using similarity transformations developed by Lie group analysis, the continuity, momentum, energy, and nanoparticle volume fraction equations are transformed into a set of coupled similarity equations. The OHAM solutions are obtained and verified by numerical results using a Runge-Kutta-Fehlberg fourth-fifth order method. The effect of the emerging flow controlling parameters on the dimensionless velocity, temperature, and nanoparticle volume fraction have been presented graphically and discussed. Good agreement is found between analytical and numerical results of the present paper with published results. This close agreement supports our analysis and the accuracy of the numerical computations. This paper also includes a representative set of numerical results for reduced Nusselt and Sherwood numbers in a table for various values of the parameters. It is concluded that the reduced Nusselt number increases with the Lewis number and reaction parameter whist it decreases with the order of the chemical reaction, thermal slip, and generation parameters.
Alekseevsky, D. V.; Cortes, V.
1997-01-01
The variation of Hodge structure of a Calabi-Yau 3-fold induces a canonical K\\"ahler metric on its Kuranishi moduli space, known as the Weil-Petersson metric. Similarly, special pseudo K\\"ahler manifolds correspond to certain (abstract) variations of Hodge structure which generalize the above example. We give the classification of homogeneous special pseudo K\\"ahler manifolds of semisimple groups with compact stabilizer.
The Merger History, AGN and Dwarf Galaxies of Hickson Compact Group 59
Konstantopoulos, I. S.; Gallagher, S. C.; Fedotov, K.; Durrell, P. R.; Tzanavaris, P.; Hill, A. R.; Zabludoff, A. I.; Maier, M. L.; Elmegreen, D. M.; Charlton, J. C.;
2011-01-01
Compact group galaxies often appear unaffected by their unusually dense environment. Closer examination can, however, reveal the subtle, cumulative effects of multiple galaxy interactions. Hickson Compact Group (HCG) 59 is an excellent example of this situation. We present a photometric study of this group in the optical (HST), infrared (Spitzer) and X-ray (Chandra) regimes aimed at characterizing the star formation and nuclear activity in its constituent galaxies and intra-group medium. We associate five dwarf galaxies with the group and update the velocity dispersion, leading to an increase in the dynamical mass of the group of up to a factor of 10 (to 2.8 x 10(exp 13) Stellar Mass), and a subsequent revision of its evolutionary stage. Star formation is proceeding at a level consistent with the morphological types of the four main galaxies, of which two are star-forming and the other two quiescent. Unlike in some other compact groups, star-forming complexes across HCG 59 closely follow mass-radius scaling relations typical of nearby galaxies. In contrast, the ancient globular cluster populations in galaxies HCG 59A and B show intriguing irregularities, and two extragalactic HII regions are found just west of B. We age-date a faint stellar stream in the intra-group medium at approx. 1 Gyr to examine recent interactions. We detect a likely low-luminosity AGN in HCG 59A by its approx. 10(exp 40) erg/s X-ray emission; the active nucleus rather than star formation can account for the UV+IR SED. We discuss the implications of our findings in the context of galaxy evolution in dense environments.
Lie bialgebras with triangular decomposition
International Nuclear Information System (INIS)
Andruskiewitsch, N.; Levstein, F.
1992-06-01
Lie bialgebras originated in a triangular decomposition of the underlying Lie algebra are discussed. The explicit formulas for the quantization of the Heisenberg Lie algebra and some motion Lie algebras are given, as well as the algebra of rational functions on the quantum Heisenberg group and the formula for the universal R-matrix. (author). 17 refs
A COMPACT GROUP OF GALAXIES AT Z = 2.48 HOSTING AN AGN-DRIVEN OUTFLOW
Energy Technology Data Exchange (ETDEWEB)
Shih, Hsin-Yi [Gemini Observatory, 670 N Aohoku Place, Hilo, HI 96720 (United States); Stockton, Alan, E-mail: jshih@gemini.edu, E-mail: stockton@ifa.hawaii.edu [Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822 (United States)
2015-12-10
We present observations of a remarkable compact group of galaxies at z = 2.48. Four galaxies, all within 40 kpc of each other, surround a powerful high-redshift radio source. This group comprises two compact red passive galaxies and a pair of merging galaxies. One of the red galaxies, with an apparent stellar mass of 3.6 × 10{sup 11}M{sub ⊙} and an effective radius of 470 pc, is one of the most extreme examples of a massive quiescent compact galaxy found so far. One of the pair of merging galaxies hosts the active galactic nucleus (AGN) producing the large powerful radio structure. The merger is massive and enriched, consistent with the mass–metallicity relation expected at this redshift. Close to the merging nuclei, the emission lines exhibit broad and asymmetric profiles that suggest outflows powered either by a very young expanding radio jet or by AGN radiation. At ≳50 kpc from the system, we found a fainter extended-emission region that may be a part of a radio-jet-driven outflow.
Directory of Open Access Journals (Sweden)
Avraham eMerzel
2015-10-01
Full Text Available Do we feel bound by our own misrepresentations? Does one act of cheating compel the cheater to make subsequent choices that maintain the false image even at a cost? To answer these questions we employed a two-task paradigm such that in the first task the participants could benefit from false reporting of private observations whereas in the second they could benefit from making a prediction in line with their actual, rather than their previously reported observations. Thus, for those participants who inflated their report during the first task, sticking with that report for the second task was likely to lead to a loss, whereas deviating from it would imply that they had lied. Data from three experiments (total N=116 indicate that, having lied, participants were ready to suffer future loss rather than admit, even if implicitly, that they had lied.
Rainer, Löwen
2017-01-01
We prove that the automorphism group of a topological parallelism on real projective 3-space is compact. In a preceding article it was proved that at least the connected component of the identity is compact. The present proof does not depend on that earlier result.
MID-INFRARED EVIDENCE FOR ACCELERATED EVOLUTION IN COMPACT GROUP GALAXIES
International Nuclear Information System (INIS)
Walker, Lisa May; Johnson, Kelsey E.; Gallagher, Sarah C.; Hibbard, John E.; Hornschemeier, Ann E.; Tzanavaris, Panayiotis; Charlton, Jane C.; Jarrett, Thomas H.
2010-01-01
Compact galaxy groups are at the extremes of the group environment, with high number densities and low velocity dispersions that likely affect member galaxy evolution. To explore the impact of this environment in detail, we examine the distribution in the mid-infrared (MIR) 3.6-8.0 μm color space of 42 galaxies from 12 Hickson compact groups (HCGs) in comparison with several control samples, including the LVL+SINGS galaxies, interacting galaxies, and galaxies from the Coma Cluster. We find that the HCG galaxies are strongly bimodal, with statistically significant evidence for a gap in their distribution. In contrast, none of the other samples show such a marked gap, and only galaxies in the Coma infall region have a distribution that is statistically consistent with the HCGs in this parameter space. To further investigate the cause of the HCG gap, we compare the galaxy morphologies of the HCG and LVL+SINGS galaxies, and also probe the specific star formation rate (SSFR) of the HCG galaxies. While galaxy morphology in HCG galaxies is strongly linked to position with MIR color space, the more fundamental property appears to be the SSFR, or star formation rate normalized by stellar mass. We conclude that the unusual MIR color distribution of HCG galaxies is a direct product of their environment, which is most similar to that of the Coma infall region. In both cases, galaxy densities are high, but gas has not been fully processed or stripped. We speculate that the compact group environment fosters accelerated evolution of galaxies from star-forming and neutral gas-rich to quiescent and neutral gas-poor, leaving few members in the MIR gap at any time.
GALAXY INTERACTIONS IN COMPACT GROUPS. I. THE GALACTIC WINDS OF HCG16
Energy Technology Data Exchange (ETDEWEB)
Vogt, Frederic P. A.; Dopita, Michael A.; Kewley, Lisa J., E-mail: fvogt@mso.anu.edu.au [Mount Stromlo Observatory, Research School of Astronomy and Astrophysics, Australian National University, Cotter Road, Weston Creek, ACT 2611 (Australia)
2013-05-10
Using the WiFeS integral field spectrograph, we have undertaken a series of observations of star-forming galaxies in compact groups. In this first paper dedicated to the project, we present the analysis of the spiral galaxy NGC 838, a member of the Hickson Compact Group 16, and of its galactic wind. Our observations reveal that the wind forms an asymmetric, bipolar, rotating structure, powered by a nuclear starburst. Emission line ratio diagnostics indicate that photoionization is the dominant excitation mechanism at the base of the wind. Mixing from slow shocks (up to 20%) increases further out along the outflow axis. The asymmetry of the wind is most likely caused by one of the two lobes of the wind bubble bursting out of its H I envelope, as indicated by line ratios and radial velocity maps. The characteristics of this galactic wind suggest that it is caught early (a few Myr) in the wind evolution sequence. The wind is also quite different from the galactic wind in the partner galaxy NGC 839 which contains a symmetric, shock-excited wind. Assuming that both galaxies have similar interaction histories, the two different winds must be a consequence of the intrinsic properties of NGC 838 and NGC 839 and their starbursts.
Directory of Open Access Journals (Sweden)
Arash Ghaani Farashahi
2015-12-01
Full Text Available This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K$ be a continuous homomorphism. Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-convolution on $L^1(G_tau$ and we show that, with respect to each of them, the function space $L^1(G_tau$ is a Banach algebra. We define $tau$-convolution as a linear combination of the left and right $tau$-convolution and we show that the $tau$-convolution is commutative if and only if $K$ is abelian. We prove that there is a $tau$-involution on $L^1(G_tau$ such that with respect to the $tau$-involution and $tau$-convolution, $L^1(G_tau$ is a non-associative Banach $*$-algebra. It is also shown that when $K$ is abelian, the $tau$-involution and $tau$-convolution make $L^1(G_tau$ into a Jordan Banach $*$-algebra. Finally, we also present the generalized notation of $tau$-convolution for other $L^p$-spaces with $p>1$.
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.)
Diagram Techniques in Group Theory
Stedman, Geoffrey E.
2009-09-01
Preface; 1. Elementary examples; 2. Angular momentum coupling diagram techniques; 3. Extension to compact simple phase groups; 4. Symmetric and unitary groups; 5. Lie groups and Lie algebras; 6. Polarisation dependence of multiphoton processes; 7. Quantum field theoretic diagram techniques for atomic systems; 8. Applications; Appendix; References; Indexes.
Ultra-compact high velocity clouds in the ALFALFA HI survey: Candidate Local Group galaxies?
Adams, Elizabeth Ann Kovenz
The increased sensitivity and spatial resolution of the ALFALFA HI survey has resulted in the detection of ultra-compact high velocity clouds (UCHVCs). These objects are good candidates to represent low mass gas-rich galaxies in the Local Group and Local Volume with stellar populations that are too faint to be detected in extant optical surveys. This idea is referred to as the "minihalo hypothesis". We identify the UCHVCs within the ALFALFA dataset via the use of a 3D matched filtering signal identification algorithm. UCHVCs are selected based on a compact size ( 120 km s-1) and isolation. Within the 40% complete ALFALFA survey (alpha.40), 59 UCHVCs are identified; 19 are in a most-isolated subset and are the best galaxy candidates. Due to the presence of large HVC complexes in the fall sky, most notably the Magellanic Stream, the association of UCHVCs with existing structure cannot be ruled out. In the spring sky, the spatial and kinematic distribution of the UCHVCs is consistent with simulations of dark matter halos within the Local Group. In addition, the HI properties of the UCHVCs (if placed at 1 Mpc) are consistent with both theoretical and observational predictions for low mass gas-rich galaxies. Importantly, the HI properties of the UCHVCs are consistent with those of two recently discovered low mass gas-rich galaxies in the Local Group and Local Volume, Leo T and Leo P. Detailed follow-up observations are key for addressing the minihalo hypothesis. High resolution HI observations can constrain the environment of a UCHVC and offer evidence for a hosting dark matter halo through evidence of rotation support and comparison to theoretical models. Observations of one UCHVC at high resolution (15'') reveal the presence of a clumpy HI distribution, similar to both low mass galaxies and circumgalactic compact HVCs. An extended envelope containing ˜50% of the HI flux is resolved out by the array configuration; observations at lower spatial resolution can recover
A Lie based 4-dimensional higher Chern-Simons theory
Zucchini, Roberto
2016-05-01
We present and study a model of 4-dimensional higher Chern-Simons theory, special Chern-Simons (SCS) theory, instances of which have appeared in the string literature, whose symmetry is encoded in a skeletal semistrict Lie 2-algebra constructed from a compact Lie group with non discrete center. The field content of SCS theory consists of a Lie valued 2-connection coupled to a background closed 3-form. SCS theory enjoys a large gauge and gauge for gauge symmetry organized in an infinite dimensional strict Lie 2-group. The partition function of SCS theory is simply related to that of a topological gauge theory localizing on flat connections with degree 3 second characteristic class determined by the background 3-form. Finally, SCS theory is related to a 3-dimensional special gauge theory whose 2-connection space has a natural symplectic structure with respect to which the 1-gauge transformation action is Hamiltonian, the 2-curvature map acting as moment map.
A Compact Group of Galaxies at z = 2.48 Hosting an AGN-driven Outflow
Shih, Hsin-Yi; Stockton, Alan
2015-12-01
We present observations of a remarkable compact group of galaxies at z = 2.48. Four galaxies, all within 40 kpc of each other, surround a powerful high-redshift radio source. This group comprises two compact red passive galaxies and a pair of merging galaxies. One of the red galaxies, with an apparent stellar mass of 3.6 × 1011M⊙ and an effective radius of 470 pc, is one of the most extreme examples of a massive quiescent compact galaxy found so far. One of the pair of merging galaxies hosts the active galactic nucleus (AGN) producing the large powerful radio structure. The merger is massive and enriched, consistent with the mass-metallicity relation expected at this redshift. Close to the merging nuclei, the emission lines exhibit broad and asymmetric profiles that suggest outflows powered either by a very young expanding radio jet or by AGN radiation. At ≳50 kpc from the system, we found a fainter extended-emission region that may be a part of a radio-jet-driven outflow. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The work is also based, in part, on data collected at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan, and on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência, Tecnologia e Inovação (Brazil), and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina).
Scaling laws, renormalization group flow and the continuum limit in non-compact lattice QED
International Nuclear Information System (INIS)
Goeckeler, M.; Horsley, R.; Rakow, P.; Schierholz, G.; Sommer, R.
1992-01-01
We investigate the ultra-violet behavior of non-compact lattice QED with light staggered fermions. The main question is whether QED is a non-trivial theory in the continuum limit, and if not, what is its range of validity as a low-energy theory. Perhaps the limited range of validity could offer an explanation of why the fine-structure constant is so small. Non-compact QED undergoes a second-order chiral phase transition at strong coupling, at which the continuum limit can be taken. We examine the phase diagram and the critical behavior of the theory in detail. Moreover, we address the question as to whether QED confines in the chirally broken phase. This is done by investigating the potential between static external charges. We then compute the renormalized charge and derive the Callan-Symanzik β-function in the critical region. No ultra-violet stable zero is found. Instead, we find that the evolution of charge is well described by renormalized perturbation theory, and that the renormalized charge vanishes at the critical point. The consequence is that QED can only be regarded as a cut-off theory. We evaluate the maximum value of the cut-off as a function of the renormalized charge. Next, we compute the masses of fermion-antifermion composite states. The scaling behavior of these masses is well described by an effective action with mean-field critical exponents plus logarithmic corrections. This indicates that also the matter sector of the theory is non-interacting. Finally, we investigate and compare the renormalization group flow of different quantities. Altogether, we find that QED is a valid theory only for samll renormalized charges. (orig.)
Compaction of a Bacterial Group I Ribozyme Coincides with the Assembly of Core Helices
International Nuclear Information System (INIS)
Perez-Salas, U.; Rangan, P.; Krueger, S.; Briber, R.; Thirumalai, D.; Woodson, S.
2004-01-01
Counterions are critical to the self-assembly of RNA tertiary structure because they neutralize the large electrostatic forces which oppose the folding process. Changes in the size and shape of the Azoarcus group I ribozyme as a function of Mg 2+ and Na + concentration were followed by small angle neutron scattering. In low salt buffer, the RNA was expanded, with an average radius of gyration (R g ) of 53 ± 1 Angstroms. A highly cooperative transition to a compact form (R g = 31.5 ± 0.5 Angstroms) was observed between 1.6 and 1.7 mM MgCl 2 . The collapse transition, which is unusually sharp in Mg 2+ , has the characteristics of a first-order phase transition. Partial digestion with ribonuclease T1 under identical conditions showed that this transition correlated with the assembly of double helices in the ribozyme core. Fivefold higher Mg 2+ concentrations were required for self-splicing, indicating that compaction occurs before native tertiary interactions are fully stabilized. No further decrease in Rg was observed between 1.7 and 20 mM MgCl 2 , indicating that the intermediates have the same dimensions as the native ribozyme, within the uncertainty of the data (± 1 Angstroms). A more gradual transition to a final R g of approximately 33.5 Angstroms was observed between 0.45 and 2 M NaCl. This confirms the expectation that monovalent ions not only are less efficient in charge neutralization but also contract the RNA less efficiently than multivalent ions
A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ Lie-Group Shooting Method
Directory of Open Access Journals (Sweden)
Chein-Shan Liu
2013-01-01
Full Text Available The boundary layer problem for power-law fluid can be recast to a third-order p-Laplacian boundary value problem (BVP. In this paper, we transform the third-order p-Laplacian into a new system which exhibits a Lie-symmetry SL(3,ℝ. Then, the closure property of the Lie-group is used to derive a linear transformation between the boundary values at two ends of a spatial interval. Hence, we can iteratively solve the missing left boundary conditions, which are determined by matching the right boundary conditions through a finer tuning of r∈[0,1]. The present SL(3,ℝ Lie-group shooting method is easily implemented and is efficient to tackle the multiple solutions of the third-order p-Laplacian. When the missing left boundary values can be determined accurately, we can apply the fourth-order Runge-Kutta (RK4 method to obtain a quite accurate numerical solution of the p-Laplacian.
Smith, Douglas P.; Busby, Cathy J.
1993-10-01
Paleomagnetic data from Albian to Turonian sedimentary rocks on Cedros Island, Mexico (28.2° N, 115.2° W) support the interpretation that Cretaceous rocks of western Baja California have moved farther northward than the 3° of latitude assignable to Neogene oblique rifting in the Gulf of California. Averaged Cretaceous paleomagnetic results from Cedros Island support 20 ± 10° of northward displacement and 14 ± 7° of clockwise rotation with respect to cratonic North America. Positive field stability tests from the Vizcaino terrane substantiate a mid-Cretaceous age for the high-temperature characteristic remanent magnetization in mid-Cretaceous strata. Therefore coincidence of characteristic magnetization directions and the expected Quaternary axial dipole direction is not due to post mid-Cretaceous remagnetization. A slump test performed on internally coherent, intrabasinal slump blocks within a paleontologically dated olistostrome demonstrates a mid-Cretaceous age of magnetization in the Valle Group. The in situ high-temperature natural remanent magnetization directions markedly diverge from the expected Quaternary axial dipole, indicating that the characteristic, high-temperature magnetization was acquired prior to intrabasinal slumping. Early acquisition of the characteristic magnetization is also supported by a regional attitude test involving three localities in coherent mid-Cretaceous Valle Group strata. Paleomagnetic inclinations in mudstone are not different from those in sandstone, indicating that burial compaction did not bias the results toward shallow inclinations in the Vizcaino terrane.
Du, Xia-Xia; Tian, Bo; Chai, Jun; Sun, Yan; Yuan, Yu-Qiang
2017-11-01
In this paper, we investigate a (3+1)-dimensional modified Zakharov-Kuznetsov equation, which describes the nonlinear plasma-acoustic waves in a multicomponent magnetised plasma. With the aid of the Hirota method and symbolic computation, bilinear forms and one-, two- and three-soliton solutions are derived. The characteristics and interaction of the solitons are discussed graphically. We present the effects on the soliton's amplitude by the nonlinear coefficients which are related to the ratio of the positive-ion mass to negative-ion mass, number densities, initial densities of the lower- and higher-temperature electrons and ratio of the lower temperature to the higher temperature for electrons, as well as by the dispersion coefficient, which is related to the ratio of the positive-ion mass to the negative-ion mass and number densities. Moreover, using the Lie symmetry group theory, we derive the Lie point symmetry generators and the corresponding symmetry reductions, through which certain analytic solutions are obtained via the power series expansion method and the (G'/G) expansion method. We demonstrate that such an equation is strictly self-adjoint, and the conservation laws associated with the Lie point symmetry generators are derived.
On the absence of order in 2-dimensional systems with compact symmetry
International Nuclear Information System (INIS)
Bruschi, M.L.; Garcia, A.A.; Masperi, L.; Garcia Canal, C.A.
1984-01-01
An alternative proof for the generalization to any compact Lie group of the absence of an ordered phase in one and two dimensional classical systems is provided using the original Bogoliubov inequality. (Author) [pt
International Nuclear Information System (INIS)
Ma Hongcai
2005-01-01
Using the (2+1)-dimensional Broer-Kaup equation as an simple example, a new direct method is developed to find symmetry groups and symmetry algebras and then exact solutions of nonlinear mathematical physical equations.
Directory of Open Access Journals (Sweden)
Fedriani Martel, Eugenio M.
2006-06-01
Full Text Available En la presente comunicación explicamos algunas de las herramientas de la Geometría Diferencial y, en concreto, de la Teoría de Lie con las que se trabaja actualmente en Economía. Se indican las condiciones que se exigen a las funciones de producción y la definición de un tipo de progreso técnico denominado de tipo Lie, consistente en exigir las tres propiedades que han de verificar los grupos de Lie. También se expone el uso del operador de Lie en interpretaciones económicas y en la cuantificación del impacto del progreso técnico. Dicho operador permite dar una respuesta a la Controversia Solow-Stigler. Por último, se indican varias aplicaciones de la Teoría de Lie en los estudios económicos, que permiten abrir futuras líneas de investigación,de las que se apuntan algunas. De este modo, nuestro objetivo principal es mostrar el uso, actual y futuro, de la Teoría de Lie en el campo de la Economía.
High-Quality Ultra-Compact Grid Layout of Grouped Networks.
Yoghourdjian, Vahan; Dwyer, Tim; Gange, Graeme; Kieffer, Steve; Klein, Karsten; Marriott, Kim
2016-01-01
Prior research into network layout has focused on fast heuristic techniques for layout of large networks, or complex multi-stage pipelines for higher quality layout of small graphs. Improvements to these pipeline techniques, especially for orthogonal-style layout, are difficult and practical results have been slight in recent years. Yet, as discussed in this paper, there remain significant issues in the quality of the layouts produced by these techniques, even for quite small networks. This is especially true when layout with additional grouping constraints is required. The first contribution of this paper is to investigate an ultra-compact, grid-like network layout aesthetic that is motivated by the grid arrangements that are used almost universally by designers in typographical layout. Since the time when these heuristic and pipeline-based graph-layout methods were conceived, generic technologies (MIP, CP and SAT) for solving combinatorial and mixed-integer optimization problems have improved massively. The second contribution of this paper is to reassess whether these techniques can be used for high-quality layout of small graphs. While they are fast enough for graphs of up to 50 nodes we found these methods do not scale up. Our third contribution is a large-neighborhood search meta-heuristic approach that is scalable to larger networks.
WITNESSING GAS MIXING IN THE METAL DISTRIBUTION OF THE HICKSON COMPACT GROUP HCG 31
International Nuclear Information System (INIS)
Torres-Flores, S.; Alfaro-Cuello, M.; De Oliveira, C. Mendes; Amram, P.; Carrasco, E. R.; De Mello, D. F.
2015-01-01
We present for the first time direct evidence that in a merger of disk galaxies, the pre-existing central metallicities will mix as a result of gas being transported in the merger interface region along the line that joins the two coalescing nuclei. This is shown using detailed two-dimensional kinematics as well as metallicity measurements for the nearby ongoing merger in the center of the compact group HCG 31. We focus on the emission line gas, which is extensive in the system. The two coalescing cores display similar oxygen abundances. While in between the two nuclei, the metallicity changes smoothly from one nucleus to the other indicating a mix of metals in this region, which is confirmed by the high-resolution Hα kinematics (R = 45,900). This nearby system is especially important because it involves the merging of two fairly low-mass and clumpy galaxies (LMC-like galaxies), making it an important system for comparison with high-redshift galaxies
WITNESSING GAS MIXING IN THE METAL DISTRIBUTION OF THE HICKSON COMPACT GROUP HCG 31
Energy Technology Data Exchange (ETDEWEB)
Torres-Flores, S.; Alfaro-Cuello, M. [Departamento de Física, Universidad de La Serena, Av. Cisternas 1200, La Serena (Chile); De Oliveira, C. Mendes [Instituto de Astronomia, Geofísica e Ciências Atmosféricas da Universidade de São Paulo, Cidade Universitária, CEP:05508-900, São Paulo, SP (Brazil); Amram, P. [Aix Marseille Université, CNRS, LAM (Laboratoire d' Astrophysique de Marseille) UMR 7326, F-13388, Marseille (France); Carrasco, E. R. [Gemini Observatory/AURA, Southern Operations Center, Casilla 603, La Serena (Chile); De Mello, D. F., E-mail: storres@dfuls.cl [Catholic University of America, Washington, DC 20064 (United States)
2015-01-01
We present for the first time direct evidence that in a merger of disk galaxies, the pre-existing central metallicities will mix as a result of gas being transported in the merger interface region along the line that joins the two coalescing nuclei. This is shown using detailed two-dimensional kinematics as well as metallicity measurements for the nearby ongoing merger in the center of the compact group HCG 31. We focus on the emission line gas, which is extensive in the system. The two coalescing cores display similar oxygen abundances. While in between the two nuclei, the metallicity changes smoothly from one nucleus to the other indicating a mix of metals in this region, which is confirmed by the high-resolution Hα kinematics (R = 45,900). This nearby system is especially important because it involves the merging of two fairly low-mass and clumpy galaxies (LMC-like galaxies), making it an important system for comparison with high-redshift galaxies.
Dynamics on the group manifolds and path integral
International Nuclear Information System (INIS)
Marinov, M.S.; Terentyev, M.V.
1979-01-01
Classical and quantum dynamics onn the compact simple Lie group and on the sphere of arbitrary dimensionality are considered. The accuracy of the semiclassical approximation for Green functions is discussed. Various path integral representations of the Green functions are presented. The special features of these representations due to the compactness and curvature are analysed. Basic results of the theory of Lie algebras and Lie groups used in the main text are presented
DEFF Research Database (Denmark)
Trinhammer, Ole
PiMinus invariant mass in B decays. We give a controversial prediction of the relative neutron to proton mass difference 0.138 % as originating in period doublings of certain parametric states. The group space dynamics communicates with real space via the exterior derivative which projects out quark and gluon...
DEFF Research Database (Denmark)
Alatalo, K.; Appleton, P. N.; Lisenfeld, U.
2014-01-01
We present [C II] and [O I] observations from Herschel and CO(1-0) maps from the Combined Array for Research in Millimeter Astronomy (CARMA) of the Hickson compact group HCG 57, focusing on the galaxies HCG 57a and HCG 57d. HCG 57a has been previously shown to contain enhanced quantities of warm ...
Start-up scenario of compact tori based on REB-injection developed in SPAC-group
International Nuclear Information System (INIS)
Ikuta, K.
1981-01-01
Quasi-static start-up of compact tori without toroidal field coil is reviewed thoroughly in a proposal of the S-1 spheromak. During the formation phase we should note that the rapid heat loss from the plasma will give a bad effect for the generation of the confinement configuration. In the case of fast start-up of the configuration plasma can safely pass over the dangerous state of the instability toward the desirable stable state with a bonus of producing hot plasma. By this reason it is intended to discuss a fast start-up scenario of the compact tori based on REB injection developed in SPAC group
ULTRAVIOLET+INFRARED STAR FORMATION RATES: HICKSON COMPACT GROUPS WITH SWIFT AND SPITZER
International Nuclear Information System (INIS)
Tzanavaris, P.; Hornschemeier, A. E.; Immler, S.; Gallagher, S. C.; Johnson, K. E.; Reines, A. E.; Gronwall, C.; Hoversten, E.; Charlton, J. C.
2010-01-01
We present Swift UVOT ultraviolet (UV; 1600-3000 A) data with complete three-band UV photometry for a sample of 41 galaxies in 11 nearby ( -1 ) Hickson Compact Groups (HCGs) of galaxies. We use UVOT uvw2-band (2000 A) photometry to estimate the dust-unobscured component, SFR UV , of the total star formation rate, SFR TOTAL . We use Spitzer MIPS 24 μm photometry to estimate SFR IR , the component of SFR TOTAL that suffers dust extinction in the UV and is re-emitted in the IR. By combining the two components, we obtain SFR TOTAL estimates for all HCG galaxies. We obtain total stellar mass, M * , estimates by means of Two Micron All Sky Survey K s -band luminosities, and use them to calculate specific star formation rates, SSFR ≡ SFR TOTAL /M * . SSFR values show a clear and significant bimodality, with a gap between low (∼ -11 yr -1 ) and high-SSFR (∼>1.2 x 10 -10 yr -1 ) systems. We compare this bimodality to the previously discovered bimodality in α IRAC , the MIR activity index from a power-law fit to the Spitzer IRAC 4.5-8 μm data for these galaxies. We find that all galaxies with α IRAC ≤ 0 ( >0) are in the high- (low-) SSFR locus, as expected if high levels of star-forming activity power MIR emission from polycyclic aromatic hydrocarbon molecules and a hot dust continuum. Consistent with this finding, all elliptical/S0 galaxies are in the low-SSFR locus, while 22 out of 24 spirals/irregulars are in the high-SSFR locus, with two borderline cases. We further divide our sample into three subsamples (I, II, and III) according to decreasing H I richness of the parent galaxy group to which a galaxy belongs. Consistent with the SSFR and α IRAC bimodality, 12 out of 15 type I (11 out of 12 type III) galaxies are in the high- (low-) SSFR locus, while type II galaxies span almost the full range of SSFR values. We use the Spitzer Infrared Nearby Galaxy Survey (SINGS) to construct a comparison subsample of galaxies that (1) match HCG galaxies in J-band total
Density character of subgroups of topological groups
Leiderman, Arkady; Morris, Sidney A.; Tkachenko, Mikhail G.
2015-01-01
A subspace Y of a separable metrizable space X is separable, but without X metrizable this is not true even If Y is a closed linear subspace of a topological vector space X. K.H. Hofmann and S.A. Morris introduced the class of pro-Lie groups which consists of projective limits of finite-dimensional Lie groups and proved that it contains all compact groups, locally compact abelian groups and connected locally compact groups and is closed under products and closed subgroups. A topological group...
International Nuclear Information System (INIS)
Olmos, C.
1990-05-01
The restricted holonomy group of a Riemannian manifold is a compact Lie group and its representation on the tangent space is a product of irreducible representations and a trivial one. Each one of the non-trivial factors is either an orthogonal representation of a connected compact Lie group which acts transitively on the unit sphere or it is the isotropy representation of a single Riemannian symmetric space of rank ≥ 2. We prove that, all these properties are also true for the representation on the normal space of the restricted normal holonomy group of any submanifold of a space of constant curvature. 4 refs
Directory of Open Access Journals (Sweden)
Khodakhast Bibak
2016-09-01
Full Text Available Graphs embedded into surfaces have many important applications, in particular, in combinatorics, geometry, and physics. For example, ribbon graphs and their counting is of great interest in string theory and quantum field theory (QFT. Recently, Koch et al. (2013 [12] gave a refined formula for counting ribbon graphs and discussed its applications to several physics problems. An important factor in this formula is the number of surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group. The aim of this paper is to give an explicit and practical formula for the number of such epimorphisms. As a consequence, we obtain an ‘equivalent’ form of Harvey's famous theorem on the cyclic groups of automorphisms of compact Riemann surfaces. Our main tool is an explicit formula for the number of solutions of restricted linear congruence recently proved by Bibak et al. using properties of Ramanujan sums and of the finite Fourier transform of arithmetic functions.
Energy Technology Data Exchange (ETDEWEB)
Bibak, Khodakhast, E-mail: kbibak@uvic.ca; Kapron, Bruce M., E-mail: bmkapron@uvic.ca; Srinivasan, Venkatesh, E-mail: srinivas@uvic.ca
2016-09-15
Graphs embedded into surfaces have many important applications, in particular, in combinatorics, geometry, and physics. For example, ribbon graphs and their counting is of great interest in string theory and quantum field theory (QFT). Recently, Koch et al. (2013) gave a refined formula for counting ribbon graphs and discussed its applications to several physics problems. An important factor in this formula is the number of surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group. The aim of this paper is to give an explicit and practical formula for the number of such epimorphisms. As a consequence, we obtain an ‘equivalent’ form of Harvey's famous theorem on the cyclic groups of automorphisms of compact Riemann surfaces. Our main tool is an explicit formula for the number of solutions of restricted linear congruence recently proved by Bibak et al. using properties of Ramanujan sums and of the finite Fourier transform of arithmetic functions.
A Higgs at 125.1 GeV and baryon mass spectra derived from a Common U(3) Lie group framework
DEFF Research Database (Denmark)
Trinhammer, Ole; Bohr, Henrik; Jensen, Mogens O Stibius
2015-01-01
Baryons are described by a Hamiltonian on an intrinsic U(3) Lie group configuration space with electroweak degrees of freedom originating in specific Bloch wave factors. By opening the Bloch degrees of freedom pairwise via a U(2) Higgs mechanism, the strong and electroweak energy scales become...... related to yield the Higgs mass 125.085+/-0.017 GeV and the usual gauge boson masses. From the same Hamiltonian we derive both the relative neutron to proton mass ratio and the N and Delta mass spectra. All compare rather well with the experimental values. We predict neutral flavour baryon singlets...... to be sought for in negative pions scattering on protons or in photoproduction on neutrons and in invariant mass like Σ+c(2455)D- from various decays above the open charm threshold, e.g. at 4499, 4652 and 4723 MeV. The fundamental predictions are based on just one length scale and the fine structure coupling...
Rubio Martí, Vicente
2016-01-01
En el presente proyecto definimos lo que es un grupo de Lie, así como su respectiva álgebra de Lie canónica como aproximación lineal a dicho grupo de Lie. El proceso de linealización, que es hallar el algebra de Lie de un grupo de Lie dado, tiene su
International Nuclear Information System (INIS)
Wu Ming-Zhong; Bai Cheng-Ming
2015-01-01
A compatible Lie algebra is a pair of Lie algebras such that any linear combination of the two Lie brackets is a Lie bracket. We construct a bialgebra theory of compatible Lie algebras as an analogue of a Lie bialgebra. They can also be regarded as a “compatible version” of Lie bialgebras, that is, a pair of Lie bialgebras such that any linear combination of the two Lie bialgebras is still a Lie bialgebra. Many properties of compatible Lie bialgebras as the “compatible version” of the corresponding properties of Lie bialgebras are presented. In particular, there is a coboundary compatible Lie bialgebra theory with a construction from the classical Yang–Baxter equation in compatible Lie algebras as a combination of two classical Yang–Baxter equations in Lie algebras. Furthermore, a notion of compatible pre-Lie algebra is introduced with an interpretation of its close relation with the classical Yang–Baxter equation in compatible Lie algebras which leads to a construction of the solutions of the latter. As a byproduct, the compatible Lie bialgebras fit into the framework to construct non-constant solutions of the classical Yang–Baxter equation given by Golubchik and Sokolov. (paper)
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)
Gradings on simple Lie algebras
Elduque, Alberto
2013-01-01
Gradings are ubiquitous in the theory of Lie algebras, from the root space decomposition of a complex semisimple Lie algebra relative to a Cartan subalgebra to the beautiful Dempwolff decomposition of E_8 as a direct sum of thirty-one Cartan subalgebras. This monograph is a self-contained exposition of the classification of gradings by arbitrary groups on classical simple Lie algebras over algebraically closed fields of characteristic not equal to 2 as well as on some nonclassical simple Lie algebras in positive characteristic. Other important algebras also enter the stage: matrix algebras, the octonions, and the Albert algebra. Most of the presented results are recent and have not yet appeared in book form. This work can be used as a textbook for graduate students or as a reference for researchers in Lie theory and neighboring areas.
Prodhan, Suryoday; Ramasesha, S.
2018-05-01
The symmetry adapted density matrix renormalization group (SDMRG) technique has been an efficient method for studying low-lying eigenstates in one- and quasi-one-dimensional electronic systems. However, the SDMRG method had bottlenecks involving the construction of linearly independent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. We have developed a modified algorithm to overcome this bottleneck. The new method incorporates end-to-end interchange symmetry (C2) , electron-hole symmetry (J ) , and parity or spin-flip symmetry (P ) in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new basis with maximum sparseness, just one nonzero matrix element per row. Using methods similar to those employed in the exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the 1980s, it is possible to construct orthogonal SDMRG basis states while bypassing the slow step of the Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited-state spectra of 1,12-benzoperylene and a narrow mixed graphene nanoribbon with a chrysene molecule as the building unit, comprising both zigzag and cove-edge structures.
Positive-definite functions and unitary representations of locally compact groups in a Hilbert space
International Nuclear Information System (INIS)
Gali, I.M.; Okb el-Bab, A.S.; Hassan, H.M.
1977-08-01
It is proved that the necessary and sufficient condition for the existence of an integral representation of a group of unitary operators in a Hilbert space is that it is positive-definite and continuous in some topology
Parks, Helen Frances
to extend POD to structured settings. In particular, we consider systems evolving on Lie groups and make use of canonical coordinates in the reduction process. We see considerable improvement in the accuracy of the reduced model over the usual structure-agnostic POD approach.
A new compact for owners and directors. The Working Group on Corporate Governance.
1991-01-01
The virtual demise of hostile takeovers and leveraged buyouts has not cooled the tensions over corporate governance. In congressional hearings, at annual meetings, and in proxy contests splashed across the business pages, senior executives and powerful shareholders continue to confront each other. The basic issues remain remarkably consistent. When do investors' legitimate needs for returns translate into destructive pressures on long-term corporate prosperity? What kinds of accountability do top managers owe shareholders in terms of strategic consultation and disclosure? What is the precise role of the board of directors as a management monitor and shareholder representative? More than a year ago, a working group of distinguished lawyers representing large public companies and leading institutional investors began a series of meetings to cut through the rancor. Their goal was to reach common ground on a set of principles that reconciles the tensions between owners and managers. Recently, the group agreed on a statement that all eight members endorsed. The statement, "A New Charter for Owners and Managers," deserves wide readership, scrutiny, and commentary. HBR is pleased the working group chose it as the exclusive forum to release its statement.
Low-dimensional gravities as gauge theories with non-compact groups
International Nuclear Information System (INIS)
Cangeni, D.
1993-01-01
In another note presented in these Proceedings it is shown that the two main lineal gravities can be given a gauge formulation. If it is already known that one of them the Sitter model - is a dimensional reduction of a Chern-Simons model in (2+1) dimensions, it was not clear whether the other one - the extended Poincare model follows from a similar reduction. The purpose of this note is to show that this is indeed the case provide we start in 2+1 dimensions with an extension ISO(2,1) of the Poincare groups as gauge group of a Chern-Simons model. We first show that this model gives a new proposal for gravity in 2*1 dimensions, since we get classically the Einstein's equations. Performing then a dimensional reduction, we recover not only the extended Poincare model but also the de Sitter one; hence, both lineal gravities get unified in the reduced model. (Author) 6 refs
Bakhurst, D
1992-01-01
This article challenges Jennifer Jackson's recent defence of doctors' rights to deceive patients. Jackson maintains there is a general moral difference between lying and intentional deception: while doctors have a prima facie duty not to lie, there is no such obligation to avoid deception. This paper argues 1) that an examination of cases shows that lying and deception are often morally equivalent, and 2) that Jackson's position is premised on a species of moral functionalism that misconstrue...
International Nuclear Information System (INIS)
Adams, Elizabeth A. K.; Giovanelli, Riccardo; Haynes, Martha P.
2013-01-01
We present a catalog of 59 ultra-compact high velocity clouds (UCHVCs) extracted from the 40% complete ALFALFA HI-line survey. The ALFALFA UCHVCs have median flux densities of 1.34 Jy km s –1 , median angular diameters of 10', and median velocity widths of 23 km s –1 . We show that the full UCHVC population cannot easily be associated with known populations of high velocity clouds. Of the 59 clouds presented here, only 11 are also present in the compact cloud catalog extracted from the commensal GALFA-HI survey, demonstrating the utility of this separate dataset and analysis. Based on their sky distribution and observed properties, we infer that the ALFALFA UCHVCs are consistent with the hypothesis that they may be very low mass galaxies within the Local Volume. In that case, most of their baryons would be in the form of gas, and because of their low stellar content, they remain unidentified by extant optical surveys. At distances of ∼1 Mpc, the UCHVCs have neutral hydrogen (H I) masses of ∼10 5 -10 6 M ☉ , H I diameters of ∼2-3 kpc, and indicative dynamical masses within the H I extent of ∼10 7 -10 8 M ☉ , similar to the Local Group ultra-faint dwarf Leo T. The recent ALFALFA discovery of the star-forming, metal-poor, low mass galaxy Leo P demonstrates that this hypothesis is true in at least one case. In the case of the individual UCHVCs presented here, confirmation of their extragalactic nature will require further work, such as the identification of an optical counterpart to constrain their distance.
Energy Technology Data Exchange (ETDEWEB)
Adams, Elizabeth A. K.; Giovanelli, Riccardo; Haynes, Martha P., E-mail: betsey@astro.cornell.edu, E-mail: riccardo@astro.cornell.edu, E-mail: haynes@astro.cornell.edu [Center for Radiophysics and Space Research, Space Sciences Building, Cornell University, Ithaca, NY 14853 (United States)
2013-05-01
We present a catalog of 59 ultra-compact high velocity clouds (UCHVCs) extracted from the 40% complete ALFALFA HI-line survey. The ALFALFA UCHVCs have median flux densities of 1.34 Jy km s{sup -1}, median angular diameters of 10', and median velocity widths of 23 km s{sup -1}. We show that the full UCHVC population cannot easily be associated with known populations of high velocity clouds. Of the 59 clouds presented here, only 11 are also present in the compact cloud catalog extracted from the commensal GALFA-HI survey, demonstrating the utility of this separate dataset and analysis. Based on their sky distribution and observed properties, we infer that the ALFALFA UCHVCs are consistent with the hypothesis that they may be very low mass galaxies within the Local Volume. In that case, most of their baryons would be in the form of gas, and because of their low stellar content, they remain unidentified by extant optical surveys. At distances of {approx}1 Mpc, the UCHVCs have neutral hydrogen (H I) masses of {approx}10{sup 5}-10{sup 6} M{sub Sun }, H I diameters of {approx}2-3 kpc, and indicative dynamical masses within the H I extent of {approx}10{sup 7}-10{sup 8} M{sub Sun }, similar to the Local Group ultra-faint dwarf Leo T. The recent ALFALFA discovery of the star-forming, metal-poor, low mass galaxy Leo P demonstrates that this hypothesis is true in at least one case. In the case of the individual UCHVCs presented here, confirmation of their extragalactic nature will require further work, such as the identification of an optical counterpart to constrain their distance.
Factorial representations of path groups
International Nuclear Information System (INIS)
Albeverio, S.; Hoegh-Krohn, R.; Testard, D.; Vershik, A.
1983-11-01
We give the reduction of the energy representation of the group of mappings from I = [ 0,1 ], S 1 , IRsub(+) or IR into a compact semi simple Lie group G. For G = SU(2) we prove the factoriality of the representation, which is of type III in the case I = IR
Lie symmetries in differential equations
International Nuclear Information System (INIS)
Pleitez, V.
1979-01-01
A study of ordinary and Partial Differential equations using the symmetries of Lie groups is made. Following such a study, an application to the Helmholtz, Line-Gordon, Korleweg-de Vries, Burguer, Benjamin-Bona-Mahony and wave equations is carried out [pt
Verschuere, B.; Spruyt, A.; Meijer, E.H.; Otgaar, H.
2011-01-01
Brain imaging studies suggest that truth telling constitutes the default of the human brain and that lying involves intentional suppression of the predominant truth response. By manipulating the truth proportion in the Sheffield lie test, we investigated whether the dominance of the truth response
Biyogmam, Guy Roger
2011-01-01
In this paper, we introduce the category of Lie $n$-racks and generalize several results known on racks. In particular, we show that the tangent space of a Lie $n$-Rack at the neutral element has a Leibniz $n$-algebra structure. We also define a cohomology theory of $n$-racks..
Vrij, Aldert; Taylor, Paul J.; Picornell, Isabel; Oxburgh, Gavin; Myklebust, Trond; Grant, Tim; Milne, Rebecca
2015-01-01
In this chapter, we discuss verbal lie detection and will argue that speech content can be revealing about deception. Starting with a section discussing the, in our view, myth that non-verbal behaviour would be more revealing about deception than speech, we then provide an overview of verbal lie
International Nuclear Information System (INIS)
Kumar, Vikas; Gupta, R. K.; Jiwari, Ram
2014-01-01
In this paper, the variable-coefficient diffusion—advection (DA) equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced second-order nonlinear ordinary differential equations. Further, an extended (G'/G)-expansion method is applied to the DA equation to construct some new non-traveling wave solutions
Medicine, lies and deceptions.
Benn, P
2001-04-01
This article offers a qualified defence of the view that there is a moral difference between telling lies to one's patients, and deceiving them without lying. However, I take issue with certain arguments offered by Jennifer Jackson in support of the same conclusion. In particular, I challenge her claim that to deny that there is such a moral difference makes sense only within a utilitarian framework, and I cast doubt on the aptness of some of her examples of non-lying deception. But I argue that lies have a greater tendency to damage trust than does non-lying deception, and suggest that since many doctors do believe there is a moral boundary between the two types of deception, encouraging them to violate that boundary may have adverse general effects on their moral sensibilities.
Bakhurst, D
1992-06-01
This article challenges Jennifer Jackson's recent defence of doctors' rights to deceive patients. Jackson maintains there is a general moral difference between lying and intentional deception: while doctors have a prima facie duty not to lie, there is no such obligation to avoid deception. This paper argues 1) that an examination of cases shows that lying and deception are often morally equivalent, and 2) that Jackson's position is premised on a species of moral functionalism that misconstrues the nature of moral obligation. Against Jackson, it is argued that both lying and intentional deception are wrong where they infringe a patient's right to autonomy or his/her right to be treated with dignity. These rights represent 'deontological constraints' on action, defining what we must not do whatever the functional value of the consequences. Medical ethics must recognise such constraints if it is to contribute to the moral integrity of medical practice.
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...
Bakhurst, D
1992-01-01
This article challenges Jennifer Jackson's recent defence of doctors' rights to deceive patients. Jackson maintains there is a general moral difference between lying and intentional deception: while doctors have a prima facie duty not to lie, there is no such obligation to avoid deception. This paper argues 1) that an examination of cases shows that lying and deception are often morally equivalent, and 2) that Jackson's position is premised on a species of moral functionalism that misconstrues the nature of moral obligation. Against Jackson, it is argued that both lying and intentional deception are wrong where they infringe a patient's right to autonomy or his/her right to be treated with dignity. These rights represent 'deontological constraints' on action, defining what we must not do whatever the functional value of the consequences. Medical ethics must recognise such constraints if it is to contribute to the moral integrity of medical practice. PMID:1619626
Carnovale, Giovanna; Caselli, Fabrizio; Concini, Corrado; Sole, Alberto
2017-01-01
Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.
On the Lie groups with the commutation relations of the type [Hsub(i), Hsub(j)]=rsub(ij)Hsub(i)(i
International Nuclear Information System (INIS)
Lebedenko, V.M.
1976-01-01
The class of PR-groups, i.e., the class of all connected and simply-connected groups of the type mentioned in the title, has been described. A number of properties has been studied and the linear realizations of arbitrary PR-groups have been considered. All the PR-groups are shown to be exponential. It follows from this fact a simple sufficient condition of applicability of the Kirillov orbit method to the construction of the harmonic analysis on concrete groups. Examples of the PR-groups are given which have been already used in theoretical physics
Abdalla, M. Sebawe; Khalil, E. M.; Obada, A. S.-F.
2017-08-01
The problem of the codirectional Kerr coupler has been considered several times from different point of view. In the present paper we introduce the interaction between a two-level atom and the codirectional Kerr nonlinear coupler in terms of su (2 ) Lie algebra. Under certain conditions we have adjusted the Kerr coupler and consequently we have managed to handle the problem. The wave function is obtained by using the evolution operator where the Heisnberg equation of motion is invoked to get the constants of the motion. We note that the Kerr parameter χ as well as the quantum number j plays the role of controlling the atomic inversion behavior. Also the maximum entanglement occurs after a short period of time when χ = 0. On the other hand for the entropy and the variance squeezing we observe that there is exchange between the quadrature variances. Furthermore, the variation in the quantum number j as well as in the parameter χ leads to increase or decrease in the number of fluctuations. Finally we examined the second order correlation function where classical and nonclassical phenomena are observed.
Graded-Lie-algebra cohomology and supergravity
International Nuclear Information System (INIS)
D'Auria, R.; Fre, P.; Regge, T.
1980-01-01
Detailed explanations of the cohomology invoked in the group-manifold approach to supergravity is given. The Chevalley cohomology theory of Lie algebras is extended to graded Lie algebras. The scheme of geometrical theories is enlarged so to include cosmological terms and higher powers of the curvature. (author)
Jurco, Branislav
2011-01-01
Let g be a simplicial Lie algebra with Moore complex Ng of length k. Let G be the simplicial Lie group integrating g, which is simply connected in each simplicial level. We use the 1-jet of the classifying space of G to construct, starting from g, a Lie k-algebra L. The so constructed Lie k-algebra L is actually a differential graded Lie algebra. The differential and the brackets are explicitly described in terms (of a part) of the corresponding k-hypercrossed complex structure of Ng. The res...
Seron, X
2014-10-01
The issue of lying occurs in neuropsychology especially when examinations are conducted in a forensic context. When a subject intentionally either presents non-existent deficits or exaggerates their severity to obtain financial or material compensation, this behaviour is termed malingering. Malingering is discussed in the general framework of lying in psychology, and the different procedures used by neuropsychologists to evidence a lack of collaboration at examination are briefly presented and discussed. When a lack of collaboration is observed, specific emphasis is placed on the difficulty in unambiguously establishing that this results from the patient's voluntary decision. Copyright © 2014. Published by Elsevier SAS.
Konstantopoulos, I. S.; Maybhate, A.; Charlton, J. C.; Fedotov, K.; Durrell, P. R.; Mulchaey, J. S.; English, J.; Desjardins, T. D.; Gallagher, S. C.; Walker, L. M.;
2013-01-01
We present a multi-wavelength analysis of three compact galaxy groups, Hickson compact groups (HCGs) 16, 22, and 42, which describe a sequence in terms of gas richness, from space- (Swift, Hubble Space Telescope (HST), and Spitzer) and ground-based (Las Campanas Observatory and Cerro Tololo Inter-American Observatory) imaging and spectroscopy.We study various signs of past interactions including a faint, dusty tidal feature about HCG 16A, which we tentatively age-date at what were thought to be double nuclei in HCG 16C and D into multiple, distinct sources, likely to be star clusters. Beyond our phenomenological treatment, we focus primarily on contrasting the stellar populations across these three groups. The star clusters show a remarkable intermediate-age population in HCG 22, and identify the time at which star formation was quenched in HCG 42. We also search for dwarf galaxies at accordant redshifts. The inclusion of 33 members and 27 "associates" (possible members) radically changes group dynamical masses, which in turn may affect previous evolutionary classifications. The extended membership paints a picture of relative isolation in HCGs 16 and 22, but shows HCG 42 to be part of a larger structure, following a dichotomy expected from recent studies. We conclude that (1) star cluster populations provide an excellent metric of evolutionary state, as they can age-date the past epochs of star formation; and (2) the extended dwarf galaxy population must be considered in assessing the dynamical state of a compact group.
Multiplication: From Thales to Lie1
Indian Academy of Sciences (India)
Addition. To describe the geometric constructions of addition, as ..... general, we could apply the implicit function theorem of calculus to solve locally the defining ... and whose multiplication and inverse are analytic maps, is called a Lie group.
Compact Information Representations
2016-08-02
Department of Defense, Executive Services, Directorate (0704-0188). Respondents should be aware that notwithstanding any other provision of law, no person...which lies in the mission of AFOSR. 15. SUBJECT TERMS sparse sampling , principal components analysis 16. SECURITY CLASSIFICATION OF: 17...approved for public release Contents 1 Training for Ph.D. Students and Postdoc Researchers 2 2 Papers 2 3 Summary of Proposed Research: Compact
Lie symmetries and superintegrability
International Nuclear Information System (INIS)
Nucci, M C; Post, S
2012-01-01
We show that a known superintegrable system in two-dimensional real Euclidean space (Post and Winternitz 2011 J. Phys. A: Math. Theor. 44 162001) can be transformed into a linear third-order equation: consequently we construct many autonomous integrals—polynomials up to order 18—for the same system. The reduction method and the connection between Lie symmetries and Jacobi last multiplier are used.
Classification and identification of Lie algebras
Snobl, Libor
2014-01-01
The purpose of this book is to serve as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address the problem of expressing a Lie algebra obtained in some arbitrary basis in a more suitable basis in which all essential features of the Lie algebra are directly visible. This includes algorithms accomplishing decomposition into a direct sum, identification of the radical and the Levi decomposition, and the computation of the nilradical and of the Casimir invariants. Examples are given for each algorithm. For low-dimensional Lie algebras this makes it possible to identify the given Lie algebra completely. The authors provide a representative list of all Lie algebras of dimension less or equal to 6 together with their important properties, including their Casimir invariants. The list is ordered in a way to make identification easy, using only basis independent properties of the Lie algebras. They also describe certain cl...
Energy Technology Data Exchange (ETDEWEB)
NONE
1996-02-01
The Department of Energy has prepared an Environmental Assessment (DOE/EA-1143) evaluating the construction, equipping and operation of the proposed Lied Transplant Center at the University of Nebraska Medical Center in Omaha, Nebraska. Based on the analysis in the EA, the DOE has determined that the proposed action does not constitute a major federal action significantly affecting the quality of the human environment within the meaning of the National Environmental Policy Act of 1969 (NEPA). Therefore, the preparation of an Environmental Statement in not required.
International Nuclear Information System (INIS)
Konstantopoulos, I. S.; Maybhate, A.; Charlton, J. C.; Gronwall, C.; Fedotov, K.; Desjardins, T. D.; Gallagher, S. C.; Durrell, P. R.; Mulchaey, J. S.; English, J.; Walker, L. M.; Johnson, K. E.; Tzanavaris, P.
2013-01-01
We present a multi-wavelength analysis of three compact galaxy groups, Hickson compact groups (HCGs) 16, 22, and 42, which describe a sequence in terms of gas richness, from space- (Swift, Hubble Space Telescope (HST), and Spitzer) and ground-based (Las Campanas Observatory and Cerro Tololo Inter-American Observatory) imaging and spectroscopy. We study various signs of past interactions including a faint, dusty tidal feature about HCG 16A, which we tentatively age-date at <1 Gyr. This represents the possible detection of a tidal feature at the end of its phase of optical observability. Our HST images also resolve what were thought to be double nuclei in HCG 16C and D into multiple, distinct sources, likely to be star clusters. Beyond our phenomenological treatment, we focus primarily on contrasting the stellar populations across these three groups. The star clusters show a remarkable intermediate-age population in HCG 22, and identify the time at which star formation was quenched in HCG 42. We also search for dwarf galaxies at accordant redshifts. The inclusion of 33 members and 27 ''associates'' (possible members) radically changes group dynamical masses, which in turn may affect previous evolutionary classifications. The extended membership paints a picture of relative isolation in HCGs 16 and 22, but shows HCG 42 to be part of a larger structure, following a dichotomy expected from recent studies. We conclude that (1) star cluster populations provide an excellent metric of evolutionary state, as they can age-date the past epochs of star formation; and (2) the extended dwarf galaxy population must be considered in assessing the dynamical state of a compact group.
Lagrangian submanifolds and dynamics on Lie algebroids
International Nuclear Information System (INIS)
Leon, Manuel de; Marrero, Juan C; MartInez, Eduardo
2005-01-01
In some previous papers, a geometric description of Lagrangian mechanics on Lie algebroids has been developed. In this topical review, we give a Hamiltonian description of mechanics on Lie algebroids. In addition, we introduce the notion of a Lagrangian submanifold of a symplectic Lie algebroid and we prove that the Lagrangian (Hamiltonian) dynamics on Lie algebroids may be described in terms of Lagrangian submanifolds of symplectic Lie algebroids. The Lagrangian (Hamiltonian) formalism on Lie algebroids permits us to deal with Lagrangian (Hamiltonian) functions not defined necessarily on tangent (cotangent) bundles. Thus, we may apply our results to the projection of Lagrangian (Hamiltonian) functions which are invariant under the action of a symmetry Lie group. As a consequence, we obtain that Lagrange-Poincare (Hamilton-Poincare) equations are the Euler-Lagrange (Hamilton) equations associated with the corresponding Atiyah algebroid. Moreover, we prove that Lagrange-Poincare (Hamilton-Poincare) equations are the local equations defining certain Lagrangian submanifolds of symplectic Atiyah algebroids. (topical review)
Lie Quasi-Bialgebras and Cohomology of Lie algebra
International Nuclear Information System (INIS)
Bangoura, Momo
2010-05-01
Lie quasi-bialgebras are natural generalisations of Lie bialgebras introduced by Drinfeld. To any Lie quasi-bialgebra structure of finite-dimensional (G, μ, γ, φ), corresponds one Lie algebra structure on D = G + G*, called the double of the given Lie quasi-bialgebra. We show that there exist on ΛG, the exterior algebra of G, a D-module structure and we establish an isomorphism of D-modules between ΛD and End(ΛG), D acting on ΛD by the adjoint action. (author) [fr
Renormalized Lie perturbation theory
International Nuclear Information System (INIS)
Rosengaus, E.; Dewar, R.L.
1981-07-01
A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another
Debey, E.; De Houwer, J.; Verschuere, B.
2014-01-01
Cognitive models of deception focus on the conflict-inducing nature of the truth activation during lying. Here we tested the counterintuitive hypothesis that the truth can also serve a functional role in the act of lying. More specifically, we examined whether the construction of a lie can involve a
Purposes and Effects of Lying.
Hample, Dale
Three exploratory studies were aimed at describing the purposes of lies and the consequences of lying. Data were collected through a partly open-ended questionnaire, a content analysis of several tape-recorded interviews, and a large-scale survey. The results showed that two of every three lies were told for selfish reasons, while three of every…
Lie-superalgebraical aspects of quantum statistics
International Nuclear Information System (INIS)
Palev, T.D.
1978-01-01
The Lie-superalgebraical properties of the ordinary quantum statistics are discussed with the aim of possible generalization in quantum theory and in theoretical physics. It is indicated that the algebra generated by n pairs of Fermi or paraFermi operators is isomorphic to the classical simple Lie algebra Bsub(n) of the SO(2n+1) orthogonal group, whereas n pairs of Bose or paraBose operators generate the simple orthosympletic superalgebra B(O,n). The transition to infinite number of creation and annihilation operators (n → infinity) does not change a superalgebraic structure. Hence, ordinary Bose and Fermi quantization can be considered as quantization over definite irreducible representations of two simple Lie superalgebras. The idea is given of how one can introduce creation and annihilation operators that satisfy the second quantization postulates and generate other simple Lie superalgebras
Indian Academy of Sciences (India)
Jyotishman Bhowmick
2015-11-07
Nov 7, 2015 ... Classical. Quantum. Background. Compact Hausdorff space. Unital C∗ algebra. Gelfand-Naimark. Compact Group. Compact Quantum Group. Woronowicz. Group Action. Coaction. Woronowicz. Riemannian manifold. Spectral triple. Connes. Isometry group. Quantum Isometry Group. To be discussed.
Exponentiation and deformations of Lie-admissible algebras
International Nuclear Information System (INIS)
Myung, H.C.
1982-01-01
The exponential function is defined for a finite-dimensional real power-associative algebra with unit element. The application of the exponential function is focused on the power-associative (p,q)-mutation of a real or complex associative algebra. Explicit formulas are computed for the (p,q)-mutation of the real envelope of the spin 1 algebra and the Lie algebra so(3) of the rotation group, in light of earlier investigations of the spin 1/2. A slight variant of the mutated exponential is interpreted as a continuous function of the Lie algebra into some isotope of the corresponding linear Lie group. The second part of this paper is concerned with the representation and deformation of a Lie-admissible algebra. The second cohomology group of a Lie-admissible algebra is introduced as a generalization of those of associative and Lie algebras in the Hochschild and Chevalley-Eilenberg theory. Some elementary theory of algebraic deformation of Lie-admissible algebras is discussed in view of generalization of that of associative and Lie algebras. Lie-admissible deformations are also suggested by the representation of Lie-admissible algebras. Some explicit examples of Lie-admissible deformation are given in terms of the (p,q)-mutation of associative deformation of an associative algebra. Finally, we discuss Lie-admissible deformations of order one
Lie Algebras and Integrable Systems
International Nuclear Information System (INIS)
Zhang Yufeng; Mei Jianqin
2012-01-01
A 3 × 3 matrix Lie algebra is first introduced, its subalgebras and the generated Lie algebras are obtained, respectively. Applications of a few Lie subalgebras give rise to two integrable nonlinear hierarchies of evolution equations from their reductions we obtain the nonlinear Schrödinger equations, the mKdV equations, the Broer-Kaup (BK) equation and its generalized equation, etc. The linear and nonlinear integrable couplings of one integrable hierarchy presented in the paper are worked out by casting a 3 × 3 Lie subalgebra into a 2 × 2 matrix Lie algebra. Finally, we discuss the elliptic variable solutions of a generalized BK equation. (general)
Group C∗-algebras without the completely bounded approximation property
DEFF Research Database (Denmark)
Haagerup, U.
2016-01-01
It is proved that: (1) The Fourier algebra A(G) of a simple Lie group G of real rank at least 2 with finite center does not have a multiplier bounded approximate unit. (2) The reduced C∗-algebra C∗ r of any lattice in a non-compact simple Lie group of real rank at least 2 with finite center does...... not have the completely bounded approximation property. Hence, the results obtained by de Canniere and the author for SOe (n, 1), n ≥ 2, and by Cowling for SU(n, 1) do not generalize to simple Lie groups of real rank at least 2. © 2016 Heldermann Verlag....
Celse, Jérémy; Chang, Kirk
2017-11-30
This research analyzed whether political leaders make people lie via priming experiments. Priming is a non-conscious and implicit memory effect in which exposure to one stimulus affects the response to another. Following priming theories, we proposed an innovative concept that people who perceive leaders to be dishonest (such as liars) are likely to lie themselves. We designed three experiments to analyze and critically discussed the potential influence of prime effect on lying behavior, through the prime effect of French political leaders (including general politicians, presidents and parties). Experiment 1 discovered that participants with non-politician-prime were less likely to lie (compared to politician-prime). Experiment 2A discovered that, compared to Hollande-prime, Sarkozy-prime led to lying behavior both in gravity (i.e., bigger lies) and frequency (i.e., lying more frequently). Experiment 2B discovered that Republicans-prime yielded an impact on more lying behavior, and Sarkozy-prime made such impact even stronger. Overall, the research findings suggest that lying can be triggered by external influencers such as leaders, presidents and politicians in the organizations. Our findings have provided valuable insights into organizational leaders and managers in their personnel management practice, especially in the intervention of lying behavior. Our findings also have offered new insights to explain non-conscious lying behavior.
Nonlinear σ-model with non-compact symmetry group and the theory of nonideal bose gas
International Nuclear Information System (INIS)
Pashaev, O.K.
1985-01-01
A continuous classical model of the Heisenberg magnet is constructed on the non-compact SU(1, 1)/U(1) manifold which is gauge equivalent to the nonlinear Schroedinger equation (MLS) of the repulsive type. It is shown that the choice of gauge transformation function as the Jost solutions for the NLS linear problem allows one to obtain solutions of the appropriate Σ-model of the magnet. Spin-wave and soliton solutions are presented. Energy, momentum and magnetization integrals are calculated. Spin waves are determined by the Bogoluybov frequency and describe precession on the hyperboloid surface with a fixed Msub(z) value. Soliton solution describes the magnetization vector yield from the precession plane. When condensate density p → O, then the spectrum coincides with the result obtained for SU(2) Heisenberg ferromagnet and with an exact solution for Bethe spin complex. In the case corresponding to unlimited length of vector S, the soliton spectrum coincides with the hole spectrum of antiferromagnet. There magnetizations related to the upper and lower sheets of the hyperboloid compensate for each other
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
Motivation and Consequences of Lying. A Qualitative Analysis of Everyday Lying
Directory of Open Access Journals (Sweden)
Beata Arcimowicz
2015-09-01
Full Text Available This article presents findings of qualitative analysis of semi-structured interviews with a group of "frequent liars" and another of "rare liars" who provided their subjective perspectives on the phenomenon of lying. Participants in this study previously had maintained a diary of their social interactions and lies over the course of one week, which allowed to assign them to one of the two groups: frequent or rare liars. Thematic analysis of the material followed by elements of theory formulation resulted in an extended lying typology that includes not only the target of the lie (the liar vs. other but also the motivation (protection vs. bringing benefits. We offer an analysis of what prevents from telling the truth, i.e. penalties, relationship losses, distress of the lied-to, and anticipated lack of criticism for telling the truth. We also focus on understanding moderatorsof consequences of lying (significance of the area of life, the type of lie and capacity to understand the liar that can be useful in future studies. URN: http://nbn-resolving.de/urn:nbn:de:0114-fqs1503318
Lie families: theory and applications
International Nuclear Information System (INIS)
Carinena, Jose F; Grabowski, Janusz; De Lucas, Javier
2010-01-01
We analyze the families of non-autonomous systems of first-order ordinary differential equations admitting a common time-dependent superposition rule, i.e. a time-dependent map expressing any solution of each of these systems in terms of a generic set of particular solutions of the system and some constants. We next study the relations of these families, called Lie families, with the theory of Lie and quasi-Lie systems and apply our theory to provide common time-dependent superposition rules for certain Lie families.
Lying in business : Insights from Hanna Arendt's 'Lying in Politics'
Eenkhoorn, P.; Graafland, J.J.
2011-01-01
The political philosopher Hannah Arendt develops several arguments regarding why truthfulness cannot be counted among the political virtues. This article shows that similar arguments apply to lying in business. Based on Hannah Arendt's theory, we distinguish five reasons why lying is a structural
Testosterone administration reduces lying in men.
Directory of Open Access Journals (Sweden)
Matthias Wibral
Full Text Available Lying is a pervasive phenomenon with important social and economic implications. However, despite substantial interest in the prevalence and determinants of lying, little is known about its biological foundations. Here we study a potential hormonal influence, focusing on the steroid hormone testosterone, which has been shown to play an important role in social behavior. In a double-blind placebo-controlled study, 91 healthy men (24.32±2.73 years received a transdermal administration of 50 mg of testosterone (n=46 or a placebo (n=45. Subsequently, subjects participated in a simple task, in which their payoff depended on the self-reported outcome of a die-roll. Subjects could increase their payoff by lying without fear of being caught. Our results show that testosterone administration substantially decreases lying in men. Self-serving lying occurred in both groups, however, reported payoffs were significantly lower in the testosterone group (p<0.01. Our results contribute to the recent debate on the effect of testosterone on prosocial behavior and its underlying channels.
DEFF Research Database (Denmark)
Brander, David; Rossman, Wayne; Schmitt, Nicholas
2010-01-01
We give an infinite dimensional generalized Weierstrass representation for spacelike constant mean curvature (CMC) surfaces in Minkowski 3-space $\\R^{2,1}$. The formulation is analogous to that given by Dorfmeister, Pedit and Wu for CMC surfaces in Euclidean space, replacing the group $SU_2$ with...
Gruppi, anelli di Lie e teoria della coomologia
Zappa, G
2011-01-01
This book includes: R. Baer: Complementation in finite gropus; M. Lazard: Groupes, anneaux de Lie et probleme de Burnside; J. Tits: Sur les groupes algebriques afffines; Theoremes fondamentaux de structure; and, Classification des groupes semisimples et geometries associees.
Lie algebraical aspects of quantum statistics
International Nuclear Information System (INIS)
Palev, T.D.
1976-01-01
It is shown that the secon quantization axioms can, in principle, be satisfied with creation and annihilation operators generating (in the case of n pairs of such operators) the Lie algebra Asub(n) of the group SL(n+1). A concept of the Fock space is introduced. The matrix elements of the operators are found
Sugawara operators for classical Lie algebras
Molev, Alexander
2018-01-01
The celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras. The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical \\mathcal{W}-algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations. An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the Harish-Chandra isomorphism connec...
Lying to patients with dementia: Attitudes versus behaviours in nurses.
Cantone, Daniela; Attena, Francesco; Cerrone, Sabrina; Fabozzi, Antonio; Rossiello, Riccardo; Spagnoli, Laura; Pelullo, Concetta Paola
2017-01-01
Using lies, in dementia care, reveals a common practice far beyond the diagnosis and prognosis, extending to the entire care process. In this article, we report results about the attitude and the behaviour of nurses towards the use of lies to patients with dementia. An epidemiological cross-sectional study was conducted between September 2016 and February 2017 in 12 elderly residential facilities and in the geriatric, psychiatric and neurological wards of six specialised hospitals of Italy's Campania Region. In all, 106 nurses compiled an attitude questionnaire (A) where the main question was 'Do you think it is ethically acceptable to use lies to patients with dementia?', instead 106 nurses compiled a behaviour questionnaire (B), where the main question was 'Have you ever used lies to patients with dementia?' Ethical considerations: Using lies in dementia care, although topic ethically still controversial, reveals a common practice far beyond the diagnosis and prognosis, extending to the entire care process. Only a small percentage of the interviewed nurses stated that they never used lies/that it is never acceptable to use lies (behaviour 10.4% and attitude 12.3%; p = 0.66). The situation in which nurses were more oriented to use lies was 'to prevent or reduce aggressive behaviors'. Indeed, only the 6.7% in the attitude group and 3.8% in the behaviour group were against using lies. On the contrary, the case in which the nurses were less oriented to use lies was 'to avoid wasting time giving explanations', in this situation were against using lies the 51.0% of the behaviour group and the 44.6% of the attitude group. Our results, according to other studies, support the hypothesis of a low propensity of nurses to ethical reflection about use of lies. In our country, the implementation of guidelines about a correct use of lie in the relationship between health operators and patients would be desirable.
Deformations of classical Lie algebras with homogeneous root system in characteristic two. I
International Nuclear Information System (INIS)
Chebochko, N G
2005-01-01
Spaces of local deformations of classical Lie algebras with a homogeneous root system over a field K of characteristic 2 are studied. By a classical Lie algebra over a field K we mean the Lie algebra of a simple algebraic Lie group or its quotient algebra by the centre. The description of deformations of Lie algebras is interesting in connection with the classification of the simple Lie algebras.
Transverse lie in labor: A study from Kaduna, Northern Nigeria ...
African Journals Online (AJOL)
Results: During the period there were 16633 deliveries and 30 women with transversely lying fetuses, giving an incidence of 1 in 554 deliveries. Forty percent of the cases were neglected transverse lies. The para 4 and above group had the highest incidence of 2.69/1000. Northern minorities ethnic group had the highest ...
Vakily, Masoomeh; Noroozi, Mahnaz; Yamani, Nikoo
2017-01-01
Training the health personnel about domestic violence would cause them to investigate and evaluate this issue more than before. Considering the new educational approaches for transferring knowledge, the goal of this research was to compare the effect of group-based and compact disk (CD)-based training on midwives' knowledge and attitude toward domestic violence. In this clinical experiment, seventy midwives working at health centers and hospitals of Isfahan were randomly allocated into two classes of group-based and CD-based trainings and were trained in the fields of recognition, prevention, and management of domestic violence. Data were collected by questionnaires which were completed by the midwives for evaluation of their knowledge and attitude. The mean score of midwives' knowledge and attitude toward domestic violence had a meaningful increase after the training (16.1, 46.9) compared to the score of before the training (12.1, 39.1) in both of the classes (group-based training: 17.7, 45.4) (CD-based training: 11.7, 38.6). No meaningful difference was observed between the two groups regarding midwives' attitude toward domestic violence after the intervention; however, regarding their knowledge level, the difference was statistically meaningful ( P = 0.001), and this knowledge increase was more in the CD-based training group. In spite of the effectiveness of both of the training methods in promoting midwives' knowledge and attitude about domestic violence, training with CD was more effective in increasing their knowledge; as a result, considering the benefits of CD-based training such as cost-effectiveness and possibility of use at any time, it is advised to be used in training programs for the health personnel.
Invariants of triangular Lie algebras
International Nuclear Information System (INIS)
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman
2007-01-01
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated
Wess-Zumino-Novikov-Witten models based on Lie superalgebras
International Nuclear Information System (INIS)
Mohammedi, N.
1994-04-01
The affine current algebra for Lie superalgebras is examined. The bilinear invariant forms of the Lie superalgebra can be either degenerate or non-degenerate. We give the conditions for a Virasoro construction, in which the currents are primary fields of weight one, to exist. In certain cases, the Virasoro central charge is an integer equal to the super dimension of the group supermanifold. A Wess-Zumino-Novikov-Witten action based on these Lie superalgebras is also found. (orig.)
Quantum group symmetry of classical and noncommutative geometry
Indian Academy of Sciences (India)
Debashish Goswami
2016-07-01
Jul 1, 2016 ... universal enveloping algebra U(L) of a Lie algebra L, (iv) ... Kustermans defined locally compact quantum groups too. .... There are other versions of quantum isometries formulated by me ..... classical connected spaces when either the space is ..... Etingof-Walton's paper, we have : (i) M0 is open and dense,.
Castillo, Encarnación; López-Ramos, Juan A.; Morales, Diego P.
2018-01-01
Security is a critical challenge for the effective expansion of all new emerging applications in the Internet of Things paradigm. Therefore, it is necessary to define and implement different mechanisms for guaranteeing security and privacy of data interchanged within the multiple wireless sensor networks being part of the Internet of Things. However, in this context, low power and low area are required, limiting the resources available for security and thus hindering the implementation of adequate security protocols. Group keys can save resources and communications bandwidth, but should be combined with public key cryptography to be really secure. In this paper, a compact and unified co-processor for enabling Elliptic Curve Cryptography along to Advanced Encryption Standard with low area requirements and Group-Key support is presented. The designed co-processor allows securing wireless sensor networks with independence of the communications protocols used. With an area occupancy of only 2101 LUTs over Spartan 6 devices from Xilinx, it requires 15% less area while achieving near 490% better performance when compared to cryptoprocessors with similar features in the literature. PMID:29337921
Parrilla, Luis; Castillo, Encarnación; López-Ramos, Juan A; Álvarez-Bermejo, José A; García, Antonio; Morales, Diego P
2018-01-16
Security is a critical challenge for the effective expansion of all new emerging applications in the Internet of Things paradigm. Therefore, it is necessary to define and implement different mechanisms for guaranteeing security and privacy of data interchanged within the multiple wireless sensor networks being part of the Internet of Things. However, in this context, low power and low area are required, limiting the resources available for security and thus hindering the implementation of adequate security protocols. Group keys can save resources and communications bandwidth, but should be combined with public key cryptography to be really secure. In this paper, a compact and unified co-processor for enabling Elliptic Curve Cryptography along to Advanced Encryption Standard with low area requirements and Group-Key support is presented. The designed co-processor allows securing wireless sensor networks with independence of the communications protocols used. With an area occupancy of only 2101 LUTs over Spartan 6 devices from Xilinx, it requires 15% less area while achieving near 490% better performance when compared to cryptoprocessors with similar features in the literature.
Directory of Open Access Journals (Sweden)
Luis Parrilla
2018-01-01
Full Text Available Security is a critical challenge for the effective expansion of all new emerging applications in the Internet of Things paradigm. Therefore, it is necessary to define and implement different mechanisms for guaranteeing security and privacy of data interchanged within the multiple wireless sensor networks being part of the Internet of Things. However, in this context, low power and low area are required, limiting the resources available for security and thus hindering the implementation of adequate security protocols. Group keys can save resources and communications bandwidth, but should be combined with public key cryptography to be really secure. In this paper, a compact and unified co-processor for enabling Elliptic Curve Cryptography along to Advanced Encryption Standard with low area requirements and Group-Key support is presented. The designed co-processor allows securing wireless sensor networks with independence of the communications protocols used. With an area occupancy of only 2101 LUTs over Spartan 6 devices from Xilinx, it requires 15% less area while achieving near 490% better performance when compared to cryptoprocessors with similar features in the literature.
"Lie to me"-Oxytocin impairs lie detection between sexes.
Pfundmair, Michaela; Erk, Wiebke; Reinelt, Annika
2017-10-01
The hormone oxytocin modulates various aspects of social behaviors and even seems to lead to a tendency for gullibility. The aim of the current study was to investigate the effect of oxytocin on lie detection. We hypothesized that people under oxytocin would be particularly susceptible to lies told by people of the opposite sex. After administration of oxytocin or a placebo, male and female participants were asked to judge the veracity of statements from same- vs. other-sex actors who either lied or told the truth. Results showed that oxytocin decreased the ability of both male and female participants to correctly classify other-sex statements as truths or lies compared to placebo. This effect was based on a lower ability to detect lies and not a stronger bias to regard truth statements as false. Revealing a new effect of oxytocin, the findings may support assumptions about the hormone working as a catalyst for social adaption. Copyright © 2017. Published by Elsevier Ltd.
Bases in Lie and quantum algebras
International Nuclear Information System (INIS)
Ballesteros, A; Celeghini, E; Olmo, M A del
2008-01-01
Applications of algebras in physics are related to the connection of measurable observables to relevant elements of the algebras, usually the generators. However, in the determination of the generators in Lie algebras there is place for some arbitrary conventions. The situation is much more involved in the context of quantum algebras, where inside the quantum universal enveloping algebra, we have not enough primitive elements that allow for a privileged set of generators and all basic sets are equivalent. In this paper we discuss how the Drinfeld double structure underlying every simple Lie bialgebra characterizes uniquely a particular basis without any freedom, completing the Cartan program on simple algebras. By means of a perturbative construction, a distinguished deformed basis (we call it the analytical basis) is obtained for every quantum group as the analytical prolongation of the above defined Lie basis of the corresponding Lie bialgebra. It turns out that the whole construction is unique, so to each quantum universal enveloping algebra is associated one and only one bialgebra. In this way the problem of the classification of quantum algebras is moved to the classification of bialgebras. In order to make this procedure more clear, we discuss in detail the simple cases of su(2) and su q (2).
Desjardins, Tyler D.; Gallagher, Sarah C.; Hornschemeier, Ann E.; Mulchaey, John S.; Walker, Lisa May; Brandt, Willian N.; Charlton, Jane C.; Johnson, Kelsey E.; Tzanavaris, Panayiotis
2014-01-01
We present an analysis of the diffuse X-ray emission in 19 compact groups (CGs) of galaxies observed with Chandra. The hottest, most X-ray luminous CGs agree well with the galaxy cluster X-ray scaling relations in L(x-T) and (L(x-sigma), even in CGs where the hot gas is associated with only the brightest galaxy. Using Spitzer photometry, we compute stellar masses and classify Hickson CGs 19, 22, 40, and 42, and RSCGs 32, 44, and 86 as fossil groups using a new definition for fossil systems that includes a broader range of masses. We find that CGs with total stellar and Hi masses are great than or equal to 10(sup (11.3) solar mass are often X-ray luminous, while lower-mass CGs only sometimes exhibit faint, localized X-ray emission. Additionally, we compare the diffuse X-ray luminosity against both the total UV and 24 micron star formation rates of each CG and optical colors of the most massive galaxy in each of the CGs. The most X-ray luminous CGs have the lowest star formation rates, likely because there is no cold gas available for star formation, either because the majority of the baryons in these CGs are in stars or the X-ray halo, or due togas stripping from the galaxies in CGs with hot halos. Finally, the optical colors that trace recent star formation histories of the most massive group galaxies do not correlate with the X-ray luminosities of the CGs, indicating that perhaps the current state of the X-ray halos is independent of the recent history of stellar mass assembly in the most massive galaxies.
Transitive Lie algebras of vector fields: an overview
Draisma, J.
2011-01-01
This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary differential equations, these algebras, or infinitesimal groups, are a recurring theme in 20th-century research on
Counting Semisimple Orbits of Finite Lie Algebras by Genus
Fulman, Jason
1999-01-01
The adjoint action of a finite group of Lie type on its Lie algebra is studied. A simple formula is conjectured for the number of split semisimple orbits of a given genus. This conjecture is proved for type A, and partial results are obtained for other types. For type A a probabilistic interpretation is given in terms of card shuffling.
Akivis, M A
2011-01-01
This book describes the life and achievements of the great French mathematician, Elie Cartan. Here readers will find detailed descriptions of Cartan's discoveries in Lie groups and algebras, associative algebras, differential equations, and differential geometry, as well of later developments stemming from his ideas. There is also a biographical sketch of Cartan's life. A monumental tribute to a towering figure in the history of mathematics, this book will appeal to mathematicians and historians alike.
Invariants of generalized Lie algebras
International Nuclear Information System (INIS)
Agrawala, V.K.
1981-01-01
Invariants and invariant multilinear forms are defined for generalized Lie algebras with arbitrary grading and commutation factor. Explicit constructions of invariants and vector operators are given by contracting invariant forms with basic elements of the generalized Lie algebra. The use of the matrix of a linear map between graded vector spaces is emphasized. With the help of this matrix, the concept of graded trace of a linear operator is introduced, which is a rich source of multilinear forms of degree zero. To illustrate the use of invariants, a characteristic identity similar to that of Green is derived and a few Racah coefficients are evaluated in terms of invariants
Energy Technology Data Exchange (ETDEWEB)
Bluemich, Bernhard; Haber-Pohlmeier, Sabina; Zia, Wasif [RWTH Aachen Univ. (Germany). Inst. fuer Technische und Makromolekulare Chemie (ITMC)
2014-06-01
Nuclear Magnetic Resonance (NMR) spectroscopy is the most popular method for chemists to analyze molecular structures, while Magnetic Resonance Imaging (MRI) is a non-invasive diagnostic tool for medical doctors that provides high-contrast images of biological tissue. In both applications, the sample (or patient) is positioned inside a large, superconducting magnet to magnetize the atomic nuclei. Interrogating radio-frequency pulses result in frequency spectra that provide the chemist with molecular information, the medical doctor with anatomic images, and materials scientist with NMR relaxation parameters. Recent advances in magnet technology have led to a variety of small permanent magnets to allow compact and low-cost instruments. The goal of this book is to provide an introduction to the practical use of compact NMR at a level nearly as basic as the operation of a smart phone.
Energy Technology Data Exchange (ETDEWEB)
Bazeia, D.; Losano, L.; Marques, M.A.; Zafalan, I. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Menezes, R. [Universidade Federal da Paraiba, Departamento de Ciencias Exatas, Rio Tinto, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil)
2017-02-15
We study a family of Maxwell-Higgs models, described by the inclusion of a function of the scalar field that represent generalized magnetic permeability. We search for vortex configurations which obey first-order differential equations that solve the equations of motion. We first deal with the asymptotic behavior of the field configurations, and then implement a numerical study of the solutions, the energy density and the magnetic field. We work with the generalized permeability having distinct profiles, giving rise to new models, and we investigate how the vortices behave, compared with the solutions of the corresponding standard models. In particular, we show how to build compact vortices, that is, vortex solutions with the energy density and magnetic field vanishing outside a compact region of the plane. (orig.)
Estevez-Delgado, Gabino; Estevez-Delgado, Joaquin
2018-05-01
An analysis and construction is presented for a stellar model characterized by two parameters (w, n) associated with the compactness ratio and anisotropy, respectively. The reliability range for the parameter w ≤ 1.97981225149 corresponds with a compactness ratio u ≤ 0.2644959374, the density and pressures are positive, regular and monotonic decrescent functions, the radial and tangential speed of sound are lower than the light speed, moreover, than the plausible stability. The behavior of the speeds of sound are determinate for the anisotropy parameter n, admitting a subinterval where the speeds are monotonic crescent functions and other where we have monotonic decrescent functions for the same speeds, both cases describing a compact object that is also potentially stable. In the bigger value for the observational mass M = 2.05 M⊙ and radii R = 12.957 Km for the star PSR J0348+0432, the model indicates that the maximum central density ρc = 1.283820319 × 1018 Kg/m3 corresponds to the maximum value of the anisotropy parameter and the radial and tangential speed of the sound are monotonic decrescent functions.
Isomorphism of Intransitive Linear Lie Equations
Directory of Open Access Journals (Sweden)
Jose Miguel Martins Veloso
2009-11-01
Full Text Available We show that formal isomorphism of intransitive linear Lie equations along transversal to the orbits can be extended to neighborhoods of these transversal. In analytic cases, the word formal is dropped from theorems. Also, we associate an intransitive Lie algebra with each intransitive linear Lie equation, and from the intransitive Lie algebra we recover the linear Lie equation, unless of formal isomorphism. The intransitive Lie algebra gives the structure functions introduced by É. Cartan.
Cartan Connections and Lie Algebroids
Directory of Open Access Journals (Sweden)
Michael Crampin
2009-06-01
Full Text Available This paper is a study of the relationship between two constructions associated with Cartan geometries, both of which involve Lie algebroids: the Cartan algebroid, due to [Blaom A.D., Trans. Amer. Math. Soc. 358 (2006, 3651–3671], and tractor calculus [Cap A., Gover A.R., Trans. Amer. Math. Soc. 354 (2001, 1511–1548].
Group actions, non-Kähler complex manifolds and SKT structures
Directory of Open Access Journals (Sweden)
Poddar Mainak
2018-02-01
Full Text Available We give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the constructions of complex structure on compact Lie groups by Samelson and Wang, and on principal torus bundles by Calabi-Eckmann and others. It also yields large classes of new examples of non-Kähler compact complex manifolds. Moreover, under suitable restrictions on the base manifold, the structure group, and characteristic classes, the total space of the principal bundle admits SKT metrics. This generalizes recent results of Grantcharov et al. We study the Picard group and the algebraic dimension of the total space in some cases. We also use a slightly generalized version of the construction to obtain (non-Kähler complex structures on tangential frame bundles of complex orbifolds.
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
Fractional supersymmetry and infinite dimensional lie algebras
International Nuclear Information System (INIS)
Rausch de Traubenberg, M.
2001-01-01
In an earlier work extensions of supersymmetry and super Lie algebras were constructed consistently starting from any representation D of any Lie algebra g. Here it is shown how infinite dimensional Lie algebras appear naturally within the framework of fractional supersymmetry. Using a differential realization of g this infinite dimensional Lie algebra, containing the Lie algebra g as a sub-algebra, is explicitly constructed
Particle-like structure of Lie algebras
Vinogradov, A. M.
2017-07-01
If a Lie algebra structure 𝔤 on a vector space is the sum of a family of mutually compatible Lie algebra structures 𝔤i's, we say that 𝔤 is simply assembled from the 𝔤i's. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the 𝔤i's, one obtains a Lie algebra assembled in two steps from 𝔤i's, and so on. We describe the process of modular disassembling of a Lie algebra into a unimodular and a non-unimodular part. We then study two inverse questions: which Lie algebras can be assembled from a given family of Lie algebras, and from which Lie algebras can a given Lie algebra be assembled. We develop some basic assembling and disassembling techniques that constitute the elements of a new approach to the general theory of Lie algebras. The main result of our theory is that any finite-dimensional Lie algebra over an algebraically closed field of characteristic zero or over R can be assembled in a finite number of steps from two elementary constituents, which we call dyons and triadons. Up to an abelian summand, a dyon is a Lie algebra structure isomorphic to the non-abelian 2-dimensional Lie algebra, while a triadon is isomorphic to the 3-dimensional Heisenberg Lie algebra. As an example, we describe constructions of classical Lie algebras from triadons.
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
A cohomological characterization of Leibniz central extensions of Lie algebras
International Nuclear Information System (INIS)
Hu Naihong; Pei Yufeng; Liu Dong
2006-12-01
Motivated by Pirashvili's spectral sequences on a Leibniz algebra, some notions such as invariant symmetric bilinear forms, dual space derivations and the Cartan-Koszul homomorphism are connected together to give a description of the second Leibniz cohomology groups with trivial coefficients of Lie algebras (as Leibniz objects), which leads to a concise approach to determining one-dimensional Leibniz central extensions of Lie algebras. As applications, we contain the discussions for some interesting classes of infinite-dimensional Lie algebras. In particular, our results include the cohomological version of Gao's main Theorem for Kac-Moody algebras and answer a question. (author)
Sophus Lie une pensée audacieuse
Stubhaug, Arild
2006-01-01
Sophus Lie (1842-1899) compte parmi les plus grandes figures norvgiennes de la science. La notorit que lui valent ses travaux n'a rien envier celle de son illustre compatriote Niels Henrik Abel. Groupes et alg bres de Lie ont acquis droit de cit dans maints domaines. Dans cette biographie dtaille, l'crivain Arild Stubhaug, puisant dans la volumineuse correspondance de Lie, dcrit l'homme et la socit norvgienne dans la seconde moiti du XIXe si cle. Le lecteur peut ainsi suivre son enfance dans un presbyt re nich au fond d'un fjord, dcouvrir les rformes de l'enseignement, voyager en Europe, frque
Filiform Lie algebras of order 3
International Nuclear Information System (INIS)
Navarro, R. M.
2014-01-01
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases
Filiform Lie algebras of order 3
Navarro, R. M.
2014-04-01
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, "Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes," Bull. Soc. Math. France 98, 81-116 (1970)]. Also we give the dimension, using an adaptation of the {sl}(2,{C})-module Method, and a basis of such infinitesimal deformations in some generic cases.
Lie-algebra approach to symmetry breaking
International Nuclear Information System (INIS)
Anderson, J.T.
1981-01-01
A formal Lie-algebra approach to symmetry breaking is studied in an attempt to reduce the arbitrariness of Lagrangian (Hamiltonian) models which include several free parameters and/or ad hoc symmetry groups. From Lie algebra it is shown that the unbroken Lagrangian vacuum symmetry can be identified from a linear function of integers which are Cartan matrix elements. In broken symmetry if the breaking operators form an algebra then the breaking symmetry (or symmetries) can be identified from linear functions of integers characteristic of the breaking symmetries. The results are applied to the Dirac Hamiltonian of a sum of flavored fermions and colored bosons in the absence of dynamical symmetry breaking. In the partially reduced quadratic Hamiltonian the breaking-operator functions are shown to consist of terms of order g 2 , g, and g 0 in the color coupling constants and identified with strong (boson-boson), medium strong (boson-fermion), and fine-structure (fermion-fermion) interactions. The breaking operators include a boson helicity operator in addition to the familiar fermion helicity and ''spin-orbit'' terms. Within the broken vacuum defined by the conventional formalism, the field divergence yields a gauge which is a linear function of Cartan matrix integers and which specifies the vacuum symmetry. We find that the vacuum symmetry is chiral SU(3) x SU(3) and the axial-vector-current divergence gives a PCAC -like function of the Cartan matrix integers which reduces to PCAC for SU(2) x SU(2) breaking. For the mass spectra of the nonets J/sup P/ = 0 - ,1/2 + ,1 - the integer runs through the sequence 3,0,-1,-2, which indicates that the breaking subgroups are the simple Lie groups. Exact axial-vector-current conservation indicates a breaking sum rule which generates octet enhancement. Finally, the second-order breaking terms are obtained from the second-order spin tensor sum of the completely reduced quartic Hamiltonian
Some quantum Lie algebras of type Dn positive
International Nuclear Information System (INIS)
Bautista, Cesar; Juarez-Ramirez, Maria Araceli
2003-01-01
A quantum Lie algebra is constructed within the positive part of the Drinfeld-Jimbo quantum group of type D n . Our quantum Lie algebra structure includes a generalized antisymmetry property and a generalized Jacobi identity closely related to the braid equation. A generalized universal enveloping algebra of our quantum Lie algebra of type D n positive is proved to be the Drinfeld-Jimbo quantum group of the same type. The existence of such a generalized Lie algebra is reduced to an integer programming problem. Moreover, when the integer programming problem is feasible we show, by means of the generalized Jacobi identity, that the Poincare-Birkhoff-Witt theorem (basis) is still true
Butler, Steve; Gass, Mike; Schoel, Jim; Murphy, Morgan; Murray, Mark; White, Will; Loggers, Otto; Renaker, Paul
1999-01-01
Describes nine group problem-solving and communication initiatives used in adventure- and experiential-education settings. Includes target group, group size, time and space requirements, activity level, props, instructions, and tips for post-activity group reflection and processing. Activities emphasize teamwork, communication skills, and a…
Particle-like structure of coaxial Lie algebras
Vinogradov, A. M.
2018-01-01
This paper is a natural continuation of Vinogradov [J. Math. Phys. 58, 071703 (2017)] where we proved that any Lie algebra over an algebraically closed field or over R can be assembled in a number of steps from two elementary constituents, called dyons and triadons. Here we consider the problems of the construction and classification of those Lie algebras which can be assembled in one step from base dyons and triadons, called coaxial Lie algebras. The base dyons and triadons are Lie algebra structures that have only one non-trivial structure constant in a given basis, while coaxial Lie algebras are linear combinations of pairwise compatible base dyons and triadons. We describe the maximal families of pairwise compatible base dyons and triadons called clusters, and, as a consequence, we give a complete description of the coaxial Lie algebras. The remarkable fact is that dyons and triadons in clusters are self-organised in structural groups which are surrounded by casings and linked by connectives. We discuss generalisations and applications to the theory of deformations of Lie algebras.
Pharmaceutical powder compaction technology
National Research Council Canada - National Science Library
Çelik, Metin
2011-01-01
... through the compaction formulation process and application. Compaction of powder constituents both active ingredient and excipients is examined to ensure consistent and reproducible disintegration and dispersion profiles...
Lying in the Name of the Collective Good: A Developmental Study
Fu, Genyue; Evans, Angela D.; Wang, Lingfeng; Lee, Kang
2008-01-01
The present study examined the developmental origin of "blue lies", a pervasive form of lying in the adult world that is told purportedly to benefit a collective. Seven, 9-, and 11-year-old Chinese children were surreptitiously placed in a real-life situation where they decided whether to lie to conceal their group's cheating behavior. Children…
Lie algebroids in derived differential topology
Nuiten, J.J.
2018-01-01
A classical principle in deformation theory asserts that any formal deformation problem is controlled by a differential graded Lie algebra. This thesis studies a generalization of this principle to Lie algebroids, and uses this to examine the interactions between the theory of Lie algebroids and the
The Centroid of a Lie Triple Algebra
Directory of Open Access Journals (Sweden)
Xiaohong Liu
2013-01-01
Full Text Available General results on the centroids of Lie triple algebras are developed. Centroids of the tensor product of a Lie triple algebra and a unitary commutative associative algebra are studied. Furthermore, the centroid of the tensor product of a simple Lie triple algebra and a polynomial ring is completely determined.
The First Honest Book about Lies.
Kincher, Jonni; Espeland, Pamela, Ed.
Readers learn how to discern the truth from lies through a series of activities, games, and experiments. This book invites young students to look at lies in a fair and balanced way. Different types of lies are examined and the purposes they serve and discussed. Problem solving activities are given. The book is organized in nine chapters,…
On a parametrization of Baker-Campbell-Hausdorf formula for bosonic superfields in Lie algebra
International Nuclear Information System (INIS)
Gabeskiria, M.A.
1984-01-01
A compact form for the Baker-Cambell-Hausdorf formula has been obtained. Here the dependence of bosonic superfields, with their values on the Crassmann hull G(LAMBDA 2 ) of Lie algebra G, on the generators LAMBDA 2 has been factorized as a single exponent
Directory of Open Access Journals (Sweden)
Dong Junyan
2016-01-01
Full Text Available Due to the poor transport system, remoteness and few channels to access to information from the outside world in most minority-inhabited areas in China, buildings in these areas are well preserved. In particular, dwellings in these places show low-tech and ecological features. Different types and the natural environment of the plateau where Shangri-La lies provide people with a variety of living resources. As living environments vary in different areas, different inhabitation forms have been formed. Tibetan people adjust measures to local conditions and excel at using local materials and appropriate technologies to build houses. In this paper, a case study is made of traditional dwellings in Tibetan-inhabited areas in Shangri-La, to analyze low-tech and ecological strategies for traditional dwellings in Tibetan-inhabited areas in Shangri-La, from three aspects: regional environment measures, building technologies and the spatial order system.
Lie-algebraic classification of effective theories with enhanced soft limits
Bogers, Mark P.; Brauner, Tomáš
2018-05-01
A great deal of effort has recently been invested in developing methods of calculating scattering amplitudes that bypass the traditional construction based on Lagrangians and Feynman rules. Motivated by this progress, we investigate the long-wavelength behavior of scattering amplitudes of massless scalar particles: Nambu-Goldstone (NG) bosons. The low-energy dynamics of NG bosons is governed by the underlying spontaneously broken symmetry, which likewise allows one to bypass the Lagrangian and connect the scaling of the scattering amplitudes directly to the Lie algebra of the symmetry generators. We focus on theories with enhanced soft limits, where the scattering amplitudes scale with a higher power of momentum than expected based on the mere existence of Adler's zero. Our approach is complementary to that developed recently in ref. [1], and in the first step we reproduce their result. That is, as far as Lorentz-invariant theories with a single physical NG boson are concerned, we find no other nontrivial theories featuring enhanced soft limits beyond the already well-known ones: the Galileon and the Dirac-Born-Infeld (DBI) scalar. Next, we show that in a certain sense, these theories do not admit a nontrivial generalization to non-Abelian internal symmetries. Namely, for compact internal symmetry groups, all NG bosons featuring enhanced soft limits necessarily belong to the center of the group. For noncompact symmetry groups such as the ISO( n) group featured by some multi-Galileon theories, these NG bosons then necessarily belong to an Abelian normal subgroup. The Lie-algebraic consistency constraints admit two infinite classes of solutions, generalizing the known multi-Galileon and multi-flavor DBI theories.
Zanette, Sarah; Gao, Xiaoqing; Brunet, Megan; Bartlett, Marian Stewart; Lee, Kang
2016-10-01
The current study used computer vision technology to examine the nonverbal facial expressions of children (6-11years old) telling antisocial and prosocial lies. Children in the antisocial lying group completed a temptation resistance paradigm where they were asked not to peek at a gift being wrapped for them. All children peeked at the gift and subsequently lied about their behavior. Children in the prosocial lying group were given an undesirable gift and asked if they liked it. All children lied about liking the gift. Nonverbal behavior was analyzed using the Computer Expression Recognition Toolbox (CERT), which employs the Facial Action Coding System (FACS), to automatically code children's facial expressions while lying. Using CERT, children's facial expressions during antisocial and prosocial lying were accurately and reliably differentiated significantly above chance-level accuracy. The basic expressions of emotion that distinguished antisocial lies from prosocial lies were joy and contempt. Children expressed joy more in prosocial lying than in antisocial lying. Girls showed more joy and less contempt compared with boys when they told prosocial lies. Boys showed more contempt when they told prosocial lies than when they told antisocial lies. The key action units (AUs) that differentiate children's antisocial and prosocial lies are blink/eye closure, lip pucker, and lip raise on the right side. Together, these findings indicate that children's facial expressions differ while telling antisocial versus prosocial lies. The reliability of CERT in detecting such differences in facial expression suggests the viability of using computer vision technology in deception research. Copyright © 2016 Elsevier Inc. All rights reserved.
On Deformations and Contractions of Lie Algebras
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Marc de Montigny
2006-05-01
Full Text Available In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras. We first discuss low-dimensional Lie algebras and illustrate thereby that whereas for every contraction there exists a reverse deformation, the converse is not true in general. Also we note that some Lie algebras belonging to parameterized families are singled out by the irreversibility of deformations and contractions. After reminding that global deformations of the Witt, Virasoro, and affine Kac-Moody algebras allow one to retrieve Lie algebras of Krichever-Novikov type, we contract the latter to find new infinite dimensional Lie algebras.
Quantum Lie theory a multilinear approach
Kharchenko, Vladislav
2015-01-01
This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin Lie algebras; and Shestakov--Umirbaev operations for the Lie theory of nonassociative products. Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.
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.
Lewis, Scott M; Christova, Peka; Jerde, Trenton A; Georgopoulos, Apostolos P
2012-01-01
We used hierarchical tree clustering to derive a functional organizational chart of 52 human cortical areas (26 per hemisphere) from zero-lag correlations calculated between single-voxel, prewhitened, resting-state BOLD fMRI time series in 18 subjects. No special "resting-state networks" were identified. There were four major features in the resulting tree (dendrogram). First, there was a strong clustering of homotopic, left-right hemispheric areas. Second, cortical areas were concatenated in multiple, partially overlapping clusters. Third, the arrangement of the areas revealed a layout that closely resembled the actual layout of the cerebral cortex, namely an orderly progression from anterior to posterior. And fourth, the layout of the cortical areas in the tree conformed to principles of efficient, compact layout of components proposed by Cherniak. Since the tree was derived on the basis of the strength of neural correlations, these results document an orderly relation between functional interactions and layout, i.e., between structure and function.
Lewis, Scott M.; Christova, Peka; Jerde, Trenton A.; Georgopoulos, Apostolos P.
2012-01-01
We used hierarchical tree clustering to derive a functional organizational chart of 52 human cortical areas (26 per hemisphere) from zero-lag correlations calculated between single-voxel, prewhitened, resting-state BOLD fMRI time series in 18 subjects. No special “resting-state networks” were identified. There were four major features in the resulting tree (dendrogram). First, there was a strong clustering of homotopic, left-right hemispheric areas. Second, cortical areas were concatenated in multiple, partially overlapping clusters. Third, the arrangement of the areas revealed a layout that closely resembled the actual layout of the cerebral cortex, namely an orderly progression from anterior to posterior. And fourth, the layout of the cortical areas in the tree conformed to principles of efficient, compact layout of components proposed by Cherniak. Since the tree was derived on the basis of the strength of neural correlations, these results document an orderly relation between functional interactions and layout, i.e., between structure and function. PMID:22973198
Challenges: a state and compact perspective
International Nuclear Information System (INIS)
Brown, H.
1987-01-01
The challenges facing states and compacts in their efforts to implement the Low-Level Waste Policy Amendments Act are described. Institutional challenges include: small-volume sites; compact maintenance; shifting agencies and changing personnel; and timing of progress. The technical challenge lies in the enormous number of plans, procedures, and regulations that have to be developed over the next four years. There are two main fiscal challenges: funding of day-to-day operations of compact commissions; and financing the siting and construction of new disposal sites. There are also two main regulatory challenges: host states must develop regulations for siting and selection of technology; and all states have to await federal regulations to be completed. The final challenge is political: whether a region can overcome public opposition and actually site a facility
Cartan calculus on quantum Lie algebras
International Nuclear Information System (INIS)
Schupp, P.; Watts, P.; Zumino, B.
1993-01-01
A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum spaces we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions au into one big algebra, the ''Cartan Calculus.''
Testosterone Administration Reduces Lying in Men
Wibral, M.; Dohmen, T.J.; Klingmüller, Dietrich; Weber, Bernd; Falk, Armin
2012-01-01
Lying is a pervasive phenomenon with important social and economic implications. However, despite substantial interest in the prevalence and determinants of lying, little is known about its biological foundations. Here we study a potential hormonal influence, focusing on the steroid hormone
Lie symmetries for systems of evolution equations
Paliathanasis, Andronikos; Tsamparlis, Michael
2018-01-01
The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the differential equations. The exact relation of the Lie symmetries with the collineations of the bimetric space is determined.
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
Computing nilpotent quotients in finitely presented Lie rings
Directory of Open Access Journals (Sweden)
Csaba Schneider
1997-12-01
Full Text Available A nilpotent quotient algorithm for finitely presented Lie rings over Z (and Q is described. The paper studies the graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented, nilpotent Lie ring. A nilpotent presentation consists of generators for the abelian group and the products expressed as linear combinations for pairs formed by generators. Using that presentation the word problem is decidable in L. Provided that the Lie ring L is graded, it is possible to determine the canonical presentation for a lower central factor of L. Complexity is studied and it is shown that optimising the presentation is NP-hard. Computational details are provided with examples, timing and some structure theorems obtained from computations. Implementation in C and GAP interface are available.
Mappings with closed range and compactness
International Nuclear Information System (INIS)
Iyahen, S.O.; Umweni, I.
1985-12-01
The motivation for this note is the result of E.O. Thorp that a normed linear space E is finite dimensional if and only if every continuous linear map for E into any normed linear space has a closed range. Here, a class of Hausdorff topological groups is introduced; called r-compactifiable topological groups, they include compact groups, locally compact Abelian groups and locally convex linear topological spaces. It is proved that a group in this class which is separable, complete metrizable or locally compact, is necessarily compact if its image by a continuous group homomorphism is necessarily closed. It is deduced then that a Hausdorff locally convex is zero if its image by a continuous additive map is necessarily closed. (author)
Realization of vector fields for quantum groups as pseudodifferential operators on quantum spaces
International Nuclear Information System (INIS)
Chu, Chong-Sun; Zumino, B.
1995-01-01
The vector fields of the quantum Lie algebra are described for the quantum groups GL q (n), SL q (N) and SO q (N) as pseudodifferential operators on the linear quantum spaces covariant under the corresponding quantum group. Their expressions are simple and compact. It is pointed out that these vector fields satisfy certain characteristic polynomial identities. The real forms SU q (N) and SO q (N,R) are discussed in detail
On the uniform perfectness of equivariant diffeomorphism groups for principal G manifolds
Directory of Open Access Journals (Sweden)
Kazuhiko Fukui
2017-01-01
Full Text Available We proved in [K. Abe, K. Fukui, On commutators of equivariant diffeomorphisms, Proc. Japan Acad. 54 (1978, 52-54] that the identity component \\(\\text{Diff}\\,^r_{G,c}(M_0\\ of the group of equivariant \\(C^r\\-diffeomorphisms of a principal \\(G\\ bundle \\(M\\ over a manifold \\(B\\ is perfect for a compact connected Lie group \\(G\\ and \\(1 \\leq r \\leq \\infty\\ (\\(r \
Vertex ring-indexed Lie algebras
International Nuclear Information System (INIS)
Fairlie, David; Zachos, Cosmas
2005-01-01
Infinite-dimensional Lie algebras are introduced, which are only partially graded, and are specified by indices lying on cyclotomic rings. They may be thought of as generalizations of the Onsager algebra, but unlike it, or its sl(n) generalizations, they are not subalgebras of the loop algebras associated with sl(n). In a particular interesting case associated with sl(3), their indices lie on the Eisenstein integer triangular lattice, and these algebras are expected to underlie vertex operator combinations in CFT, brane physics, and graphite monolayers
Representations of some quantum tori Lie subalgebras
International Nuclear Information System (INIS)
Jiang, Jingjing; Wang, Song
2013-01-01
In this paper, we define the q-analog Virasoro-like Lie subalgebras in x ∞ =a ∞ (b ∞ , c ∞ , d ∞ ). The embedding formulas into x ∞ are introduced. Irreducible highest weight representations of A(tilde sign) q , B(tilde sign) q , and C(tilde sign) q -series of the q-analog Virasoro-like Lie algebras in terms of vertex operators are constructed. We also construct the polynomial representations of the A(tilde sign) q , B(tilde sign) q , C(tilde sign) q , and D(tilde sign) q -series of the q-analog Virasoro-like Lie algebras.
Quartic trace identity for exceptional Lie algebras
International Nuclear Information System (INIS)
Okubo, S.
1979-01-01
Let X be a representation matrix of generic element x of a simple Lie algebra in generic irreducible representation ]lambda] of the Lie algebra. Then, for all exceptional Lie algebras as well as A 1 and A 2 , we can prove the validity of a quartic trace identity Tr(X 4 ) =K (lambda)[Tr(X 2 )] 2 , where the constant K (lambda) depends only upon the irreducible representation ]lambda], and its explicit form is calculated. Some applications of second and fourth order indices have also been discussed
Lie-Nambu and Lie-Poisson structures in linear and nonlinear quantum mechanics
International Nuclear Information System (INIS)
Czachor, M.
1996-01-01
Space of density matrices in quantum mechanics can be regarded as a Poisson manifold with the dynamics given by certain Lie-Poisson bracket corresponding to an infinite dimensional Lie algebra. The metric structure associated with this Lie algebra is given by a metric tensor which is not equivalent to the Cartan-Killing metric. The Lie-Poisson bracket can be written in a form involving a generalized (Lie-)Nambu bracket. This bracket can be used to generate a generalized, nonlinear and completely integrable dynamics of density matrices. (author)
Directory of Open Access Journals (Sweden)
Shabanali Khansanami
2013-07-01
Full Text Available Background and Objectives: Emphasis is placed on the correction of reading the prayer as an important precept in Islamic culture, and it is essential to use an effective teaching method to promote the status of reading the prayers in youth. This study was conducted with the aim of comparing the effect of the methods of group teaching, personal (face-to-face teaching and using compact disc (CD on correcting the pronunciation and reading of the prayer in the students of Qom University of Medical Sciences in 2011.Methods: This semi-experimental study was done on the students of the Faculty of Nursery and Midwifery of Qom University of Medical Sciences. The samples were randomly assigned into three groups, and the number of students in each group was 22. A checklist of reading mistakes was completed before the intervention, and then, teaching content was given to them in the form of group and face-to-face teaching and CD. In the following, reading mistakes of the students’ prayer were recorded one month after intervention. Data was analyzed using descriptive statistics, and Kruskal–Wallis and Wilcoxon tests at a significance level of p0.05.Conclusion: Based on the findings of this study, the effect of teaching methods of group, personal, and CD was the same in correcting the students’ reading of the prayer. Therefore, it is suggested that considering the students’ interest and current circumstances, various methods could be used for correction of the students’ reading of the prayer.
International Nuclear Information System (INIS)
Schmidt, J.
1987-01-01
The author discusses his lab's plan for completing the Compact Ignition Tokamak (CIT) conceptual design during calendar year 1987. Around July 1 they froze the subsystem envelopes on the device to continue with the conceptual design. They did this by formalizing a general requirements document. They have been developing the management plan and submitted a version to the DOE July 10. He describes a group of management activities. They released the vacuum vessel Request For Proposals (RFP) on August 5. An RFP to do a major part of the system engineering on the device is being developed. They intend to assemble the device outside of the test cell, then move it into the the test cell, install it there, and bring to the test cell many of the auxiliary facilities from TFTR, for example, power supplies
When is a lie acceptable? Work and private life lying acceptance depends on its beneficiary.
Cantarero, Katarzyna; Szarota, Piotr; Stamkou, Eftychia; Navas, Marisol; Dominguez Espinosa, Alejandra Del Carmen
2018-01-01
In this article we show that when analyzing attitude towards lying in a cross-cultural setting, both the beneficiary of the lie (self vs other) and the context (private life vs. professional domain) should be considered. In a study conducted in Estonia, Ireland, Mexico, The Netherlands, Poland, Spain, and Sweden (N = 1345), in which participants evaluated stories presenting various types of lies, we found usefulness of relying on the dimensions. Results showed that in the joint sample the most acceptable were other-oriented lies concerning private life, then other-oriented lies in the professional domain, followed by egoistic lies in the professional domain; and the least acceptance was shown for egoistic lies regarding one's private life. We found a negative correlation between acceptance of a behavior and the evaluation of its deceitfulness.
Freestall maintenance: effects on lying behavior of dairy cattle.
Drissler, M; Gaworski, M; Tucker, C B; Weary, D M
2005-07-01
In a series of 3 experiments, we documented how sand-bedding depth and distribution changed within freestalls after new bedding was added and the effect of these changes on lying behavior. In experiment 1, we measured changes in bedding depth over a 10-d period at 43 points in 24 freestalls. Change in depth of sand was the greatest the day after new sand was added and decreased over time. Over time, the stall surface became concave, and the deepest part of the stall was at the center. Based on the results of experiment 1, we measured changes in lying behavior when groups of cows had access to freestalls with sand bedding that was 0, 3.5, 5.2, or 6.2 cm at the deepest point, below the curb, while other dimensions remained fixed. We found that daily lying time was 1.15 h shorter in stalls with the lowest levels of bedding compared with stalls filled with bedding. Indeed, for every 1-cm decrease in bedding, cows spent 11 min less time lying down during each 24-h period. In a third experiment, we imposed 4 treatments that reflected the variation in sand depth within stalls: 0, 6.2, 9.9, and 13.7 cm below the curb. Again, lying times reduced with decreasing bedding, such that cows using the stalls with the least amount of bedding (13.7 cm below curb) spent 2.33 h less time per day lying down than when housed with access to freestalls filled with sand (0 cm below curb).
New examples of continuum graded Lie algebras
International Nuclear Information System (INIS)
Savel'ev, M.V.
1989-01-01
Several new examples of continuum graded Lie algebras which provide an additional elucidation of these algebras are given. Here, in particular, the Kac-Moody algebras, the algebra S 0 Diff T 2 of infinitesimal area-preserving diffeomorphisms of the torus T 2 , the Fairlie, Fletcher and Zachos sine-algebras, etc., are described as special cases of the cross product Lie algebras. 8 refs
Huang, Yong-Heng; Jankowski, Aleksander; Cheah, Kathryn S E; Prabhakar, Shyam; Jauch, Ralf
2015-05-27
The SOXE transcription factors SOX8, SOX9 and SOX10 are master regulators of mammalian development directing sex determination, gliogenesis, pancreas specification and neural crest development. We identified a set of palindromic SOX binding sites specifically enriched in regulatory regions of melanoma cells. SOXE proteins homodimerize on these sequences with high cooperativity. In contrast to other transcription factor dimers, which are typically rigidly spaced, SOXE group proteins can bind cooperatively at a wide range of dimer spacings. Using truncated forms of SOXE proteins, we show that a single dimerization (DIM) domain, that precedes the DNA binding high mobility group (HMG) domain, is sufficient for dimer formation, suggesting that DIM : HMG rather than DIM:DIM interactions mediate the dimerization. All SOXE members can also heterodimerize in this fashion, whereas SOXE heterodimers with SOX2, SOX4, SOX6 and SOX18 are not supported. We propose a structural model where SOXE-specific intramolecular DIM:HMG interactions are allosterically communicated to the HMG of juxtaposed molecules. Collectively, SOXE factors evolved a unique mode to combinatorially regulate their target genes that relies on a multifaceted interplay between the HMG and DIM domains. This property potentially extends further the diversity of target genes and cell-specific functions that are regulated by SOXE proteins.
Huang, Yong-Heng; Jankowski, Aleksander; Cheah, Kathryn S. E.; Prabhakar, Shyam; Jauch, Ralf
2015-01-01
The SOXE transcription factors SOX8, SOX9 and SOX10 are master regulators of mammalian development directing sex determination, gliogenesis, pancreas specification and neural crest development. We identified a set of palindromic SOX binding sites specifically enriched in regulatory regions of melanoma cells. SOXE proteins homodimerize on these sequences with high cooperativity. In contrast to other transcription factor dimers, which are typically rigidly spaced, SOXE group proteins can bind cooperatively at a wide range of dimer spacings. Using truncated forms of SOXE proteins, we show that a single dimerization (DIM) domain, that precedes the DNA binding high mobility group (HMG) domain, is sufficient for dimer formation, suggesting that DIM : HMG rather than DIM:DIM interactions mediate the dimerization. All SOXE members can also heterodimerize in this fashion, whereas SOXE heterodimers with SOX2, SOX4, SOX6 and SOX18 are not supported. We propose a structural model where SOXE-specific intramolecular DIM:HMG interactions are allosterically communicated to the HMG of juxtaposed molecules. Collectively, SOXE factors evolved a unique mode to combinatorially regulate their target genes that relies on a multifaceted interplay between the HMG and DIM domains. This property potentially extends further the diversity of target genes and cell-specific functions that are regulated by SOXE proteins. PMID:26013289
Okamura, Hajime; Ouchi, Masahiro
2003-01-01
Self-compacting concrete was first developed in 1988 to achieve durable concrete structures. Since then, various investigations have been carried out and this type of concrete has been used in practical structures in Japan, mainly by large construction companies. Investigations for establishing a rational mix-design method and self-compactability testing methods have been carried out from the viewpoint of making self-compacting concrete a standard concrete.
Compact Polarimetry Potentials
Truong-Loi, My-Linh; Dubois-Fernandez, Pascale; Pottier, Eric
2011-01-01
The goal of this study is to show the potential of a compact-pol SAR system for vegetation applications. Compact-pol concept has been suggested to minimize the system design while maximize the information and is declined as the ?/4, ?/2 and hybrid modes. In this paper, the applications such as biomass and vegetation height estimates are first presented, then, the equivalence between compact-pol data simulated from full-pol data and compact-pol data processed from raw data as such is shown. Finally, a calibration procedure using external targets is proposed.
Pharmaceutical powder compaction technology
National Research Council Canada - National Science Library
Çelik, Metin
2011-01-01
"Revised to reflect modern pharmaceutical compacting techniques, this Second Edition guides pharmaceutical engineers, formulation scientists, and product development and quality assurance personnel...
Federal Laboratory Consortium — Facility consists of a folded compact antenna range including a computer controlled three axis position table, parabolic reflector and RF sources for the measurement...
Energy Technology Data Exchange (ETDEWEB)
Sati, Hisham [University of Pittsburgh,Pittsburgh, PA, 15260 (United States); Mathematics Program, Division of Science and Mathematics, New York University Abu Dhabi,Saadiyat Island, Abu Dhabi (United Arab Emirates); Schreiber, Urs [Mathematics Institute of the Academy,Žitna 25, Praha 1, 115 67 (Czech Republic)
2017-03-16
We uncover higher algebraic structures on Noether currents and BPS charges. It is known that equivalence classes of conserved currents form a Lie algebra. We show that at least for target space symmetries of higher parameterized WZW-type sigma-models this naturally lifts to a Lie (p+1)-algebra structure on the Noether currents themselves. Applied to the Green-Schwarz-type action functionals for super p-brane sigma-models this yields super Lie (p+1)-algebra refinements of the traditional BPS brane charge extensions of supersymmetry algebras. We discuss this in the generality of higher differential geometry, where it applies also to branes with (higher) gauge fields on their worldvolume. Applied to the M5-brane sigma-model we recover and properly globalize the M-theory super Lie algebra extension of 11-dimensional superisometries by 2-brane and 5-brane charges. Passing beyond the infinitesimal Lie theory we find cohomological corrections to these charges in higher analogy to the familiar corrections for D-brane charges as they are lifted from ordinary cohomology to twisted K-theory. This supports the proposal that M-brane charges live in a twisted cohomology theory.
Fu, Genyue; Xu, Fen; Cameron, Catherine Ann; Leyman, Gail; Lee, Kang
2007-01-01
This study examined cross-cultural differences and similarities in children's moral understanding of individual- or collective-oriented lies and truths. Seven-, 9-, and 11-year-old Canadian and Chinese children were read stories about story characters facing moral dilemmas about whether to lie or tell the truth to help a group but harm an…
Unitary Representations of Gauge Groups
Huerfano, Ruth Stella
I generalize to the case of gauge groups over non-trivial principal bundles representations that I. M. Gelfand, M. I. Graev and A. M. Versik constructed for current groups. The gauge group of the principal G-bundle P over M, (G a Lie group with an euclidean structure, M a compact, connected and oriented manifold), as the smooth sections of the associated group bundle is presented and studied in chapter I. Chapter II describes the symmetric algebra associated to a Hilbert space, its Hilbert structure, a convenient exponential and a total set that later play a key role in the construction of the representation. Chapter III is concerned with the calculus needed to make the space of Lie algebra valued 1-forms a Gaussian L^2-space. This is accomplished by studying general projective systems of finitely measurable spaces and the corresponding systems of sigma -additive measures, all of these leading to the description of a promeasure, a concept modeled after Bourbaki and classical measure theory. In the case of a locally convex vector space E, the corresponding Fourier transform, family of characters and the existence of a promeasure for every quadratic form on E^' are established, so the Gaussian L^2-space associated to a real Hilbert space is constructed. Chapter III finishes by exhibiting the explicit Hilbert space isomorphism between the Gaussian L ^2-space associated to a real Hilbert space and the complexification of its symmetric algebra. In chapter IV taking as a Hilbert space H the L^2-space of the Lie algebra valued 1-forms on P, the gauge group acts on the motion group of H defining in an straight forward fashion the representation desired.
Uniaxial backfill block compaction
International Nuclear Information System (INIS)
Koskinen, V.
2012-05-01
The main parts of the project were: to make a literature survey of the previous uniaxial compaction experiments; do uniaxial compaction tests in laboratory scale; and do industrial scale production tests. Object of the project was to sort out the different factors affecting the quality assurance chain of the backfill block uniaxial production and solve a material sticking to mould problem which appeared during manufacturing the blocks of bentonite and cruched rock mixture. The effect of mineralogical and chemical composition on the long term functionality of the backfill was excluded from the project. However, the used smectite-rich clays have been tested for mineralogical consistency. These tests were done in B and Tech OY according their SOPs. The objective of the Laboratory scale tests was to find right material- and compaction parameters for the industrial scale tests. Direct comparison between the laboratory scale tests and industrial scale tests is not possible because the mould geometry and compaction speed has a big influence for the compaction process. For this reason the selected material parameters were also affected by the previous compaction experiments. The industrial scale tests were done in summer of 2010 in southern Sweden. Blocks were done with uniaxial compaction. A 40 tons of the mixture of bentonite and crushed rock blocks and almost 50 tons of Friedland-clay blocks were compacted. (orig.)
Compaction properties of isomalt
Bolhuis, Gerad K.; Engelhart, Jeffrey J. P.; Eissens, Anko C.
Although other polyols have been described extensively as filler-binders in direct compaction of tablets, the polyol isomalt is rather unknown as pharmaceutical excipient, in spite of its description in all the main pharmacopoeias. In this paper the compaction properties of different types of
African Journals Online (AJOL)
The currently proposed model compaction equation was derived from data sourced from the. Niger Delta and it relates porosity to depth for sandstones under hydrostatic pressure condition. The equation is useful in predicting porosity and compaction trend in hydrostatic sands of the. Niger Delta. GEOLOGICAL SETTING OF ...
Casimir elements of epsilon Lie algebras
International Nuclear Information System (INIS)
Scheunert, M.
1982-10-01
The classical framework for investigating the Casimir elements of a Lie algebra is generalized to the case of an epsilon Lie algebra L. We construct the standard L-module isomorphism of the epsilon-symmetric algebra of L onto its enveloping algebra and we introduce the Harish-Chandra homomorphism. In case the generators of L can be written in a canonical two-index form, we construct the associated standard sequence of Casimir elements and derive a formula for their eigenvalues in an arbitrary highest weight module. (orig.)
Stabilization of compactible waste
International Nuclear Information System (INIS)
Franz, E.M.; Heiser, J.H. III; Colombo, P.
1990-09-01
This report summarizes the results of series of experiments performed to determine the feasibility of stabilizing compacted or compactible waste with polymers. The need for this work arose from problems encountered at disposal sites attributed to the instability of this waste in disposal. These studies are part of an experimental program conducted at Brookhaven National Laboratory (BNL) investigating methods for the improved solidification/stabilization of DOE low-level wastes. The approach taken in this study was to perform a series of survey type experiments using various polymerization systems to find the most economical and practical method for further in-depth studies. Compactible dry bulk waste was stabilized with two different monomer systems: styrene-trimethylolpropane trimethacrylate (TMPTMA) and polyester-styrene, in laboratory-scale experiments. Stabilization was accomplished by wetting or soaking compactible waste (before or after compaction) with monomers, which were subsequently polymerized. Three stabilization methods are described. One involves the in-situ treatment of compacted waste with monomers in which a vacuum technique is used to introduce the binder into the waste. The second method involves the alternate placement and compaction of waste and binder into a disposal container. In the third method, the waste is treated before compaction by wetting the waste with the binder using a spraying technique. A series of samples stabilized at various binder-to-waste ratios were evaluated through water immersion and compression testing. Full-scale studies were conducted by stabilizing two 55-gallon drums of real compacted waste. The results of this preliminary study indicate that the integrity of compacted waste forms can be readily improved to ensure their long-term durability in disposal environments. 9 refs., 10 figs., 2 tabs
Dimensional reduction of exceptional E6,E8 gauge groups and flavour chirality
International Nuclear Information System (INIS)
Koca, M.
1984-01-01
Ten-dimensional Yang - Mills gauge theories based on the exceptional groups E 6 and E 8 are reduced to four-dimensional flavour-chiral Yang - Mills - Higgs theories where the extra six dimensions are identified with the compact G 2 /SU(3) and SO(7)/SO(6) coset spaces. A ten-dimensional E 8 theory leads to three families of SU(5), one of which lies in the 144-dimensional representation of SO(10)
Lying in Business : Insights from Hannah Arendt’s ‘Lying in Politics’
Eenkhoorn, P.; Graafland, J.J.
2010-01-01
The famous political philosopher Hannah Arendt develops several arguments why truthfulness cannot be counted among the political virtues. This article shows that similar arguments apply to lying in business. Based on Hannah Arendt’s theory, we distinguish five reasons why lying is a structural
Teaching the Truth about Lies to Psychology Students: The Speed Lying Task
Pearson, Matthew R.; Richardson, Thomas A.
2013-01-01
To teach the importance of deception in everyday social life, an in-class activity called the "Speed Lying Task" was given in an introductory social psychology class. In class, two major research findings were replicated: Individuals detected deception at levels no better than expected by chance and lie detection confidence was unrelated…
Discrete finite nilpotent Lie analogs: New models for unified gauge field theory
International Nuclear Information System (INIS)
Kornacker, K.
1978-01-01
To each finite dimensional real Lie algebra with integer structure constants there corresponds a countable family of discrete finite nilpotent Lie analogs. Each finite Lie analog maps exponentially onto a finite unipotent group G, and is isomorphic to the Lie algebra of G. Reformulation of quantum field theory in discrete finite form, utilizing nilpotent Lie analogs, should elminate all divergence problems even though some non-Abelian gauge symmetry may not be spontaneously broken. Preliminary results in the new finite representation theory indicate that a natural hierarchy of spontaneously broken symmetries can arise from a single unbroken non-Abelian gauge symmetry, and suggest the possibility of a new unified group theoretic interpretation for hadron colors and flavors
Compaction of spent nuclear fuel cans
International Nuclear Information System (INIS)
Sullivan, H.
1985-01-01
Hydraulic press apparatus for compacting waste material eg. spent nuclear fuel cans comprises a fixed frame, a movable cross head, a press crown and three groups of piston/cylinder devices; having their pistons connected to the cross head and their cylinders secured to the press crown. A control means connects the first group of devices to hydraulic fluid in a reservoir which is pressurised initially by gas from gas accumulators to move the cross head and a quill secured thereto towards the frame base to compact the waste at a first high rate under a first high loading. Compaction then proceeds at a lower second rate at a lower second loading as the hydraulic fluid in the reservoir is pressurised by a pump. At two subsequent stages of compaction of the waste at which resistance increases causing a pressure rise in cylinders the control means causes hydraulic fluid to be passed to the second group of devices and thence to the third group of devices, the compaction rate reducing at each stage but the compaction force increasing. (author)
Mapping the geometry of the F4 group
International Nuclear Information System (INIS)
Bernardoni, Fabio; Cacciatori, Sergio L.; Scotti, Antonio; Cerchiai, Bianca L.
2007-01-01
In this paper, we present a construction of the compact form of the exceptional Lie group F4 by exponentiating the corresponding Lie algebra f4. We realize F4 as the automorphisms group of the exceptional Jordan algebra, whose elements are 3 x 3 Hermitian matrices with octonionic entries. We use a parametrization which generalizes the Euler angles for SU(2) and is based on the fibration of F4 via a Spin(9) subgroup as a fiber. This technique allows us to determine an explicit expression for the Haar invariant measure on the F4 group manifold. Apart from shedding light on the structure of F4 and its coset manifold OP2 = F4/Spin(9), the octonionic projective plane, these results are a prerequisite for the study of E6, of which F4 is a (maximal) subgroup
Growth of some varieties of Lie superalgebras
International Nuclear Information System (INIS)
Zaicev, M V; Mishchenko, S P
2007-01-01
We study numerical characteristics of varieties of Lie superalgebras and, in particular, the growth of codimensions. An example of an insoluble variety of almost polynomial growth is constructed. We prove that the exponent of this variety is equal to three and calculate the growth exponents for two earlier known soluble varieties
Lie Algebras for Constructing Nonlinear Integrable Couplings
International Nuclear Information System (INIS)
Zhang Yufeng
2011-01-01
Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti-Johnson (GJ) hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational identity their Hamiltonian structures are also generated. The approach presented in the paper can also provide nonlinear integrable couplings of other soliton hierarchies of evolution equations. (general)
Lie algebras and linear differential equations.
Brockett, R. W.; Rahimi, A.
1972-01-01
Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.
ASSOCIATIVE RINGS SOLVED AS LIE RINGS
Directory of Open Access Journals (Sweden)
M. B. Smirnov
2011-01-01
Full Text Available The paper has proved that an associative ring which is solvable of a n- class as a Lie ring has a nilpotent ideal of the nilpotent class not more than 3×10n–2 and a corresponding quotient ring satisfies an identity [[x1, x2, [x3, x4
Associative and Lie deformations of Poisson algebras
Remm, Elisabeth
2011-01-01
Considering a Poisson algebra as a non associative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this non associative algebra. This gives a natural interpretation of deformations which preserves the underlying associative structure and we study deformations which preserve the underlying Lie algebra.
Star formation suppression in compact group galaxies
DEFF Research Database (Denmark)
Alatalo, K.; Appleton, P. N.; Lisenfeld, U.
2015-01-01
, bars, rings, tidal tails, and possibly nuclear outflows, though the molecular gas morphologies are more consistent with spirals and earlytype galaxies than mergers and interacting systems. Our CO-imaged HCG galaxies, when plotted on the Kennicutt-Schmidt relation, shows star formation (SF) suppression...... color space. This supports the idea that at least some galaxies in HCGs are transitioning objects, where a disruption of the existing molecular gas in the system suppresses SF by inhibiting the molecular gas from collapsing and forming stars efficiently. These observations, combined with recent work...
White, M D; Bissiere, S; Alvarez, Y D; Plachta, N
2016-01-01
Compaction is a critical first morphological event in the preimplantation development of the mammalian embryo. Characterized by the transformation of the embryo from a loose cluster of spherical cells into a tightly packed mass, compaction is a key step in the establishment of the first tissue-like structures of the embryo. Although early investigation of the mechanisms driving compaction implicated changes in cell-cell adhesion, recent work has identified essential roles for cortical tension and a compaction-specific class of filopodia. During the transition from 8 to 16 cells, as the embryo is compacting, it must also make fundamental decisions regarding cell position, polarity, and fate. Understanding how these and other processes are integrated with compaction requires further investigation. Emerging imaging-based techniques that enable quantitative analysis from the level of cell-cell interactions down to the level of individual regulatory molecules will provide a greater understanding of how compaction shapes the early mammalian embryo. © 2016 Elsevier Inc. All rights reserved.
Noether and Lie symmetries for charged perfect fluids
International Nuclear Information System (INIS)
Kweyama, M C; Govinder, K S; Maharaj, S D
2011-01-01
We study the underlying nonlinear partial differential equation that governs the behaviour of spherically symmetric charged fluids in general relativity. We investigate the conditions for the equation to admit a first integral or be reduced to quadratures using symmetry methods for differential equations. A general Noether first integral is found. We also undertake a comprehensive group analysis of the underlying equation using Lie point symmetries. The existence of a Lie symmetry is subject to solving an integro-differential equation in general; we investigate the conditions under which it can be reduced to quadratures. Earlier results for uncharged fluids and particular first integrals for charged matter are regained as special cases of our treatment.
Normalization in Lie algebras via mould calculus and applications
Paul, Thierry; Sauzin, David
2017-11-01
We establish Écalle's mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to reduce the Lie-theoretic problem to a mould equation, the solutions of which are remarkably explicit and can be fully described by means of a gauge transformation group. The dynamical applications include the construction of Poincaré-Dulac formal normal forms for a vector field around an equilibrium point, a formal infinite-order multiphase averaging procedure for vector fields with fast angular variables (Hamiltonian or not), or the construction of Birkhoff normal forms both in classical and quantum situations. As a by-product we obtain, in the case of harmonic oscillators, the convergence of the quantum Birkhoff form to the classical one, without any Diophantine hypothesis on the frequencies of the unperturbed Hamiltonians.
On the exceptional generalised Lie derivative for d≥7
International Nuclear Information System (INIS)
Rosabal, J.A.
2015-01-01
In this work we revisit the E_8×ℝ"+ generalised Lie derivative encoding the algebra of diffeomorphisms and gauge transformations of compactifications of M-theory on eight-dimensional manifolds, by extending certain features of the E_7×ℝ"+ one. Compared to its E_d×ℝ"+, d≤7 counterparts, a new term is needed for consistency. However, we find that no compensating parameters need to be introduced, but rather that the new term can be written in terms of the ordinary generalised gauge parameters by means of a connection. This implies that no further degrees of freedom, beyond those of the field content of the E_8 group, are needed to have a well defined theory. We discuss the implications of the structure of the E_8×ℝ"+ generalised transformation on the construction of the d=8 generalised geometry. Finally, we suggest how to lift the generalised Lie derivative to eleven dimensions.
Kubi's, W; Kubi\\'s, Wieslaw; Michalewski, Henryk
2005-01-01
We prove a preservation theorem for the class of Valdivia compact spaces, which involves inverse sequences of ``simple'' retractions. Consequently, a compact space of weight $\\loe\\aleph_1$ is Valdivia compact iff it is the limit of an inverse sequence of metric compacta whose bonding maps are retractions. As a corollary, we show that the class of Valdivia compacta of weight at most $\\aleph_1$ is preserved both under retractions and under open 0-dimensional images. Finally, we characterize the class of all Valdivia compacta in the language of category theory, which implies that this class is preserved under all continuous weight preserving functors.
The Effect of Telling Lies on Belief in the Truth
Directory of Open Access Journals (Sweden)
Danielle Polage
2017-11-01
Full Text Available The current study looks at the effect of telling lies, in contrast to simply planning lies, on participants’ belief in the truth. Participants planned and told a lie, planned to tell a lie but didn’t tell it, told an unplanned lie, or neither planned nor told a lie (control about events that did not actually happen to them. Participants attempted to convince researchers that all of the stories told were true. Results show that telling a lie plays a more important role in inflating belief scores than simply preparing the script of a lie. Cognitive dissonance may lead to motivated forgetting of information that does not align with the lie. This research suggests that telling lies may lead to confusion as to the veracity of the lie leading to inflated belief scores.
Symmetries and groups in particle physics
International Nuclear Information System (INIS)
Scherer, Stefan
2016-01-01
The aim of this book consists of a didactic introduction to the group-theoretical considerations and methods, which have led to an ever deeper understanding of the interactions of the elementary particles. The first three chapters deal primarily with the foundations of the representation theory of primarily finite groups, whereby many results are also transferable to compact Lie groups. In the third chapter we discuss the concept of Lie groups and their connection with Lie algebras. In the remaining chapter it is mainly about the application of group theory in physics. Chapter 4 deals with the groups SO(3) and SU(2), which occur in connection with the description of the angular momentum in quantum mechanics. We discuss the Wigner-Eckar theorem together with some applications. In chapter 5 we are employed to the composition properties of strongly interacting systems, so called hadrons, and discuss extensively the transformation properties of quarks with relation to the special unitary groups. The Noether theorem is generally treated in connection to the conservation laws belonging to the Galilei group and the Poincare group. We confine us in chapter 6 to internal symmetries, but explain for that extensively the application to quantum field theory. Especially an outlook on the effect of symmetries in form of so called Ward identities is granted. In chapter 7 we turn towards the gauge principle and discuss first the construction of quantum electrodynamics. In the following we generalize the gauge principle to non-Abelian groups (Yang-Mills theories) and formulate the quantum chromodynamics (QCD). Especially we take a view of ''random'' global symmetries of QCD, especially the chiral symmetry. In chapter 8 we illuminate the phenomenon of spontaneous symmetry breaking both for global and for local symmetries. In the final chapter we work out the group-theoretical structure of the Standard Model. Finally by means of the group SU(5) we take a view to
Hirschberg, J. G.
1979-01-01
Proposed monitor that detects back-reflected infrared radiation makes in situ turbidity measurements of lakes, streams, and other bodies of water. Monitor is compact, works well in daylight as at night, and is easily operated in rough seas.
The derivation of the conventional basis for the classical Lie algebra generators
International Nuclear Information System (INIS)
Karadayi, H.R.
1982-01-01
The explicit construction of the classical Lie algebra generators in the conventional Gell-Mann basis is derived for all irreducible unitary representations of all classical groups. The main framework is based on a description of the simple roots of the classical Lie algebras such that the inter-relations implied by the Cartan matrix of the group among these simple roots are explicit within this description. (author)
International Nuclear Information System (INIS)
Unge, Rikard von
2002-01-01
We extend the path-integral formalism for Poisson-Lie T-duality to include the case of Drinfeld doubles which can be decomposed into bi-algebras in more than one way. We give the correct shift of the dilaton, correcting a mistake in the literature. We then use the fact that the six dimensional Drinfeld doubles have been classified to write down all possible conformal Poisson-Lie T-duals of three dimensional space times and we explicitly work out two duals to the constant dilaton and zero anti-symmetric tensor Bianchi type V space time and show that they satisfy the string equations of motion. This space-time was previously thought to have no duals because of the tracefulness of the structure constants. (author)
Does a point lie inside a polygon
International Nuclear Information System (INIS)
Milgram, M.S.
1988-01-01
A superficially simple problem in computational geometry is that of determining whether a query point P lies in the interior of a polygon if it lies in the polygon's plane. Answering this question is often required when tracking particles in a Monte Carlo program; it is asked frequently and an efficient algorithm is crucial. Littlefield has recently rediscovered Shimrat's algorithm, while in separate works, Wooff, Preparata and Shamos and Mehlhorn, as well as Yamaguchi, give other algorithms. A practical algorithm answering this question when the polygon's plane is skewed in space is not immediately evident from most of these methods. Additionally, all but one fails when two sides extend to infinity (open polygons). In this paper the author review the above methods and present a new, efficient algorithm, valid for all convex polygons, open or closed, and topologically connected in n-dimensional space (n ≥ 2)
On split Lie triple systems II
Indian Academy of Sciences (India)
the proof is complete. Acknowledgements. The first author was supported by the PCI of the UCA 'Teorıa de Lie y Teorıa de Espacios de Banach', by the PAI with project numbers FQM-298, FQM-3737, FQM-2467, by the project of the Spanish Ministerio de Educación y Ciencia MTM2004-06580-C02-02 and with fondos ...
Simple Lie algebras and Dynkin diagrams
International Nuclear Information System (INIS)
Buccella, F.
1983-01-01
The following theorem is studied: in a simple Lie algebra of rank p there are p positive roots such that all the other n-3p/2 positive roots are linear combinations of them with integer non negative coefficients. Dykin diagrams are built by representing the simple roots with circles and drawing a junction between the roots. Five exceptional algebras are studied, focusing on triple junction algebra, angular momentum algebra, weights of the representation, antisymmetric tensors, and subalgebras
Unitary representations of basic classical Lie superalgebras
International Nuclear Information System (INIS)
Gould, M.D.; Zhang, R.B.
1990-01-01
We have obtained all the finite-dimensional unitary irreps of gl(mvertical stroken) and C(n), which also exhaust such irreps of all the basic classical Lie superalgebras. The lowest weights of such irreps are worked out explicitly. It is also shown that the contravariant and covariant tensor irreps of gl(mvertical stroken) are unitary irreps of type (1) and type (2) respectively, explaining the applicability of the Young diagram method to these two types of tensor irreps. (orig.)
Preschoolers' Understanding of Lies and Innocent and Negligent Mistakes.
Siegal, Michael; Peterson, Candida C.
1998-01-01
Examined preschoolers' ability to distinguish innocent and negligent mistakes from lies. Found that, when asked to identify a mistake or lie about a food's contact with contaminants and identify a bystander's reaction, children distinguished mistakes from lies; they could also discriminate between lies and both negligent mistakes that generate…
Legitimate lies : The relationship between omission, commission, and cheating
Pittarello, Andrea; Rubaltelli, Enrico; Motro, Daphna
Across four experiments, we show that when people can serve their self-interest, they are more likely to refrain from reporting the truth ( lie of omission) than actively lie ( lie of commission). We developed a novel online "Heads or Tails" task in which participants can lie to win a monetary
A survey on stability and rigidity results for Lie algebras
Crainic, Marius; Schätz, Florian; Struchiner, Ivan
2014-01-01
We give simple and unified proofs of the known stability and rigidity results for Lie algebras, Lie subalgebras and Lie algebra homomorphisms. Moreover, we investigate when a Lie algebra homomorphism is stable under all automorphisms of the codomain (including outer automorphisms).
Cooling of hypernuclear compact stars
Raduta, Adriana R.; Sedrakian, Armen; Weber, Fridolin
2018-04-01
We study the thermal evolution of hypernuclear compact stars constructed from covariant density functional theory of hypernuclear matter and parametrizations which produce sequences of stars containing two-solar-mass objects. For the input in the simulations, we solve the Bardeen-Cooper-Schrieffer gap equations in the hyperonic sector and obtain the gaps in the spectra of Λ, Ξ0, and Ξ- hyperons. For the models with masses M/M⊙ ≥ 1.5 the neutrino cooling is dominated by hyperonic direct Urca processes in general. In the low-mass stars the (Λp) plus leptons channel is the dominant direct Urca process, whereas for more massive stars the purely hyperonic channels (Σ-Λ) and (Ξ-Λ) are dominant. Hyperonic pairing strongly suppresses the processes on Ξ-s and to a lesser degree on Λs. We find that intermediate-mass 1.5 ≤ M/M⊙ ≤ 1.8 models have surface temperatures which lie within the range inferred from thermally emitting neutron stars, if the hyperonic pairing is taken into account. Most massive models with M/M⊙ ≃ 2 may cool very fast via the direct Urca process through the (Λp) channel because they develop inner cores where the S-wave pairing of Λs and proton is absent.
Fu, Genyue; Xu, Fen; Cameron, Catherine Ann; Heyman, Gail; Lee, Kang
2008-01-01
This study examined cross-cultural differences and similarities in children’s moral understanding of individual- or collective-oriented lies and truths. Seven-, 9-, and 11-year-old Canadian and Chinese children were read stories about story characters facing moral dilemmas about whether to lie or tell the truth to help a group but harm an individual or vice versa. Participants chose to lie or to tell the truth as if they were the character (Experiments 1 and 2) and categorized and evaluated the story characters’ truthful and untruthful statements (Experiments 3 and 4). Most children in both cultures labeled lies as lies and truths as truths. The major cultural differences lay in choices and moral evaluations. Chinese children chose lying to help a collective but harm an individual, and they rated it less negatively than lying with opposite consequences. Chinese children rated truth telling to help an individual but harm a group less positively than the alternative. Canadian children did the opposite. These findings suggest that cross-cultural differences in emphasis on groups versus individuals affect children’s choices and moral judgments about truth and deception. PMID:17352539
Lie algebra of conformal Killing–Yano forms
International Nuclear Information System (INIS)
Ertem, Ümit
2016-01-01
We provide a generalization of the Lie algebra of conformal Killing vector fields to conformal Killing–Yano forms. A new Lie bracket for conformal Killing–Yano forms that corresponds to slightly modified Schouten–Nijenhuis bracket of differential forms is proposed. We show that conformal Killing–Yano forms satisfy a graded Lie algebra in constant curvature manifolds. It is also proven that normal conformal Killing–Yano forms in Einstein manifolds also satisfy a graded Lie algebra. The constructed graded Lie algebras reduce to the graded Lie algebra of Killing–Yano forms and the Lie algebras of conformal Killing and Killing vector fields in special cases. (paper)
Stoop, B.T.J.; Larbi, J.A.; Heijnen, W.M.M.
1996-01-01
It is shown that it is possible to produce compacted gypsum with a low porosity and a high strength on a laboratory scale by uniaxial compaction of flue gas desulphurization (FGD-) gypsum powder. Compacted FGD-gypsum cylinders were produced at a compaction pres-sure between 50 and 500 MPa yielding
Internally connected graphs and the Kashiwara-Vergne Lie algebra
Felder, Matteo
2018-02-01
It is conjectured that the Kashiwara-Vergne Lie algebra \\widehat{krv}_2 is isomorphic to the direct sum of the Grothendieck-Teichmüller Lie algebra grt_1 and a one-dimensional Lie algebra. In this paper, we use the graph complex of internally connected graphs to define a nested sequence of Lie subalgebras of \\widehat{krv}_2 whose intersection is grt_1 , thus giving a way to interpolate between these two Lie algebras.
Harmonic Analysis and Group Representation
Figa-Talamanca, Alessandro
2011-01-01
This title includes: Lectures - A. Auslander, R. Tolimeri - Nilpotent groups and abelian varieties, M Cowling - Unitary and uniformly bounded representations of some simple Lie groups, M. Duflo - Construction de representations unitaires d'un groupe de Lie, R. Howe - On a notion of rank for unitary representations of the classical groups, V.S. Varadarajan - Eigenfunction expansions of semisimple Lie groups, and R. Zimmer - Ergodic theory, group representations and rigidity; and, Seminars - A. Koranyi - Some applications of Gelfand pairs in classical analysis.
Matrix groups for undergraduates
Tapp, Kristopher
2005-01-01
Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori.
Olver, Peter J; the American Mathematical Society on Lie Algebras, Cohomology and New Applications to Quantum Mechanics
1994-01-01
This volume is devoted to a range of important new ideas arising in the applications of Lie groups and Lie algebras to Schrödinger operators and associated quantum mechanical systems. In these applications, the group does not appear as a standard symmetry group, but rather as a "hidden" symmetry group whose representation theory can still be employed to analyze at least part of the spectrum of the operator. In light of the rapid developments in this subject, a Special Session was organized at the AMS meeting at Southwest Missouri State University in March 1992 in order to bring together, perhaps for the first time, mathematicians and physicists working in closely related areas. The contributions to this volume cover Lie group methods, Lie algebras and Lie algebra cohomology, representation theory, orthogonal polynomials, q-series, conformal field theory, quantum groups, scattering theory, classical invariant theory, and other topics. This volume, which contains a good balance of research and survey papers, p...
The Relative Lie Algebra Cohomology of the Weil Representation
Ralston, Jacob
We study the relative Lie algebra cohomology of so(p,q) with values in the Weil representation piof the dual pair Sp(2k, R) x O(p,q ). Using the Fock model defined in Chapter 2, we filter this complex and construct the associated spectral sequence. We then prove that the resulting spectral sequence converges to the relative Lie algebra cohomology and has E0 term, the associated graded complex, isomorphic to a Koszul complex, see Section 3.4. It is immediate that the construction of the spectral sequence of Chapter 3 can be applied to any reductive subalgebra g ⊂ sp(2k(p + q), R). By the Weil representation of O( p,|q), we mean the twist of the Weil representation of the two-fold cover O(pq)[special character omitted] by a suitable character. We do this to make the center of O(pq)[special character omitted] act trivially. Otherwise, all relative Lie algebra cohomology groups would vanish, see Proposition 4.10.2. In case the symplectic group is large relative to the orthogonal group (k ≥ pq), the E 0 term is isomorphic to a Koszul complex defined by a regular sequence, see 3.4. Thus, the cohomology vanishes except in top degree. This result is obtained without calculating the space of cochains and hence without using any representation theory. On the other hand, in case k BMR], this author wrote with his advisor John Millson and Nicolas Bergeron of the University of Paris.
Advances in geometry and Lie algebras from supergravity
Frè, Pietro Giuseppe
2018-01-01
This book aims to provide an overview of several topics in advanced Differential Geometry and Lie Group Theory, all of them stemming from mathematical problems in supersymmetric physical theories. It presents a mathematical illustration of the main development in geometry and symmetry theory that occurred under the fertilizing influence of supersymmetry/supergravity. The contents are mainly of mathematical nature, but each topic is introduced by historical information and enriched with motivations from high energy physics, which help the reader in getting a deeper comprehension of the subject. .
Bond behavior of self compacting concrete
Directory of Open Access Journals (Sweden)
Ponmalar S.
2018-03-01
Full Text Available The success of an optimum design lies in the effective load transfer done by the bond forces at the steel-concrete interface. Self Compacting Concrete, is a new innovative concrete capable of filling intrinsic reinforcement and gets compacted by itself, without the need of external mechanical vibration. For this reason, it is replacing the conventional vibrated concrete in the construction industry. The present paper outlays the materials and methods adopted for attaining the self compacting concrete and describes about the bond behavior of this concrete. The bond stress-slip curve is similar in the bottom bars for both SCC and normal concrete whereas a higher bond stress and stiffness is experienced in the top and middle bars, for SCC compared to normal concrete. Also the interfacial properties revealed that the elastic modulus and micro-strength of interfacial transition zone [ITZ] were better on the both top and bottom side of horizontal steel bar in the SCC mixes than in normal vibrated concrete. The local bond strength of top bars for SCC is about 20% less than that for NC. For the bottom bars, however, the results were almost the same.
Bond behavior of self compacting concrete
Ponmalar, S.
2018-03-01
The success of an optimum design lies in the effective load transfer done by the bond forces at the steel-concrete interface. Self Compacting Concrete, is a new innovative concrete capable of filling intrinsic reinforcement and gets compacted by itself, without the need of external mechanical vibration. For this reason, it is replacing the conventional vibrated concrete in the construction industry. The present paper outlays the materials and methods adopted for attaining the self compacting concrete and describes about the bond behavior of this concrete. The bond stress-slip curve is similar in the bottom bars for both SCC and normal concrete whereas a higher bond stress and stiffness is experienced in the top and middle bars, for SCC compared to normal concrete. Also the interfacial properties revealed that the elastic modulus and micro-strength of interfacial transition zone [ITZ] were better on the both top and bottom side of horizontal steel bar in the SCC mixes than in normal vibrated concrete. The local bond strength of top bars for SCC is about 20% less than that for NC. For the bottom bars, however, the results were almost the same.
Vector fields and nilpotent Lie algebras
Grayson, Matthew; Grossman, Robert
1987-01-01
An infinite-dimensional family of flows E is described with the property that the associated dynamical system: x(t) = E(x(t)), where x(0) is a member of the set R to the Nth power, is explicitly integrable in closed form. These flows E are of the form E = E1 + E2, where E1 and E2 are the generators of a nilpotent Lie algebra, which is either free, or satisfies some relations at a point. These flows can then be used to approximate the flows of more general types of dynamical systems.
Inhomogeneous compact extra dimensions
Energy Technology Data Exchange (ETDEWEB)
Bronnikov, K.A. [Center of Gravity and Fundamental Metrology, VNIIMS, 46 Ozyornaya st., Moscow 119361 (Russian Federation); Budaev, R.I.; Grobov, A.V.; Dmitriev, A.E.; Rubin, Sergey G., E-mail: kb20@yandex.ru, E-mail: buday48@mail.ru, E-mail: alexey.grobov@gmail.com, E-mail: alexdintras@mail.ru, E-mail: sergeirubin@list.ru [National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409 Moscow (Russian Federation)
2017-10-01
We show that an inhomogeneous compact extra space possesses two necessary features— their existence does not contradict the observable value of the cosmological constant Λ{sub 4} in pure f ( R ) theory, and the extra dimensions are stable relative to the 'radion mode' of perturbations, the only mode considered. For a two-dimensional extra space, both analytical and numerical solutions for the metric are found, able to provide a zero or arbitrarily small Λ{sub 4}. A no-go theorem has also been proved, that maximally symmetric compact extra spaces are inconsistent with 4D Minkowski space in the framework of pure f ( R ) gravity.
Effects of bedding quality on lying behavior of dairy cows.
Fregonesi, J A; Veira, D M; von Keyserlingk, M A G; Weary, D M
2007-12-01
Cows prefer to spend more time lying down in free stalls with more bedding, but no research to date has addressed the effects of bedding quality. Bedding in stalls often becomes wet either from exposure to the elements or from feces and urine. The aim of this study was to test the effect of wet bedding on stall preference and use. Four groups of 6 nonlactating Holstein cows were housed in free stalls bedded daily with approximately 0.1 m of fresh sawdust. Following a 5-d adaptation period, each group of cows was tested sequentially with access to stalls with either dry or wet sawdust bedding (86.4 +/- 2.1 vs. 26.5 +/- 2.1% dry matter), each for 2 d. These no-choice phases were followed by a 2-d free-choice phase during which cows had simultaneous access to stalls containing either wet or dry bedding. Stall usage was assessed by using 24-h video recordings scanned at 10-min intervals, and responses were analyzed by using a mixed model, with group (n = 4) as the observational unit. The minimum and maximum environmental temperatures during the experiment were 3.4 +/- 2.2 and 6.8 +/- 2.5 degrees C, respectively. When cows had access only to stalls with wet bedding, they spent 8.8 +/- 0.8 h/d lying down, which increased to 13.8 +/- 0.8 h/d when stalls with dry bedding were provided. Cows spent more time standing with their front 2 hooves in the stall when provided with wet vs. dry bedding (92 +/- 10 vs. 32 +/- 10 min/d). During the free-choice phase, all cows spent more time lying down in the dry stalls, spending 12.5 +/- 0.3 h/d in the dry stalls vs. 0.9 +/- 0.3 h/ d in stalls with wet bedding. In conclusion, dairy cows show a clear preference for a dry lying surface, and they spend much more time standing outside the stall when only wet bedding is available.
Some quantum Lie algebras of type D{sub n} positive
Energy Technology Data Exchange (ETDEWEB)
Bautista, Cesar [Facultad de Ciencias de la Computacion, Benemerita Universidad Autonoma de Puebla, Edif 135, 14 sur y Av San Claudio, Ciudad Universitaria, Puebla Pue. CP 72570 (Mexico); Juarez-Ramirez, Maria Araceli [Facultad de Ciencias Fisico-Matematicas, Benemerita Universidad Autonoma de Puebla, Edif 158 Av San Claudio y Rio Verde sn Ciudad Universitaria, Puebla Pue. CP 72570 (Mexico)
2003-03-07
A quantum Lie algebra is constructed within the positive part of the Drinfeld-Jimbo quantum group of type D{sub n}. Our quantum Lie algebra structure includes a generalized antisymmetry property and a generalized Jacobi identity closely related to the braid equation. A generalized universal enveloping algebra of our quantum Lie algebra of type D{sub n} positive is proved to be the Drinfeld-Jimbo quantum group of the same type. The existence of such a generalized Lie algebra is reduced to an integer programming problem. Moreover, when the integer programming problem is feasible we show, by means of the generalized Jacobi identity, that the Poincare-Birkhoff-Witt theorem (basis) is still true.
On Lie point symmetry of classical Wess-Zumino-Witten model
International Nuclear Information System (INIS)
Maharana, Karmadeva
2001-06-01
We perform the group analysis of Witten's equations of motion for a particle moving in the presence of a magnetic monopole, and also when constrained to move on the surface of a sphere, which is the classical example of Wess-Zumino-Witten model. We also consider variations of this model. Our analysis gives the generators of the corresponding Lie point symmetries. The Lie symmetry corresponding to Kepler's third law is obtained in two related examples. (author)
International Nuclear Information System (INIS)
Zhang Mei-Ling; Wang Xiao-Xiao; Xie Yin-Li; Jia Li-Qun; Sun Xian-Ting
2011-01-01
Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results. (general)
Characterization of ceramic powder compacts
International Nuclear Information System (INIS)
Yanai, K.; Ishimoto, S.; Kubo, T.; Ito, K.; Ishikawa, T.; Hayashi, H.
1995-01-01
UO 2 and Al 2 O 3 powder packing structures in cylindrical powder compacts are observed by scanning electron microscopy using polished cross sections of compacts fixed by low viscosity epoxy resin. Hard aggregates which are not destroyed during powder compaction are observed in some of the UO 2 powder compacts. A technique to measure local density in powder compacts is developed based on counting characteristic X-ray intensity by energy dispersive X-ray analysis (EDX). The local density of the corner portion of the powder compact fabricated by double-acting dry press is higher than that of the inner portion. ((orig.))
Manufacturability of compact synchrotron mirrors
Douglas, Gary M.
1997-11-01
While many of the government funded research communities over the years have put their faith and money into increasingly larger synchrotrons, such as Spring8 in Japan, and the APS in the United States, a viable market appears to exist for smaller scale, research and commercial grade, compact synchrotrons. These smaller, and less expensive machines, provide the research and industrial communities with synchrotron radiation beamline access at a portion of the cost of their larger and more powerful counterparts. A compact synchrotron, such as the Aurora-2D, designed and built by Sumitomo Heavy Industries, Ltd. of japan (SHI), is a small footprint synchrotron capable of sustaining 20 beamlines. Coupled with a Microtron injector, with 150 MeV of injection energy, an entire facility fits within a 27 meter [88.5 ft] square floorplan. The system, controlled by 2 personal computers, is capable of producing 700 MeV electron energy and 300 mA stored current. Recently, an Aurora-2D synchrotron was purchased from SHI by the University of Hiroshima. The Rocketdyne Albuquerque Operations Beamline Optics Group was approached by SHI with a request to supply a group of 16 beamline mirrors for this machine. These mirrors were sufficient to supply 3 beamlines for the Hiroshima machine. This paper will address engineering issues which arose during the design and manufacturing of these mirrors.
Short communication: Association of lying behavior and subclinical ketosis in transition dairy cows.
Kaufman, E I; LeBlanc, S J; McBride, B W; Duffield, T F; DeVries, T J
2016-09-01
The objective of this study was to characterize the association of lying behavior and subclinical ketosis (SCK) in transition dairy cows. A total of 339 dairy cows (107 primiparous and 232 multiparous) on 4 commercial dairy farms were monitored for lying behavior and SCK from 14d before calving until 28 d after calving. Lying time, frequency of lying bouts, and average lying bout length were measured using automated data loggers 24h/d. Cows were tested for SCK 1×/wk by taking a blood sample and analyzing for β-hydroxybutyrate; cows with β-hydroxybutyrate ≥1.2mmol/L postpartum were considered to have SCK. Cases of retained placenta, metritis, milk fever, or mastitis during the study period were recorded and cows were categorized into 1 of 4 groups: healthy (HLT) cows had no SCK or any other health problem (n=139); cows treated for at least 1 health issue other than SCK (n=50); SCK (HYK) cows with no other health problems during transition (n=97); or subclinically ketotic plus (HYK+) cows that had SCK and 1 or more other health problems (n=53). Daily lying time was summarized by week and comparisons were made between HLT, HYK, and HYK+, respectively. We found no difference among health categories in lying time, bout frequency, or bout length fromwk -2 towk +4 relative to calving for first-lactation cows. Differences in lying time for multiparous cows were seen inwk +1, when HYK+ cows spent 92±24.0 min/d more time lying down than HLT cows, and duringwk +3 and +4 when HYK cows spent 44±16.7 and 41±18.9 min/d, respectively, more time lying down than HLT cows. Increased odds of HYK+ were found to be associated with higher parity, longer dry period, and greater stall stocking density inwk -1 and longer lying time duringwk +1. When comparing HYK to HLT cows, the same variables were associated with odds of SCK; however, lying time was not retained in the final model. These results suggest that monitoring lying time may contribute to identifying multiparous cows
On Quantum Lie Nilpotency of Order 2
Directory of Open Access Journals (Sweden)
E. A. Kireeva
2016-01-01
Full Text Available The paper investigates the free algebras of varieties of associative algebras modulo identities of quantum Lie nilpotency of order 1 and 2. Let q be an invertible element of the ground field K (or of its extension. The element[x,y]q = xy-qyxof the free associative algebra is called a quantum commutator. We consider the algebras modulo identities [x,y]q = 0 (1and [[x,y]q ,z]q = 0. (2It is natural to consider the aforementioned algebras as the quantum analogs of commutative algebras and algebras of Lie nilpotency of order 2. The free algebras of the varieties of associative algebras modulo the identity of Lie nilpotency of order 2, that is the identity[[x,y] ,z] =0,where [x,y]=xy-yx is a Lie commutator, are of great interest in the theory of algebras with polynomial identities, since it was proved by A.V.Grishin for algebras over fields of characteristic 2, and V.V.Shchigolev for algebras over fields of characteristic p>2, that these algebras contain non-finitely generated T-spaces.We prove in the paper that the algebras modulo identities (1 and (2 are nilpotent in the usual sense and calculate precisely the nilpotency order of these algebras. More precisely, we prove that the free algebra of the variety of associative algebras modulo identity (1 is nilpotent of order 2 if q ≠ ± 1, and nilpotent of order 3 if q = - 1 and the characteristic of K is not equal to 2. It is also proved that the free algebra of the variety of associative algebras modulo identity (2 is nilpotent of order 3 if q3 ≠ 1, q ≠ ± 1, nilpotent of order 4 if q3 = 1, q ≠ 1, and nilpotent of
A generalization of the Lie derivative
International Nuclear Information System (INIS)
Dolan, P.
1984-01-01
If X=xisup(i)deltasub(i) and Y=etasup(i)deltasub(i) are vector fields then it is well-known that the Lie derivative Poundsub(X)Y equivalent to [X,Y] (xisup(s)deltasub(s) etasup(s)deltasub(s)xisup(i))deltasub(i) is also a vector field under general coordinate transformations. A generalization of this result, due to previous workers, allows a definition of Poundsub(F)G, where F,G are arbitrary contravariant tensor fields. The formulae are linear in the first partial derivatives of F and G. An application to the theory of Killing-Yano tensor fields on Riemannian manifolds is given. (author)
Energy Technology Data Exchange (ETDEWEB)
Riva, A.
2000-07-01
This report details the work undertaken by the Study Group 8.3 during the triennium 1997-2000 on environmental management and reporting through the use of results of inquiries and the analysis of published documents. For environmental management it presents a review of standards, guidelines, documents and practices for industrial sectors. The results of a survey on the application of environmental management systems within the gas industry are presented with information on their structure and on the organisation adopted for the implementation. The gas industry has been gaining experience in environmental reporting in recent years. The contents recommended for environmental reports by international guidelines are presented. A review of several reports published by gas industries lead to identify the most relevant contents that can be used by gas companies as reference in preparing environmental reports. Challenges and benefits for the adoption of environmental management systems and the publication of environmental reports are evaluated and recommendations for the gas industry are given. Case studies on experiences of the gas industry in developing environmental management systems are described. (author)
Biderivations of finite dimensional complex simple Lie algebras
Tang, Xiaomin
2016-01-01
In this paper, we prove that a biderivation of a finite dimensional complex simple Lie algebra without the restriction of skewsymmetric is inner. As an application, the biderivation of a general linear Lie algebra is presented. In particular, we find a class of a non-inner and non-skewsymmetric biderivations. Furthermore, we also get the forms of linear commuting maps on the finite dimensional complex simple Lie algebra or general linear Lie algebra.
The geometry of lie algebras and broken SO(6) symmetries
International Nuclear Information System (INIS)
Lawrence, T.R.
2001-10-01
Non-linear realisations of the groups SU(2), SO(1,4) and SO(2,4) are analysed, described by the coset spaces SU(2)/U(1), SO(1,4)/SO(1,3) and SO(2,4)/SO(1,3) x SO(1,1). The Lie algebras of certain special unitary and special orthogonal groups are studied and their projection operators are determined in order to facilitate the above analyses, in particular that of SO(2,4)/SO(l,3) x SO(1,1). The analysis consists of determining the transformation properties of the Goldstone bosons, constructing the most general possible Lagrangian for the realisations and finding the metric of the coset space. (author)
Accurately Detecting Students' Lies regarding Relational Aggression by Correctional Instructions
Dickhauser, Oliver; Reinhard, Marc-Andre; Marksteiner, Tamara
2012-01-01
This study investigates the effect of correctional instructions when detecting lies about relational aggression. Based on models from the field of social psychology, we predict that correctional instruction will lead to a less pronounced lie bias and to more accurate lie detection. Seventy-five teachers received videotapes of students' true denial…
Lie n-derivations on 7 -subspace lattice algebras
Indian Academy of Sciences (India)
all x ∈ K and all A ∈ Alg L. Based on this result, a complete characterization of linear n-Lie derivations on Alg L is obtained. Keywords. J -subspace lattice algebras; Lie derivations; Lie n-derivations; derivations. 2010 Mathematics Subject Classification. 47B47, 47L35. 1. Introduction. Let A be an algebra. Recall that a linear ...
Dimension of the c-nilpotent multiplier of Lie algebras
Indian Academy of Sciences (India)
Abstract. The purpose of this paper is to derive some inequalities for dimension of the c-nilpotent multiplier of finite dimensional Lie algebras and their factor Lie algebras. We further obtain an inequality between dimensions of c-nilpotent multiplier of Lie algebra L and tensor product of a central ideal by its abelianized factor ...
Weakly compact operators and interpolation
Maligranda, Lech
1992-01-01
The class of weakly compact operators is, as well as the class of compact operators, a fundamental operator ideal. They were investigated strongly in the last twenty years. In this survey, we have collected and ordered some of this (partly very new) knowledge. We have also included some comments, remarks and examples. The class of weakly compact operators is, as well as the class of compact operators, a fundamental operator ideal. They were investigated strongly in the last twenty years. I...
Lie detection based on nonverbal expressions - study of the Czech Republic Police employees
Directory of Open Access Journals (Sweden)
Hedvika Boukalová
2014-12-01
Full Text Available Lie detection based on nonverbal behavior is not a standard method, it is an intuitive process, applied by lay persons, but also professionals. Some of the major sources (e.g. widespread Interrogation Manual by F. Inbau et al., 2004 offer clear recommendations about the nonverbal behavior of liars to investigators of serious crime. These findings are not supported by the research, moreover they can lead to lowering the ability to detect lie (Blair, Kooi 2004. Another topic is mapping the skills of professionals (police officers, members of the secret services and non-specialists to detect lies by nonverbal signs. Across the studies (with few exceptions a low performance in the task of detecting lies by nonverbal expressions (Ekman P., 1996; Vrij, 2004 and others is found. The levels of success are usually around the level of chance. The potential reasons for such results are analyzed (e.g. Blair, Kooi, 2004. However a group of psychologists led by P. Ekman and M. O'Sullivan (O'Sullivan, 2007 managed to find in their years lasting research a group of people whose ability to detect lies is well above the population average. This group is diverse in terms of age, interests and professions, all of them come from the USA. There were certain common features found in this group and also a focus on similar phenomena in the detection of lying. The main goal and research question is to find out: what is the success rate of differentiation between lies and truths in this specific professional group of Czech population, is it the same or different from the results reported in the context of available resources. The research will focus on the ability of respondents to determine the truth or deceit on the basis of non-verbal and paraverbal expressions of observed subjects, with focus on specific professional groups - mainly police workers. We assume, that the police officers are frequently in the contact with people, who are not willing to reveal critical
Directory of Open Access Journals (Sweden)
W. Sinkala
2012-01-01
Full Text Available We use Lie symmetry analysis to solve a boundary value problem that arises in chemical engineering, namely, mass transfer during the contact of a solid slab with an overhead flowing fluid. This problem was earlier tackled using Adomian decomposition method (Fatoorehchi and Abolghasemi 2011, leading to the Adomian series form of solution. It turns out that the application of Lie group analysis yields an elegant form of the solution. After introducing the governing mathematical model and some preliminaries of Lie symmetry analysis, we compute the Lie point symmetries admitted by the governing equation and use these to construct the desired solution as an invariant solution.
Lie and conditional symmetries of the three-component diffusive Lotka–Volterra system
International Nuclear Information System (INIS)
Cherniha, Roman; Davydovych, Vasyl’
2013-01-01
Lie and Q-conditional symmetries of the classical three-component diffusive Lotka–Volterra system in the case of one space variable are studied. The group-classification problems for finding Lie symmetries and Q-conditional symmetries of the first type are completely solved. Notably, non-Lie symmetries (Q-conditional symmetry operators) for a multi-component nonlinear reaction–diffusion system are constructed for the first time. The results are compared with those derived for the two-component diffusive Lotka–Volterra system. The conditional symmetry obtained for the non-Lie reduction of the three-component system used for modeling competition between three species in population dynamics is applied and the relevant exact solutions are found. Particularly, the exact solution describing different scenarios of competition between three species is constructed. (paper)
The Blue Compact Dwarf Galaxy IZw18
Musella, I.; Marconi, M.; Fiorentino, G.; Clementini, G.; Aloisi, A.; Annibali, F.; Contreras, R.; Saha, A.; Tosi, M.; van der Marel, R. P.
2012-01-01
We present the results obtained for the Blue compact galaxy IZw18 on the basis of ACS HST data obtained from our group. In particular, we discuss the stellar population and the variable stars content of this galaxy to get information about its star formation history and distance.
Duality results for co-compact Gabor systems
DEFF Research Database (Denmark)
Jakobsen, Mads Sielemann; Lemvig, Jakob
2015-01-01
In this paper we give an account of recent developments in the duality theory of Gabor frames. We prove the Wexler-Raz biorthogonality relations and the duality principle for co-compact Gabor systems on second countable, locally compact abelian groups G. Our presentation does not rely on the exis...
Compact stellarators as reactors
International Nuclear Information System (INIS)
Lyon, J.F.; Valanju, P.; Zarnstorff, M.C.; Hirshman, S.; Spong, D.A.; Strickler, D.; Williamson, D.E.; Ware, A.
2001-01-01
Two types of compact stellarators are examined as reactors: two- and three-field-period (M=2 and 3) quasi-axisymmetric devices with volume-average =4-5% and M=2 and 3 quasi-poloidal devices with =10-15%. These low-aspect-ratio stellarator-tokamak hybrids differ from conventional stellarators in their use of the plasma-generated bootstrap current to supplement the poloidal field from external coils. Using the ARIES-AT model with B max =12T on the coils gives Compact Stellarator reactors with R=7.3-8.2m, a factor of 2-3 smaller R than other stellarator reactors for the same assumptions, and neutron wall loadings up to 3.7MWm -2 . (author)
International Nuclear Information System (INIS)
Lyon, J.F.; Carreras, B.A.; Lynch, V.E.; Tolliver, J.S.; Sviatoslavsky, I.N.
1988-05-01
Low-aspect-ratio torsatron configurations could lead to compact stellarator reactors with R 0 = 8--11m, roughly one-half to one-third the size of more conventional stellarator reactor designs. Minimum-size torsatron reactors are found using various assumptions. Their size is relatively insensitive to the choice of the conductor parameters and depends mostly on geometrical constraints. The smallest size is obtained by eliminating the tritium breeding blanket under the helical winding on the inboard side and by reducing the radial depth of the superconducting coil. Engineering design issues and reactor performance are examined for three examples to illustrate the feasibility of this approach for compact reactors and for a medium-size (R 0 ≅ 4 m,/bar a/ /approx lt/ 1 m) copper-coil ignition experiment. 26 refs., 11 figs., 7 tabs
Energy Technology Data Exchange (ETDEWEB)
Placidi, M.; Jung, J. -Y.; Ratti, A.; Sun, C.
2014-07-25
This paper describes beam distribution schemes adopting a novel implementation based on low amplitude vertical deflections combined with horizontal ones generated by Lambertson-type septum magnets. This scheme offers substantial compactness in the longitudinal layouts of the beam lines and increased flexibility for beam delivery of multiple beam lines on a shot-to-shot basis. Fast kickers (FK) or transverse electric field RF Deflectors (RFD) provide the low amplitude deflections. Initially proposed at the Stanford Linear Accelerator Center (SLAC) as tools for beam diagnostics and more recently adopted for multiline beam pattern schemes, RFDs offer repetition capabilities and a likely better amplitude reproducibility when compared to FKs, which, in turn, offer more modest financial involvements both in construction and operation. Both solutions represent an ideal approach for the design of compact beam distribution systems resulting in space and cost savings while preserving flexibility and beam quality.
CERN. Geneva
2015-01-01
Fusion research is currently to a large extent focused on tokamak (ITER) and inertial confinement (NIF) research. In addition to these large international or national efforts there are private companies performing fusion research using much smaller devices than ITER or NIF. The attempt to achieve fusion energy production through relatively small and compact devices compared to tokamaks decreases the costs and building time of the reactors and this has allowed some private companies to enter the field, like EMC2, General Fusion, Helion Energy, Lawrenceville Plasma Physics and Lockheed Martin. Some of these companies are trying to demonstrate net energy production within the next few years. If they are successful their next step is to attempt to commercialize their technology. In this presentation an overview of compact fusion reactor concepts is given.
International Nuclear Information System (INIS)
Kiselev, V.V.; Churakov, Yu.A.; Danchenko, Yu.V.; Bylkin, B.K.; Tsvetkov, S.V.
1983-01-01
Different constructions of racks for compact storage of spent fuel assemblies (FA) in ''coolin''g pools (CP) of NPPs with the BWR and PWR type reactors are described. Problems concerning nuclear and radiation safety and provision of necessary thermal conditions arising in such rack design are discussed. It is concluded that the problem of prolonged fuel storage at NPPs became Very actual for many countries because of retapdation of the rates of fuel reprocessing centers building. Application of compact storage racks is a promising solution of the problem of intermediate FA storage at NPPs. Such racks of stainless boron steel and with neutron absorbers in the from of boron carbide panels enable to increase the capacity of the present CP 2-2.6 times, and the period of FA storage in them up to 5-10 years
Analysis of laboratory compaction methods of roller compacted concrete
Trtík, Tomáš; Chylík, Roman; Bílý, Petr; Fládr, Josef
2017-09-01
Roller-Compacted Concrete (RCC) is an ordinary concrete poured and compacted with machines typically used for laying of asphalt road layers. One of the problems connected with this technology is preparation of representative samples in the laboratory. The aim of this work was to analyse two methods of preparation of RCC laboratory samples with bulk density as the comparative parameter. The first method used dynamic compaction by pneumatic hammer. The second method of compaction had a static character. The specimens were loaded by precisely defined force in laboratory loading machine to create the same conditions as during static rolling (in the Czech Republic, only static rolling is commonly used). Bulk densities obtained by the two compaction methods were compared with core drills extracted from real RCC structure. The results have shown that the samples produced by pneumatic hammer tend to overestimate the bulk density of the material. For both compaction methods, immediate bearing index test was performed to verify the quality of compaction. A fundamental difference between static and dynamic compaction was identified. In static compaction, initial resistance to penetration of the mandrel was higher, after exceeding certain limit the resistance was constant. This means that the samples were well compacted just on the surface. Specimens made by pneumatic hammer actively resisted throughout the test, the whole volume was uniformly compacted.
On generalized Melvin solution for the Lie algebra E6
International Nuclear Information System (INIS)
Bolokhov, S.V.; Ivashchuk, V.D.
2017-01-01
A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra G is considered. The gravitational model in D dimensions, D ≥ 4, contains n 2-forms and l ≥ n scalar fields, where n is the rank of G. The solution is governed by a set of n functions H s (z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). The polynomials H s (z), s = 1,.., 6, for the Lie algebra E 6 are obtained and a corresponding solution for l = n = 6 is presented. The polynomials depend upon integration constants Q s , s = 1,.., 6. They obey symmetry and duality identities. The latter ones are used in deriving asymptotic relations for solutions at large distances. The power-law asymptotic relations for E 6 -polynomials at large z are governed by the integer-valued matrix ν = A -1 (I + P), where A -1 is the inverse Cartan matrix, I is the identity matrix and P is a permutation matrix, corresponding to a generator of the Z 2 -group of symmetry of the Dynkin diagram. The 2-form fluxes Φ s , s = 1,.., 6, are calculated. (orig.)
Wychowaniec, J.; Griffiths, I.; Gay, A.; Mughal, A.
2013-01-01
We report on simple shaking experiments to measure the compaction of a column of Firth oat grain. Such grains are elongated anisotropic particles with a bimodal polydispersity. In these experiments, the particle configurations start from an initially disordered, low-packing-fraction state and under vertical shaking evolve to a dense state with evidence of nematic-like structure at the surface of the confining tube. This is accompanied by an increase in the packing fraction of the grain.
International Nuclear Information System (INIS)
Juric, S.I.
1975-01-01
A compact nuclear reactor of the pressurized-water variety is described which has two separate parts separably engageable for ease of inspection, maintenance and repair. One of the parts is a pressure vessel having an active core and the other of the parts is a closure adapted on its lower surface with an integral steam generator. An integral pump, external pressurizer and control rods are provided which communicate with the active core when engaged to form a total unit. (U.S.)
International Nuclear Information System (INIS)
Wetch, J.R.; Dieckamp, H.M.; Wilson, L.A.
1978-01-01
There is disclosed a small compact nuclear reactor operating in the epithermal neutron energy range for supplying power at remote locations, as for a satellite. The core contains fuel moderator elements of Zr hydride with 7 w/o of 93% enriched uranium alloy. The core has a radial beryllium reflector and is cooled by liquid metal coolant such as NaK. The reactor is controlled and shut down by moving portions of the reflector
International Nuclear Information System (INIS)
Anon.
1995-01-01
The milestone workshops on LHC experiments in Aachen in 1990 and at Evian in 1992 provided the first sketches of how LHC detectors might look. The concept of a compact general-purpose LHC experiment based on a solenoid to provide the magnetic field was first discussed at Aachen, and the formal Expression of Interest was aired at Evian. It was here that the Compact Muon Solenoid (CMS) name first became public. Optimizing first the muon detection system is a natural starting point for a high luminosity (interaction rate) proton-proton collider experiment. The compact CMS design called for a strong magnetic field, of some 4 Tesla, using a superconducting solenoid, originally about 14 metres long and 6 metres bore. (By LHC standards, this warrants the adjective 'compact'.) The main design goals of CMS are: 1 - a very good muon system providing many possibilities for momentum measurement (physicists call this a 'highly redundant' system); 2 - the best possible electromagnetic calorimeter consistent with the above; 3 - high quality central tracking to achieve both the above; and 4 - an affordable detector. Overall, CMS aims to detect cleanly the diverse signatures of new physics by identifying and precisely measuring muons, electrons and photons over a large energy range at very high collision rates, while also exploiting the lower luminosity initial running. As well as proton-proton collisions, CMS will also be able to look at the muons emerging from LHC heavy ion beam collisions. The Evian CMS conceptual design foresaw the full calorimetry inside the solenoid, with emphasis on precision electromagnetic calorimetry for picking up photons. (A light Higgs particle will probably be seen via its decay into photon pairs.) The muon system now foresaw four stations. Inner tracking would use silicon microstrips and microstrip gas chambers, with over 10 7 channels offering high track finding efficiency. In the central CMS barrel, the tracking elements are
Polygraph lie detection on real events in a laboratory setting.
Bradley, M T; Cullen, M C
1993-06-01
This laboratory study dealt with real-life intense emotional events. Subjects generated embarrassing stories from their experience, then submitted to polygraph testing and, by lying, denied their stories and, by telling the truth, denied a randomly assigned story. Money was given as an incentive to be judged innocent on each story. An interrogator, blind to the stories, used Control Question Tests and found subjects more deceptive when lying than when truthful. Stories interacted with order such that lying on the second story was more easily detected than lying on the first. Embarrassing stories provide an alternative to the use of mock crimes to study lie detection in the laboratory.
Internally connected graphs and the Kashiwara-Vergne Lie algebra
Felder, Matteo
2016-01-01
It is conjectured that the Kashiwara-Vergne Lie algebra $\\widehat{\\mathfrak{krv}}_2$ is isomorphic to the direct sum of the Grothendieck-Teichm\\"uller Lie algebra $\\mathfrak{grt}_1$ and a one-dimensional Lie algebra. In this paper, we use the graph complex of internally connected graphs to define a nested sequence of Lie subalgebras of $\\widehat{\\mathfrak{krv}}_2$ whose intersection is $\\mathfrak{grt}_1$, thus giving a way to interpolate between these two Lie algebras.
On the q-exponential of matrix q-Lie algebras
Directory of Open Access Journals (Sweden)
Ernst Thomas
2017-01-01
Full Text Available In this paper, we define several new concepts in the borderline between linear algebra, Lie groups and q-calculus.We first introduce the ring epimorphism r, the set of all inversions of the basis q, and then the important q-determinant and corresponding q-scalar products from an earlier paper. Then we discuss matrix q-Lie algebras with a modified q-addition, and compute the matrix q-exponential to form the corresponding n × n matrix, a so-called q-Lie group, or manifold, usually with q-determinant 1. The corresponding matrix multiplication is twisted under τ, which makes it possible to draw diagrams similar to Lie group theory for the q-exponential, or the so-called q-morphism. There is no definition of letter multiplication in a general alphabet, but in this article we introduce new q-number systems, the biring of q-integers, and the extended q-rational numbers. Furthermore, we provide examples of matrices in suq(4, and its corresponding q-Lie group. We conclude with an example of system of equations with Ward number coeficients.
Diffusion through statically compacted clay
International Nuclear Information System (INIS)
Ho, C.L.; Shebl, M.A.A.
1994-01-01
This paper presents experimental work on the effect of compaction on contaminant flow through clay liners. The experimental program included evaluation of soil properties, compaction, permeability and solute diffusion. A permeameter was built of non reactive materials to test samples compacted at different water contents and compactive efforts. The flow of a permeating solute, LiCl, was monitored. Effluent samples were collected for solute concentration measurements. The concentrations were measured by performing atomic adsorption tests. The analyzed results showed different diffusion characteristics when compaction conditions changed. At each compactive effort, permeability decreased as molding water content increased. Consequently, transit time (measured at relative concentration 50%) increased and diffusivity decreased. As compactive effort increased for soils compacted dry of optimum, permeability and diffusion decreased. On the other hand, as compactive effort increased for soils compacted wet of optimum, permeability and diffusivity increased. Tortuosity factor was indirectly measured from the diffusion and retardation rate. Tortuosity factor also decreased as placement water content was increased from dry of optimum to wet of optimum. Then decreases were more pronounced for low compactive effort tests. 27 refs., 7 figs., 5 tabs
Devious Lies: Adventures in Freelance Science Outreach
Fatland, D. R.
2003-12-01
Observations are given from two freelance science outreach projects undertaken by the author: Tutoring at-risk secondary students and teaching astronomy to 5th-7th graders in a camp retreat environment. Two recurring thematic challenges in these experiences are considered: First the 'Misperception Problem', the institutionalized chasm between the process of doing science and K-12 science education (wherein science is often portrayed as something distant and inaccessible, while ironically children are necessarily excellent scientists). And second the 'Engagement Problem', engaging a student's attention and energy by matching teaching material and--more importantly--teaching techniques to the student's state of development. The objective of this work is twofold: To learn how to address these two challenges and to empower the students in a manner independent of the scientific content of any particular subject. An underlying hypothesis is that confidence to problem solve (a desirable life-skill) can be made more accessible through a combination of problem solving by the student and seeing how others have solved seemingly impossible problems. This hypothesis (or agenda) compels an emphasis on critical thinking and raises the dilemma of reconciling non-directed teaching with very pointed conclusions about the verity of pseudo-science and ideas prevalent about science in popular culture. An interesting pedagogical found-object in this regard is the useful 'devious lie' which can encourage a student to question the assumption that the teacher (and by extension any professed expert) has the right answers.
Quantum integrable systems related to lie algebras
International Nuclear Information System (INIS)
Olshanetsky, M.A.; Perelomov, A.M.
1983-01-01
Some quantum integrable finite-dimensional systems related to Lie algebras are considered. This review continues the previous review of the same authors (1981) devoted to the classical aspects of these systems. The dynamics of some of these systems is closely related to free motion in symmetric spaces. Using this connection with the theory of symmetric spaces some results such as the forms of spectra, wave functions, S-matrices, quantum integrals of motion are derived. In specific cases the considered systems describe the one-dimensional n-body systems interacting pairwise via potentials g 2 v(q) of the following 5 types: vsub(I)(q)=q - 2 , vsub(II)(q)=sinh - 2 q, vsub(III)(q)=sin - 2 q, vsub(IV)(q)=P(q), vsub(V)(q)=q - 2 +#betta# 2 q 2 . Here P(q) is the Weierstrass function, so that the first three cases are merely subcases on the fourth. The system characterized by the Toda nearest-neighbour potential exp(qsub(j)-qsub(j+1)) is moreover considered. This review presents from a general and universal point of view results obtained mainly over the past fifteen years. Besides, it contains some new results both of physical and mathematical interest. (orig.)
Moving Picture, Lying Image: Unreliable Cinematic Narratives
Directory of Open Access Journals (Sweden)
Csönge Tamás
2015-08-01
Full Text Available By coining the term “unreliable narrator” Wayne Booth hypothesized another agent in his model besides the author, the implicit author, to explain the double coding of narratives where a distorted view of reality and the exposure of this distortion are presented simultaneously. The article deals with the applicability of the concept in visual narratives. Since unreliability is traditionally considered to be intertwined with first person narratives, it works through subjective mediators. According to scholarly literature on the subject, the narrator has to be strongly characterized, or in other words, anthropomorphized. In the case of film, the main problem is that the narrator is either missing or the narration cannot be attributed entirely to them. There is a medial rupture where the apparatus mediates the story instead of a character’s oral or written discourse. The present paper focuses on some important but overlooked questions about the nature of cinematic storytelling through a re-examination of |the lying flashback in Alfred Hitchcock's Stage Fright. Can a character-narrator control the images the viewer sees? How can the filmic image still be unreliable without having an anthropomorphic narrator? How useful is the term focalization when we are dealing with embedded character-narratives in film?
Introduction to topological groups
Husain, Taqdir
2018-01-01
Concise treatment covers semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras. 1966 edition.
White Lies in Hand: Are Other-Oriented Lies Modified by Hand Gestures? Possibly Not
Directory of Open Access Journals (Sweden)
Katarzyna Cantarero
2017-06-01
Full Text Available Previous studies have shown that the hand-over-heart gesture is related to being more honest as opposed to using self-centered dishonesty. We assumed that the hand-over-heart gesture would also relate to other-oriented dishonesty, though the latter differs highly from self-centered lying. In Study 1 (N = 79, we showed that performing a hand-over-heart gesture diminished the tendency to use other-oriented white lies and that the fingers crossed behind one’s back gesture was not related to higher dishonesty. We then pre-registered and conducted Study 2 (N = 88, which was designed following higher methodological standards than Study 1. Contrary, to the findings of Study 1, we found that using the hand-over-heart gesture did not result in refraining from using other-oriented white lies. We discuss the findings of this failed replication indicating the importance of strict methodological guidelines in conducting research and also reflect on relatively small effect sizes related to some findings in embodied cognition.
White Lies in Hand: Are Other-Oriented Lies Modified by Hand Gestures? Possibly Not.
Cantarero, Katarzyna; Parzuchowski, Michal; Dukala, Karolina
2017-01-01
Previous studies have shown that the hand-over-heart gesture is related to being more honest as opposed to using self-centered dishonesty. We assumed that the hand-over-heart gesture would also relate to other-oriented dishonesty, though the latter differs highly from self-centered lying. In Study 1 ( N = 79), we showed that performing a hand-over-heart gesture diminished the tendency to use other-oriented white lies and that the fingers crossed behind one's back gesture was not related to higher dishonesty. We then pre-registered and conducted Study 2 ( N = 88), which was designed following higher methodological standards than Study 1. Contrary, to the findings of Study 1, we found that using the hand-over-heart gesture did not result in refraining from using other-oriented white lies. We discuss the findings of this failed replication indicating the importance of strict methodological guidelines in conducting research and also reflect on relatively small effect sizes related to some findings in embodied cognition.
Moduli space of self-dual connections in dimension greater than four for abelian Gauge groups
Cappelle, Natacha
2018-01-01
In 1954, C. Yang and R. Mills created a Gauge Theory for strong interaction of Elementary Particles. More generally, they proved that it is possible to define a Gauge Theory with an arbitrary compact Lie group as Gauge group. Within this context, it is interesting to find critical values of a functional defined on the space of connections: the Yang-Mills functional. If the based manifold is four dimensional, there exists a natural notion of (anti-)self-dual 2-form, which gives a natural notio...
MECHANICS OF DYNAMIC POWDER COMPACTION PROCESS
Nurettin YAVUZ
1996-01-01
In recent years, interest in dynamic compaction methods of metal powders has increased due to the need to improve compaction properties and to increase production rates of compacts. In this paper, review of dynamic and explosive compaction of metal powders are given. An attempt is made to get a better understanding of the compaction process with the mechanicis of powder compaction.
A new approach for categorizing pig lying behaviour based on a Delaunay triangulation method.
Nasirahmadi, A; Hensel, O; Edwards, S A; Sturm, B
2017-01-01
Machine vision-based monitoring of pig lying behaviour is a fast and non-intrusive approach that could be used to improve animal health and welfare. Four pens with 22 pigs in each were selected at a commercial pig farm and monitored for 15 days using top view cameras. Three thermal categories were selected relative to room setpoint temperature. An image processing technique based on Delaunay triangulation (DT) was utilized. Different lying patterns (close, normal and far) were defined regarding the perimeter of each DT triangle and the percentages of each lying pattern were obtained in each thermal category. A method using a multilayer perceptron (MLP) neural network, to automatically classify group lying behaviour of pigs into three thermal categories, was developed and tested for its feasibility. The DT features (mean value of perimeters, maximum and minimum length of sides of triangles) were calculated as inputs for the MLP classifier. The network was trained, validated and tested and the results revealed that MLP could classify lying features into the three thermal categories with high overall accuracy (95.6%). The technique indicates that a combination of image processing, MLP classification and mathematical modelling can be used as a precise method for quantifying pig lying behaviour in welfare investigations.
International Nuclear Information System (INIS)
Madhavi, V.; Phatak, P.R.; Bahadur, C.; Bayala, A.K.; Jakati, R.K.; Sathian, V.
2003-01-01
Full text: A compact size neutron flux monitor has been developed incorporating standard boards developed for smart radiation monitors. The sensitivity of the monitors is 0.4cps/nV. It has been tested up to 2075 nV flux with standard neutron sources. It shows convincing results even in high flux areas like 6m away from the accelerator in RMC (Parel) for 106/107 nV. These monitors have a focal and remote display, alarm function with potential free contacts for centralized control and additional provision of connectivity via RS485/Ethernet. This paper describes the construction, working and results of the above flux monitor
International Nuclear Information System (INIS)
Angelini, A.; Coppi, B.; Nassi, M.
1992-01-01
This paper reports on high magnetic field experiments which can be designed to investigate D-T ignition conditions based on present-day experimental results and theoretical understanding of plasma phenomena. The key machine elements are: large plasma currents, compact dimensions, tight aspect ratios, moderate elongations and significant triangularities of the plasma column. High plasma densities, strong ohmic heating, the needed degree of energy confinement, good plasma purity and robust stability against ideal and resistive instabilities can be achieved simultaneously. The Ignitor design incorporates all these characteristics and involves magnet technology developments, started with the Alcator experiment, that use cryogenically cooled normal conductors
International Nuclear Information System (INIS)
Kurennoy, S.S.; O'Hara, J.F.; Rybarcyk, L.J.
2008-01-01
We are developing a compact deuteron-beam accelerator up to the deuteron energy of a few MeV based on room-temperature inter-digital H-mode (IH) accelerating structures with the transverse beam focusing using permanent-magnet quadrupoles (PMQ). Combining electromagnetic 3-D modeling with beam dynamics simulations and thermal-stress analysis, we show that IHPMQ structures provide very efficient and practical accelerators for light-ion beams of considerable currents at the beam velocities around a few percent of the speed of light. IH-structures with PMQ focusing following a short RFQ can also be beneficial in the front end of ion linacs.
Compact electron storage rings
International Nuclear Information System (INIS)
Williams, G.P.
1987-01-01
There have been many recent developments in the area of compact storage rings. Such rings would have critical wavelengths of typically 10 A, achieved with beam energies of several hundreds of MeV and superconducting dipole fields of around 5 Tesla. Although the primary motivation for progress in this area is that of commercial x-ray lithography, such sources might be an attractive source for college campuses to operate. They would be useful for many programs in materials science, solid state, x-ray microscopy and other biological areas. We discuss the properties of such sources and review developments around the world, primarily in the USA, japan and W. Germany
Compact synchrotron radiation source
International Nuclear Information System (INIS)
Liu, N.; Wang, T.; Tian, J.; Lin, Y.; Chen, S.; He, W.; Hu, Y.; Li, Q.
1985-01-01
A compact 800 MeV synchrotron radiation source is discussed. The storage ring has a circumference of 30.3 m, two 90 degree and four 45 degree bending magnet sections, two long straight sections and four short straight sections. The radius of the bending magnet is 2.224m. The critical wave length is 24A. The injector is a 15 Mev Microtron Electrons are accelerated from 15 Mev to 800 Mev by ramping the field of the ring. The expected stored current will be around 100 ma
International Nuclear Information System (INIS)
Linford, R.K.; Armstrong, W.T.; Bartsch, R.R.
1981-01-01
The Compact Torus (CT) concept includes any axisymmetric toroidal plasma configuration, which does not require the linking of any material through the hole in the torus. Thus, the magnet coils, vacuum vessel, etc., have a simple cylindrical or spherical geometry instead of the toroidal geometry required for Tokamaks and RFP's. This simplified geometry results in substantial engineering advantages in CT reactor embodiments while retaining the good confinement properties afforded by an axisymmetric toroidal plasma-field geometry. CT's can be classified into three major types by using the ion gyro radius rho/sub i/ and the magnitude of the maximum toroidal field B/sub tm/
Energy Technology Data Exchange (ETDEWEB)
Bazeia, D., E-mail: bazeia@fisica.ufpb.br [Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, PB (Brazil); Losano, L.; Marques, M.A. [Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, PB (Brazil); Menezes, R. [Departamento de Ciências Exatas, Universidade Federal da Paraíba, 58297-000 Rio Tinto, PB (Brazil); Departamento de Física, Universidade Federal de Campina Grande, 58109-970 Campina Grande, PB (Brazil); Rocha, R. da [Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-580 Santo André (Brazil)
2016-07-10
In this work we deal with non-topological solutions of the Q-ball type in two space–time dimensions, in models described by a single complex scalar field that engenders global symmetry. The main novelty is the presence of stable Q-balls solutions that live in a compact interval of the real line and appear from a family of models controlled by two distinct parameters. We find analytical solutions and study their charge and energy, and show how to control the parameters to make the Q-balls classically and quantum mechanically stable.
Lie transforms and their use in Hamiltonian perturbation theory
International Nuclear Information System (INIS)
Cary, J.R.
1978-06-01
A review is presented of the theory of Lie transforms as applied to Hamiltonian systems. We begin by presenting some general background on the Hamiltonian formalism and by introducing the operator notation for canonical transformations. We then derive the general theory of Lie transforms. We derive the formula for the new Hamiltonian when one uses a Lie transform to effect a canonical transformation, and we use Lie transforms to prove a very general version of Noether's theorem, or the symmetry-equals-invariant theorem. Next we use the general Lie transform theory to derive Deprit's perturbation theory. We illustrate this perturbation theory by application to two well-known problems in classical mechanics. Finally we present a chapter on conventions. There are many ways to develop Lie transforms. The last chapter explains the reasons for the choices made here
Lie-Hamilton systems on curved spaces: a geometrical approach
Herranz, Francisco J.; de Lucas, Javier; Tobolski, Mariusz
2017-12-01
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional Lie algebra, a Vessiot-Guldberg Lie algebra, of Hamiltonian vector fields relative to a Poisson structure. Its general solution can be written as an autonomous function, the superposition rule, of a generic finite family of particular solutions and a set of constants. We pioneer the study of Lie-Hamilton systems on Riemannian spaces (sphere, Euclidean and hyperbolic plane), pseudo-Riemannian spaces (anti-de Sitter, de Sitter, and Minkowski spacetimes) as well as on semi-Riemannian spaces (Newtonian spacetimes). Their corresponding constants of motion and superposition rules are obtained explicitly in a geometric way. This work extends the (graded) contraction of Lie algebras to a contraction procedure for Lie algebras of vector fields, Hamiltonian functions, and related symplectic structures, invariants, and superposition rules.
Scalable Nonlinear Compact Schemes
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Debojyoti [Argonne National Lab. (ANL), Argonne, IL (United States); Constantinescu, Emil M. [Univ. of Chicago, IL (United States); Brown, Jed [Univ. of Colorado, Boulder, CO (United States)
2014-04-01
In this work, we focus on compact schemes resulting in tridiagonal systems of equations, specifically the fifth-order CRWENO scheme. We propose a scalable implementation of the nonlinear compact schemes by implementing a parallel tridiagonal solver based on the partitioning/substructuring approach. We use an iterative solver for the reduced system of equations; however, we solve this system to machine zero accuracy to ensure that no parallelization errors are introduced. It is possible to achieve machine-zero convergence with few iterations because of the diagonal dominance of the system. The number of iterations is specified a priori instead of a norm-based exit criterion, and collective communications are avoided. The overall algorithm thus involves only point-to-point communication between neighboring processors. Our implementation of the tridiagonal solver differs from and avoids the drawbacks of past efforts in the following ways: it introduces no parallelization-related approximations (multiprocessor solutions are exactly identical to uniprocessor ones), it involves minimal communication, the mathematical complexity is similar to that of the Thomas algorithm on a single processor, and it does not require any communication and computation scheduling.
Compact magnetic fusion systems
Energy Technology Data Exchange (ETDEWEB)
Linford, R.K.
1983-12-01
If the core (first wall, blanket, shield, and magnet coils) of fusion reactor systems could be made smaller in mass and volume for a given net electric power output than is usually predicted for the mainline tokamak/sup 1/ and mirror concepts, the cost of the technological development of the core and the construction of power plants might be significantly reduced. Although progress in plasma physics and engineering approaches should continue to yield improvements in reactor designs, certain physics features of the mainline concepts may prevent major reductions in the size of the core without straining the limits of technology. However, more than a factor of ten reduction in volume and mass of the core, at constant output power, may be possible for a class of toroidal confinement concepts in which the confining magnetic fields are supported more by currents flowing in the plasma than those in the external coils. In spite of this dramatic increase in power density (ratio of total thermal output power to the volume of the core), the design of compact systems need not rely on any materials requirements that are qualitatively more difficult than those proposed for the lower-power-density mainline fusion concepts. In some respects compact systems require less of an extension of existing technology, e.g. magnetics.
Compact magnetic fusion systems
International Nuclear Information System (INIS)
Linford, R.K.
1983-01-01
If the core (first wall, blanket, shield, and magnet coils) of fusion reactor systems could be made smaller in mass and volume for a given net electric power output than is usually predicted for the mainline tokamak 1 and mirror concepts, the cost of the technological development of the core and the construction of power plants might be significantly reduced. Although progress in plasma physics and engineering approaches should continue to yield improvements in reactor designs, certain physics features of the mainline concepts may prevent major reductions in the size of the core without straining the limits of technology. However, more than a factor of ten reduction in volume and mass of the core, at constant output power, may be possible for a class of toroidal confinement concepts in which the confining magnetic fields are supported more by currents flowing in the plasma than those in the external coils. In spite of this dramatic increase in power density (ratio of total thermal output power to the volume of the core), the design of compact systems need not rely on any materials requirements that are qualitatively more difficult than those proposed for the lower-power-density mainline fusion concepts. In some respects compact systems require less of an extension of existing technology, e.g. magnetics
Diffusion in compacted betonite
International Nuclear Information System (INIS)
Muurinen, A.; Rantanen, J.
1985-01-01
The objective of this report is to collect the literature bearing on the diffusion in compacted betonite, which has been suggested as possible buffer material for the disposal of spent fuel. Diffusion in a porous, water-saturated material is usually described as diffusion in the pore-water where sorption on the solid matter can delay the migration in the instationary state. There are also models which take into consideration that the sorbed molecules can also move while being sorbed. Diffusion experiments in compacted bentonite have been reported by many authors. Gases, anions, cations and actinides have been used as diffusing molecules. The report collects the results and the information on the measurement methods. On the basis of the results can be concluded that different particles possibly follow different diffusion mechanisms. The parameters which affect the diffusion seem to be for example the size, the electric charge and the sorption properties of the diffusing molecule. The report also suggest the parameters to be used in the diffusion calculation of the safety analyses of spent fuel disposal. (author)
Zuckerwar, Allan J.; Shams, Qamar A.; Sealey, Bradley S.; Comeaux, Toby
2005-01-01
A compact windscreen has been conceived for a microphone of a type used outdoors to detect atmospheric infrasound from a variety of natural and manmade sources. Wind at the microphone site contaminates received infrasonic signals (defined here as sounds having frequencies <20 Hz), because a microphone cannot distinguish between infrasonic pressures (which propagate at the speed of sound) and convective pressure fluctuations generated by wind turbulence. Hence, success in measurement of outdoor infrasound depends on effective screening of the microphone from the wind. The present compact windscreen is based on a principle: that infrasound at sufficiently large wavelength can penetrate any barrier of practical thickness. Thus, a windscreen having solid, non-porous walls can block convected pressure fluctuations from the wind while transmitting infrasonic acoustic waves. The transmission coefficient depends strongly upon the ratio between the acoustic impedance of the windscreen and that of air. Several materials have been found to have impedance ratios that render them suitable for use in constructing walls that have practical thicknesses and are capable of high transmission of infrasound. These materials (with their impedance ratios in parentheses) are polyurethane foam (222), space shuttle tile material (332), balsa (323), cedar (3,151), and pine (4,713).
Compact electrostatic comb actuator
Rodgers, M. Steven; Burg, Michael S.; Jensen, Brian D.; Miller, Samuel L.; Barnes, Stephen M.
2000-01-01
A compact electrostatic comb actuator is disclosed for microelectromechanical (MEM) applications. The actuator is based upon a plurality of meshed electrostatic combs, some of which are stationary and others of which are moveable. One or more restoring springs are fabricated within an outline of the electrostatic combs (i.e. superposed with the moveable electrostatic combs) to considerably reduce the space required for the actuator. Additionally, a truss structure is provided to support the moveable electrostatic combs and prevent bending or distortion of these combs due to unbalanced electrostatic forces or external loading. The truss structure formed about the moveable electrostatic combs allows the spacing between the interdigitated fingers of the combs to be reduced to about one micron or less, thereby substantially increasing the number of active fingers which can be provided in a given area. Finally, electrostatic shields can be used in the actuator to substantially reduce unwanted electrostatic fields to further improve performance of the device. As a result, the compact electrostatic comb actuator of the present invention occupies only a fraction of the space required for conventional electrostatic comb actuators, while providing a substantial increase in the available drive force (up to one-hundred times).
Development task of compact reactor
International Nuclear Information System (INIS)
Kurushima, Morihiro
1982-01-01
In the Ministry of International Trade and Industry, studies proceed on the usage of compact medium and small LWRs. As such, the reactors from 100 to 200 MW may meet varieties of demands in scale and kind in view of the saving of petroleum and the economy of nuclear power. In this case, the technology of light water reactors with already established safety will be suitable for the development of compact reactors. The concept of ''nuclear power community'' using the compact reactors in local society and industrial zones was investigated. The following matters are described: need for the introduction of compact reactors, the survey on the compact reactor systems, and the present status and future problems for compact reactor usage. (J.P.N.)
The United Nations Global Compact
DEFF Research Database (Denmark)
Rasche, Andreas; Waddock, Sandra; McIntosh, Malcolm
2013-01-01
This article reviews the interdisciplinary literature on the UN Global Compact. The review identifies three research perspectives, which scholars have used to study the UN Global Compact so far: a historical perspective discussing the Global Compact in the context of UN-business relations...... key empirical as well as conceptual scholarly contributions. The remainder of this article contains focused summaries of the articles selected for this Special Issue. All articles are introduced and evaluated against the background of the three research perspectives....
Low-dimensional filiform Lie algebras over finite fields
Falcón Ganfornina, Óscar Jesús; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vasek, Vladimir (Coordinador); Shmaliy, Yuriy S. (Coordinador); Trcek, Denis (Coordinador); Kobayashi, Nobuhiko P. (Coordinador); Choras, Ryszard S. (Coordinador); Klos, Zbigniew (Coordinador)
2011-01-01
In this paper we use some objects of Graph Theory to classify low-dimensional filiform Lie algebras over finite fields. The idea lies in the representation of each Lie algebra by a certain type of graphs. Then, some properties on Graph Theory make easier to classify the algebras. As results, which can be applied in several branches of Physics or Engineering, for instance, we find out that there exist, up to isomorphism, six 6-dimensional filiform Lie algebras over Z/pZ, for p = 2, 3, 5. Pl...
Expansion of the Lie algebra and its applications
International Nuclear Information System (INIS)
Guo Fukui; Zhang Yufeng
2006-01-01
We take the Lie algebra A1 as an example to illustrate a detail approach for expanding a finite dimensional Lie algebra into a higher-dimensional one. By making use of the late and its resulting loop algebra, a few linear isospectral problems with multi-component potential functions are established. It follows from them that some new integrable hierarchies of soliton equations are worked out. In addition, various Lie algebras may be constructed for which the integrable couplings of soliton equations are obtained by employing the expanding technique of the the Lie algebras
3-Lie bialgebras (Lb,Cd and (Lb,Ce
Directory of Open Access Journals (Sweden)
Bai Ruipu
2016-05-01
Full Text Available Four dimensional $3$-Lie coalgebras with two-dimensional derived algebras, and four-dimensional $3$-Lie bialgebras of type $(L_b, C_c$ are classified. It is proved that there exist three classes of four dimensional $3$-Lie coalgebras with two-dimensional derived algebra which are $(L, C_{c_i}$, $i=1, 2, 3$ (Lemma 3.1, and ten classes of four dimensional $3$-Lie bialgebras of type $(L_b, C_c$ (Theorem 3.2.
Matrix groups for undergraduates
Tapp, Kristopher
2016-01-01
Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe the basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, maximal tori, homogeneous spaces, and roots. This second edition includes two new chapters that allow for an easier transition to the general theory of Lie groups. From reviews of the First Edition: This book could be used as an excellent textbook for a one semester course at university and it will prepare students for a graduate course on Lie groups, Lie algebras, etc. … The book combines an intuitive style of writing w...
General Relativity and Compact Stars
International Nuclear Information System (INIS)
Glendenning, Norman K.
2005-01-01
Compact stars--broadly grouped as neutron stars and white dwarfs--are the ashes of luminous stars. One or the other is the fate that awaits the cores of most stars after a lifetime of tens to thousands of millions of years. Whichever of these objects is formed at the end of the life of a particular luminous star, the compact object will live in many respects unchanged from the state in which it was formed. Neutron stars themselves can take several forms--hyperon, hybrid, or strange quark star. Likewise white dwarfs take different forms though only in the dominant nuclear species. A black hole is probably the fate of the most massive stars, an inaccessible region of spacetime into which the entire star, ashes and all, falls at the end of the luminous phase. Neutron stars are the smallest, densest stars known. Like all stars, neutron stars rotate--some as many as a few hundred times a second. A star rotating at such a rate will experience an enormous centrifugal force that must be balanced by gravity or else it will be ripped apart. The balance of the two forces informs us of the lower limit on the stellar density. Neutron stars are 10 14 times denser than Earth. Some neutron stars are in binary orbit with a companion. Application of orbital mechanics allows an assessment of masses in some cases. The mass of a neutron star is typically 1.5 solar masses. They can therefore infer their radii: about ten kilometers. Into such a small object, the entire mass of our sun and more, is compressed
Uniform estimate of a compact convex set by a ball in an arbitrary norm
International Nuclear Information System (INIS)
Dudov, S I; Zlatorunskaya, I V
2000-01-01
The problem of the best uniform approximation of a compact convex set by a ball with respect to an arbitrary norm in the Hausdorff metric corresponding to that norm is considered. The question is reduced to a convex programming problem, which can be studied by means of convex analysis. Necessary and sufficient conditions for the solubility of this problem are obtained and several properties of its solution are described. It is proved, in particular, that the centre of at least one ball of best approximation lies in the compact set under consideration; in addition, conditions ensuring that the centres of all balls of best approximation lie in this compact set and a condition for unique solubility are obtained
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
Energy Technology Data Exchange (ETDEWEB)
Elizondo-Decanini, Juan M.
2017-08-29
A compact particle accelerator having an input portion configured to receive power to produce particles for acceleration, where the input portion includes a switch, is provided. In a general embodiment, a vacuum tube receives particles produced from the input portion at a first end, and a plurality of wafer stacks are positioned serially along the vacuum tube. Each of the plurality of wafer stacks include a dielectric and metal-oxide pair, wherein each of the plurality of wafer stacks further accelerate the particles in the vacuum tube. A beam shaper coupled to a second end of the vacuum tube shapes the particles accelerated by the plurality of wafer stacks into a beam and an output portion outputs the beam.
Compact vacuum insulation embodiments
Benson, D.K.; Potter, T.F.
1992-04-28
An ultra-thin compact vacuum insulation panel is comprised of two hard, but bendable metal wall sheets closely spaced apart from each other and welded around the edges to enclose a vacuum chamber. Glass or ceramic spacers hold the wall sheets apart. The spacers can be discrete spherical beads or monolithic sheets of glass or ceramic webs with nodules protruding therefrom to form essentially point' or line' contacts with the metal wall sheets. In the case of monolithic spacers that form line' contacts, two such spacers with the line contacts running perpendicular to each other form effectively point' contacts at the intersections. Corrugations accommodate bending and expansion, tubular insulated pipes and conduits, and preferred applications are also included. 26 figs.
Benson, D.K.; Potter, T.F.
1993-01-05
An ultra-thin compact vacuum insulation panel is comprised of two hard, but bendable metal wall sheets closely spaced apart from each other and welded around the edges to enclose a vacuum chamber. Glass or ceramic spacers hold the wall sheets apart. The spacers can be discrete spherical beads or monolithic sheets of glass or ceramic webs with nodules protruding therefrom to form essentially point'' or line'' contacts with the metal wall sheets. In the case of monolithic spacers that form line'' contacts, two such spacers with the line contacts running perpendicular to each other form effectively point'' contacts at the intersections. Corrugations accommodate bending and expansion, tubular insulated pipes and conduits, and preferred applications are also included.
Compact cryocooler heat exchangers
International Nuclear Information System (INIS)
Luna, J.; Frederking, T.H.K.
1991-01-01
Compact heat exchangers are subject to different constraints as a room temperature gas is cooled down by a cold stream returning from a JT valve (or a similar cryoprocess component). In particular, the optimization of exchangers for liquid helium systems has to cover a wide range in temperature and density of the fluid. In the present work we address the following thermodynamic questions: 1. The optimization of intermediate temperatures which optimize stage operation (a stage is assumed to have a constant cross section); 2. The optimum temperature difference available for best overall economic performance values. The results are viewed in the context of porous media concepts applied to rather low speeds of fluid flow in narrow passages. In this paper examples of fluid/solid constraints imposed in this non-classical low temperature area are presented
Yu, Siyuan; Lourtioz, Jean-Michel
2014-01-01
This book brings together in a single volume a unique contribution by the top experts around the world in the field of compact semiconductor lasers to provide a comprehensive description and analysis of the current status as well as future directions in the field of micro- and nano-scale semiconductor lasers. It is organized according to the various forms of micro- or nano-laser cavity configurations with each chapter discussing key technical issues, including semiconductor carrier recombination processes and optical gain dynamics, photonic confinement behavior and output coupling mechanisms, carrier transport considerations relevant to the injection process, and emission mode control. Required reading for those working in and researching the area of semiconductors lasers and micro-electronics.
Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities
International Nuclear Information System (INIS)
Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Torres, Pedro J.
2007-01-01
Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schroedinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves
Lie-Telling Behavior in Children with Autism and Its Relation to False-Belief Understanding
Talwar, Victoria; Zwaigenbaum, Lonnie; Goulden, Keith J.; Manji, Shazeen; Loomes, Carly; Rasmussen, Carmen
2012-01-01
Children's lie-telling behavior and its relation to false-belief understanding was examined in children with autism spectrum disorders (ASD; n = 26) and a comparison group of typically developing children (n = 27). Participants were assessed using a temptation resistance paradigm, in which children were told not to peek at a forbidden toy while…
Description of a class of superstring compactifications related to semi-simple Lie algebras
International Nuclear Information System (INIS)
Markushevich, D.I.; Ol'shanetskij, M.A.; Perelomov, A.M.
1986-01-01
A class of vacuum configurations in the superstring theory obtained by compactification of physical dimensions from ten to four is constructed. The compactification scheme involves taking quotients of tori of semisimple Lie algebras by finite symmetry group actions. The complete list of such configurations arising from actions by a Coxeter transformation is given. Some topological invariants having physical interpretations are calculated
Closure of the gauge algebra, generalized Lie equations and Feynman rules
International Nuclear Information System (INIS)
Batalin, I.A.
1984-01-01
A method is given by which an open gauge algebra can always be closed and even made abelian. As a preliminary the generalized Lie equations for the open group are obtained. The Feynman rules for gauge theories with open algebras are derived by reducing the gauge theory to a non-gauge one. (orig.)
The eyes don't have it: lie detection and Neuro-Linguistic Programming.
Directory of Open Access Journals (Sweden)
Richard Wiseman
Full Text Available Proponents of Neuro-Linguistic Programming (NLP claim that certain eye-movements are reliable indicators of lying. According to this notion, a person looking up to their right suggests a lie whereas looking up to their left is indicative of truth telling. Despite widespread belief in this claim, no previous research has examined its validity. In Study 1 the eye movements of participants who were lying or telling the truth were coded, but did not match the NLP patterning. In Study 2 one group of participants were told about the NLP eye-movement hypothesis whilst a second control group were not. Both groups then undertook a lie detection test. No significant differences emerged between the two groups. Study 3 involved coding the eye movements of both liars and truth tellers taking part in high profile press conferences. Once again, no significant differences were discovered. Taken together the results of the three studies fail to support the claims of NLP. The theoretical and practical implications of these findings are discussed.
How (not) to Lie with Benefit-Cost Analysis
Scott Farrow
2013-01-01
Benefit-cost analysis is seen by some as a controversial activity in which the analyst can significantly bias the results. This note highlights some of the ways that analysts can "lie" in a benefit-cost analysis but more importantly, provides guidance on how not to lie and how to better inform public decisionmakers.
Lie and Noether symmetries of systems of complex ordinary ...
Indian Academy of Sciences (India)
2014-07-02
Jul 2, 2014 ... Abstract. The Lie and Noether point symmetry analyses of a kth-order system of m complex ordi- nary differential equations (ODEs) with m dependent variables are performed. The decomposition of complex symmetries of the given system of complex ODEs yields Lie- and Noether-like opera- tors.
Lie Algebroids in Classical Mechanics and Optimal Control
Directory of Open Access Journals (Sweden)
Eduardo Martínez
2007-03-01
Full Text Available We review some recent results on the theory of Lagrangian systems on Lie algebroids. In particular we consider the symplectic and variational formalism and we study reduction. Finally we also consider optimal control systems on Lie algebroids and we show how to reduce Pontryagin maximum principle.