ALGEBRAIC DEFINITION OF TOPOLOGICAL W GRAVITY

1992 ◽  
Vol 07 (21) ◽  
pp. 5193-5211
Author(s):  
SHINOBU HOSONO
Keyword(s):  
Lie Algebra ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Simple Lie Algebra ◽  
Topological Gravity ◽  
Definition Of ◽  
Extended Theories

We propose a definition of the topological W gravity using some properties of the principal three-dimensional subalgebra of a simple Lie algebra due to Kostant. In our definition, structures of the two-dimensional topological gravity are naturally embedded in the extended theories. In accordance with the definition, we will present some explicit calculations for the W3 gravity.

scholarly journals ELEMENTARY PARABOLIC TWIST

2002 ◽  
Vol 01 (04) ◽  
pp. 413-424 ◽  
Author(s):  
V. D. LYAKHOVSKY ◽  
M. E. SAMSONOV
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Borel Subalgebra ◽  
Main Element ◽  
Two Dimensional ◽  
Parabolic Subalgebra ◽  
Simple Lie Algebras ◽  
Simple Lie Algebra

The twist deformations for simple Lie algebras [Formula: see text] whose twisting elements ℱ are known explicitly are usually defined on the carrier subspace injected in the Borel subalgebra [Formula: see text]. We consider the case where the carrier of the twist intersects nontrivially with both [Formula: see text] and [Formula: see text]. The main element of the new deformation is the parabolic twist ℱ℘ whose carrier is the minimal parabolic subalgebra of simple Lie algebra [Formula: see text]. It has the structure of the algebra of two-dimensional motions, contains [Formula: see text] and intersects nontrivially with [Formula: see text]. The twist ℱ℘ is constructed as a composition of the extended jordanian twist [Formula: see text] and the factor [Formula: see text]. The latter can be considered as a special deformed version of the jordanian twist. The twisted costructure is found for [Formula: see text] and the corresponding universal ℛ-matrix is presented. The parabolic twist can be composed with certain types of chains of extended jordanian twists for algebras A2(n-1). The chains enlarged by the parabolic factor ℱ℘ perform the explicit quantization of the new set of classical r-matrices.

scholarly journals Weyl modules and Weyl functors for hyper-map algebras

2020 ◽  
pp. 2140007
Author(s):  
Angelo Bianchi ◽  
Samuel Chamberlin
Keyword(s):  
Lie Algebra ◽  
Finitely Generated ◽  
Weyl Modules ◽  
Simple Lie Algebra ◽  
Finite Dimensional ◽  
Universal Properties ◽  
Definition Of ◽  
Unitary Algebra

We investigate the representations of the hyperalgebras associated to the map algebras [Formula: see text], where [Formula: see text] is any finite-dimensional complex simple Lie algebra and [Formula: see text] is any associative commutative unitary algebra with a multiplicatively closed basis. We consider the natural definition of the local and global Weyl modules, and the Weyl functor for these algebras. Under certain conditions, we prove that these modules satisfy certain universal properties, and we also give conditions for the local or global Weyl modules to be finite-dimensional or finitely generated, respectively.

Exploration of Non-Revolved Parts Modeling Based on MBD and Pro/ENGINEER

2013 ◽  
Vol 712-715 ◽  
pp. 1171-1174 ◽  
Author(s):  
Li Xin Wang ◽  
Yu Guo ◽  
Ming Yue Guo
Keyword(s):  
Three Dimensional ◽  
Great Change ◽  
Two Dimensional ◽  
Modeling Methods ◽  
Model Based ◽  
Boeing Company ◽  
The World ◽  
Definition Of ◽  
Key Steps ◽  
Product Definition

A great change in mechanical industry has occurred after several successful practices using MBD (Model Based Definition) of The Boeing Company. It is an inevitable trend from two-dimensional product definition to three-dimensional product definition in mechanical industry. Several standards for MBD have emerged around the world. This paper explores the non-revolved parts modeling methods based on MBD and Pro/ENGINEER, presents several key steps about full-annotated model per MBD and then makes a conclusion. Following these methods we successfully build a typical non-revolved model which conforms to MBD standards correctly and efficiently.

Three-dimensional impulsive vortex formation from slender orifices

2011 ◽  
Vol 666 ◽  
pp. 506-520 ◽  
Author(s):  
F. DOMENICHINI
Keyword(s):  
Stokes Equations ◽  
Intermediate Phase ◽  
Vortex Formation ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Vortex Ring Formation ◽  
Long Time ◽  
Definition Of

The vortex formation behind an orifice is a widely investigated phenomenon, which has been recently studied in several problems of biological relevance. In the case of a circular opening, several works in the literature have shown the existence of a limiting process for vortex ring formation that leads to the concept of critical formation time. In the different geometric arrangement of a planar flow, which corresponds to an opening with straight edges, it has been recently outlined that such a concept does not apply. This discrepancy opens the question about the presence of limiting conditions when apertures with irregular shape are considered. In this paper, the three-dimensional vortex formation due to the impulsively started flow through slender openings is studied with the numerical solution of the Navier–Stokes equations, at values of the Reynolds number that allow the comparison with previous two-dimensional findings. The analysis of the three-dimensional results reveals the two-dimensional nature of the early vortex formation phase. During an intermediate phase, the flow evolution appears to be driven by the local curvature of the orifice edge, and the time scale of the phenomena exhibits a surprisingly good agreement with those found in axisymmetric problems with the same curvature. The long-time evolution shows the complete development of the three-dimensional vorticity dynamics, which does not allow the definition of further unifying concepts.

scholarly journals CANONICAL TRANSFORMATIONS IN THREE-DIMENSIONAL PHASE-SPACE

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4769-4788 ◽  
Author(s):  
TEKİN DERELİ ◽  
ADNAN TEĞMEN ◽  
TUĞRUL HAKİOĞLU
Keyword(s):  
Phase Space ◽  
Canonical Transformation ◽  
Generating Functions ◽  
General Framework ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Canonical Transformations ◽  
Dimensional Phase Space ◽  
Nambu Bracket ◽  
Definition Of

Canonical transformation in a three-dimensional phase-space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them are listed. Infinitesimal canonical transformations are also discussed. Finally, we show that the decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one.

Divided by a Common Language: Political Theory and the Concept of Power

Politics ◽  
1997 ◽  
Vol 17 (1) ◽  
pp. 45-52 ◽  
Author(s):  
Colin Hay
Keyword(s):  
Political Theory ◽  
Three Dimensional ◽  
Fundamental Concept ◽  
Common Language ◽  
Two Dimensional ◽  
Dimensional Approach ◽  
Political Analysis ◽  
Heated Debate ◽  
The Subject ◽  
Definition Of

Power is probably the most universal and fundamental concept of political analysis. It has been, and continues to be, the subject of extended and heated debate. In this article I critically review the contributions of Bachrach and Baratz, and Lukes to our understanding of the multiple faces of power. I suggest that although the former's two-dimensional approach to power is ultimately compromised by the residues of behaviouralism that it inherits from classic pluralism, the latter's three-dimensional view suggests a potential route out of this pluralist impasse. To seize the opportunity he provides, however, requires that we rethink the concept of power. In the second half of the paper I advance a definition of power as context-shaping and demonstrate how this helps us to disentangle the notions of power, responsibility and culpability that Lukes conflates. In so doing I suggest the we differentiate clearly between analytical questions concerning the identification of power within social and political contexts, and normative questions concerning the critique of the distribution and exercise of power thus identified.

scholarly journals Embedding the Cartesian Space Principles in a Smile, an Inclusive Learning Method for K12.

10.29007/9n6r ◽  
2020 ◽  
Author(s):  
Stefano Vuga ◽  
Eleonora Vuga
Keyword(s):  
Modular Forms ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Emotional Memory ◽  
Free Play ◽  
Two Dimensional ◽  
Real Representation ◽  
Cognitive Intelligence ◽  
Cartesian Space ◽  
Definition Of

It is now well established that the negative emotions the child experiences for not understanding a mathematical topic mark their emotional memory associated with that topic. We’ve been investigating which tangible and accessible tools prevent the development of a pathological allergy to a fundamental concept as it is the Cartesian space, seeking for kid-friendly gates to the subject. When fear and pain for not understanding traces an escape pattern from this topic at a young age the child’s ability to relate to all its didactic applications can be seriously jeopardized, marking (when not identified) the school career and sub-sequent attitudes towards all the fields of theoretical and practical application of it.The elementary approach in explaining the Cartesian space principles to the children remains mainly linked to traditional visualization models of three-dimensional images on two-dimensional space, e.g., paper, blackboard, and screens. Only recently, augmented reality has been used as a teaching aid for visualizing objects in the actual three-dimensional space. Those systems are suitable for children naturally predisposed to mathematical and/or visual-cognitive intelligence, who are not suffering from any visual impairment. This is a non-inclusive system of access to understanding such fundamental topic as the Cartesian space. Topic which is later essential to an extended comprehension of geometry, mathematics, representation of objects, and concepts. The aim of the research was to find and test a support system to complement the standard two-dimensional and visual-only approach and to guarantee a complete and consistent sensorial experience of the definition of the Cartesian space through physical, material, and modular forms. We sought to create a bond between the concept and its real representation. This system should be extended to different ages of development and types of intelligence and backgrounds, transversal to environments and contexts of usage (family/school), also for visually impaired children. The developed tools pro-vide the child an early and positive emotional bond, prior to any traditional scholastic approach, with the fundamental principles of the Cartesian space through methods such as free play, trial and error, experimentation and share of the emotions while engaging in cooperative activities.

The Three-Dimensional Necker Cube

2017 ◽  
Author(s):  
Nicola Bruno
Keyword(s):  
Necker Cube ◽  
Three Dimensional ◽  
Visual Illusions ◽  
Two Dimensional ◽  
Reversible Figure ◽  
Sensory Signals ◽  
Dimensional Version ◽  
Definition Of ◽  
Theoretical Issues

The Necker cube is a widely known example of a reversible figure. Perceptual reversals were first observed in engravings of crystals by the Swiss geologist Louis Albert Necker in 1832. Although Necker’s engravings were not exactly of regular cubes, the figure as it is used now can be perceived in two alternative arrangements of a three-dimensional (3D) cube. Although less widely known than the popular two-dimensional version, the 3D Necker cube is a surprisingly rich model for psychophysical investigation. This chapter summarizes relevant main results and their implications for diverse theoretical issues such as the definition of visual illusions, the role of global three-dimensional interpretations in the integration of local sensory signals, and the exploratory and multisensory nature of perceptual processes.

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