ON A ONE-PARAMETER FAMILY OF EXOTIC SUPERSPACES IN TWO DIMENSIONS

1991 ◽  
Vol 06 (35) ◽  
pp. 3239-3250 ◽  
Author(s):  
MURAT GÜNAYDIN
Keyword(s):  
Two Dimensions ◽  
Parameter Family ◽  
Oscillator Algebra ◽  
Jordan Superalgebras ◽  
Special Values ◽  
Finite Dimensional ◽  
Operator Realization ◽  
The One ◽  
Conformal Superalgebras ◽  
Bosonic Oscillator

Using Jordan algebraic techniques we define and study a family of exotic superspaces in two dimensions with two bosonic and two fermionic coordinates. They are defined by the one-parameter family of Jordan superalgebras JD (2/2)α. For two special values of α the JD (2/2)α can be realized in terms of a single fermionic or a single bosonic oscillator, respectively. For other values of α it can be interpreted as defining an exotic oscillator algebra. The derivation, reduced structure and Möbius superalgebras of JD (2/2)α are identified with the rotation, Lorentz and finite-dimensional conformal superalgebras of the corresponding superspaces. The conformal superalgebras turn out to be the superalgebras D(2,1;α) with the even subgroup SO(2,2)×SU(2) . We give an explicit differential operator realization of the actions of D(2,1;α) on these superspaces.

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

scholarly journals Assessing a Linear Nanosystem's Limiting Reliability from its Components

2008 ◽  
Vol 45 (03) ◽  
pp. 879-887 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Present State ◽  
Size Range ◽  
Two Dimensions ◽  
The Other ◽  
One Dimension ◽  
Present Moment ◽  
One Dimensional ◽  
The One ◽  
Fixed Moment ◽  
Nanosized Systems

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

scholarly journals On the forces that cable webs under tension can support and how to design cable webs to channel stresses

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180781 ◽  
Author(s):  
Guy Bouchitté ◽  
Ornella Mattei ◽  
Graeme W. Milton ◽  
Pierre Seppecher
Keyword(s):  
Linear Programming ◽  
Convex Hull ◽  
Structural Engineering ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Dimensional ◽  
Necessary And Sufficient

In many applications of structural engineering, the following question arises: given a set of forces f 1 ,  f 2 , …,  f N applied at prescribed points x 1 ,  x 2 , …,  x N , under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points x 1 ,  x 2 , …,  x N in the two- and three-dimensional cases. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two dimensions, we show that any such web can be replaced by one in which there are at most P elementary loops, where elementary means that the loop cannot be subdivided into subloops, and where P is the number of forces f 1 ,  f 2 , …,  f N applied at points strictly within the convex hull of x 1 ,  x 2 , …,  x N . In three dimensions, we show that, by slightly perturbing f 1 ,  f 2 , …,  f N , there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for channelling stress in desired ways.

scholarly journals A measure of the variability of revenue in auctions: A look at the revenue equivalence theorem

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
Fernando Beltrán ◽  
Natalia Santamaría
Keyword(s):  
Equivalence Theorem ◽  
Auction Theory ◽  
Two Dimensions ◽  
Revenue Equivalence ◽  
Extensive Simulation ◽  
Value Set ◽  
Equilibrium Bidding ◽  
The One

One not-so-intuitive result in auction theory is the revenue equivalence theorem, which states that as long as an auction complies with some conditions, it will on average generate the same revenue to an auctioneer as the revenue generated by any other auction that complies with them. Surprisingly, the conditions are not defined on the payment rules to the bidders but on the fact that the bidders do not bid below a reserve value—set by the auctioneer—the winner is the one with the highest bidding and there is a common equilibrium bidding function used by all bidders. In this paper, we verify such result using extensive simulation of a broad range of auctions and focus on the variability or fluctuations of the results around the average. Such fluctuations are observed and measured in two dimensions for each type of auction: as the number of auctions grows and as the number of bidders increases.

scholarly journals Psychological autonomy and hierarchical relatedness as organizers of developmental pathways

2016 ◽  
Vol 371 (1686) ◽  
pp. 20150070 ◽  
Author(s):  
Heidi Keller
Keyword(s):  
Two Dimensions ◽  
Global Perspective ◽  
Developmental Pathways ◽  
Cultural Constructs ◽  
Human Needs ◽  
Subsistence Farmer ◽  
The Hierarchical Structure ◽  
Psychological Autonomy ◽  
The One ◽  
Definition Of

The definition of self and others can be regarded as embodying the two dimensions of autonomy and relatedness. Autonomy and relatedness are two basic human needs and cultural constructs at the same time. This implies that they may be differently defined yet remain equally important. The respective understanding of autonomy and relatedness is socialized during the everyday experiences of daily life routines from birth on. In this paper, two developmental pathways are portrayed that emphasize different conceptions of autonomy and relatedness that are adaptive in two different environmental contexts with very different affordances and constraints. Western middle-class children are socialized towards psychological autonomy, i.e. the primacy of own intentions, wishes, individual preferences and emotions affording a definition of relatedness as psychological negotiable construct. Non-Western subsistence farmer children are socialized towards hierarchical relatedness, i.e. positioning oneself into the hierarchical structure of a communal system affording a definition of autonomy as action oriented, based on responsibility and obligations. Infancy can be regarded as a cultural lens through which to study the different socialization agendas. Parenting strategies that aim at supporting these different socialization goals in German and Euro-American parents on the one hand and Nso farmers from North Western Cameroon on the other hand are described. It is concluded that different pathways need to be considered in order to understand human psychology from a global perspective.

scholarly journals The Role of Crisis Prevention from the Perspective of the Biggest Polish Companies and Public Relations Agencies on the Basis of Expert Research

2019 ◽  
Vol 31 (1) ◽  
pp. 109-130
Author(s):  
Dariusz Tworzydło ◽  
Przemysław Szuba
Keyword(s):  
Public Relations ◽  
Two Dimensions ◽  
Prevention Measures ◽  
Point Model ◽  
Communication Management ◽  
Crisis Prevention ◽  
Current Trends ◽  
Business Survey ◽  
The One

Summary The article constitutes a presentation of the results of research devoted to the current trends in crisis PR. The authors of the work made an attempt to diagnose crisis prevention in a cross-section of two dimensions. On the one hand the perspective of business (survey of companies) was presented and on the other hand experts’ opinions (survey of the leaders of public relations agencies) were shown. As a result of analyses a point model of an immune system, which takes into consideration the key instruments of crisis methodology (developed procedures in form of communication management book, dedicated anti-crisis structures in an organization, crisis team with a fixed membership and a system of communication trainings) was designed. Diagnosis of prevention measures of the leaders of Polish business — based on the years 2007–2017 showed major deficiencies in the degree of companies’ preparation for the risk of crisis.

scholarly journals ON THE SPECIAL VALUES OF L-FUNCTIONS OF CM-BASE CHANGE FOR HILBERT MODULAR FORMS

2013 ◽  
Vol 56 (1) ◽  
pp. 57-63
Author(s):  
CRISTIAN VIRDOL
Keyword(s):  
Finite Order ◽  
Modular Forms ◽  
Number Fields ◽  
Base Change ◽  
Hilbert Modular Forms ◽  
Special Values ◽  
Finite Dimensional ◽  
Arbitrary Base ◽  
Hilbert Modular

AbstractIn this paper we generalize some results, obtained by Shimura, on the special values of L-functions of l-adic representations attached to quadratic CM-base change of Hilbert modular forms twisted by finite order characters. The generalization is to the case of the special values of L-functions of arbitrary base change to CM-number fields of l-adic representations attached to Hilbert modular forms twisted by some finite-dimensional representations.

scholarly journals On the Dynamics of the Unified Chaotic System Between Lorenz and Chen Systems

2015 ◽  
Vol 25 (09) ◽  
pp. 1550122 ◽  
Author(s):  
Jaume Llibre ◽  
Ana Rodrigues
Keyword(s):  
Chaotic System ◽  
Parameter Family ◽  
Algebraic Surfaces ◽  
Hopf Bifurcations ◽  
Global Dynamics ◽  
Differential Systems ◽  
Special Values ◽  
Unified Chaotic System ◽  
Invariant Algebraic Surfaces ◽  
The Family

A one-parameter family of differential systems that bridges the gap between the Lorenz and the Chen systems was proposed by Lu, Chen, Cheng and Celikovsy. The goal of this paper is to analyze what we can say using analytic tools about the dynamics of this one-parameter family of differential systems. We shall describe its global dynamics at infinity, and for two special values of the parameter a we can also describe the global dynamics in the whole ℝ3using the invariant algebraic surfaces of the family. Additionally we characterize the Hopf bifurcations of this family.

Internet Memes, Memory, and Orders of Repackaging

2021 ◽  
Vol 2 (1) ◽  
pp. 111-136
Author(s):  
Julija Korostenskiene
Keyword(s):  
Human Memory ◽  
Two Dimensions ◽  
The Other ◽  
Methodological Framework ◽  
Internal Dimension ◽  
External Dimension ◽  
The One ◽  
Taxonomic Relations

Abstract The present study explores the construction of humor in internet memes along two dimensions. The external dimension is concerned with humor in internet memes as opposed to verbal humor on the one hand and as opposed to humor in comics and caricatures on the other. The perceptive differences, stemming from the workings of the human memory, and the medium are posited as the two main differentiating factors. On the internal dimension, we explore manifestations of humor in light of the communicative situation and taxonomic relations at both the intermedial and intramedial levels of internet memes, taking as an example a family of You Wouldn’t Get It image macros. Our analysis employs elements of intertextuality theory and the notion of orders of indexicality. The study aims to contribute to the growing theoretical and methodological framework for multifactorial analyses of internet memes.

Preliminary Investigation of Mesh Stability for Linear Systems

1999 ◽  
Author(s):  
Pete Seiler ◽  
Aniruddha Pant ◽  
J. K. Hedrick
Keyword(s):  
Linear Systems ◽  
Mimo Systems ◽  
Preliminary Investigation ◽  
Two Dimensions ◽  
String Stability ◽  
Significant Research ◽  
Simple Class ◽  
The Subject ◽  
A Chain ◽  
The One

Abstract Damping of disturbances as they propagate through a chain of interconnected systems, termed string stability, has been the subject of significant research. In this paper, we investigate mesh stability, which is the two-dimensional extension of string stability. We review the key results used for string stability analysis and then generalize the conditions for MIMO systems. These results are then applied to a simple class of linear systems which form a mesh in two-dimensions. It is shown (as in the one-dimensional case) that communicating the velocity and acceleration of the lead vehicle to all subsystems is sufficient for mesh stability. This result is then verified by simulation.

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