scholarly journals Howe duality of Higgs – Hahn algebra for 8D harmonic oscillator

2019 ◽  
Vol 55 (2) ◽  
pp. 216-224
Author(s):  
А. N. Lavrenov ◽  
I. A. Lavrenov
Keyword(s):  
Tensor Product ◽  
Harmonic Oscillator ◽  
Symmetry Algebra ◽  
Dual Pair ◽  
Two Dimensions ◽  
Discrete Version ◽  
Oscillator Representation ◽  
Higgs Algebra ◽  
Howe Duality ◽  
The One

In the light of the Howe duality, two different, but isomorphic representations of one algebra as Higgs algebra and Hahn algebra are considered in this article. The first algebra corresponds to the symmetry algebra of a harmonic oscillator on a 2-sphere and a polynomially deformed algebra SU(2), and the second algebra encodes the bispectral properties of corresponding homogeneous orthogonal polynomials and acts as a symmetry algebra for the Hartmann and certain ring-shaped potentials as well as the singular oscillator in two dimensions. The realization of this algebra is shown in explicit form, on the one hand, as the commutant O(4) ⊕ O(4) of subalgebra U(8) in the oscillator representation of universal algebra U (u(8)) and, on the other hand, as the embedding of the discrete version of the Hahn algebra in the double tensor product SU(1,1) ⊗ SU(1,1). These two realizations reflect the fact that SU(1,1) and U(8) form a dual pair in the state space of the harmonic oscillator in eight dimensions. The N-dimensional, N-fold tensor product SU(1,1)⊗N аnd q-generalizations are briefly discussed.

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 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.

THE RESPONSE FUNCTION OF THE 4He, 16O AND 40Ca NUCLEI IN THE HARMONIC OSCILLATOR SHELL MODEL AND THE IMPULSE APPROXIMATIONS

2013 ◽  
Vol 22 (02) ◽  
pp. 1350011
Author(s):  
M. MODARRES ◽  
Y. YOUNESIZADEH
Keyword(s):  
Harmonic Oscillator ◽  
Shell Model ◽  
Momentum Distribution ◽  
Impulse Approximation ◽  
Distribution Functions ◽  
Heavy Nuclei ◽  
Momentum Distribution Function ◽  
Oscillator Shell ◽  
Nucleus Scattering ◽  
The One

In this work, the response functions (RFs) of the 4 He , 16 O and 40 Ca nuclei are calculated in the harmonic oscillator shell model (HOSM) and the impulse approximation (IA). First, the one-body momentum distribution and the one-body spectral functions for these nuclei are written in the HOSM configuration. Then, their RFs are calculated, in the two frameworks, namely the spectral and the momentum distribution functions, within the IA. Unlike our previous work, no further assumption is made to reduce the analytical complications. For each nucleus, it is shown that the (RF) evaluated using the corresponding spectral function has a sizable shift, with respect to the one calculated in terms of the momentum distribution function. It is concluded that for the heavier nuclei, this shift increases and reaches nearly to a constant value (approximately 62 MeV), i.e., similar to that of nuclear matter. It is discussed that in the nuclei with the few nucleons, the above shift can approximately be ignored. This result reduces the theoretical complication for the explanation of the ongoing deep inelastic scattering (DIS) experiments of 3 H or 3 H nucleus target in the Jefferson Laboratory. On the other hand, it is observed that in the heavier nuclei, the RF heights (width) decrease (increase), i.e., the comparison between the theoretical and the experimental electron nucleus scattering cross-section is more sensible for heavy nuclei rather than the light ones.

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 Time-dependent quantum harmonic oscillator: a continuous route from adiabatic to sudden changes

2021 ◽  
Author(s):  
Daniel M. Tibaduiza ◽  
Luis Barbosa Pires ◽  
Carlos Farina
Keyword(s):  
Harmonic Oscillator ◽  
Simple Expression ◽  
Time Dependent ◽  
Frequency Change ◽  
Quantum Harmonic Oscillator ◽  
Transition Analysis ◽  
Adiabatic Theorem ◽  
Significant Difference ◽  
The One ◽  
Proper Interpretation

Abstract In this work, we give a quantitative answer to the question: how sudden or how adiabatic is a frequency change in a quantum harmonic oscillator (HO)? We do that by studying the time evolution of a HO which is initially in its fundamental state and whose time-dependent frequency is controlled by a parameter (denoted by ε) that can continuously tune from a totally slow process to a completely abrupt one. We extend a solution based on algebraic methods introduced recently in the literature that is very suited for numerical implementations, from the basis that diagonalizes the initial hamiltonian to the one that diagonalizes the instantaneous hamiltonian. Our results are in agreement with the adiabatic theorem and the comparison of the descriptions using the different bases together with the proper interpretation of this theorem allows us to clarify a common inaccuracy present in the literature. More importantly, we obtain a simple expression that relates squeezing to the transition rate and the initial and final frequencies, from which we calculate the adiabatic limit of the transition. Analysis of these results reveals a significant difference in squeezing production between enhancing or diminishing the frequency of a HO in a non-sudden way.

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.

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

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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