scholarly journals The Harish-Chandra homomorphism for a quantized classical hermitian symmetric pair

1999 ◽  
Vol 49 (4) ◽  
pp. 1179-1214
Author(s):  
Welleda Baldoni ◽  
Pierluigi Möseneder Frajria
Keyword(s):  
Symmetric Pair ◽  
Hermitian Symmetric Pair

scholarly journals R-spaces associated with a Hermitian symmetric pair

1986 ◽  
Vol 10 (1) ◽  
pp. 165-170
Author(s):  
Hiroyuki Tasaki ◽  
Osami Yasukura
Keyword(s):  
Symmetric Pair ◽  
Hermitian Symmetric Pair

Gelfand–Kirillov Dimensions of Highest Weight Harish-Chandra Modules for $\boldsymbol{{SU}(p,q)}$

2017 ◽  
Vol 2019 (14) ◽  
pp. 4392-4418 ◽  
Author(s):  
Zhanqiang Bai ◽  
Xun Xie
Keyword(s):  
Symmetric Pair ◽  
Combinatorial Algorithm ◽  
Compact Type ◽  
Highest Weight Module ◽  
Highest Weight ◽  
Integral Weight ◽  
Positive Roots ◽  
Hermitian Symmetric Pair ◽  
Associated Variety ◽  
Gk Dimension

Abstract Let $(G,K)$ be an irreducible Hermitian symmetric pair of non-compact type with $G={SU}(p,q)$, and let $\lambda$ be an integral weight such that the simple highest weight module $L(\lambda)$ is a Harish-Chandra $({\mathfrak{g}},K)$-module. We give a combinatorial algorithm for the Gelfand–Kirillov (GK) dimension of $L(\lambda)$. This enables us to prove that the GK dimension of $L(\lambda)$ decreases as the integer $\langle{\lambda+\rho},{\beta}^{\vee} \rangle$ increases, where $\rho$ is the half sum of positive roots and $\beta$ is the maximal non-compact root. Finally by the combinatorial algorithm, we obtain a description of the associated variety of $L(\lambda)$.

Symmetric-pair antennas for beam steering, direction finding or isotropic-reception gain

1991 ◽  
Vol 138 (4) ◽  
pp. 368 ◽  
Author(s):  
R. Benjamin ◽  
W. Titze ◽  
P.V. Brennan ◽  
H.D. Griffiths
Keyword(s):  
Beam Steering ◽  
Direction Finding ◽  
Symmetric Pair

3D Printing — The Basins of Tristability in the Lorenz System

2017 ◽  
Vol 27 (08) ◽  
pp. 1750128 ◽  
Author(s):  
Anda Xiong ◽  
Julien C. Sprott ◽  
Jingxuan Lyu ◽  
Xilu Wang
Keyword(s):  
Lorenz System ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Basins Of Attraction ◽  
Symmetric Pair ◽  
State Space Approach ◽  
3D Printers ◽  
The Lorenz System ◽  
Almost All ◽  
Space Approach

The famous Lorenz system is studied and analyzed for a particular set of parameters originally proposed by Lorenz. With those parameters, the system has a single globally attracting strange attractor, meaning that almost all initial conditions in its 3D state space approach the attractor as time advances. However, with a slight change in one of the parameters, the chaotic attractor coexists with a symmetric pair of stable equilibrium points, and the resulting tri-stable system has three intertwined basins of attraction. The advent of 3D printers now makes it possible to visualize the topology of such basins of attraction as the results presented here illustrate.

scholarly journals Autonomous emergence of connectivity assemblies via spike triplet interactions

2019 ◽  
Author(s):  
Lisandro Montangie ◽  
Julijana Gjorgjieva
Keyword(s):  
Random Network ◽  
Transmission Function ◽  
Higher Order ◽  
External Input ◽  
Spike Timing ◽  
Symmetric Pair ◽  
Graph Theoretic ◽  
Stdp Rule ◽  
Triplet Model ◽  
External Stimuli

AbstractNon-random connectivity can emerge without structured external input driven by activity-dependent mechanisms of synaptic plasticity based on precise spiking patterns. Here we analyze the emergence of global structures in recurrent networks based on a triplet model of spike timing dependent plasticity (STDP) which depends on the interactions of three precisely-timed spikes and can describe plasticity experiments with varying spike frequency better than the classical pair-based STDP rule. We describe synaptic changes arising from emergent higher-order correlations, and investigate their influence on different connectivity motifs in the network. Our motif expansion framework reveals novel motif structures under the triplet STDP rule, which support the formation of bidirectional connections and loops in contrast to the classical pair-based STDP rule. Therefore, triplet STDP drives the spontaneous emergence of self-connected groups of neurons, or assemblies, proposed to represent functional units in neural circuits. Assembly formation has often been associated with plasticity driven by firing rates or external stimuli. We propose that assembly structure can emerge without the need for externally patterned inputs or assuming a symmetric pair-based STDP rule commonly assumed in previous studies. The emergence of non-random network structure under triplet STDP occurs through internally-generated higher-order correlations, which are ubiquitous in natural stimuli and neuronal spiking activity, and important for coding. We further demonstrate how neuromodulatory mechanisms that modulate the shape of triplet STDP or the synaptic transmission function differentially promote connectivity motifs underlying the emergence of assemblies, and quantify the differences using graph theoretic measures.

scholarly journals More nonexistence results for symmetric pair coverings

2015 ◽  
Vol 487 ◽  
pp. 43-73
Author(s):  
Nevena Francetić ◽  
Sarada Herke ◽  
Daniel Horsley
Keyword(s):  
Symmetric Pair

scholarly journals Stellar Orbits in Barred Galaxies with Nuclear Rings

1996 ◽  
Vol 157 ◽  
pp. 467-469
Author(s):  
Clayton H. Heller ◽  
Isaac Shlosman
Keyword(s):  
Large Range ◽  
Symmetric Pair ◽  
Dynamical Response ◽  
Instability Strip ◽  
Stellar Orbits ◽  
Barred Galaxies ◽  
Jacobi Integral ◽  
Elliptical Ring ◽  
Lindblad Resonance ◽  
Inner Lindblad Resonance

AbstractWe investigate the dynamical response of stellar orbits in a rotating barred galaxy potential to the perturbation by a nuclear gaseous ring. The change in 3D periodic orbit families is examined as the gas accumulates near the inner Lindblad resonance. It is found that the x2/x3 loop extends to higher Jacobi energy and a vertical instability strip forms in each family. These strips are connected by a symmetric/anti-symmetric pair of 2:2:1 3D orbital families. A significant distortion of the x1 orbits is observed in the vicinity of the ring, which leads to the intersection between orbits over a large range of the Jacobi integral. We also find that a moderately elliptical ring oblique to the stellar bar produces significant phase shifts in the x1 orbital response.

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