On some semi-spherical representations of an Hermitian symmetric pair of the tubular type

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 $L(\lambda)$.

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

IEE Proceedings H Microwaves Antennas and Propagation ◽

10.1049/ip-h-2.1991.0060 ◽

1991 ◽

Vol 138 (4) ◽

pp. 368 ◽

Cited By ~ 1

Author(s):

R. Benjamin ◽

W. Titze ◽

P.V. Brennan ◽

H.D. Griffiths

Keyword(s):

Beam Steering ◽

Direction Finding ◽

Symmetric Pair

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Effects of amplitude and phase errors on performance of symmetric-pair arrays

Electronics Letters ◽

10.1049/el:19910976 ◽

1991 ◽

Vol 27 (17) ◽

pp. 1557

Author(s):

W. Titze

Keyword(s):

Symmetric Pair ◽

Phase Errors ◽

Amplitude And Phase Errors

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Analysis of Parameters for Producing High-Purity Hydrogen from Natural Gas in a Tubular Type Membrane-Catalytic Module

Chemical and Petroleum Engineering ◽

10.1007/s10556-021-00833-z ◽

2021 ◽

Vol 56 (9-10) ◽

pp. 715-720

Author(s):

A. B. Vandyshev ◽

V. A. Kulikov

Keyword(s):

Natural Gas ◽

High Purity ◽

Tubular Type ◽

Catalytic Module ◽

High Purity Hydrogen

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Geometrical Scaling of Antiresonant Hollow-Core Fibers for Mid-Infrared Beam Delivery

Crystals ◽

10.3390/cryst11040420 ◽

2021 ◽

Vol 11 (4) ◽

pp. 420

Author(s):

Ang Deng ◽

Wonkeun Chang

Keyword(s):

Structural Parameters ◽

Transmission Band ◽

Confinement Loss ◽

Hollow Core ◽

Core Size ◽

Core Diameter ◽

Mid Infrared ◽

The Core ◽

Tubular Type ◽

Beam Delivery

We numerically investigate the effect of scaling two key structural parameters in antiresonant hollow-core fibers—dielectric wall thickness of the cladding elements and core size—in view of low-loss mid-infrared beam delivery. We demonstrate that there exists an additional resonance-like loss peak in the long-wavelength limit of the first transmission band in antiresonant hollow-core fibers. We also find that the confinement loss in tubular-type hollow-core fibers depends strongly on the core size, where the degree of the dependence varies with the cladding tube size. The loss scales with the core diameter to the power of approximately −5.4 for commonly used tubular-type hollow-core fiber designs.

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Leachate Minimization by Reverse Osmosis

Water Science & Technology ◽

10.2166/wst.1992.0084 ◽

1992 ◽

Vol 25 (3) ◽

pp. 117-120 ◽

Cited By ~ 23

Author(s):

T. Bilstad ◽

M. V. Madland

Keyword(s):

Reverse Osmosis ◽

Suspended Solids ◽

Membrane Separation ◽

Water Phase ◽

Major Portion ◽

Tubular Type ◽

Iron Copper ◽

Copper Chromium ◽

Direct Discharge

Leachates from chemical and domestic landfills are defined as hazardous wastewater. Quantitative and qualitative control of leachate can be performed by membrane separation of the total produced leachate volume. Dissolved and suspended solids in the leachate are removed from the major portion of the water phase and either returned to the landfill or further treated. The particle - free permeate meets the effluent requirements for direct discharge to virtually any watercourse. An untreated leachate flow is concentrated thirteen times by tubular type reverse osmosis. The separation efficiencies are 99% for iron, copper, chromium and zinc. For suspended solids the removal is 100%.

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