Complete Hall Research Articles

Finite groups all of whose subgroups are σ-subnormal or σ-abnormal

ABSTRACTLet σ = {σi|i∈I} be a partition of the set of all primes ℙ and G a finite group. A set ℋ of subgroups of G is said to be a complete Hall σ-set of G if every member ≠1 of ℋ is a Hall σi-subgroup of G for some i∈I, and ℋ contains exact one Hall σi-subgroup of G for every i such that σi∩π(G)≠∅. A group is said to be σ-primary if it is a finite σi-group for some i. A subgroup A of G is said to be: σ-permutable or σ-quasinormal in G if G possesses a complete Hall σ-set ℋ such that for all H∈ℋ and all x∈G; σ-subnormal in G if there is a subgroup chain such that either or is σ-primary for all i = 1,…,t; σ-abnormal in G if L∕KL is not σ-primary whenever A≤K<L≤G. In this paper, answering to Question 7.7 in [17], we describe finite groups in which every subgroup is either σ-subnormal or σ-abnormal, and we use this result to classify finite groups G such that every subgroup of G is either σ-quasinormal or σ-abnormal in G.

On $$\Pi $$ Π -quasinormal subgroups of finite groups

Let \(\sigma =\{\sigma _{i} | i\in I\}\) be some partition of the set of all primes \(\mathbb {P}\) and \(\Pi \) a non-empty subset of the set \(\sigma \). A set \(\mathcal{H}\) of subgroups of a finite group G is said to be a complete Hall \(\Pi \) -set of G if every member \(\ne 1\) of \(\mathcal{H}\) is a Hall \(\sigma _{i}\)-subgroup of G for some \(\sigma _{i}\in \Pi \) and \(\mathcal{H}\) contains exactly one Hall \(\sigma _{i}\)-subgroup of G for every \(\sigma _{i}\in \Pi \) such that \(\sigma _i\cap \pi (G)\ne \emptyset \). A subgroup H of G is called \(\Pi \)-permutable or \(\Pi \)-quasinormal in G if G possesses a complete Hall \(\Pi \)-set \(\mathcal{H}\) such that \(AH^{x}=H^{x}A\) for all \(H\in \mathcal{H}\) and \(x\in G\). We study the embedding properties of H under the hypothesis that H is \(\Pi \)-permutable in G. Some well-known results are generalized.

Groups with maximal subgroups of Sylow subgroups σ-permutably embedded

Abstract Let σ = { σ i : i ∈ I } ${\sigma=\{\sigma_{i}:i\in I\}}$ be some partition of the set of all primes ℙ ${\mathbb{P}}$ , G a finite group and σ ⁢ ( G ) = { σ i : σ i ∩ π ⁢ ( G ) ≠ ∅ } ${\sigma(G)=\{\sigma_{i}:\sigma_{i}\cap\pi(G)\neq\emptyset\}}$ . A set 1 ∈ ℋ ${1\in{\mathcal{H}}}$ of subgroups of G is said to be a complete Hall σ-set of G if every non-identity group in ℋ ${{\mathcal{H}}}$ is a Hall σ i ${\sigma_{i}}$ -subgroup of G for some σ i ∈ σ ⁢ ( G ) ${\sigma_{i}\in\sigma(G)}$ and ℋ ${{\mathcal{H}}}$ contains exactly one Hall σ i ${\sigma_{i}}$ -subgroup of G for every σ i ∈ σ ⁢ ( G ) ${\sigma_{i}\in\sigma(G)}$ . A subgroup H of G is called σ-permutable (resp. σ-permutably embedded) in G if G possesses a complete Hall σ-set ℋ = { 1 , H 1 , … , H t } ${{\mathcal{H}}=\{1,H_{1},\ldots,H_{t}\}}$ such that A ⁢ H i x = H i x ⁢ A ${AH_{i}^{x}=H_{i}^{x}A}$ for any i and all x ∈ G ${x\in G}$ (resp. if H has a complete Hall σ-set and every Hall σ i ${\sigma_{i}}$ -subgroup of H is also a Hall σ i ${\sigma_{i}}$ -subgroup of some σ-permutable subgroup of G). In this paper, we classify the finite groups G such that either every maximal subgroup of every Sylow subgroup of G is σ-permutable in G or every maximal subgroup of every Sylow subgroup of G is σ-permutably embedded in G.

Low-noise epitaxial graphene on SiC Hall effect element for commercial applications

In this report, we demonstrate a complete Hall effect element that is based on quasi-free-standing monolayer graphene synthesized on a semi-insulating on-axis Si-terminated 6H-SiC substrate in an epitaxial Chemical Vapor Deposition process. The device offers the current-mode sensitivity of 87 V/AT and low excess noise (Hooge's parameter αH &amp;lt; 2 × 10−3) enabling room-temperature magnetic resolution of 650 nT/Hz0.5 at 10 Hz, 95 nT/Hz0.5 at 1 kHz, and 14 nT/Hz0.5 at 100 kHz at the total active area of 0.1275 mm2. The element is passivated with a silicone encapsulant to ensure its electrical stability and environmental resistance. Its processing cycle is suitable for large-scale commercial production and it is available in large quantities through a single growth run on an up to 4-in SiC wafer.

On σ-subnormal and σ-permutable subgroups of finite groups

Let σ={σi|i∈I} be some partition of the set P of all primes, that is, P=∪i∈Iσi and σi∩σj=∅ for all i≠j. Let G be a finite group. We say that G is: σ-primary if G is a σi-group for some i∈I; σ-soluble if every chief factor of G is σ-primary. We say that a set H={H1,…,Ht} of Hall subgroups of G, where Hi is σ-primary (i=1,…,t), is a complete Hall set of type σ of G if (|Hi|,|Hj|)=1 for all i≠j and π(G)=π(H1)∪⋯∪π(Ht). We say that a subgroup A of G is: σ-subnormal in G if there is a subgroup chain A=A0≤A1≤⋯≤An=G such that either Ai−1 is normal in Ai or Ai/(Ai−1)Ai is σ-primary for all i=1,…,t; σ-permutable in G if G has a complete Hall set H of type σ such that A is HG-permutable in G, that is, AHx=HxA for all x∈G and all H∈H. We study the relationship between the σ-subnormal and σ-permutable subgroups of G. In particular, we prove that every σ-permutable subgroup of G is σ-subnormal, and we classify finite σ-soluble groups in which every σ-subnormal subgroup is σ-permutable.

Variable Acoustics Design of a Small Proscenium Concert Hall

The 403-seat Kung Hsue She (KHS) Concert Hall features a small proscenium stage designed to accommodate a wide range of performances. Attention to room acoustical design emphasized broadening the variability, while recitals by pianists and singers were considered primary. These competing purposes were realized by integrating stage curtains with the stage shell and the coupled volume outside the shell. Detached lateral reflectors were introduced to minimize sound level drop due to use of moveable curtains around the audience. The proposed design strategies were tested using a scale model and were verified in the completed hall.

Comparison of modeled versus measured room acoustic parameters in the recently completed Shaghoian Concert Hall in Clovis, California.

The Shaghoian Concert Hall in Clovis, CA is a popular new variable acoustic music venue in the greater Fresno, CA area. The design process for this hall included CATT‐Acoustic (TM) modeling for analysis and verification of essential room acoustic parameters based upon the settings of the variable acoustic devices. The model of the final design produced parameters that were closely in line with ideal values for a hall of this size and use. Model results will be compared to measured parameters in the completed hall.

Developments in the Acoustic Design of Concert Halls from the Royal Festival Hall, London, to the Segerstrom Hall, California

Research over the last forty years has resulted in many new factors being considered in the acoustical design of concert halls. In this paper a brief account is given of this research and how halls designed since the nineteen fifties have been progressively influenced by this work. The Segerstrom Hall in California is an example of a hall where acoustical considerations have been given great importance at all stages of the design process and a team of consultants has ensured that recent research findings have been applied to good effect. The design approach is discussed and model experiments performed in the course of the design process are described. Finally the results of objective and subjective measurements carried out in the completed hall are described.

Room acoustic prediction and auralization based on an extended image source model

During the 1980s, an exciting new technique was developed that put great demands on prediction methods. This new technique, called ‘‘auralization’’ in an analogy to visualization, enables the designer of a concert hall to get an aural impression of the hall before it has been built. By the calculation of highly detailed octave-band echograms, the use of signal-processing techniques and measured head-related transfer functions, a binaural room impulse response can be synthesized. This response is convolved with anechoically recorded music to give an impression of how the music would sound in the completed hall. This paper describes auralization using the image source model. This model, as well as others, has its share of short comings. In an attempt to compensate for some of these, the basic model has been extended. The two most important extensions are the treatment of scattering and the use of ray tracing to estimate the late part of the echogram. The combined method enables reasonably fast calculations, highly detailed early parts of the echograms, and smooth transitions to the late parts. The predicted measures compare well with measurements and the aural impressions created sound natural.

A convolutional model for simulating the response of an electro-acoustic system inside a hall

In a hall that is equipped with an electroacoustic system (EAS) for the enhancement of reverberation, the reflected sound field is built up by contributions of both system and hall. To quantify the transmission of the sound field from source to listener, from source to EAS microphones, and from EAS loudspeakers to listener, the appropriate hall transfer function should be taken into account. Also, the acoustic coupling between EAS microphones and loudspeakers may play an important role. In this paper, a convolutional model to calculate the complete hall and EAS response will be discussed, using a version of the image source algorithm that can also handle diffuse reflection at room boundaries. The EAS is divided in an early reflection module and a reverberation module. Examples will be shown, ranging from simple situations to complex configurations. Results are in good agreement with measurements.

Variable magnetic field Hall effect measurements and analyses of high purity, Hg vacancy (p-type) HgCdTe

This paper reports on complete Hall characterization of Hg vacancy ( p-type) HgCdTe with very high purity and compositional uniformity. The x-values of the Hg1−xCdxTe samples ranged from 0.180 to 0.300 with carrier concentrations of 6×1015 to 3×1017. Each sample was of very uniform composition with Δx&amp;lt;0.0015, as verified from room temperature infrared transmission measurements. This characterization couples variable magnetic field (up to 150 000 G) and temperature (from 15 to 160 K) data with an analysis procedure which includes heavy holes, light holes, and electrons. The measurements and analyses yield unambiguous determination of the two Hg vacancy ionization energies, one shallow level at 12–14 meV for x=0.216 HgCdTe and one deeper level at 40% of the band gap measured from the valence band edge. In addition, not only can the majority carrier (heavy holes) temperature dependent concentrations and mobilities be determined by this technique, but both the minority carrier (electron) and the light hole concentrations and mobilities have been determined as a function of temperature. At magnetic field strengths of 40 000 G and above, the heavy hole concentration was observed to decrease with increasing magnetic field. This occurred at all temperatures (15 to 160 K) investigated. This effect is commonly referred to as magnetic ‘‘freeze out’’ and is reported here for HgCdTe for the first time.

The hall of the University of Warwick

The acoustic design of a 1300-seat multi-purpose concert hall is described and the uncertainties, practical difficulties and compromises inherent in orthodox practice are mentioned. Listeners' and performers' comments during the first six months of use are compared with the results of extensive objective measurements made in the completed hall. Major features of the design are the use of bleacher retractable seating, a terrace on three sides of the orchestra, exposed roof structure and ventilation trunking and novel techniques to provide good acoustic conditions for the performers.

Instability of vortex lines in the presence of axial normal fluid flow

We show that a normal mode analysis of the complete Hall two-fluid equations in rotating He II yields a critical velocity for axial normal fluid flow which is identical to the critical velocity derived in an earlier paper from the superfluid equation alone. We also present a simplified derivation of the critical velocity based on consideration of the forces acting on an isolated vortex line. The analysis is extended to 3 He- 4 He solutions and it is shown that rather small impurity concentrations can greatly increase the critical heat current in axial thermal counterflow.

Acoustics of the Jesse H. Jones Performing Arts Hall, Houston Texas

This multipurpose, multiform hall, opened in October 1966, accommodates the full range of musical and theatrical events. The ceiling of the hall consists of an array of hexagon-shaped damped steel panels that can be moved in groups to adjust the hall's seating capacity and its acoustical environment. The ceiling can be lowered to exclude the upper balcony, reducing the seating capacity from 3000 to 2400. Mesh curtains toward the rear mezzanine and orchestra level reduce the seating capacity to 1800. A stage enclosure of damped steel construction can be either 40 ft deep for full orchestra or 25 ft for smaller groups. The reverberation time of the hall at midfrequencies is 1.8 sec in the symphony and opera configurations (3000 seats) and 1.4 sec in the drama configuration (1800 or 2400 seats, all draperies exposed). This paper compares acoustical data obtained in a 110-scale model with measurements in the completed hall.

Acoustics of the Binyanei Ha'Oomah Jerusalem Congress Hall

The 3200-seat Congress Hall in Jerusalem, Israel was completed in the spring of 1960 after a construction period of some 10 years. The original primary design goal was to provide a place for large assemblies the most important of which was the biennial meeting of the World Zionist Congress. During construction, the repeated use of the partially completed “unroofed” structure for out door concerts led to the reconsideration of the original design goals to give primary emphasis to music. The hall now has become the Jerusalem home of the Israeli Philharmonic while still serving its function for congresses and other uses. This paper traces the development of the acoustical design goals as well as discusses the important acoustical design features, the results of measurements made in the completed hall, and the reactions of musicians who have played in the hall.

Acoustics of the Jerusalem Congress Hall (Binyanae Ha'oomah)

The 3200-seat Congress Hall in Jerusalem, Israel, was completed in the spring of 1960 after a construction period of some ten years. The original primary design goal was to provide a place for large assemblies, the most important of which was the semiannual meeting of the World Zionist Congress. During construction, the repeated use of the partially completed “unroofed” structure for outdoor concerts led to the reconsideration of the original design goals to give primary emphasis to music. The hall now has become the home of the Israeli Philharmonic while still serving its function for congresses and other uses. This paper traces the development of the acoustical design goals as well as discusses the important acoustical design features, the results of measurements made in the completed hall, and the reactions of musicians who have played in the hall.