Bounding the number of generators of a polycyclic group

1981 ◽  
Vol 37 (1) ◽  
pp. 7-17 ◽  
Author(s):  
P. A. Linnell ◽  
D. Warhurst
Keyword(s):  
Polycyclic Group ◽  
Number Of Generators

On some polycyclic groups with small Hirsch length II

2019 ◽  
Vol 18 (09) ◽  
pp. 1950169
Author(s):  
Heguo Liu ◽  
Fang Zhou ◽  
Tao Xu
Keyword(s):  
Abelian Subgroup ◽  
Polycyclic Group ◽  
Normal Abelian Subgroup ◽  
Number Of Generators ◽  
Finite Quotient ◽  
Polycyclic Groups

A polycyclic group [Formula: see text] is called a [Formula: see text]-group ([Formula: see text]-group) if every normal abelian subgroup (abelian subgroup) of any finite quotient of [Formula: see text] is generated by [Formula: see text], or fewer, elements and [Formula: see text] is the least integer with this property. In this paper, we describe the structures of [Formula: see text]-groups and [Formula: see text]-groups, and bound the number of generators of [Formula: see text]-groups and the derived lengths of [Formula: see text]-groups, which is a continuation of [H. G. Liu, F. Zhou and T. Xu, On some polycyclic groups with small Hirsch length, J. Algebra Appl. 16(11) (2017) 17502371–175023710].

Study on the Modes of Operation of a Multi-Machine Installations with Mechanical Reduction

2019 ◽  
pp. 12-22
Author(s):  
A. M. Oleynikov ◽  
L. N. Kanov
Keyword(s):  
Mathematical Description ◽  
Reactive Power ◽  
Maximum Efficiency ◽  
Wind Flow ◽  
System Of Equations ◽  
Mechanical Equilibrium ◽  
Synchronous Generators ◽  
Electromagnetic Excitation ◽  
Number Of Generators ◽  
Wide Range

The paper gives the description of the original wind electrical installation with mechanical reduction in which the output of vertical axis wind turbine with rather low rotation speed over multiplicator is distributed to a certain number of generators. The number of acting generators is determined by the output of actual operating wind stream at each moment. According to this constructive scheme, it is possible to provide effective and with maximum efficiency installation work in a wide range of wind speeds and under any schedule issued to the consumer of electricity. As there are no any experience in using such complexes, mathematical description of its main elements is given, namely windwheels, generators with electromagnetic excitation of magnetic electrical type, then their interaction with windwheel, and also the results of mathematical modeling of work system regimes under using the offered system of equations. The basis for the mathematical description of the main elements of the installation – synchronous generators – are the system of equations of electrical and mechanical equilibrium in relative units in rotating coordinates without considering saturation of the magnetic circuit. The equation of mechanical equilibrium systems includes torque and brake windwheel electromagnetic moments of generators with taking into account the reduction coefficients and friction. In addition, we specify the alternator rotor dynamics resulting from continuous torque of windwheel fluctuations under the influence of unsteady wind flow and wind speed serving as the original variable is modeled by a set of sinusoids. Model simplification is achieved by equivalization of similar generators and by disregarding these transitions with a small time constant. Calculation the installation with synchronous generators of two types of small and medium capacity taking into account the operational factors allowed us to demonstrate the logic of interactions in the main elements of the reported complex in the process of converting wind flow into the generated active and reactive power. We have shown the possibility of stable system work under changeable wind stream condition by regulating of the plant blade angle and with simultaneous varying of generator number of different types. All these are in great interest for project organizations and power producers.

On the Number of Generators for Transeunt Triangles

1999 ◽  
Author(s):  
J. T. Butler ◽  
G. W. Dueck ◽  
S. N. Yanushkevich ◽  
V. P. Shmerko
Keyword(s):  
Number Of Generators

scholarly journals Univariate Ideal Membership Parameterized by Rank, Degree, and Number of Generators

2021 ◽  
Author(s):  
V. Arvind ◽  
Abhranil Chatterjee ◽  
Rajit Datta ◽  
Partha Mukhopadhyay
Keyword(s):  
Number Of Generators ◽  
Ideal Membership

scholarly journals Quasi-powerful 𝑝-groups

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
James Williams
Keyword(s):  
Large Family ◽  
Power Structure ◽  
Number Of Generators

Abstract In this paper, we introduce the notion of a quasi-powerful 𝑝-group for odd primes 𝑝. These are the finite 𝑝-groups 𝐺 such that G / Z ⁢ ( G ) G/Z(G) is powerful in the sense of Lubotzky and Mann. We show that this large family of groups shares many of the same properties as powerful 𝑝-groups. For example, we show that they have a regular power structure, and we generalise a result of Fernández-Alcober on the order of commutators in powerful 𝑝-groups to this larger family of groups. We also obtain a bound on the number of generators of a subgroup of a quasi-powerful 𝑝-group, expressed in terms of the number of generators of the group, and we give an example which demonstrates this bound is close to best possible.

On Parseval Wavelet Frames with Two or Three Generators via the Unitary Extension Principle

2014 ◽  
Vol 57 (2) ◽  
pp. 254-263 ◽  
Author(s):  
Ole Christensen ◽  
Hong Oh Kim ◽  
Rae Young Kim
Keyword(s):  
Extension Principle ◽  
Sufficient Condition ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Wavelet System ◽  
Number Of Generators ◽  
Unitary Extension

AbstractThe unitary extension principle (UEP) by A. Ron and Z. Shen yields a sufficient condition for the construction of Parseval wavelet frames with multiple generators. In this paper we characterize the UEP-type wavelet systems that can be extended to a Parseval wavelet frame by adding just one UEP-type wavelet system. We derive a condition that is necessary for the extension of a UEP-type wavelet system to any Parseval wavelet frame with any number of generators and prove that this condition is also sufficient to ensure that an extension with just two generators is possible.

scholarly journals Comparing powers of edge ideals

2019 ◽  
Vol 18 (10) ◽  
pp. 1950184 ◽  
Author(s):  
Mike Janssen ◽  
Thomas Kamp ◽  
Jason Vander Woude
Keyword(s):  
Symbolic Power ◽  
Edge Ideal ◽  
Homogeneous Ideal ◽  
Edge Ideals ◽  
Ideal Formula ◽  
Number Of Generators ◽  
Recent Interest ◽  
Odd Cycle ◽  
Ordinary Power

Given a nontrivial homogeneous ideal [Formula: see text], a problem of great recent interest has been the comparison of the [Formula: see text]th ordinary power of [Formula: see text] and the [Formula: see text]th symbolic power [Formula: see text]. This comparison has been undertaken directly via an exploration of which exponents [Formula: see text] and [Formula: see text] guarantee the subset containment [Formula: see text] and asymptotically via a computation of the resurgence [Formula: see text], a number for which any [Formula: see text] guarantees [Formula: see text]. Recently, a third quantity, the symbolic defect, was introduced; as [Formula: see text], the symbolic defect is the minimal number of generators required to add to [Formula: see text] in order to get [Formula: see text]. We consider these various means of comparison when [Formula: see text] is the edge ideal of certain graphs by describing an ideal [Formula: see text] for which [Formula: see text]. When [Formula: see text] is the edge ideal of an odd cycle, our description of the structure of [Formula: see text] yields solutions to both the direct and asymptotic containment questions, as well as a partial computation of the sequence of symbolic defects.

scholarly journals Distributed Generation Placement in Radial Distribution Networks using a Bat-inspired Algorithm

DYNA ◽  
2015 ◽  
Vol 82 (192) ◽  
pp. 60-67 ◽  
Author(s):  
John Edwin Candelo-Becerra ◽  
Helman Hernández-Riaño
Keyword(s):  
Distributed Generation ◽  
Radial Distribution ◽  
Distribution Systems ◽  
Reactive Power ◽  
Distribution Networks ◽  
Power Losses ◽  
Number Of Generators ◽  
Metaheuristic Techniques ◽  
Distributed Generation Placement ◽  
Made In

<p>Distributed generation (DG) is an important issue for distribution networks due to the improvement in power losses, but the location and size of generators could be a difficult task for exact techniques. The metaheuristic techniques have become a better option to determine good solutions and in this paper the application of a bat-inspired algorithm (BA) to a problem of location and size of distributed generation in radial distribution systems is presented. A comparison between particle swarm optimization (PSO) and BA was made in the 33-node and 69-node test feeders, using as scenarios the change in active and reactive power, and the number of generators. PSO and BA found good results for small number and capacities of generators, but BA obtained better results for difficult problems and converged faster for all scenarios. The maximum active power injections to reduce power losses in the distribution networks were found for the five scenarios.</p>

On the number of generators of a finite group

1989 ◽  
Vol 53 (6) ◽  
pp. 521-523 ◽  
Author(s):  
Robert M. Guralnick
Keyword(s):  
Finite Group ◽  
Number Of Generators ◽  
A Finite Group
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