scholarly journals Circulant association schemes on triples

10.53733/106 ◽  
2021 ◽  
Vol 52 ◽  
pp. 153-165
Author(s):  
Cheryl Praeger ◽  
Prabir Bhattacharya
Keyword(s):  
Cyclic Subgroup ◽  
Automorphism Groups ◽  
Three Dimensional ◽  
Association Schemes ◽  
Permutation Groups ◽  
Open Questions ◽  
Transitive Groups ◽  
Regular Partitions ◽  
The Given ◽  
Complete Characterisation

Association Schemes and coherent configurations (and the related Bose-Mesner algebra and coherent algebras) are well known in combinatorics with many applications. In the 1990s, Mesner and Bhattacharya introduced a three-dimensional generalisation of association schemes which they called an {\em association scheme on triples} (AST) and constructed examples of several families of ASTs. Many of their examples used 2-transitive permutation groups: the non-trivial ternary relations of the ASTs were sets of ordered triples of pairwise distinct points of the underlying set left invariant by the group; and the given permutation group was a subgroup of automorphisms of the AST. In this paper, we consider ASTs that do not necessarily admit 2-transitive groups as automorphism groups but instead a transitive cyclic subgroup of the symmetric group acts as automorphisms. Such ASTs are called {\em circulant} ASTs and the corresponding ternary relations are called {\em circulant relations}. We give a complete characterisation of circulant ASTs in terms of AST-regular partitions of the underlying set. We also show that a special type of circulant, that we call a {\em thin circulant}, plays a key role in describing the structure of circulant ASTs. We outline several open questions.  

On locally graded barely transitive groups

2013 ◽  
Vol 11 (7) ◽  
Author(s):  
Cansu Betin ◽  
Mahmut Kuzucuoğlu
Keyword(s):  
Finite Index ◽  
Cyclic Subgroup ◽  
Transitive Group ◽  
Transitive Groups ◽  
Point Stabilizer

AbstractWe show that a barely transitive group is totally imprimitive if and only if it is locally graded. Moreover, we obtain the description of a barely transitive group G for the case G has a cyclic subgroup 〈x〉 which intersects non-trivially with all subgroups and for the case a point stabilizer H of G has a subgroup H 1 of finite index in H satisfying the identity χ(H 1) = 1, where χ is a multi-linear commutator of weight w.

Automorphism groups of arithmetically saturated models

2006 ◽  
Vol 71 (1) ◽  
pp. 203-216 ◽  
Author(s):  
Ermek S. Nurkhaidarov
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Open Subgroup ◽  
Peano Arithmetic ◽  
Standard System ◽  
Permutation Groups ◽  
Saturated Model ◽  
Saturated Models ◽  
Homogeneous Set ◽  
Image Position

In this paper we study the automorphism groups of countable arithmetically saturated models of Peano Arithmetic. The automorphism groups of such structures form a rich class of permutation groups. When studying the automorphism group of a model, one is interested to what extent a model is recoverable from its automorphism group. Kossak-Schmerl [12] show that if M is a countable, arithmetically saturated model of Peano Arithmetic, then Aut(M) codes SSy(M). Using that result they prove:Let M1. M2 be countable arithmetically saturated models of Peano Arithmetic such that Aut(M1) ≅ Aut(M2). Then SSy(M1) = SSy(M2).We show that if M is a countable arithmetically saturated of Peano Arithmetic, then Aut(M) can recognize if some maximal open subgroup is a stabilizer of a nonstandard element, which is smaller than any nonstandard definable element. That fact is used to show the main theorem:Let M1, M2be countable arithmetically saturated models of Peano Arithmetic such that Aut(M1) ≅ Aut(M2). Then for every n < ωHere RT2n is Infinite Ramsey's Theorem stating that every 2-coloring of [ω]n has an infinite homogeneous set. Theorem 0.2 shows that for models of a false arithmetic the converse of Kossak-Schmerl Theorem 0.1 is not true. Using the results of Reverse Mathematics we obtain the following corollary:There exist four countable arithmetically saturated models of Peano Arithmetic such that they have the same standard system but their automorphism groups are pairwise non-isomorphic.

An Inverse Inviscid Method for the Design of Quasi-Three-Dimensional Turbomachinery Cascades

1993 ◽  
Vol 115 (1) ◽  
pp. 121-127 ◽  
Author(s):  
E. Bonataki ◽  
P. Chaviaropoulos ◽  
K. D. Papailiou
Keyword(s):  
Differential Equation ◽  
Three Dimensional ◽  
Test Cases ◽  
Elliptic Type ◽  
Flow Angle ◽  
Blade Shape ◽  
Closure Conditions ◽  
Type Boundary ◽  
Absolute Frame ◽  
The Given

The calculation of the blade shape, when the desired velocity distribution is imposed, has been the object of numerous investigations in the past. The object of this paper is to present a new method suitable for the design of turbomachinery stator and rotor blade sections, lying on an arbitrary axisymmetric stream-surface with varying streamtube width. The flow is considered irrotational in the absolute frame of reference and compressible. The given data are the streamtube geometry, the number of blades, the inlet flow conditions and the suction and pressure side velocity distributions as functions of the normalized arc-length. The output of the computation is the blade shape that satisfies the above data. The method solves an elliptic type partial differential equation for the velocity modulus with Dirichlet and periodic type boundary conditions on the (potential function, stream function)-plane (Φ, Ψ). The flow angle field is subsequently calculated solving an ordinary differential equation along the iso-Φ or iso-Ψ lines. The blade coordinates are, finally, computed by numerical integration. A set of closure conditions has been developed and discussed in the paper. The method is validated on several test cases and a discussion is held concerning its application and limitations.

Calculation of Complete Three-Dimensional Flow in a Centrifugal Rotor With Splitter Blades

1988 ◽  
Author(s):  
Liu Dian-Kui ◽  
Ji Le-Jian
Keyword(s):  
Mass Flow ◽  
Three Dimensional ◽  
Present Calculation ◽  
Flow Ratio ◽  
Three Dimensional Flow ◽  
Stream Surface ◽  
Dimensional Flow ◽  
Flow Capacity ◽  
The Given ◽  
Mass Flow Ratio

The flow within a centrifugal rotor has strong characteristics of three-dimensional effect. A procedure called “stream-surface coordinates iteration” for the calculation of complete three dimensional flow in turbo-machinery is first described. Splitter blade techniques have been used in many rotors, especially in centrifugal compressors and pumps with high flow capacity. The difficulty of the calculation of the flow field for this type of rotor lies on that the mass flow ratio between the two sub-channels is unknown for the given total flow capacity. In the second part of this paper, an assumption about how to determine this mass flow ratio and a procedure to calculate the complete three-dimensional flow are presented. Finally, some design criteria about the splitter blades are put forward. Experimental data from two centrifugal pump impellers equipped with different splitter blades are also given to demonstrate the availability of the present calculation method.

scholarly journals ADAPTIVE ALGORITHM FOR DETERMINING THE PARAMETERS OF AN INACCESSIBLE POINT OF AN OBJECT

2021 ◽  
pp. 58-70
Author(s):  
Aleksandr Brailov ◽  
Vitaliy Panchenko
Keyword(s):  
Adaptive Algorithm ◽  
Minimum Distance ◽  
Three Dimensional ◽  
Geometrical Model ◽  
Multiple Variables ◽  
The Common ◽  
Relative Errors ◽  
The Given ◽  
Real Experimental Data

In the present research the optimizing approach to the determination of the parameters of an inaccessible point of an object is developed. The common issues are revealed and essential steps of their resolution are identified. The essence of the problem is an objective contradiction between a requirement for the location of points A and B of the centers of the sighting tubes of optical devices in the same horizontal plane P1 and the lack of a real possibility to perform such to achieve this an identical one-level arrangement without error. The aim of the study is to develop strategies for determining the position of an inaccessible point of an object in the minimum domain between intersecting sighting rays as well as an adaptive algorithm for determining the values of the parameters of an inaccessible point under the given absolute and relative errors. To achieve this aim, the following problems are formulated and solved in the paper: 1. Develop strategies for determining the position of the inaccessible point of the object in the minimum domain between the intersecting sighting rays. 2. Develop an adaptive algorithm for determining the values of the parameters of an inaccessible point based on the specified absolute and relative errors. In the proposed optimizing approach, the three-dimensional geometrical model with crossed directional rays for the determination of coordinates of the inaccessible point of an object is developed. It is discussed that points С and C', coordinated of which to be determined, locates in domain [CDM, CEM], [C'D'M, C'E'M] of the minimum distance ρmin between crossed directional rays. The optimizing problem of the determination of coordinates of an inaccessible point of an object in space is reduced to a problem of the determination of the minimum distance between two crossed directional rays. It’s known from the theory of function of multiple variables that function ρ = f (tC'D', tC'E') reaches its extremum ρmin when its partial derivatives by each variable are equal to zero. Three strategies for selecting the position of the inaccessible point C (xC, yC, zC) in the found minimum region [CDM, CEM] are proposed. The required point C' (xC', yC', zC') can be located, for example, in the middle of the minimum segment [C'D'M, C'E'M]. The essence of the adaptive algorithm is in optimizing the variation of the initial values of data α, α', β, γ, γ', AB, at which the absolute and relative errors of the coordinates of the inaccessible point satisfy the error values set by the customer (0.0001-1.2%) The proposed approach is verified using real experimental data.

scholarly journals Analysis of wireless network security systems problems and those solutions

2020 ◽  
pp. 139-140
Author(s):  
Ibraim Didmanidze ◽  
Zebur Beridze ◽  
Vladimir Zaslavski
Keyword(s):  
Wireless Networks ◽  
Network Security ◽  
Wireless Network ◽  
Research Paper ◽  
Network Routing ◽  
Security Systems ◽  
Security Issues ◽  
Wireless Network Security ◽  
Open Questions ◽  
The Given

In the people's lives wireless networks play a big role. It is necessary to understand the basic concept of wireless networks, to consider the security issues related to them, and then observe how they work and what benefits they can bring in different cases. In this regard the given research paper presents the fundamental principles of security as well as related open questions. It reviews the security issues of the wireless networks. Security of protocols of wireless network routing has become an urgent necessity to stimulate the network launching and expand the area of its usage. Therefore, the presented research paper proposes and defines different solutions and concepts for security.  

scholarly journals On generation and propagation of tsunamis in a shallow running ocean

1978 ◽  
Vol 1 (3) ◽  
pp. 373-390
Author(s):  
Lokenath Debnath ◽  
Uma Basu
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Relative Magnitude ◽  
Ocean Floor ◽  
Surface Elevation ◽  
Free Surface Elevation ◽  
Surface Disturbance ◽  
Fourier And Laplace Transforms ◽  
The Given ◽  
Integral Solutions

A theory is presented of the generation and propagation of the two and the three dimensional tsunamis in a shallow running ocean due to the action of an arbitrary ocean floor or ocean surface disturbance. Integral solutions for both two and three dimensional problems are obtained by using the generalized Fourier and Laplace transforms. An asymptotic analysis is carried out for the investigation of the principal features of the free surface elevation. It is found that the propagation of the tsunamis depends on the relative magnitude of the given speed of the running ocean and the wave speed of the shallow ocean. When the speed of the running ocean is less than the speed of the shallow ocean wave, both the two and the three dimensional free surface elevation represent the generation and propagation of surface waves which decay asymptotically ast−12for the two dimensional case and ast−1for the three dimensional tsunamis. Several important features of the solution are discussed in some detail. As an application of the general theory, some physically realistic ocean floor disturbances are included in this paper.

Remedy for Misalignment of Bilobe Cargo Tanks in Liquefied Petroleum Gas Carriers

2004 ◽  
Vol 20 (03) ◽  
pp. 133-146
Author(s):  
Ivo Senjanovi ◽  
Smiljko Rudan ◽  
Ana Maria Ljustina
Keyword(s):  
Water Pressure ◽  
Three Dimensional ◽  
Additional Stress ◽  
Liquefied Petroleum Gas ◽  
Hydraulic Test ◽  
Dimensional Finite Element ◽  
Reliable Solution ◽  
Three Dimensional Finite Element ◽  
The Given ◽  
Design Pressure

The work describes independent tanks of different shapes, which are further subdivided into A, B, and C types related to design pressure. Special attention is paid to the remedy for misalignment resulting from manufacturing difficulties in a 3,000-m3 bilobe cargo tank of a 8,350-m3 liquefied petroleum gas (LPG) carrier. Namely, some eccentricity in the Y joint of tank shells and longitudinal bulkhead usually remains during fabrication, which causes additional stress concentration. This problem is first considered analytically and then numerically. A complete and reliable solution is achieved by a three-dimensional finite element method analysis of a tank segment between two vacuum rings. Reinforcement of the Y joint by a set of knees and bars, according to the value of the shell's eccentricity, is recommended in order to reduce the stress level below the allowable value. The obtained results are presented in a practical diagram for general use. Following the given instructions, the cargo tanks of the considered LPG are reinforced and submitted to the hydraulic test with water pressure 50% higher than the design pressure. Having passed this test successfully, the approval of the relevant classification society is obtained.

scholarly journals Numerical Modeling of Force-Stiffness Response of Cross-Linked Actin Networks Using Tensegrity Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Xian Xu ◽  
Yafeng Wang ◽  
Yaozhi Luo
Keyword(s):  
Three Dimensional ◽  
Structural Response ◽  
Postbuckling Behavior ◽  
Actin Networks ◽  
Tensegrity Structure ◽  
Tensegrity Systems ◽  
Order Polynomial ◽  
The Mean ◽  
The Given ◽  
Tensegrity Model

A three-dimensional tensegrity structure is used as a computational model for cross-linked actin networks. The postbuckling behavior of the members under compression is considered and the constitutive relation of the postbuckling members is modeled as a second-order polynomial. A numerical scheme incorporating the equivalent constitution of the postbuckling members is used to predict the structural response of the tensegrity model under compression loads. The numerical simulation shows that the stiffness of the tensegrity structure nonlinearly increases before member buckling and abruptly decreases to a lower level as soon as members buckle. This result qualitatively mimics the experimentally observed stiffness to compression stress response of cross-linked actin networks. In order to take member length variety into account, a large number of simulations with the length of buckling members varying in the given range are also carried out. It is found that the mean response of the simulations using different buckling member length exhibits more resemblance to the experimental observation.

scholarly journals EMBEDDING PERMUTATION GROUPS INTO WREATH PRODUCTS IN PRODUCT ACTION

2012 ◽  
Vol 92 (1) ◽  
pp. 127-136 ◽  
Author(s):  
CHERYL E. PRAEGER ◽  
CSABA SCHNEIDER
Keyword(s):  
Permutation Group ◽  
Wreath Product ◽  
Automorphism Groups ◽  
Wreath Products ◽  
Error Correcting Codes ◽  
Permutation Groups ◽  
Graph Products ◽  
Product Action ◽  
Hamming Graphs

AbstractWe consider the wreath product of two permutation groups G≤Sym Γ and H≤Sym Δ as a permutation group acting on the set Π of functions from Δ to Γ. Such groups play an important role in the O’Nan–Scott theory of permutation groups and they also arise as automorphism groups of graph products and codes. Let X be a subgroup of Sym Γ≀Sym Δ. Our main result is that, in a suitable conjugate of X, the subgroup of SymΓ induced by a stabiliser of a coordinate δ∈Δ only depends on the orbit of δ under the induced action of X on Δ. Hence, if X is transitive on Δ, then X can be embedded into the wreath product of the permutation group induced by the stabiliser Xδ on Γ and the permutation group induced by X on Δ. We use this result to describe the case where X is intransitive on Δ and offer an application to error-correcting codes in Hamming graphs.

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