A constructive approach to the finite congruence lattice representation problem

2000 ◽  
Vol 43 (2-3) ◽  
pp. 279-293 ◽  
Author(s):  
John W. Snow
Keyword(s):  
Congruence Lattice ◽  
Constructive Approach ◽  
Representation Problem ◽  
Lattice Representation

A MINIMAL CONGRUENCE LATTICE REPRESENTATION FOR

2020 ◽  
Vol 108 (3) ◽  
pp. 332-340
Author(s):  
ROGER BUNN ◽  
DAVID GROW ◽  
MATT INSALL ◽  
PHILIP THIEM
Keyword(s):  
Congruence Lattice ◽  
Dihedral Group ◽  
Unary Algebra ◽  
Left Translation ◽  
Lattice Representation

Let $p$ be an odd prime. The unary algebra consisting of the dihedral group of order $2p$, acting on itself by left translation, is a minimal congruence lattice representation of $\mathbb{M}_{p+1}$.

Directors' Liability in Negligence – Challenging the "Elements of the Tort" Approach

2016 ◽  
Vol 47 (3) ◽  
pp. 485
Author(s):  
Victoria Stace
Keyword(s):  
Third Parties ◽  
Duty Of Care ◽  
Constructive Approach ◽  
Two Stage ◽  
Policy Issues ◽  
Threshold Test

This article suggests that the "elements of the tort" approach to directors' liability in negligence to third parties should be discontinued on the basis that assumption of responsibility as a threshold test is not an element of the tort of negligence or negligent misstatement and a more constructive approach would be to address the policy issues associated with imposing liability on directors as part of the two-stage duty of care inquiry.

scholarly journals A constructive approach to accessible group classes

2021 ◽  
Author(s):  
Francesco de Giovanni ◽  
Marco Trombetti
Keyword(s):  
Constructive Approach ◽  
Class A ◽  
Formula Group

AbstractLet $${\mathfrak {X}}$$ X be a group class. A group G is an opponent of $${\mathfrak {X}}$$ X if it is not an $${\mathfrak {X}}$$ X -group, but all its proper subgroups belong to $${\mathfrak {X}}$$ X . Of course, every opponent of $${\mathfrak {X}}$$ X is a cohopfian group and the aim of this paper is to describe the smallest group class containing $${\mathfrak {X}}$$ X and admitting no such a kind of cohopfian groups.

An analysis of the Pólya point process

1983 ◽  
Vol 15 (01) ◽  
pp. 39-53 ◽  
Author(s):  
Ed Waymire ◽  
Vijay K. Gupta
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Critical Value ◽  
General Representation ◽  
Infinitely Divisible ◽  
Generating Functional ◽  
Representation Problem ◽  
Polya Process ◽  
Pólya Process ◽  
Stochastic Point Processes

The Pólya process is employed to illustrate certain features of the structure of infinitely divisible stochastic point processes in connection with the representation for the probability generating functional introduced by Milne and Westcott in 1972. The Pólya process is used to provide a counterexample to the result of Ammann and Thall which states that the class of stochastic point processes with the Milne and Westcott representation is the class of regular infinitely divisble point processes. So the general representation problem is still unsolved. By carrying the analysis of the Pólya process further it is possible to see the extent to which the general representation is valid. In fact it is shown in the case of the Pólya process that there is a critical value of a parameter above which the representation breaks down. This leads to a proper version of the representation in the case of regular infinitely divisible point processes.

Path polynomials of a circuit: a constructive approach

1998 ◽  
Vol 44 (4) ◽  
pp. 313-325 ◽  
Author(s):  
C.M. DA Fonseca ◽  
J. Petronilho
Keyword(s):  
Constructive Approach

HETEROCLINIC ORBITS FOR MONOTONE TWIST MAPS THROUGH A VARIATIONAL PRINCIPLE

2001 ◽  
Vol 11 (09) ◽  
pp. 2451-2461
Author(s):  
TIFEI QIAN
Keyword(s):  
Variational Principle ◽  
Variational Method ◽  
Fixed Points ◽  
Heteroclinic Orbit ◽  
Geometric Method ◽  
Heteroclinic Orbits ◽  
Constructive Approach ◽  
Connecting Orbits ◽  
Relative Ease ◽  
Twist Maps

The variational method has shown many advantages over the geometric method in proving the existence of connecting orbits since it requires much weaker hyperbolicity and less smoothness. Many results known to be difficult to obtain by the geometric method can now be obtained by a variational principle with relative ease. In particular, a variational principle provides a constructive approach to the existence of heteroclinic orbits. In this paper a variational principle is used to construct a heteroclinic orbit between an adjacent minimal pair of fixed points for monotone twist maps on (ℝ/ℤ) × ℝ. Application of our results to a standard map is also given.

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