scholarly journals Semifields in Class ${\cal F}_4^{(a)}$

10.37236/142 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Gary Ebert ◽  
Giuseppe Marino ◽  
Olga Polverino ◽  
Rocco Trombetti
Keyword(s):  
Algebraic Curves ◽  
Two Dimensional ◽  
Linear Sets ◽  
Odd Order ◽  
Middle Nucleus ◽  
The Right

The semifields of order $q^6$ which are two-dimensional over their left nucleus and six-dimensional over their center have been geometrically partitioned into six classes by using the associated linear sets in $PG(3,q^3)$. One of these classes has been partitioned further (again geometrically) into three subclasses. In this paper algebraic curves are used to construct two infinite families of odd order semifields belonging to one of these subclasses, the first such families shown to exist in this subclass. Moreover, using similar techniques it is shown that these are the only semifields in this subclass which have the right or middle nucleus which is two-dimensional over the center. This work is a non-trivial step towards the classification of all semifields that are six-dimensional over their center and two-dimensional over their left nucleus.

scholarly journals Is It the Right Ansatz?

2001 ◽  
Vol 7 (4) ◽  
pp. 355-365 ◽  
Author(s):  
Dominique Gross ◽  
Barry McMullin
Keyword(s):  
Artificial Life ◽  
Two Dimensional ◽  
Simulation Framework ◽  
Third Order ◽  
Artificial Chemistry ◽  
The Right ◽  
Order Structures

This article is a response to Rasmussen et al. [Artificial Life, 7, 329–350], in which the authors suggest that, within a particular simulation “framework,” there is a tight correspondence between the complexity of the primitive objects and the emergence of dynamical hierarchies. As an example they report a two-dimensional artificial chemistry that supports the spontaneous emergence of micellar structures, which they classify as third-order structures. We report in this article that essentially comparable phenomena can be produced with relatively simpler primitive objects. We also question the order classification of the micellar structures.

Awareness and Decision Making in Professional Ethics

2000 ◽  
Vol 5 (1) ◽  
pp. 19-27 ◽  
Author(s):  
Ronny Swain
Keyword(s):  
Decision Making ◽  
Professional Ethics ◽  
Ethical Decision Making ◽  
Code Of Ethics ◽  
Professional Autonomy ◽  
Ethical Awareness ◽  
Ethical Decisions ◽  
The Right ◽  
Aid Decision

The paper describes the development of the 1998 revision of the Psychological Society of Ireland's Code of Professional Ethics. The Code incorporates the European Meta-Code of Ethics and an ethical decision-making procedure borrowed from the Canadian Psychological Association. An example using the procedure is presented. To aid decision making, a classification of different kinds of stakeholder (i.e., interested party) affected by ethical decisions is offered. The author contends (1) that psychologists should assert the right, which is an important aspect of professional autonomy, to make discretionary judgments, (2) that to be justified in doing so they need to educate themselves in sound and deliberative judgment, and (3) that the process is facilitated by a code such as the Irish one, which emphasizes ethical awareness and decision making. The need for awareness and judgment is underlined by the variability in the ethical codes of different organizations and different European states: in such a context, codes should be used as broad yardsticks, rather than precise templates.

On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Space

2020 ◽  
Vol 14 (6) ◽  
pp. 1232-1239
Author(s):  
P. M. Pustovoit ◽  
E. G. Yashina ◽  
K. A. Pshenichnyi ◽  
S. V. Grigoriev
Keyword(s):  
Dimensional Space ◽  
Two Dimensional

scholarly journals On local and integrated stress-tensor commutators

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Mert Besken ◽  
Jan de Boer ◽  
Grégoire Mathys
Keyword(s):  
Stress Tensor ◽  
Free Field ◽  
Virasoro Algebra ◽  
Light Sheet ◽  
Operator Product ◽  
Local Form ◽  
Two Dimensional ◽  
Conformal Embedding ◽  
General Aspects ◽  
The Right

Abstract We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE. We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor. We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincaré algebra, and the Virasoro algebra of two-dimensional CFT. We then consider commutators of light-ray operators built from the stress-tensor. Using simplifying features of the light sheet limit in four-dimensional CFT we provide a direct computation of the BMS algebra formed by a specific set of light-ray operators in theories with no light scalar conformal primaries. In four-dimensional CFT we define a new infinite set of light-ray operators constructed from the stress-tensor, which all have well-defined matrix elements. These are a direct generalization of the two-dimensional Virasoro light-ray operators that are obtained from a conformal embedding of Minkowski space in the Lorentzian cylinder. They obey Hermiticity conditions similar to their two-dimensional analogues, and also share the property that a semi-infinite subset annihilates the vacuum.

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