scholarly journals THE VELDKAMP SPACE OF THE SMALLEST SLIM DENSE NEAR HEXAGON

2012 ◽  
Vol 10 (02) ◽  
pp. 1250082 ◽  
Author(s):  
R. M. GREEN ◽  
METOD SANIGA
Keyword(s):  
Black Holes ◽  
Quantum Information ◽  
Automorphism Group ◽  
Complete Classification ◽  
Recent Emergence ◽  
Different Types ◽  
Geometrical Concepts ◽  
Stabilizer Group ◽  
Near Hexagon

We give a detailed description of the Veldkamp space of the smallest slim dense near hexagon. This space is isomorphic to PG(7,2) and its 28- 1 = 255 Veldkamp points (that is, geometric hyperplanes of the near hexagon) fall into five distinct classes, each of which is uniquely characterized by the number of points/lines as well as by a sequence of the cardinalities of points of given orders and/or that of (grid-)quads of given types. For each type we also give its weight, stabilizer group within the full automorphism group of the near hexagon and the total number of copies. The totality of (255 choose 2)/3 = 10,795 Veldkamp lines split into 41 different types. We give a complete classification of them in terms of the properties of their cores (i.e. subconfigurations of points and lines common to all the three hyperplanes comprising a given Veldkamp line) and the types of the hyperplanes they are composed of. These findings may lend themselves into important physical applications, especially in view of recent emergence of a variety of closely related finite geometrical concepts linking quantum information with black holes.

scholarly journals CONFORMAL SUPERFIELDS AND BPS STATES IN AdS4/7 GEOMETRIES

2000 ◽  
Vol 14 (22n23) ◽  
pp. 2315-2333 ◽  
Author(s):  
SERGIO FERRARA ◽  
EMERY SOKATCHEV
Keyword(s):  
Black Holes ◽  
De Sitter ◽  
Harmonic Superspace ◽  
Supergravity Theory ◽  
Conformally Invariant ◽  
Highest Weight ◽  
Ads Black Holes ◽  
Different Types ◽  
Bps States

We carry out a general analysis of the representations of the superconformal algebras OSp(8/4, ℝ) and OSp(8*/2N) in terms of harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different types of massless conformal superfields ("supersingletons"). Particular attention is paid to the so-called "short multiplets". Representations undergoing shortening have "protected dimension" and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.

scholarly journals REPRESENTATIONS OF SUPERCONFORMAL ALGEBRAS IN THE AdS7/4/CFT6/3 CORRESPONDENCE

2001 ◽  
Vol 16 (05) ◽  
pp. 976-989 ◽  
Author(s):  
SERGIO FERRARA ◽  
EMERY SOKATCHEV
Keyword(s):  
Black Holes ◽  
De Sitter ◽  
Harmonic Superspace ◽  
Supergravity Theory ◽  
Conformally Invariant ◽  
Highest Weight ◽  
Ads Black Holes ◽  
Different Types ◽  
Bps States

We perform a general analysis of representations of the superconformal algebras OSp (8/4, ℝ) and OSp (8*/2N) in harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different types of massless conformal superfields ("supersingletons"). In particular, all "short multiplets" are classified. Representations undergoing shortening have "protected dimension" and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.

scholarly journals Automorphisms of surfaces of general type with acting trivially in cohomology

2013 ◽  
Vol 149 (10) ◽  
pp. 1667-1684 ◽  
Author(s):  
Jin-Xing Cai ◽  
Wenfei Liu ◽  
Lei Zhang
Keyword(s):  
Automorphism Group ◽  
Minimal Surfaces ◽  
General Type ◽  
Cohomology Ring ◽  
Complete Classification ◽  
Surfaces Of General Type

AbstractIn this paper we prove that surfaces of general type with irregularity $q\geq 3$ are rationally cohomologically rigidified, and so are minimal surfaces $S$ with $q(S)= 2$ unless ${ K}_{S}^{2} = 8\chi ({ \mathcal{O} }_{S} )$. Here a surface $S$ is said to be rationally cohomologically rigidified if its automorphism group $\mathrm{Aut} (S)$ acts faithfully on the cohomology ring ${H}^{\ast } (S, \mathbb{Q} )$. As examples we give a complete classification of surfaces isogenous to a product with $q(S)= 2$ that are not rationally cohomologically rigidified.

scholarly journals Pentavalent Symmetric Graphs of Order $12p$

10.37236/720 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Song-Tao Guo ◽  
Jin-Xin Zhou ◽  
Yan-Quan Feng
Keyword(s):  
Automorphism Group ◽  
Complete Classification ◽  
Symmetric Graph ◽  
Symmetric Graphs

A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, a complete classification of connected pentavalent symmetric graphs of order $12p$ is given for each prime $p$. As a result, a connected pentavalent symmetric graph of order $12p$ exists if and only if $p=2$, $3$, $5$ or $11$, and up to isomorphism, there are only nine such graphs: one for each $p=2$, $3$ and $5$, and six for $p=11$.

scholarly journals Two-geodesic-transitive graphs which are neighbor cubic or neighbor tetravalent

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2483-2488
Author(s):  
Wei Jin ◽  
Li Tan
Keyword(s):  
Automorphism Group ◽  
Complete Classification ◽  
Transitive Graphs

A vertex triple (u, v, w) with v adjacent to both u and w is called a 2-geodesic if u ? w and u,w are not adjacent. A graph ? is said to be 2-geodesic-transitive if its automorphism group is transitive on both arcs and 2-geodesics. In this paper, a complete classification of 2-geodesic-transitive graphs is given which are neighbor cubic or neighbor tetravalent.

Dual stain kit for the microscopic gram classification of ocular infection bacteria

1993 ◽  
Vol 51 ◽  
pp. 248-249
Author(s):  
Jacob S. Hanker ◽  
Dale N. Holdren ◽  
Kenneth L. Cohen ◽  
Beverly L. Giammara
Keyword(s):  
Contact Lenses ◽  
Ocular Infection ◽  
Gram Negative Bacteria ◽  
Gram Negative ◽  
Gram Staining ◽  
Ocular Infections ◽  
Different Types ◽  
Culture Positive ◽  
Increased Susceptibility

Keratitis and conjunctivitis (infections of the cornea or conjunctiva) are ocular infections caused by various bacteria, fungi, viruses or parasites; bacteria, however, are usually prominent. Systemic conditions such as alcoholism, diabetes, debilitating disease, AIDS and immunosuppressive therapy can lead to increased susceptibility but trauma and contact lens use are very important factors. Gram-negative bacteria are most frequently cultured in these situations and Pseudomonas aeruginosa is most usually isolated from culture-positive ulcers of patients using contact lenses. Smears for staining can be obtained with a special swab or spatula and Gram staining frequently guides choice of a therapeutic rinse prior to the report of the culture results upon which specific antibiotic therapy is based. In some cases staining of the direct smear may be diagnostic in situations where the culture will not grow. In these cases different types of stains occasionally assist in guiding therapy.

Explanatory Power for Medical Expert Systems: Studies in the Representation of Causal Relationships for Clinical Consultations

1982 ◽  
Vol 21 (03) ◽  
pp. 127-136 ◽  
Author(s):  
J. W. Wallis ◽  
E. H. Shortliffe
Keyword(s):  
Explanatory Power ◽  
Prototype System ◽  
Inference Rules ◽  
Medical Expert ◽  
Comprehensive Knowledge ◽  
Different Types ◽  
Medical Expert Systems ◽  
Explanation System ◽  
Systems Studies

This paper reports on experiments designed to identify and implement mechanisms for enhancing the explanation capabilities of reasoning programs for medical consultation. The goals of an explanation system are discussed, as is the additional knowledge needed to meet these goals in a medical domain. We have focussed on the generation of explanations that are appropriate for different types of system users. This task requires a knowledge of what is complex and what is important; it is further strengthened by a classification of the associations or causal mechanisms inherent in the inference rules. A causal representation can also be used to aid in refining a comprehensive knowledge base so that the reasoning and explanations are more adequate. We describe a prototype system which reasons from causal inference rules and generates explanations that are appropriate for the user.

scholarly journals Multiplicative automatic sequences

2021 ◽  
Author(s):  
Jakub Konieczny ◽  
Mariusz Lemańczyk ◽  
Clemens Müllner
Keyword(s):  
Complete Classification ◽  
Automatic Sequences ◽  
Complex Valued

AbstractWe obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

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