scholarly journals Classification of subsets with minimal width and dual width in Grassmann, bilinear forms and dual polar graphs

2006 ◽  
Vol 113 (5) ◽  
pp. 903-910 ◽  
Author(s):  
Hajime Tanaka
Keyword(s):  
Bilinear Forms ◽  
Minimal Width

On constructions of Lie (super) algebras and (𝜀,δ)-Freudenthal–Kantor triple systems defined by bilinear forms

2019 ◽  
Vol 19 (11) ◽  
pp. 2050223
Author(s):  
Noriaki Kamiya ◽  
Daniel Mondoc
Keyword(s):  
Lie Algebras ◽  
Complex Structure ◽  
Bilinear Forms ◽  
Simple Lie Algebras ◽  
Triple Systems ◽  
Dynkin Diagrams

In this work, we discuss a classification of [Formula: see text]-Freudenthal–Kantor triple systems defined by bilinear forms and give all examples of such triple systems. From these results, we may see a construction of some simple Lie algebras or superalgebras associated with their Freudenthal–Kantor triple systems. We also show that we can associate a complex structure into these ([Formula: see text]-Freudenthal–Kantor triple systems. Further, we introduce the concept of Dynkin diagrams associated to such [Formula: see text]-Freudenthal–Kantor triple systems and the corresponding Lie (super) algebra construction.

scholarly journals Vertex Subsets with Minimal Width and Dual Width in $Q$-Polynomial Distance-Regular Graphs

10.37236/654 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Hajime Tanaka
Keyword(s):  
Point Of View ◽  
Regular Graphs ◽  
Minimal Width ◽  
Distance Regular Graphs ◽  
Classical Parameters

We study $Q$-polynomial distance-regular graphs from the point of view of what we call descendents, that is to say, those vertex subsets with the property that the width $w$ and dual width $w^*$ satisfy $w+w^*=d$, where $d$ is the diameter of the graph. We show among other results that a nontrivial descendent with $w\geq 2$ is convex precisely when the graph has classical parameters. The classification of descendents has been done for the $5$ classical families of graphs associated with short regular semilattices. We revisit and characterize these families in terms of posets consisting of descendents, and extend the classification to all of the $15$ known infinite families with classical parameters and with unbounded diameter.

On non-compact groups I. Classification of non-compact real simple Lie groups and groups containing the Lorentz group

1965 ◽  
Vol 287 (1411) ◽  
pp. 519-531 ◽  
Keyword(s):  
Lie Groups ◽  
Lorentz Group ◽  
Compact Groups ◽  
Bilinear Forms ◽  
Unimodular Group ◽  
Simple Lie Groups ◽  
Real Complex

The classification of all simple real Lie groups is discussed and given explicitly in the form of tables. In particular four classes of groups are identified which contain the Lorentz group. These are the groups which leave bilinear forms in real, complex and quaternionic spaces invariant, and the unimodular group in n -dimension.

scholarly journals The classification of rank 3 reflective hyperbolic lattices over

2016 ◽  
Vol 164 (2) ◽  
pp. 221-257
Author(s):  
ALICE MARK
Keyword(s):  
Finite Index ◽  
Standard Method ◽  
Quadratic Forms ◽  
Computation Time ◽  
Reflection Group ◽  
Bilinear Forms ◽  
Time Required ◽  
Hyperbolic Lattices ◽  
Real Quadratic

AbstractThere are 432 strongly squarefree symmetric bilinear forms of signature (2, 1) defined over$\mathbb{Z}[\sqrt{2}]$whose integral isometry groups are generated up to finite index by finitely many reflections. We adapted Allcock's method (based on Nikulin's) of analysis for the 2-dimensional Weyl chamber to the real quadratic setting, and used it to produce a finite list of quadratic forms which contains all of the ones of interest to us as a sub-list. The standard method for determining whether a hyperbolic reflection group is generated up to finite index by reflections is an algorithm of Vinberg. However, for a large number of our quadratic forms the computation time required by Vinberg's algorithm was too long. We invented some alternatives, which we present here.

Note on the spectral classification of carbon stars in the photographic infrared region

1966 ◽  
Vol 24 ◽  
pp. 21-23
Author(s):  
Y. Fujita
Keyword(s):  
Infrared Region ◽  
Spectral Classification ◽  
Carbon Stars

We have investigated the spectrograms (dispersion: 8Å/mm) in the photographic infrared region fromλ7500 toλ9000 of some carbon stars obtained by the coudé spectrograph of the 74-inch reflector attached to the Okayama Astrophysical Observatory. The names of the stars investigated are listed in Table 1.

Diagnostic Value of Electron Microscopy in Soft Tissue Tumors

1970 ◽  
Vol 28 ◽  
pp. 220-221
Author(s):  
Gerald Fine ◽  
Azorides R. Morales
Keyword(s):  
Cardiac Myxoma ◽  
Osteogenic Sarcoma ◽  
Diagnostic Value ◽  
Soft Tissue Tumors ◽  
Amelanotic Melanoma ◽  
Growth Patterns ◽  
Light Microscopic Level ◽  
Mesenchymal Tumors ◽  
Good Agreement

For years the separation of carcinoma and sarcoma and the subclassification of sarcomas has been based on the appearance of the tumor cells and their microscopic growth pattern and information derived from certain histochemical and special stains. Although this method of study has produced good agreement among pathologists in the separation of carcinoma from sarcoma, it has given less uniform results in the subclassification of sarcomas. There remain examples of neoplasms of different histogenesis, the classification of which is questionable because of similar cytologic and growth patterns at the light microscopic level; i.e. amelanotic melanoma versus carcinoma and occasionally sarcoma, sarcomas with an epithelial pattern of growth simulating carcinoma, histologically similar mesenchymal tumors of different histogenesis (histiocytoma versus rhabdomyosarcoma, lytic osteogenic sarcoma versus rhabdomyosarcoma), and myxomatous mesenchymal tumors of diverse histogenesis (myxoid rhabdo and liposarcomas, cardiac myxoma, myxoid neurofibroma, etc.)

Ultrastructure of mesotheliomas

1984 ◽  
Vol 42 ◽  
pp. 98-101
Author(s):  
Irving Dardick
Keyword(s):  
Electron Microscopy ◽  
Latent Period ◽  
Spindle Cell ◽  
Spindle Cell Sarcoma ◽  
Metastatic Adenocarcinoma ◽  
Cell Sarcoma ◽  
Cytological Features ◽  
Industrial Use ◽  
Degree Of Differentiation

With the extensive industrial use of asbestos in this century and the long latent period (20-50 years) between exposure and tumor presentation, the incidence of malignant mesothelioma is now increasing. Thus, surgical pathologists are more frequently faced with the dilemma of differentiating mesothelioma from metastatic adenocarcinoma and spindle-cell sarcoma involving serosal surfaces. Electron microscopy is amodality useful in clarifying this problem.In utilizing ultrastructural features in the diagnosis of mesothelioma, it is essential to appreciate that the classification of this tumor reflects a variety of morphologic forms of differing biologic behavior (Table 1). Furthermore, with the variable histology and degree of differentiation in mesotheliomas it might be expected that the ultrastructure of such tumors also reflects a range of cytological features. Such is the case.

Interpreting HVEM of muscle-cell impulse networks

1992 ◽  
Vol 50 (1) ◽  
pp. 126-127
Author(s):  
Paul DeCosta ◽  
Kyugon Cho ◽  
Stephen Shemlon ◽  
Heesung Jun ◽  
Stanley M. Dunn
Keyword(s):  
Structural Analysis ◽  
Muscle Cell ◽  
Electron Micrographs ◽  
Relative Size ◽  
Automatic Classification ◽  
Nerve Fibers ◽  
Analysis Algorithm ◽  
Structural Networks

Introduction: The analysis and interpretation of electron micrographs of cells and tissues, often requires the accurate extraction of structural networks, which either provide immediate 2D or 3D information, or from which the desired information can be inferred. The images of these structures contain lines and/or curves whose orientation, lengths, and intersections characterize the overall network.Some examples exist of studies that have been done in the analysis of networks of natural structures. In, Sebok and Roemer determine the complexity of nerve structures in an EM formed slide. Here the number of nodes that exist in the image describes how dense nerve fibers are in a particular region of the skin. Hildith proposes a network structural analysis algorithm for the automatic classification of chromosome spreads (type, relative size and orientation).

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