An Elementary proof of the Classification of Surfaces in the Projective 3-Space

1978 ◽  
Vol 72 (1) ◽  
pp. 191
Author(s):  
J. H. C. Creighton
Keyword(s):  
Elementary Proof

scholarly journals A complete classification of three-dimensional algebras over ℝ and ℂ — (visiting old, learn new)

2020 ◽  
pp. 2150131
Author(s):  
Yuji Kobayashi ◽  
Kiyoshi Shirayanagi ◽  
Makoto Tsukada ◽  
Sin-Ei Takahasi
Keyword(s):  
19Th Century ◽  
Complex Number ◽  
Elementary Proof ◽  
Three Dimensional ◽  
Number Fields ◽  
Complete Classification ◽  
Associative Algebras ◽  
Multiplication Tables ◽  
The 19Th Century

We provide a complete classification of three-dimensional associative algebras over the real and complex number fields based on a completely elementary proof. We list up all the multiplication tables of the algebras up to isomorphism. We compare our results with those given by mathematicians in the 19th century and this century.

Some Characterizations of a Normal Subgroup of a Group and Isotopic Classes of Transversals

2016 ◽  
Vol 23 (03) ◽  
pp. 409-422 ◽  
Author(s):  
Vipul Kakkar ◽  
R. P. Shukla
Keyword(s):  
Normal Subgroup ◽  
Finite Index ◽  
Dihedral Group ◽  
Elementary Proof ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Right Loop

Let G be a group and H be a subgroup of G which is either finite or of finite index in G. In this paper, we give some characterizations for the normality of H in G. As a consequence we get a very short and elementary proof of the main theorem of a paper of Lal and Shukla, which avoids the use of the classification of finite simple groups. Further, we study the isotopy between the transversals in some groups and determine the number of isotopy classes of transversals of a subgroup of order 2 in D2p, the dihedral group of order 2p, where p is an odd prime and the isotopism classes are formed with respect to induced right loop structures.

On affine classification of permutations on the space GF(2)3

2019 ◽  
Vol 29 (6) ◽  
pp. 363-371
Author(s):  
Fedor M. Malyshev
Keyword(s):  
Elementary Proof ◽  
Affine Equivalence ◽  
Left And Right ◽  
Affine Permutations ◽  
Coordinate Functions ◽  
Number Of Classes

Abstract We give an elementary proof that by multiplication on left and right by affine permutations A, B ∈ AGL(3, 2) each permutation π : GF(2)3 → GF(2)3 may be reduced to one of the 4 permutations for which the 3 × 3-matrices consisting of the coefficients of quadratic terms of coordinate functions have as an invariant the rank, which is either 3, or 2, or 1, or 0, respectively. For comparison, we evaluate the number of classes of affine equivalence by the Pólya enumerative theory.

Structure Theory for Montgomery-Samelson Fiberings between Manifolds, II

1969 ◽  
Vol 21 ◽  
pp. 180-186 ◽  
Author(s):  
Peter L. Antonelli
Keyword(s):  
Euler Characteristic ◽  
Betti Number ◽  
Elementary Proof ◽  
Total Space ◽  
Structure Theory ◽  
Singular Set ◽  
Sphere Bundle ◽  
Simply Connected

Let f: Mn→ Npbe the projection map of an MS-fibering of manifolds β with finite non-empty singular set Aand simply connected total space (see 1). Results of Timourian (10) imply that (n, p) = (4, 3), (8, 5) or (16, 9), while a theorem of Conner (2) yields that #(A), the cardinality of the singular set, is equal to the Euler characteristic of Mn. We give an elementary proof of this fact and, in addition, prove that #(A) is actually determined by bn/2(Mn), the middle betti number of Mn, or what is the same, by bn/2(Np – f(A)). It is then shown that β is topologically the suspension of a (Hopf) sphere bundle when Np is a sphere and bn/2(Mn) = 0. It follows as a corollary that β must also be a suspension when Mn is n/4-connected with vanishing bn/2. Examples where bn/2 is not zero are constructed and we state a couple of conjectures concerning the classification of such objects.

scholarly journals TOPOLOGICAL QUANTUM NUMBERS AND CURVATURE — EXAMPLES AND APPLICATIONS

2009 ◽  
Vol 06 (03) ◽  
pp. 533-553 ◽  
Author(s):  
JERZY SZCZȨSNY ◽  
MAREK BIESIADA ◽  
MAREK SZYDŁOWSKI
Keyword(s):  
Riemannian Geometry ◽  
Vector Fields ◽  
Elementary Proof ◽  
Dimension Vector ◽  
Smooth Mapping ◽  
Quantum Numbers ◽  
Topological Quantum ◽  
Bonnet Theorem ◽  
Hopf Theorem

Using the idea of the degree of a smooth mapping between two manifolds of the same dimension we present here the topological (homotopical) classification of the mappings between spheres of the same dimension, vector fields, monopole and instanton solutions. Starting with a review of the elements of Riemannian geometry we also present an original elementary proof of the Gauss–Bonnet theorem and also one of the Poincaré–Hopf theorem.

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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