An invariant of graph-links valued in graphs and an almost classification of graph-links

2020 ◽  
Vol 29 (09) ◽  
pp. 2050063
Author(s):  
Denis P. Ilyutko ◽  
Vassily O. Manturov
Keyword(s):  
Main Property ◽  
Link Invariant ◽  
Linear Combinations ◽  
Free Graph ◽  
Graph Link

In [V. O. Manturov, An almost classification of free knots, Dokl. Math. 88(2) (2013) 556–558.] the second author constructed an invariant which in some sense generalizes the quantum [Formula: see text] link invariant of Kuperberg to the case of free links. In this paper, we generalize this construction to free graph-links. As a result, we obtain an invariant of free graph-links with values in linear combinations of graphs. The main property of this invariant is that under certain conditions on the representative of the free graph-link, we can recover this representative from the value invariant on it. In addition, this invariant allows one to partially classify free graph-links.

1-REGULAR CAYLEY GRAPHS OF VALENCY 7

2013 ◽  
Vol 88 (3) ◽  
pp. 479-485 ◽  
Author(s):  
JING JIAN LI ◽  
GENG RONG ZHANG ◽  
BO LING
Keyword(s):  
Cayley Graphs ◽  
Free Graph

AbstractA graph $\mit{\Gamma} $ is called $1$-regular if $ \mathsf{Aut} \mit{\Gamma} $ acts regularly on its arcs. In this paper, a classification of $1$-regular Cayley graphs of valency $7$ is given; in particular, it is proved that there is only one core-free graph up to isomorphism.

scholarly journals The rich frequency spectrum of the triple-mode variable AC And

2013 ◽  
Vol 9 (S301) ◽  
pp. 443-444
Author(s):  
Géza Kovács ◽  
Gáspár A. Bakos ◽  
Joel D. Hartman
Keyword(s):  
Fourier Analysis ◽  
Light Curve ◽  
Frequency Spectrum ◽  
Linear Combinations ◽  
Period Increase ◽  
Frequency Structure ◽  
The Rich ◽  
Triple Mode ◽  
Three Components

AbstractFourier analysis of the light curve of AC And from the HATNet database reveals the rich frequency structure of this object. Above 30 components are found down to the amplitude of 3 mmag. Several of these frequencies are not the linear combinations of the three basic components. We detect period increase in all three components that may lend support to the Population I classification of this variable.

Potentials and point symmetries of Klein–Gordon equations in space-time homogenous Gödel-type metrics

2017 ◽  
Vol 14 (05) ◽  
pp. 1750070 ◽  
Author(s):  
Sameerah Jamal
Keyword(s):  
Gordon Equation ◽  
Analytic Solutions ◽  
Space Time ◽  
Primary Sources ◽  
Linear Combinations ◽  
Invariant Functions ◽  
Group Invariant ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this paper, we study the geometric properties of generators for the Klein–Gordon equation on classes of space-time homogeneous Gödel-type metrics. Our analysis complements the study involving the “Symmetries of geodesic motion in Gödel-type spacetimes” by U. Camci (J. Cosmol. Astropart. Phys., doi: 10.1088/1475-7516/2014/07/002 ). These symmetries or Killing vectors (KVs) are used to construct potential functions admitted by the Klein–Gordon equation. The criteria for the potential function originates from three primary sources, viz. through generators that are identically the Killing algebra, or with the KV fields that are recast into linear combinations and third, real subalgebras within the Killing algebra. This leads to a classification of the [Formula: see text] Klein–Gordon equation according to the catalogue of infinitesimal Lie and Noether point symmetries admitted. A comprehensive list of group invariant functions is provided and their application to analytic solutions is discussed.

scholarly journals Property RD and the classification of traces on reduced group C∗-algebras of hyperbolic groups

2017 ◽  
Vol 09 (04) ◽  
pp. 707-716
Author(s):  
Sherry Gong
Keyword(s):  
Conjugacy Class ◽  
Hyperbolic Group ◽  
Hyperbolic Groups ◽  
Linear Combinations ◽  
Rapid Decay ◽  
C Algebras ◽  
Rapid Decay Property ◽  
Finite Conjugacy ◽  
Finite Conjugacy Class

In this paper, we show that if [Formula: see text] is a non-elementary word hyperbolic group, [Formula: see text] is an element, and the conjugacy class of [Formula: see text] is infinite, then all traces [Formula: see text] vanish on [Formula: see text]. Moreover, we completely classify all traces by showing that traces [Formula: see text] are linear combinations of traces [Formula: see text] given by [Formula: see text] where [Formula: see text] is an element with finite conjugacy class, denoted [Formula: see text]. We demonstrate these two statements by introducing a new method to study traces that uses Sobolev norms and the rapid decay property.

scholarly journals THE CONCEPT OF TECHNOLOGICAL ORDER AS THE MAIN DIRECTION OF THE THEORY OF LONG WAVES IN ECONOMY

2016 ◽  
Vol 2016 (5) ◽  
pp. 326-332
Author(s):  
Александр Таранов ◽  
Aleksandr Taranov
Keyword(s):  
Main Property ◽  
Long Waves ◽  
Technological Innovations ◽  
The Core ◽  
Technological Structure ◽  
Empirical Level ◽  
Key Factor ◽  
World Economic ◽  
Methodological Approaches

The article deals with the concept of technological order as urgent and empirically justified continuation of the known theory of long waves in economy. The theory of long waves allows to predict world economic crises and economic growth at the empirical level for 50 years. Genesis of long waves theory by means of retrospective author's classification of long waves theo-ries according to technological, economic, institutional, administrative and social features is analyzed. The main group of authors who have created modern and urgent theory of long waves checked by time and strengthened by empirical calculations is: N.D. Kon-dratiev, G. Mensh, J. Dosi, Sh. Perez, S.Yu. Glazyev. The academician Glazyev has formed the concept of the technological order which is empirically proved continuation of the long waves theory. In this concept the main statements-laws, and the need of methodological approaches for technological, economic, institutional, administrative and sociological areas are revealed. An obvious property of the technological coherence of productions is considered. The logic of formation and interaction of technological units is described in detail. The conclusions are drawn about the presence of technological order. The technological innovations defining the core formation of technological way and revolutionizing technological structure of economy have received the name "key factor". Such factor now and for the next 50 years is nanotechnologies. Conclusions are drawn concerning the main property of the technological order which is a self-reproducing integrity because of that technical development of economy is only possible by consecutive change of technological orders.

The valence bands in two-dimensional graphite

1955 ◽  
Vol 227 (1170) ◽  
pp. 330-349 ◽  
Keyword(s):  
Normal Structure ◽  
Theoretical Treatment ◽  
Two Dimensional ◽  
Linear Combinations ◽  
X Ray ◽  
Atomic Orbitals ◽  
Idempotent Operators ◽  
Valence Bands ◽  
The One

A group-theoretical treatment of the spatial symmetry of two-dimensional graphite leads to a classification of the one-electron eigenstates. The method of idempotent operators is used to derive Bloch orbitals for the crystal valence bands as linear combinations of the atomic orbitals 2 p x , 2 p y and 2 s . The functions 2 p z form the conduction band. The energy of the electrons in such orbitals is estimated in terms of four overlap integrals between nearest neighbour atoms, and four corresponding Hamiltonian integrals. The deduced band structure is not sensitive to the precise values of these integrals, and cannot be changed materially by the inclusion of further neighbours. The states form three touching bands, all fully occupied by electrons in the normal structure. The large band width of some 10 eV affects previous discussions of soft X-ray experiments.

BOUNDARY COMPONENT PRESERVING SYMMETRIES OF GRAPH LINK EXTERIORS

2011 ◽  
Vol 20 (12) ◽  
pp. 1669-1683
Author(s):  
TORU IKEDA
Keyword(s):  
Boundary Component ◽  
Complete Classification ◽  
Construction Method ◽  
Strong Inversion ◽  
Graph Link ◽  
Component Graph ◽  
Specific Construction

We consider a graph link L in S3 which admits a symmetry of the exterior given by a boundary component preserving periodic homeomorphism f (orientation-preserving or not). This paper shows that L is obtained by a specific construction method if f is not a strong inversion. As an application, we provide a complete classification of 2-component graph links with symmetries of the exteriors which are not extendable to symmetries of S3.

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.

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