Classification of Dq-equivariant gradient bifurcation problems

1993 ◽  
pp. 89-99
Author(s):  
Thomas J. Bridges ◽  
Jacques E. Furter
Keyword(s):  
Bifurcation Problems

scholarly journals NONDEGENERATE UMBILICS, THE PATH FORMULATION AND GRADIENT BIFURCATION PROBLEMS

2009 ◽  
Vol 19 (09) ◽  
pp. 2965-2977 ◽  
Author(s):  
JACQUES-ELIE FURTER ◽  
ANGELA MARIA SITTA
Keyword(s):  
Cylindrical Panel ◽  
Point Of View ◽  
Singular Behavior ◽  
Universal Unfolding ◽  
Buckling Modes ◽  
The Core ◽  
Bifurcation Problems ◽  
Multiparameter Bifurcation ◽  
Special Parameter

Parametrized contact-equivalence is a successful theory for the understanding and classification of the qualitative local behavior of bifurcation diagrams and their perturbations. Path formulation is an alternative point of view making explicit the singular behavior due to the core of the bifurcation germ (when the parameters vanish) from the effects of the way parameters enter. We show how to use path formulation to classify and structure efficiently multiparameter bifurcation problems in corank 2 problems. In particular, the nondegenerate umbilics singularities are the generic cores in four situations: the general or gradient problems, with or without ℤ2 symmetry where ℤ2 acts on the second component of ℝ2 via κ(x,y) = (x,-y). The universal unfolding of the umbilic singularities have an interesting "Russian doll" type of structure of miniversal unfoldings in all those categories. With the path formulation approach we can handle one, or more, parameter situations using the same framework. We can even consider some special parameter structure (for instance, some internal hierarchy of parameters). We classify the generic bifurcations with 1, 2 or 3 parameters that occur in those cases. Some results are known with one bifurcation parameter, but the others are new. We discuss some applications to the bifurcation of a loaded cylindrical panel. This problem has many natural parameters that provide concrete examples of our generic diagrams around the first interaction of the buckling modes.

scholarly journals Origin Preserving Path Formulation for Multiparameter ℤ2-Equivariant Corank 2 Bifurcation Problems

2020 ◽  
Vol 30 (09) ◽  
pp. 2050140
Author(s):  
Jacques-Elie Furter
Keyword(s):  
Singularity Theory ◽  
Cylindrical Panel ◽  
Qualitative Behavior ◽  
Partial Classification ◽  
Equivariant Bifurcation ◽  
Bifurcation Problems ◽  
Multiparameter Bifurcation ◽  
Generic Bifurcation ◽  
Minimal Modification

A singularity theory, in the form of path formulation, is developed to analyze and organize the qualitative behavior of multiparameter [Formula: see text]-equivariant bifurcation problems of corank 2 and their deformations when the trivial solution is preserved as parameters vary. Path formulation allows for an efficient discussion of different parameter structures with a minimal modification of the algebra between cases. We give a partial classification of one-parameter problems. With a couple of parameter hierarchies, we show that the generic bifurcation problems are 2-determined and of topological codimension-0. We also show that the preservation of the trivial solutions is an important hypotheses for multiparameter bifurcation problems. We apply our results to the bifurcation of a cylindrical panel under axial compression.

CHAOS IN CROSS-COUPLED BVP OSCILLATORS

2005 ◽  
Vol 15 (10) ◽  
pp. 3359-3366 ◽  
Author(s):  
TETSUSHI UETA ◽  
HIROSHI KAWAKAMI
Keyword(s):  
Periodic Solutions ◽  
Bifurcation Diagram ◽  
Coupled Oscillator ◽  
Chaotic Motions ◽  
Independent State ◽  
State Variable ◽  
Bifurcation Problems ◽  
The Cross

In this letter, we investigate the cross-coupled BVP oscillators. A single BVP oscillator has two terminals which can extract an independent state variable, so in the preceding works, several coupling systems have been studied. Synchronization modes and chaos in these systems are classified as results of bifurcation problems. We revisit a coupled oscillator, and clarify new results which have not been reported before, i.e. stable tori and its breakdown, and chaotic motions. Also classification of synchronized periodic solutions is done by a bifurcation diagram.

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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