Analytic extension of holomorphic mappings and problems of holomorphic classification of multidimensional domains

The classical-quantum duality at the basis of quantum theory is here extended to the Planck scale domain. The classical/semiclassical gravity (G) domain is dual (in the precise sense of the classical-quantum duality) to the quantum (Q) elementary particle domain: [Formula: see text], [Formula: see text] being the Planck scale. This duality is universal. From the gravity (G) and quantum (Q) variables [Formula: see text], we define new quantum gravity (QG) variables [Formula: see text] which include all (classical, semiclassical and QG) domains passing through the Planck scale and the elementary particle domain. The QG variables are more complete than the usual ([Formula: see text], [Formula: see text]) ones which cover only one domain (Q or G). Two [Formula: see text] or [Formula: see text] values [Formula: see text] are needed for each value of [Formula: see text] (reflecting the two dual ways of reaching the Planck scale). We perform the complete analytic extension of the QG variables through analytic (holomorphic) mappings which preserve the light-cone structure. This allows us to reveal the classical-quantum duality of the Schwarzschild–Kruskal spacetime: exterior regions are classical or semiclassical while the interior is totally quantum: its boundaries being the Planck scale. Exterior and interior lose their difference near the horizon: four Planck scale hyperbolae border the horizons as a quantum dressing or width: “l’horizon habillé”. QG variables are naturally invariant under [Formula: see text]. Spacetime reflections, antipodal symmetry and PT or CPT symmetry are contained in the QG symmetry, which also shed insight on the global properties of the Kruskal manifold and its present renewed interest.

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

Symposium - International Astronomical Union ◽

10.1017/s0074180900053080 ◽

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.

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Diagnostic Value of Electron Microscopy in Soft Tissue Tumors

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100068096 ◽

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.)

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Ultrastructure of mesotheliomas

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100110775 ◽

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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