Analytic Hopf Surfaces

1962 ◽  
Vol 14 ◽  
pp. 329-333 ◽  
Author(s):  
H. G. Helfenstein
Keyword(s):  
Analytic Manifold ◽  
Binary Composition ◽  
Complex Analytic Manifold ◽  
Image Position ◽  
Topological Concept

The topological concept of H-space (7) has an analytic counterpart which so far has not been considered in the literature. We define: A complex-analytic manifold S will be called an analytic H-space if it is capable of carrying a continuous binary compositionwith the following properties (i) and (ii).

scholarly journals A Note on Holomorphic Vector Bundles Over Quotient Manifolds With Respect to Nilpotent Groups

1972 ◽  
Vol 48 ◽  
pp. 183-188
Author(s):  
Hisasi Morikawa
Keyword(s):  
Vector Bundle ◽  
Endomorphism Ring ◽  
Vector Bundles ◽  
Holomorphic Vector Bundle ◽  
Nilpotent Groups ◽  
Projective Bundle ◽  
Analytic Manifold ◽  
Transition Functions ◽  
Holomorphic Vector Bundles ◽  
Complex Analytic Manifold

A holomorphic vector bundle E over a complex analytic manifold is said to be simple, if its global endomorphism ring Endc (E) is isomorphic to C. Projectifying the fibers of E, we get the associated projective bundle P(E) of E, If we can choose a system of constant transition functions of P(Exs), the projective bundle P(E) is said to be locally flat.

Topological H-Surfaces

1965 ◽  
Vol 17 ◽  
pp. 847-849 ◽  
Author(s):  
H. G. Helfenstein
Keyword(s):  
Topological Space ◽  
Binary Composition ◽  
Image Position

An H-space is a topological space T for which it is possible to define a continuous binary compositionwith the following properties: there exists a homotopy unit, i.e. an element u ∊ T such that

scholarly journals The Partition Function in the Four-Dimensional Schwarz-Type Topological Half-Flat Two-Form Gravity

1997 ◽  
Vol 12 (06) ◽  
pp. 381-392 ◽  
Author(s):  
Mitsuko Abe
Keyword(s):  
Partition Function ◽  
Gravity Model ◽  
Moduli Spaces ◽  
Partition Functions ◽  
K3 Surface ◽  
Analytic Manifold ◽  
Rham Complex ◽  
De Rham ◽  
Complex Analytic Manifold ◽  
Equivalent Class

We derive the partition functions of the Schwarz-type four-dimensional topological half-flat two-form gravity model on K3-surface or T4 up to on-shell one-loop corrections. In this model the bosonic moduli spaces describe an equivalent class of a trio of the Einstein–Kähler forms (the hyper-Kähler forms). The integrand of the partition function is represented by the product of some [Formula: see text]-torsions. [Formula: see text]-torsion is the extension of R-torsion for the de Rham complex to that for the [Formula: see text]-complex of a complex analytic manifold.

scholarly journals Duality, Quantum Mechanics and (Almost) Complex Manifolds

2003 ◽  
Vol 18 (28) ◽  
pp. 1975-1990 ◽  
Author(s):  
José M. Isidro
Keyword(s):  
Degrees Of Freedom ◽  
Complex Structure ◽  
Classical Mechanics ◽  
Quantum Mechanical ◽  
Complex Structures ◽  
Analytic Manifold ◽  
Duality Transformation ◽  
Almost Complex Manifolds ◽  
Almost Complex ◽  
Complex Analytic Manifold

The classical mechanics of a finite number of degrees of freedom requires a symplectic structure on phase space [Formula: see text], but it is independent of any complex structure. On the contrary, the quantum theory is intimately linked with the choice of a complex structure on [Formula: see text]. When the latter is a complex-analytic manifold admitting just one complex structure, there is a unique quantization whose classical limit is [Formula: see text]. Then the notion of coherence is the same for all observers. However, when [Formula: see text] admits two or more nonbiholomorphic complex structures, there is one different quantization per different complex structure on [Formula: see text]. The lack of analyticity in transforming between nonbiholomorphic complex structures can be interpreted as the loss of quantum-mechanical coherence under the corresponding transformation. Observers using one complex structure perceive as coherent the states that other observers, using a different complex structure, do not perceive as such. This is the notion of a quantum-mechanical duality transformation: the relativity of the notion of a quantum.

Simple Identification of Electron Diffraction Ring Patterns

1969 ◽  
Vol 27 ◽  
pp. 160-161
Author(s):  
Carolyn Nohr ◽  
Ann Ayres
Keyword(s):  
Electron Microscope ◽  
Electron Diffraction ◽  
Diffraction Ring ◽  
Image Position

Texts on electron diffraction recommend that the camera constant of the electron microscope be determine d by calibration with a standard crystalline specimen, using the equation

Atomic orientation effects in proton stopping at low velocity

1983 ◽  
Vol 41 ◽  
pp. 708-709
Author(s):  
Kin Lam
Keyword(s):  
Polycrystalline Material ◽  
Charged Particles ◽  
Target Material ◽  
Stopping Power ◽  
Low Velocity ◽  
Electronic Density ◽  
Interatomic Distances ◽  
Frame Work ◽  
Image Position ◽  
Atomic Orientation

The energy of moving ions in solid is dependent on the electronic density as well as the atomic structural properties of the target material. These factors contribute to the observable effects in polycrystalline material using the scanning ion microscope. Here we outline a method to investigate the dependence of low velocity proton stopping on interatomic distances and orientations.The interaction of charged particles with atoms in the frame work of the Fermi gas model was proposed by Lindhard. For a system of atoms, the electronic Lindhard stopping power can be generalized to the formwhere the stopping power function is defined as

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