scholarly journals Some cross-section theorems on the tangent bundle over a finslerian manifold

1972 ◽  
Vol 92 (1) ◽  
Author(s):  
Tanjiro Okubo ◽  
C. S. Houh
Keyword(s):  
Cross Section ◽  
Tangent Bundle ◽  
Finslerian Manifold

XXII.—Tensor Fields and Connections on Cross-Sections in the tangent bundle of a differentiable manifold

1967 ◽  
Vol 67 (4) ◽  
pp. 277-288
Author(s):  
Kentaro Yano
Keyword(s):  
Vector Field ◽  
Cross Section ◽  
Tangent Bundle ◽  
Complex Structure ◽  
Linear Connection ◽  
Differentiable Manifold ◽  
Tensor Fields ◽  
Linear Connections ◽  
Almost Complex ◽  
The Cross

SynopsisTensor fields and linear connections in an n-dimensional differentiable manifold M can be extended, in a natural way, to the tangent bundle T(M) of M to give tensor fields of the same type and linear connections in T(M) respectively. We call such extensions complete lifts to T(M) of tensor fields and linear connections in M.On the other hand, when a vector field V is given in M, V determines a cross-section which is an n-dimensional submanifold in the 2n-dimensional tangent bundle T(M).We study first the behaviour of complete lifts of tensor fields on such a cross-section. The complete lift of an almost complex structure being again an almost complex structure, we study especially properties of the cross-section as a submanifold in an almost complex manifold.We also study properties of cross-sections with respect to the linear connection which is the complete lift of a linear connection in M and with respect to the linear connection induced by the latter on the cross-section. To quote a typical result: A necessary and sufficient condition for a cross-section to be totally geodesic is that the vector field V in M defining the cross-section in T(M) be an affine Killing vector field in M.

scholarly journals The backward continued fraction map and geodesic flow

1984 ◽  
Vol 4 (4) ◽  
pp. 487-492 ◽  
Author(s):  
Roy L. Adler ◽  
Leopold Flatto
Keyword(s):  
Cross Section ◽  
Tangent Bundle ◽  
Geodesic Flow ◽  
Continued Fraction ◽  
Fractional Part ◽  
Unit Interval ◽  
Modular Surface ◽  
Alternative Derivation ◽  
Unit Tangent Bundle ◽  
Factor Map

AbstractThe ‘backward continued fraction’ map studied by A. Reyni is defined by y = g(x) where g(x) equals the fractional part of 1/(1−x) for 0 < x < 1. We show that it is a factor map of a special cross-section map for the geodesic flow on the unit tangent bundle of the modular surface. This gives an alternative derivation of the fact that this map preserves the infinite measure dx/x on the unit interval.

XUV Absorption Spectra of Carbon Ions

1988 ◽  
Vol 102 ◽  
pp. 71-73
Author(s):  
E. Jannitti ◽  
P. Nicolosi ◽  
G. Tondello
Keyword(s):  
Absorption Spectra ◽  
Cross Section ◽  
Theoretical Calculations ◽  
Photoionization Cross Section ◽  
Carbon Ions

AbstractThe photoabsorption spectra of the carbon ions have been obtained by using two laser-produced plasmas. The photoionization cross-section of the CV has been absolutely measured and the value at threshold, σ=(4.7±0.5) × 10−19cm2, as well as its behaviour at higher energies agrees quite well with the theoretical calculations.

Elastic Scattering in Electron Microscopy

1973 ◽  
Vol 31 ◽  
pp. 252-253
Author(s):  
J. Langmore ◽  
M. Isaacson ◽  
J. Wall ◽  
A. V. Crewe
Keyword(s):  
Electron Microscopy ◽  
Elastic Scattering ◽  
Cross Section ◽  
Quantum Noise ◽  
Dark Field ◽  
Elastic Cross Section ◽  
Biological Molecules ◽  
Dark Field Microscopy ◽  
Field Systems ◽  
Effects Of Radiation

High resolution dark field microscopy is becoming an important tool for the investigation of unstained and specifically stained biological molecules. Of primary consideration to the microscopist is the interpretation of image Intensities and the effects of radiation damage to the specimen. Ignoring inelastic scattering, the image intensity is directly related to the collected elastic scattering cross section, σɳ, which is the product of the total elastic cross section, σ and the eficiency of the microscope system at imaging these electrons, η. The number of potentially bond damaging events resulting from the beam exposure required to reduce the effect of quantum noise in the image to a given level is proportional to 1/η. We wish to compare η in three dark field systems.

A New Approach to the Demonstration of Oxidase-Localization Using Tannic Acid Or Catechin

1973 ◽  
Vol 31 ◽  
pp. 698-699
Author(s):  
V. Mizuhira ◽  
Y. Futaesaku
Keyword(s):  
Cross Section ◽  
Tannic Acid ◽  
Elastic Fiber ◽  
The Other ◽  
New Approach ◽  
Tissue Block ◽  
Active Reaction ◽  
The Cross

Previously we reported that tannic acid is a very effective fixative for proteins including polypeptides. Especially, in the cross section of microtubules, thirteen submits in A-tubule and eleven in B-tubule could be observed very clearly. An elastic fiber could be demonstrated very clearly, as an electron opaque, homogeneous fiber. However, tannic acid did not penetrate into the deep portion of the tissue-block. So we tried Catechin. This shows almost the same chemical natures as that of proteins, as tannic acid. Moreover, we thought that catechin should have two active-reaction sites, one is phenol,and the other is catechole. Catechole site should react with osmium, to make Os- black. Phenol-site should react with peroxidase existing perhydroxide.

Electron Irradiation Effects in Polyoxymethylene Crystals Grown Inside Trioxane Crystals

1971 ◽  
Vol 29 ◽  
pp. 78-79
Author(s):  
J. P. Colson ◽  
D. H. Reneker
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Detailed Examination ◽  
The Other ◽  
Electron Micrograph ◽  
Irradiation Effects ◽  
Threefold Axis ◽  
Typical Sample ◽  
Polymer Crystals ◽  
Chain Axis

Polyoxymethylene (POM) crystals grow inside trioxane crystals which have been irradiated and heated to a temperature slightly below their melting point. Figure 1 shows a low magnification electron micrograph of a group of such POM crystals. Detailed examination at higher magnification showed that three distinct types of POM crystals grew in a typical sample. The three types of POM crystals were distinguished by the direction that the polymer chain axis in each crystal made with respect to the threefold axis of the trioxane crystal. These polyoxymethylene crystals were described previously.At low magnifications the three types of polymer crystals appeared as slender rods. One type had a hexagonal cross section and the other two types had rectangular cross sections, that is, they were ribbonlike.

Freeze-Fracture Replication of Frozen Outer Segments of Rat Retinal Rods

1969 ◽  
Vol 27 ◽  
pp. 392-393
Author(s):  
Thomas S. Leeson ◽  
C. Roland Leeson
Keyword(s):  
Electron Microscopy ◽  
Cross Section ◽  
Outer Segment ◽  
Freeze Fracture ◽  
X Ray Diffraction ◽  
X Ray ◽  
Outer Segments ◽  
Retinal Rods ◽  
Temperature Electron ◽  
Freeze Etching

Numerous previous studies of outer segments of retinal receptors have demonstrated a complex internal structure of a series of transversely orientated membranous lamellae, discs, or saccules. In cones, these lamellae probably are invaginations of the covering plasma membrane. In rods, however, they appear to be isolated and separate discs although some authors report interconnections and some continuities with the surface near the base of the outer segment, i.e. toward the inner segment. In some species, variations have been reported, such as longitudinally orientated lamellae and lamellar whorls. In cross section, the discs or saccules show one or more incisures. The saccules probably contain photolabile pigment, with resulting potentials after dipole formation during bleaching of pigment. Continuity between the lamina of rod saccules and extracellular space may be necessary for the detection of dipoles, although such continuity usually is not found by electron microscopy. Particles on the membranes have been found by low angle X-ray diffraction, by low temperature electron microscopy and by freeze-etching techniques.

A quantitative approach to inner shell losses

1978 ◽  
Vol 36 (1) ◽  
pp. 526-527 ◽  
Author(s):  
R.D. Leapman ◽  
P. Rez ◽  
D.F. Mayers
Keyword(s):  
Energy Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Accurate Determination ◽  
Background Intensity ◽  
Core Excitation ◽  
Quantitative Basis ◽  
Cross Section Differential ◽  
Bound Electrons

Microanalysis by EELS has been developing rapidly and though the general form of the spectrum is now understood there is a need to put the technique on a more quantitative basis (1,2). Certain aspects important for microanalysis include: (i) accurate determination of the partial cross sections, σx(α,ΔE) for core excitation when scattering lies inside collection angle a and energy range ΔE above the edge, (ii) behavior of the background intensity due to excitation of less strongly bound electrons, necessary for extrapolation beneath the signal of interest, (iii) departures from the simple hydrogenic K-edge seen in L and M losses, effecting σx and complicating microanalysis. Such problems might be approached empirically but here we describe how computation can elucidate the spectrum shape.The inelastic cross section differential with respect to energy transfer E and momentum transfer q for electrons of energy E0 and velocity v can be written as

Oxygen K near edge structures studied with multiple scattering calculations

1988 ◽  
Vol 46 ◽  
pp. 504-505
Author(s):  
Xudong Weng ◽  
Peter Rez
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Partial Cross Section ◽  
Energy Window ◽  
Edge Structure ◽  
Fine Structures ◽  
Hydrogenic Model ◽  
Electron Energy Loss ◽  
Quantitative Chemical

In electron energy loss spectroscopy, quantitative chemical microanalysis is performed by comparison of the intensity under a specific inner shell edge with the corresponding partial cross section. There are two commonly used models for calculations of atomic partial cross sections, the hydrogenic model and the Hartree-Slater model. Partial cross sections could also be measured from standards of known compositions. These partial cross sections are complicated by variations in the edge shapes, such as the near edge structure (ELNES) and extended fine structures (ELEXFS). The role of these solid state effects in the partial cross sections, and the transferability of the partial cross sections from material to material, has yet to be fully explored. In this work, we consider the oxygen K edge in several oxides as oxygen is present in many materials. Since the energy window of interest is in the range of 20-100 eV, we limit ourselves to the near edge structures.

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