scholarly journals Quasi-special Osserman manifolds

Filomat ◽  
2014 ◽  
Vol 28 (3) ◽  
pp. 623-633 ◽  
Author(s):  
Vladica Andrejic
Keyword(s):  
Curvature Tensor ◽  
Jacobi Operator ◽  
Duality Principle ◽  
Insight Into

In this paper we deal with a pseudo-Riemannian Osserman curvature tensor whose reduced Jacobi operator is diagonalizable with exactly two distinct eigenvalues. The main result gives new insight into the theory of the duality principle for pseudo-Riemannian Osserman manifolds. We concern with special Osserman curvature tensor and propose new ways to exclude some additional duality principle conditions from its definition.

scholarly journals On Lorentzian spaces of constant sectional curvature

2018 ◽  
Vol 103 (117) ◽  
pp. 7-15
Author(s):  
Vladica Andrejic
Keyword(s):  
Sectional Curvature ◽  
Curvature Tensor ◽  
Jacobi Operator ◽  
Constant Sectional Curvature ◽  
Duality Principle ◽  
Lorentzian Manifolds ◽  
Algebraic Curvature Tensor ◽  
Algebraic Curvature ◽  
Curvature Tensors

We investigate Osserman-like conditions for Lorentzian curvature tensors that imply constant sectional curvature. It is known that Osserman (moreover zwei-stein) Lorentzian manifolds have constant sectional curvature. We prove that some generalizations of the Rakic duality principle (Lorentzian totally Jacobi-dual or four-dimensional Lorentzian Jacobi-dual) imply constant sectional curvature. Moreover, any four-dimensional Jacobi-dual algebraic curvature tensor such that the Jacobi operator for some nonnull vector is diagonalizable, is Osserman. Additionally, any Lorentzian algebraic curvature tensor such that the reduced Jacobi operator for all nonnull vectors has a single eigenvalue has a constant sectional curvature.

scholarly journals On quasi-Clifford Osserman curvature tensors

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1241-1247
Author(s):  
Vladica Andrejic ◽  
Katarina Lukic
Keyword(s):  
Curvature Tensor ◽  
Sufficient Conditions ◽  
Duality Principle ◽  
Algebraic Curvature ◽  
Curvature Tensors

We consider pseudo-Riemannian generalizations of Osserman, Clifford, and the duality principle properties for algebraic curvature tensors and investigate relations between them. We introduce quasi- Clifford curvature tensors using a generalized Clifford family and show that they are Osserman. This allows us to discover an Osserman curvature tensor that does not satisfy the duality principle. We give some necessary and some sufficient conditions for the total duality principle.

scholarly journals CONFORMALLY OSSERMAN MANIFOLDS AND CONFORMALLY COMPLEX SPACE FORMS

2004 ◽  
Vol 01 (01n02) ◽  
pp. 97-106 ◽  
Author(s):  
N. BLAŽIĆ ◽  
P. GILKEY
Keyword(s):  
Curvature Tensor ◽  
Complex Space ◽  
Jacobi Operator ◽  
Space Forms ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Weyl Curvature Tensor ◽  
Complex Space Forms ◽  
Weyl Conformal Curvature Tensor ◽  
Complex Projective

We characterize manifolds which are locally conformally equivalent to either complex projective space or to its negative curvature dual in terms of their Weyl curvature tensor. As a byproduct of this investigation, we classify the conformally complex space forms if the dimension is at least 8. We also study when the Jacobi operator associated to the Weyl conformal curvature tensor of a Riemannian manifold has constant eigenvalues on the bundle of unit tangent vectors and classify such manifolds which are not conformally flat in dimensions congruent to 2 mod 4.

Calibration problems in hydrogen luminosities

1966 ◽  
Vol 24 ◽  
pp. 322-330
Author(s):  
A. Beer
Keyword(s):  
Galactic Structure ◽  
B Stars ◽  
Insight Into

The investigations which I should like to summarize in this paper concern recent photo-electric luminosity determinations of O and B stars. Their final aim has been the derivation of new stellar distances, and some insight into certain patterns of galactic structure.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

Skeletal elements of crinoid echinoderms: High-resolution structural and microanalytical results

1983 ◽  
Vol 41 ◽  
pp. 194-195
Author(s):  
D. F. Blake ◽  
L. F. Allard ◽  
D. R. Peacor
Keyword(s):  
High Resolution ◽  
Marine Invertebrates ◽  
Sea Urchins ◽  
Structural Features ◽  
Sea Stars ◽  
High Resolution Tem ◽  
Relationship Of ◽  
The Relationship ◽  
Insight Into

Echinodermata is a phylum of marine invertebrates which has been extant since Cambrian time (c.a. 500 m.y. before the present). Modern examples of echinoderms include sea urchins, sea stars, and sea lilies (crinoids). The endoskeletons of echinoderms are composed of plates or ossicles (Fig. 1) which are with few exceptions, porous, single crystals of high-magnesian calcite. Despite their single crystal nature, fracture surfaces do not exhibit the near-perfect {10.4} cleavage characteristic of inorganic calcite. This paradoxical mix of biogenic and inorganic features has prompted much recent work on echinoderm skeletal crystallography. Furthermore, fossil echinoderm hard parts comprise a volumetrically significant portion of some marine limestones sequences. The ultrastructural and microchemical characterization of modern skeletal material should lend insight into: 1). The nature of the biogenic processes involved, for example, the relationship of Mg heterogeneity to morphological and structural features in modern echinoderm material, and 2). The nature of the diagenetic changes undergone by their ancient, fossilized counterparts. In this study, high resolution TEM (HRTEM), high voltage TEM (HVTEM), and STEM microanalysis are used to characterize tha ultrastructural and microchemical composition of skeletal elements of the modern crinoid Neocrinus blakei.

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

Radiation Damage Studies with the HVEM

1972 ◽  
Vol 30 ◽  
pp. 680-681
Author(s):  
J. J. Laidler ◽  
B. Mastel
Keyword(s):  
Radiation Damage ◽  
Stainless Steels ◽  
Volume Expansion ◽  
Austenitic Stainless Steels ◽  
Test Facility ◽  
Fast Breeder Reactors ◽  
Breeder Reactors ◽  
Under Construction ◽  
Development Laboratory ◽  
Insight Into

One of the major materials problems encountered in the development of fast breeder reactors for commercial power generation is the phenomenon of swelling in core structural components and fuel cladding. This volume expansion, which is due to the retention of lattice vacancies by agglomeration into large polyhedral clusters (voids), may amount to ten percent or greater at goal fluences in some austenitic stainless steels. From a design standpoint, this is an undesirable situation, and it is necessary to obtain experimental confirmation that such excessive volume expansion will not occur in materials selected for core applications in the Fast Flux Test Facility, the prototypic LMFBR now under construction at the Hanford Engineering Development Laboratory (HEDL). The HEDL JEM-1000 1 MeV electron microscope is being used to provide an insight into trends of radiation damage accumulation in stainless steels, since it is possible to produce atom displacements at an accelerated rate with 1 MeV electrons, while the specimen is under continuous observation.

Failure Analysis With the Scanning Electron Microscope

1972 ◽  
Vol 30 ◽  
pp. 482-483
Author(s):  
John R. Devaney
Keyword(s):  
Electron Microscope ◽  
Scanning Electron Microscope ◽  
Integrated Circuits ◽  
Failure Analysis ◽  
High Reliability ◽  
Military Applications ◽  
Small Structure ◽  
Useful Life ◽  
Insight Into ◽  
Scanning Electron

Occasionally in history, an event may occur which has a profound influence on a technology. Such an event occurred when the scanning electron microscope became commercially available to industry in the mid 60's. Semiconductors were being increasingly used in high-reliability space and military applications both because of their small volume but, also, because of their inherent reliability. However, they did fail, both early in life and sometimes in middle or old age. Why they failed and how to prevent failure or prolong “useful life” was a worry which resulted in a blossoming of sophisticated failure analysis laboratories across the country. By 1966, the ability to build small structure integrated circuits was forging well ahead of techniques available to dissect and analyze these same failures. The arrival of the scanning electron microscope gave these analysts a new insight into failure mechanisms.

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