scholarly journals Hodge numbers and invariant complex structures of compact nilmanifolds

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Takumi Yamada

AbstractIn this paper, we consider several invariant complex structures on a compact real nilmanifold, and we study relations between invariant complex structures and Hodge numbers.

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Takumi Yamada

AbstractIf N is a simply connected real nilpotent Lie group with a Γ-rational complex structure, where Γ is a lattice in N, then for each s, t.We study relations between invariant complex structures and Hodge numbers of compact nilmanifolds from a viewpoint of Lie algberas.


2017 ◽  
Vol 4 (1) ◽  
pp. 73-83
Author(s):  
Takumi Yamada

AbstractLet N be a simply connected real nilpotent Lie group, n its Lie algebra, and € a lattice in N. If a left-invariant complex structure on N is Γ-rational, then HƏ̄s,t(Γ/N) ≃ HƏ̄s,t(nC) for each s; t. We can construct different left-invariant complex structures on one nilpotent Lie group by using the complexification and the scalar restriction. We investigate relationships to Hodge numbers of associated compact complex nilmanifolds.


2000 ◽  
Vol 352 (12) ◽  
pp. 5405-5433 ◽  
Author(s):  
Luis A. Cordero ◽  
Marisa Fernández ◽  
Alfred Gray ◽  
Luis Ugarte

Author(s):  
M. Marko ◽  
A. Leith ◽  
D. Parsons

The use of serial sections and computer-based 3-D reconstruction techniques affords an opportunity not only to visualize the shape and distribution of the structures being studied, but also to determine their volumes and surface areas. Up until now, this has been done using serial ultrathin sections.The serial-section approach differs from the stereo logical methods of Weibel in that it is based on the Information from a set of single, complete cells (or organelles) rather than on a random 2-dimensional sampling of a population of cells. Because of this, it can more easily provide absolute values of volume and surface area, especially for highly-complex structures. It also allows study of individual variation among the cells, and study of structures which occur only infrequently.We have developed a system for 3-D reconstruction of objects from stereo-pair electron micrographs of thick specimens.


Author(s):  
J.R. McIntosh ◽  
D.L. Stemple ◽  
William Bishop ◽  
G.W. Hannaway

EM specimens often contain 3-dimensional information that is lost during micrography on a single photographic film. Two images of one specimen at appropriate orientations give a stereo view, but complex structures composed of multiple objects of graded density that superimpose in each projection are often difficult to decipher in stereo. Several analytical methods for 3-D reconstruction from multiple images of a serially tilted specimen are available, but they are all time-consuming and computationally intense.


Author(s):  
V. Serin ◽  
K. Hssein ◽  
G. Zanchi ◽  
J. Sévely

The present developments of electron energy analysis in the microscopes by E.E.L.S. allow an accurate recording of the spectra and of their different complex structures associated with the inner shell electron excitation by the incident electrons (1). Among these structures, the Extended Energy Loss Fine Structures (EXELFS) are of particular interest. They are equivalent to the well known EXAFS oscillations in X-ray absorption spectroscopy. Due to the EELS characteristic, the Fourier analysis of EXELFS oscillations appears as a promising technique for the characterization of composite materials, the major constituents of which are low Z elements. Using EXELFS, we have developed a microstructural study of carbon fibers. This analysis concerns the carbon K edge, which appears in the spectra at 285 eV. The purpose of the paper is to compare the local short range order, determined by this way in the case of Courtauld HTS and P100 ex-polyacrylonitrile carbon fibers, which are high tensile strength (HTS) and high modulus (HM) fibers respectively.


Author(s):  
S. E. Keckler ◽  
D. M. Dabbs ◽  
N. Yao ◽  
I. A. Aksay

Cellular organic structures such as wood can be used as scaffolds for the synthesis of complex structures of organic/ceramic nanocomposites. The wood cell is a fiber-reinforced resin composite of cellulose fibers in a lignin matrix. A single cell wall, containing several layers of different fiber orientations and lignin content, is separated from its neighboring wall by the middle lamella, a lignin-rich region. In order to achieve total mineralization, deposition on and in the cell wall must be achieved. Geological fossilization of wood occurs as permineralization (filling the void spaces with mineral) and petrifaction (mineralizing the cell wall as the organic component decays) through infiltration of wood with inorganics after growth. Conversely, living plants can incorporate inorganics into their cells and in some cases into the cell walls during growth. In a recent study, we mimicked geological fossilization by infiltrating inorganic precursors into wood cells in order to enhance the properties of wood. In the current work, we use electron microscopy to examine the structure of silica formed in the cell walls after infiltration of tetraethoxysilane (TEOS).


Author(s):  
P.M. Frederik ◽  
K.N.J. Burger ◽  
M.C.A. Stuart ◽  
A.J. Verkleij

Cellular membranes are often composed of phospholipid mixtures in which one or more components have a tendency to adopt a type II non-bilayer lipid structure such as the inverted hexagonal (H||) phase. The formation of a type II non-bilayer intermediate, the inverted lipid micel is proposed as the initial step in membrane fusion (Verkleij 1984, Siegel, 1986). In the various forms of cellular transport mediated by carrier vesicles (e.g. exocytosis, endocytosis) the regulation of membrane fusion, and hence of inverted lipid micel formation, is of vital importance.We studied the phase behaviour of simple and complex lipid mixtures by cryo-electron microscopy to gain more insight in the ultrastructure of different lipid phases (e.g. Pβ’, Lα, H||) and in the complex membrane structures arising after Lα < - > H|| phase changes (e.g. isotropic, cubic). To prepare hydrated thin films a 700 mesh hexagonal grid (without supporting film) was dipped into and withdrawn from a liposome suspension. The excess fluid was blotted against filter paper and the thin films that form between the bars of the specimen grid were immediately (within 1 second) vitrified by plunging of the carrier grids into ethane cooled to its melting point by liquid nitrogen (Dubochet et al., 1982). Surface active molecules such as phospholipids play an important role in the formation and thinning of these aqueous thin films (Frederik et al., 1989). The formation of two interfacial layers at the air-water interfaces requires transport of surface molecules from the suspension as well as the orientation of these molecules at the interfaces. During the spontaneous thinning of the film the interfaces approach each other, initially driven by capillary forces later by Van der Waals attraction. The process of thinning results in the sorting by size of the suspended material and is also accompanied by a loss of water from the thinner parts of the film. This loss of water may result in the concentration and eventually in partial dehydration of suspended material even if thin films are vitrified within 1 sec after their formation. Film formation and vitrification were initiated at temperatures between 20-60°C by placing die equipment in an incubator provided widi port holes for the necessary manipulations. Unilamellar vesicles were made from dipalmitoyl phosphatidyl choline (DPPC) by an extrusion method and showed a smooth (Lα) or a rippled (PB’.) structure depending on the temperature of the suspensions and the temperature of film formation (50°C resp. 39°C) prior to vitrification. The thermotropic phases of hydrated phospholipids are thus faithfully preserved in vitrified thin films (fig. a,b). Complex structures arose when mixtures of dioleoylphosphatidylethanol-amine (DOPE), dioleoylphosphatidylcholine (DOPC) and cholesterol (molar ratio 3/1/2) are heated and used for thin film formation. The tendency of DOPE to adopt the H|| phase is responsible for the formation of complex structures in this lipid mixture. Isotropic and cubic areas (fig. c,d) having a bilayer structure are found in coexistence with H|| cylinders (fig. e). The formation of interlamellar attachments (ILA’s) as observed in isotropic and cubic structures is also thought to be of importance in biological fusion events. Therefore the study of the fusion activity of influenza B virus with liposomes (DOPE/DOPC/cholesterol/ganglioside in a molar ratio 1/1/2/0.2) was initiated. At neutral pH only adsorption of virus to liposomes was observed whereas 2 minutes after a drop in pH (7.4 - > 5.4) fusion between virus and liposome membranes was demonstrated (fig. f). The micrographs illustrate the exciting potential of cryo-electron microscopy to study lipid-lipid and lipid-protein interactions in hydrated specimens.


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