scholarly journals Complex structures on real vector lattices

2016 ◽  
Vol 440 (2) ◽  
pp. 741-749
Author(s):  
Z.A. Kusraeva
Keyword(s):  
Complex Structures ◽  
Real Vector ◽  
Vector Lattices

scholarly journals Countable vector lattices

1974 ◽  
Vol 10 (3) ◽  
pp. 371-376 ◽  
Author(s):  
Paul F. Conrad
Keyword(s):  
Vector Space ◽  
Vector Lattice ◽  
Real Vector Space ◽  
Vector Spaces ◽  
Real Vector ◽  
Real Numbers ◽  
Vector Lattices ◽  
Direct Sum ◽  
Ordered Vector Spaces ◽  
Countable Dimension

In his paper “On the structure of ordered real vector spaces” (Publ. Math. Debrecen 4 (1955–56), 334–343), Erdös shows that a totally ordered real vector space of countable dimension is order isomorphic to a lexicographic direct sum of copies of the group of real numbers. Brown, in “Valued vector spaces of countable dimension” (Publ. Math. Debrecen 18 (1971), 149–151), extends the result to a valued vector space of countable dimension and greatly simplifies the proof. In this note it is shown that a finite valued vector lattice of countable dimension is order isomorphic to a direct sum of o–simple totally ordered vector spaces. One obtains as corollaries the result of Erdös and the applications that Brown makes to totally ordered spaces.

An unpleasant set in a non-locally-convex vector lattice

1973 ◽  
Vol 18 (3) ◽  
pp. 229-233
Author(s):  
J. D. Pryce
Keyword(s):  
Convex Hull ◽  
Vector Lattice ◽  
Linear Topological Space ◽  
Real Vector ◽  
Vector Lattices ◽  
Köthe Spaces ◽  
The Common ◽  
Solid Hull ◽  
Image Position ◽  
Locally Convex

In a linear topological space E one often carries out various “ smoothing ” operations on a subset A, such as taking the convex hull co A and the closure A-. If E is also a (real) vector lattice, the solid hullis also a natural “ smoothing out ” of A. If sol A = A then A is called solid, and if E has a base of solid neighbourhoods of 0 as do all the common topological vector lattices such as C(X), Lp, Köthe spaces and so on—then E is called a locally solid space.

Some Homological Pathology in Vector Lattices

1965 ◽  
Vol 17 ◽  
pp. 411-428 ◽  
Author(s):  
David M. Topping
Keyword(s):  
Chain Condition ◽  
Boolean Algebras ◽  
Real Vector ◽  
Linear Lattice ◽  
Free Objects ◽  
Vector Lattices ◽  
Countable Chain Condition ◽  
Projective Vector ◽  
Countable Chain ◽  
Lattice Homomorphisms

The purpose of this paper is to point out a number of curious phenomena in the category of (real) vector lattices and linear lattice homomorphisms. Birkhoff (3, p. 221, Ex. 2 and Problem 96) called attention to the question of constructing models of the free objects with more than one generator in this category, a problem recently solved by E. C. Weinberg (9). In §6 we construct a more manageable class of (non-free) projective vector lattices. Here, however, there is a countability restriction which suggests strong connections with free and projective Boolean algebras (in the category of Boolean algebras and their homomorphisms, such algebras must satisfy the countable chain condition (6)).

scholarly journals On almost complex structures from classical linear connections

2017 ◽  
Vol 71 (1) ◽  
pp. 55
Author(s):  
Jan Kurek ◽  
Włodzimierz M. Mikulski
Keyword(s):  
Vector Spaces ◽  
Complex Structures ◽  
Real Vector ◽  
Local Diffeomorphisms ◽  
Linear Connections ◽  
Almost Complex Structures ◽  
Linear Maps ◽  
Almost Complex ◽  
Natural Operators

Let \(\mathcal{M} f_m\) be the category of \(m\)-dimensional manifolds and local diffeomorphisms and  let \(T\) be the tangent functor on \(\mathcal{M} f_m\). Let \(\mathcal{V}\) be the category of real vector spaces and linear maps and let \(\mathcal{V}_m\) be the category of \(m\)-dimensional real vector spaces and linear isomorphisms. We characterize all regular covariant functors \(F:\mathcal{V}_m\to\mathcal{V}\) admitting \(\mathcal{M} f_m\)-natural operators \(\tilde J\) transforming classical linear connections \(\nabla\) on \(m\)-dimensional manifolds \(M\) into almost complex structures \(\tilde J(\nabla)\) on \(F(T)M=\bigcup_{x\in M}F(T_xM)\).

Cell morphology, volume, and surface area determinations from multilevel contouring within HVEM micrographs of serial sections and whole-cell mounts

1987 ◽  
Vol 45 ◽  
pp. 588-589
Author(s):  
M. Marko ◽  
A. Leith ◽  
D. Parsons
Keyword(s):  
Surface Area ◽  
Electron Micrographs ◽  
Cell Morphology ◽  
Individual Variation ◽  
Serial Section ◽  
Stereo Pair ◽  
Complex Structures ◽  
Serial Sections ◽  
Surface Areas ◽  
Computer Based

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.

Stereo modeling of HVEM specimens by serial tilting and computer graphics

1986 ◽  
Vol 44 ◽  
pp. 34-35
Author(s):  
J.R. McIntosh ◽  
D.L. Stemple ◽  
William Bishop ◽  
G.W. Hannaway
Keyword(s):  
Computer Graphics ◽  
Analytical Methods ◽  
Photographic Film ◽  
Complex Structures ◽  
Multiple Objects ◽  
Multiple Images ◽  
3 Dimensional

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.

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