A Combinatorial Definition of Homotopy Groups

1958 ◽  
Vol 67 (2) ◽  
pp. 282 ◽  
Author(s):  
Daniel M. Kan
Keyword(s):  
Homotopy Groups ◽  
Definition Of

l′-Isolated Maps and Localizations

1983 ◽  
Vol 35 (2) ◽  
pp. 193-217
Author(s):  
Sara Hurvitz
Keyword(s):  
Finite Number ◽  
Free Algebra ◽  
Nilpotent Groups ◽  
Homotopy Groups ◽  
Homology Groups ◽  
Rational Cohomology ◽  
Locally Nilpotent Groups ◽  
Definition Of ◽  
Simply Connected ◽  
Path Connected

Let P be the set of primes, l ⊆ P a subset and l′ = P – l Recall that an H0-space is a space the rational cohomology of which is a free algebra.Cassidy and Hilton defined and investigated l′-isolated homomorphisms between locally nilpotent groups. Zabrodsky [8] showed that if X and Y are simply connected H0-spaces either with a finite number of homotopy groups or with a finite number of homology groups, then every rational equivalence f : X → Y can be decomposed into an l-equivalence and an l′-equivalence.In this paper we define and investigate l′-isolated maps between pointed spaces, which are of the homotopy type of path-connected nilpotent CW-complexes. Our definition of an l′-isolated map is analogous to the definition of an l′-isolated homomorphism. As every homomorphism can be decomposed into an l-isomorphism and an l′-isolated homomorphism, every map can be decomposed into an l-equivalence and an l′-isolated map.

scholarly journals Algebraic K-Theory of ∞-Operads

2014 ◽  
Vol 14 (3) ◽  
pp. 614-641 ◽  
Author(s):  
Thomas Nikolaus
Keyword(s):  
Homotopy Groups ◽  
Combinatorial Model ◽  
K Theory ◽  
Definition Of ◽  
Exact Sequences

AbstractThe theory of dendroidal sets has been developed to serve as a combinatorial model for homotopy coherent operads, see [MW07, CM13b]. An ∞-operad is a dendroidal setDsatisfying certain lifting conditions.In this paper we give a definition of K-groupsKn(D) for a dendroidal setD. These groups generalize the K-theory of symmetric monoidal (resp. permutative) categories and algebraic K-theory of rings. We establish some useful properties like invariance under the appropriate equivalences and long exact sequences which allow us to compute these groups in some examples. Using results from [Heu11b] and [BN12] we show that theK-theory groups ofDcan be realized as homotopy groups of a K-theory spectrum.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Symbiotic Stars at Optical, Infrared and Radio Wavelengths

1979 ◽  
Vol 46 ◽  
pp. 125-149 ◽  
Author(s):  
David A. Allen
Keyword(s):  
Temperature Regime ◽  
Type Star ◽  
Stellar Systems ◽  
Symbiotic Stars ◽  
Lower Excitation ◽  
Definition Of ◽  
Original Type

No paper of this nature should begin without a definition of symbiotic stars. It was Paul Merrill who, borrowing on his botanical background, coined the termsymbioticto describe apparently single stellar systems which combine the TiO absorption of M giants (temperature regime ≲ 3500 K) with He II emission (temperature regime ≳ 100,000 K). He and Milton Humason had in 1932 first drawn attention to three such stars: AX Per, CI Cyg and RW Hya. At the conclusion of the Mount Wilson Ha emission survey nearly a dozen had been identified, and Z And had become their type star. The numbers slowly grew, as much because the definition widened to include lower-excitation specimens as because new examples of the original type were found. In 1970 Wackerling listed 30; this was the last compendium of symbiotic stars published.

Immunoferritin localization of intracellular antigens in positively stained frozen sections

1978 ◽  
Vol 36 (2) ◽  
pp. 168-169
Author(s):  
K. T. Tokuyasu
Keyword(s):  
Surface Tension ◽  
Water Surface ◽  
Thin Layers ◽  
The Other ◽  
Positive Staining ◽  
Frozen Sections ◽  
The Past ◽  
Ultrathin Frozen Sections ◽  
Definition Of

During the past investigations of immunoferritin localization of intracellular antigens in ultrathin frozen sections, we found that the degree of negative staining required to delineate u1trastructural details was often too dense for the recognition of ferritin particles. The quality of positive staining of ultrathin frozen sections, on the other hand, has generally been far inferior to that attainable in conventional plastic embedded sections, particularly in the definition of membranes. As we discussed before, a main cause of this difficulty seemed to be the vulnerability of frozen sections to the damaging effects of air-water surface tension at the time of drying of the sections.Indeed, we found that the quality of positive staining is greatly improved when positively stained frozen sections are protected against the effects of surface tension by embedding them in thin layers of mechanically stable materials at the time of drying (unpublished).

Initial Polymerization Sites Indicated During Mitochondrial Oxidation of Diaminobenzidine after Toluene Treatment

1977 ◽  
Vol 35 ◽  
pp. 408-409
Author(s):  
W. A. Shannon ◽  
M. A. Matlib
Keyword(s):  
Membrane Permeability ◽  
Cytochrome Oxidase ◽  
Rat Liver ◽  
Precise Definition ◽  
Cytochemical Localization ◽  
Oxidative Reaction ◽  
Mitochondrial Oxidation ◽  
Definition Of ◽  
Exogenous Substrates

Numerous studies have dealt with the cytochemical localization of cytochrome oxidase via cytochrome c. More recent studies have dealt with indicating initial foci of this reaction by altering incubation pH (1) or postosmication procedure (2,3). The following study is an attempt to locate such foci by altering membrane permeability. It is thought that such alterations within the limits of maintaining morphological integrity of the membranes will ease the entry of exogenous substrates resulting in a much quicker oxidation and subsequently a more precise definition of the oxidative reaction.The diaminobenzidine (DAB) method of Seligman et al. (4) was used. Minced pieces of rat liver were incubated for 1 hr following toluene treatment (5,6). Experimental variations consisted of incubating fixed or unfixed tissues treated with toluene and unfixed tissues treated with toluene and subsequently fixed.

Application of Scanning Electron Microscopy to Medical Research

1969 ◽  
Vol 27 ◽  
pp. 12-13
Author(s):  
J. D. Hutchison
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Medical Research ◽  
Prosthetic Heart Valve ◽  
School Of Medicine ◽  
Transmission Electron ◽  
Definition Of ◽  
Mechanism Of Failure ◽  
The Brain ◽  
Scanning Electron

When the transmission electron microscope was commercially introduced a few years ago, it was heralded as one of the most significant aids to medical research of the century. It continues to occupy that niche; however, the scanning electron microscope is gaining rapidly in relative importance as it fills the gap between conventional optical microscopy and transmission electron microscopy.IBM Boulder is conducting three major programs in cooperation with the Colorado School of Medicine. These are the study of the mechanism of failure of the prosthetic heart valve, the study of the ultrastructure of lung tissue, and the definition of the function of the cilia of the ventricular ependyma of the brain.

Selection and Preparation of Specific Tissue Regions For Tem Using Large Epoxy-Embedded Blocks

1973 ◽  
Vol 31 ◽  
pp. 324-325 ◽  
Author(s):  
P. M. Lowrie ◽  
W. S. Tyler
Keyword(s):  
Electron Microscopy ◽  
Anatomical Structures ◽  
Ultrastructural Studies ◽  
Transmission Electron ◽  
Microscopic Evaluation ◽  
Embedded Blocks ◽  
Specific Tissue ◽  
Definition Of ◽  
Areas Of Interest ◽  
Selection Of

The importance of examining stained 1 to 2μ plastic sections by light microscopy has long been recognized, both for increased definition of many histologic features and for selection of specimen samples to be used in ultrastructural studies. Selection of specimens with specific orien ation relative to anatomical structures becomes of critical importance in ultrastructural investigations of organs such as the lung. The uantity of blocks necessary to locate special areas of interest by random sampling is large, however, and the method is lacking in precision. Several methods have been described for selection of specific areas for electron microscopy using light microscopic evaluation of paraffin, epoxy-infiltrated, or epoxy-embedded large blocks from which thick sections were cut. Selected areas from these thick sections were subsequently removed and re-embedded or attached to blank precasted blocks and resectioned for transmission electron microscopy (TEM).

Transmission electron microscopy of composite materials

1988 ◽  
Vol 46 ◽  
pp. 1012-1015
Author(s):  
K.P.D. Lagerlof
Keyword(s):  
Composite Materials ◽  
Physical Properties ◽  
Structural Defects ◽  
Structural Composites ◽  
Multiphase Materials ◽  
Structural Reinforcement ◽  
Transmission Electron ◽  
Reinforced Fiber ◽  
Particulate Reinforced Composites ◽  
Definition Of

Although most materials contain more than one phase, and thus are multiphase materials, the definition of composite materials is commonly used to describe those materials containing more than one phase deliberately added to obtain certain desired physical properties. Composite materials are often classified according to their application, i.e. structural composites and electronic composites, but may also be classified according to the type of compounds making up the composite, i.e. metal/ceramic, ceramic/ceramie and metal/semiconductor composites. For structural composites it is also common to refer to the type of structural reinforcement; whisker-reinforced, fiber-reinforced, or particulate reinforced composites [1-4].For all types of composite materials, it is of fundamental importance to understand the relationship between the microstructure and the observed physical properties, and it is therefore vital to properly characterize the microstructure. The interfaces separating the different phases comprising the composite are of particular interest to understand. In structural composites the interface is often the weakest part, where fracture will nucleate, and in electronic composites structural defects at or near the interface will affect the critical electronic properties.

Sign in / Sign up

Export Citation Format

Share Document