scholarly journals Minimum numbers and Wecken theorems in topological coincidence theory. I

2011 ◽  
Vol 10 (1) ◽  
pp. 3-36 ◽  
Author(s):  
Ulrich Koschorke
Keyword(s):  
Coincidence Theory ◽  
Minimum Numbers

scholarly journals FIXED POINTS AND COINCIDENCES IN TORUS BUNDLES

2011 ◽  
Vol 03 (02) ◽  
pp. 177-212 ◽  
Author(s):  
ULRICH KOSCHORKE
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Careful Analysis ◽  
Natural Generalization ◽  
Homotopy Classes ◽  
Nielsen Numbers ◽  
Coincidence Theory ◽  
Torus Bundles ◽  
Odd Order ◽  
Minimum Numbers

Minimum numbers of fixed points or of coincidence components (realized by maps in given homotopy classes) are the principal objects of study in topological fixed point and coincidence theory. In this paper, we investigate fiberwise analoga and present a general approach e.g. to the question when two maps can be deformed until they are coincidence free. Our method involves normal bordism theory, a certain pathspace EB and a natural generalization of Nielsen numbers. As an illustration we determine the minimum numbers for all maps between torus bundles of arbitrary (possibly different) dimensions over spheres and, in particular, over the unit circle. Our results are based on a careful analysis of the geometry of generic coincidence manifolds. They also allow a simple algebraic description in terms of the Reidemeister invariant (a certain selfmap of an abelian group) and its orbit behavior (e.g. the number of odd order orbits which capture certain nonorientability phenomena). We carry out several explicit sample computations, e.g. for fixed points in (S1)2-bundles. In particular, we obtain existence criteria for fixed point free fiberwise maps.

scholarly journals Microsatellite and Chromosome Evolution of Parthenogenetic Sitobion Aphids in Australia

Genetics ◽  
1996 ◽  
Vol 144 (2) ◽  
pp. 747-756 ◽  
Author(s):  
Paul Sunnucks ◽  
Phillip R England ◽  
Andrea C Taylor ◽  
Dinah F Hales
Keyword(s):  
Sexual Reproduction ◽  
Chromosome Evolution ◽  
Genetic Recombination ◽  
Allelic Variation ◽  
Repeat Unit ◽  
Chromosomal Evolution ◽  
Microsatellite Variation ◽  
Wide Range ◽  
Sexual Recombination ◽  
Minimum Numbers

Abstract Single-locus microsatellite variation correlated perfectly with chromosome number in Sitobion miscanthi aphids. The microsatellites were highly heterozygous, with up to 10 alleles per locus in this species. Despite this considerable allelic variation, only seven different S. miscanthi genotypes were discovered in 555 individuals collected from a wide range of locations, hosts and sampling periods. Relatedness between genotypes suggests only two successful colonizations of Australia. There was no evidence for genetic recombination in 555 S. miscanthi so the occurrence of recent sexual reproduction must be near zero. Thus diversification is by mutation and chromosomal rearrangement alone. Since the aphids showed no sexual recombination, microsatellites can mutate without meiosis. Five of seven microsatellite differences were a single repeat unit, and one larger jump is likely. The minimum numbers of changes between karyotypes corresponded roughly one-to-one with microsatellite allele changes, which suggests very rapid chromosomal evolution. A chromosomal fission occurred in a cultured line, and a previously unknown chromosomal race was detected. All 121 diverse S. near fragariae were heterozygous but revealed only one genotype. This species too must have a low rate of sexual reproduction and few colonizations of Australia.

Yeasts isolated from the South Saskatchewan, a polluted river

1970 ◽  
Vol 16 (11) ◽  
pp. 1051-1057 ◽  
Author(s):  
J. F. T. Spencer ◽  
P. A. J. Gorin ◽  
N. R. Gardner
Keyword(s):  
Magnetic Resonance ◽  
The South ◽  
Polluted River ◽  
Sewage System ◽  
Minimum Numbers ◽  
The City ◽  
Magnetic Resonance Spectra

Minimum numbers of yeasts isolated from the Saskatchewan River in the summers of 1964 and 1965 ranged from 400 to 500 cells/liter upstream from the city of Saskatoon, to 4600 cells/liter immediately downstream. In the summer of 1968, a period of extremely low water, the counts were 150 cells/liter upstream from the city and 30 000 cells/liter downstream.Proton magnetic resonance spectra of the mannose-containing polysaccharides from representative cultures of the different species isolated were used as an aid in classification. Most of the species were asporogenous, and included representatives of the genera Candida, Trichosporon, Rhodotorula, Torulopsis, and Cryptococcus. Some species of Pichia, Saccharomyces, and Debaryomyces were isolated. The yeasts were mostly introduced into the river with the effluent from the Saskatoon sewage system.

scholarly journals Car Scrap Yards Network in Slovakia

ECONOMICS ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 51-59
Author(s):  
Juraj Pekár ◽  
Ivan Brezina ◽  
Zuzana Čičková
Keyword(s):  
Allocation Problem ◽  
Specific Location ◽  
Location Allocation ◽  
Minimum Numbers ◽  
Location Allocation Problem

Abstract The paper is focused on specific location-allocation problem aimed to determine a set of scrap yards for vehicle decommissioning in Slovakia. The goal is to determine scrap yards network so that it is not prohibitive to pass old car for dismantling and further processing wherever former owner lives. Two approaches are considered. Once we consider the case when it is necessary to construct a completely new network of scrap yards, which results to setting of their minimum numbers and also their location. In the latter case, the already existing network of scrap yards is considered, while the model provides its extension, in order to achieve the desired values of accessibility for all residents. The results were applied to an existing network of scrap yards identifying locations to build new scrap yards. Areas where whole new network of scrap yards must be built were also identified.

scholarly journals Synchronization and Bursting Activity in the Model for Two Predator-Prey Systems Coupled By Predator Migration

2019 ◽  
Vol 14 (2) ◽  
pp. 588-611
Author(s):  
M.P. Kulakov ◽  
E.V. Kurilova ◽  
E.Ya. Frisman
Keyword(s):  
Phase Synchronization ◽  
Oscillation Period ◽  
Logistic Growth ◽  
Predator Prey ◽  
Different Types ◽  
The Difference ◽  
Minimum Numbers ◽  
Fast Oscillations ◽  
Bursting Activity ◽  
Type Ii Functional Response

The papers is devoted to a model for two non-identical predator-prey communities coupled by migration and characterized by logistic growth of prey and Holling type II functional response. The coupling is a predator migration at constant weak rate. The non-identity is the difference in the prey growth rates or predator mortalities in each patch. We studied the equilibrium states of model and scenarios of loss of their stability and emerge of complex periodic solutions. It was shown that in some domains of the parameter space there is a bursting activity which are that the dynamics of two communities contain segments of slowly resting dynamic (as part of a fast-slow cycle or canard) and regular bursts of spikes. In the resting part, the dynamics of the second community, as a rule, follow the slow changes in the first community, i.e. the dynamics in different patches are synchronous. But in the fast part there is only phase synchronization between the fast-slow cycle in first patch and bursts in second. We classified the scenarios of transition between different types of bursting activity by location spiking manifold and canard. These types differ not so much in size, shape or numbers of spikes as in the order of bursts emerge relative a slow-fast cycle. In a typical case the start of burst (divergent fast oscillations) coincides with the minimum numbers or quasi-extinction of prey in the first patch. After a rapid increase in the prey number in the first patch, diverging fluctuations give way to damped in the second patch. Such dynamics correspond to the rhombus-wave shape of spikes cluster. Another case is interesting, when the burst of spikes is formed after the full recovery of prey and with a certain predator number in the first patch. In this case, the spikes cluster takes the shape of a triangle-wave or a truncated rhombus-wave. It was shown that transitions between these types of bursts are accompanied by a change in the oscillation period and the degree of synchronization. Triangular-wave bursters correspond to complete synchronization of the predator dynamics in the resting part and rhomboid-wave correspond to antiphase synchronization. In the fast part with many spikes, communities are completely asynchronous to each other.

scholarly journals A Topological Coincidence Theory for Multifunctions via Homotopy

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 427
Author(s):  
Donal O’Regan
Keyword(s):  
Simple Result ◽  
Coincidence Theory ◽  
Transversality Theorem

A new simple result is presented which immediately yields the topological transversality theorem for coincidences.

scholarly journals National mapping and estimation of forest area by dominant tree species using Sentinel-2 data

2020 ◽  
Author(s):  
Johannes Breidenbach ◽  
Lars T. Waser ◽  
Misganu Debella-Gilo ◽  
Johannes Schumacher ◽  
Johannes Rahlf ◽  
...  
Keyword(s):  
Tree Species ◽  
Deciduous Forest ◽  
National Level ◽  
National Forest Inventory ◽  
Forest Area ◽  
Forest Resource ◽  
Species Specific ◽  
Minimum Numbers ◽  
Generate Model ◽  
Sentinel 2

Nation-wide Sentinel-2 mosaics were used with National Forest Inventory (NFI) plot data for modelling and subsequent mapping of spruce-, pine- and deciduous-dominated forest in Norway at a 16m×16m resolution. The accuracies of the best model ranged between 74% for spruce and 87% for deciduous forest. An overall accuracy of 90% was found on stand level using independent data from more than 42,000 stands. Errors mostly resulting from a forest mask reduced the model accuracies by approximately 10%. The produced map was subsequently used to generate model-assisted (MA) and post stratified (PS) estimates of species-specific forest area. At the national level, efficiencies of the estimates increased by 20% to 50% for MA and up to 90% for PS. Greater minimum numbers of observations constrained the use of PS. For MA estimates of municipalities, efficiencies improved by up to a factor of 8 but were sometimes also less than 1. PS estimates were always equally as or more precise than direct and MA estimates but were applicable in fewer municipalities. The tree species prediction map is part of the Norwegian forest resource map and is used, among others, to improve maps of other variables of interest such as timber volume and biomass.

Minimum numbers

The Knee ◽  
2020 ◽  
Vol 27 (5) ◽  
pp. 1688-1689
Author(s):  
P. Hopgood ◽  
J. Miles ◽  
R. Carrington
Keyword(s):  
Minimum Numbers
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