For an inverse sequence on 0,1 with interval-valued functions, we establish necessary conditions on the bonding functions for chainability of the inverse limit space. We also characterize ...chainability of the inverse limit in this setting in terms of properties of the bonding functions fi and the induced functions Fn:0,1→G′(f1,…,fn−1). The properties, in both cases, are related to how triods arise in the partial graphs associated with the inverse sequence when each graph G(fi) is chainable.
For an inverse sequence on 0,1 with interval-valued functions, it is shown that chainability of the graphs of the bonding functions, and chainability of the partial graphs associated with the inverse ...sequence are necessary conditions for an atriodic tree-like inverse limit. An analogous result is proved for inverse sequences with functions fi where each fi−1 is interval-valued. It follows that non-chainable, atriodic tree-like continua cannot be realized as inverse limits on 0,1 with functions from either of these subclasses of set-valued functions.
Let X be a metric continuum. For each positive integer n, we denote by 2X and Fn(X) the hyperspaces of all nonempty closed subsets of X and of all nonempty subsets of X with at most n points. A mean ...for X is a retraction r:F2(X)→F1(X). It is known that continua of type N do not admit means and it is an open question if this result can be extended to continua (or dendroids) of generalized type N. In 2012, F. Capulín, F. Orozco-Zitli and I. Puga gave an alternative definition of continuum of generalized type N (which we call COP-generalized type N) because apparently the previous definition was inadequate. Each continuum of COP-generalized type N is of generalized type N. In this paper, we present a dendroid of generalized type N admitting a mean. We also prove the non-existence of means for the most natural dendroids of generalized type N with a simple triod as limit; including the most natural dendroid of COP-generalized type N with a simple triod as limit. Finally, we show a contractible, non-selectible planar dendroid X which admits a retraction r:2X→F1(X) and, in consequence, it admits a mean.
The function ω ƒ on simple n-ods Vidal-Escobar, Ivon; Garcia-Ferreira, Salvador
Applied general topology,
10/2019, Letnik:
20, Številka:
2
Journal Article
Recenzirano
Odprti dostop
Given a discrete dynamical system (X, ƒ), we consider the function ωƒ-limit set from X to 2x asωƒ(x) = {y ∈ X : there exists a sequence of positive integers
n1 < n2 < … such that limk→∞ ƒnk (x) = ...y},for each x ∈ X. In the article 1, A. M. Bruckner and J. Ceder established several conditions which are equivalent to the continuity of the function ωƒ where ƒ: 0,1 → 0,1 is continuous surjection. It is natural to ask whether or not some results of 1 can be extended to finite graphs. In this direction, we study the function ωƒ when the phase space is a n-od simple T. We prove that if ωƒ is a continuous map, then Fix(ƒ2) and Fix(ƒ3) are connected sets. We will provide examples to show that the inverse implication fails when the phase space is a simple triod. However, we will prove that:Theorem A 2. If ƒ: T → T is a continuous function where T is a simple triod then ωƒ is a continuous set valued function iff the family {ƒ0, ƒ1, ƒ2,} is equicontinuous.As a consequence of our results concerning the ωƒ function on the simple triod, we obtain the following characterization of the unit interval.Theorem A 1. Let G be a finite graph. Then G is an arc iff for each continuous function ƒ: G → G the following conditions are equivalent:
(1) The function ωƒ is continuous.
(2) The set of all fixed points of ƒ2 is nonempty and connected.
The structure of Whitney blocks Aguilera, Maria Elena; Illanes, Alejandro
Topology and its applications,
06/2016, Letnik:
206
Journal Article
Recenzirano
Odprti dostop
Let X be a metric continuum and C(X) the hyperspace of subcontinua of X. A Whitney block is a set of the form μ−1(s,t), where μ:C(X)→0,1 is a Whitney map and 0≤s<t<1. In this paper we study continua ...for which Whitney blocks are homeomorphic to X×0,1. We characterize an arc, a simple closed curve and simple n-ods in terms of Whitney blocks. We also show that if X is arc-like, then each Whitney block for C(X) is 2-cell-like; and if X is circle-like, then each Whitney block of the form μ−1(0,t) is ring-like.
To deeply understand neuromorphic electronic systems,a basic chemical synapse model is given by logistic Euler inverse mapping and transformation in tandem,3T-MOS triod-trigger-topology（3T3） is ...designed in sub-threshold region at 100 mV supply for compact synaptic circuit,and the power consumption of synapse in brain-circuitry（ion-bump-city） is compared with its five mimic blocks of HfOx/AlOx typed memristor,modified 2T-MOS-K＋-bump circuit,3T3 synaptic circuit and 4T-Schmitt-oscillator based synaptic circuit,and Chua＇s circuit on Power-delay-products＇（PDP） levels.Above works will match searching for novel feature operators during pushing forward brain health microelectronics.
Nuclear detection in embryos is an indispensable process for quantitative analysis of the development of multicellular organisms. Due to the overlap in the distribution of pixel intensity of nuclear ...and cytoplasmic regions and the large variation of pixel intensity even within the same type of cellular components in different embryos, it is difficult to separate nuclear regions from the surrounding cytoplasmic region in differential interference contrast (DIC) microscope image. This study explores a discriminative representation of a local patch around a fixed pixel, called top-ranked intensity-ordered descriptor (TRIOD), which is prospected to distinguish the smoothed texture in the nucleus from the irregular texture in cytoplasm containing yolk granules. Then, a probability process is employed to model nuclear TRIOD prototypes, and the enhanced nuclear probability map can be constructed with the TRIODs of all pixels in a DIC microscope image. Finally, a distance-regularized level set method, which not only considers the probability change in a nearby pixel but also regularizes the contour smoothness, is applied to refine the initial localization by simply thresholding on the enhanced probability map. Experimental results show that the proposed strategy can give much better performance for segmentation of nuclear regions than the conventional strategies.
Rječnik crkvenoslavenskoga jezika makedonske redakcije omogućava proučavanje značenja himnografskih tekstova predstavljenih u Bitolskom, Zagrebačkom, Šafařikovu, Orbelskom i Hludovljevu triodu, kao i ...u Vataškom mineju koji se odlikuju stilsko-izražajnim sredstvima, leksičkim osobitostima, apstraktnom i figurativnom uporabom leksema. U navedenim su izvorima posvjedočeni leksemi nepotvrđeni u drugim makedonskim tekstovima: весельнèкъ, мокрота, дебельство, собьствèе, kao i grčke posuđenice: аколоyтè˙, продромъ, соyдарь itd. Prefiksalna i sufiksalna je tvorba značajna za konstrukciju strofičnih struktura, a za žanrovsku osobitost mineja i trioda karakteristična je npr. česta upotreba prefiksa прý-: прýбогатьнъ, прýвысокъ, прýестьствьнъ, kao i prefiksa съ-: състрадатè, съоyбèтè, съоyкрýплýтè, kombinacija prefiksa со- i čestice не-: неопалèмъ, прýнесквръньнъ, kao i glagoli s dvojnim prefiksima: прýдъèзрещè, прèсърýстè, съвъзèтè, složenice: благопокорьно, велегласьнъ, вьседýèствьнъ, вьселèкъствьнъ, добролèствьнъ, доброславьнъ, трьбогатьнъ, трьвелèкъ itd.
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