scholarly journals Maximal point spaces of posets with relative lower topology

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2645-2661
Author(s):  
Chong Shen ◽  
Xiaoyong Xi ◽  
Dongsheng Zhao
Keyword(s):  
Topological Space ◽  
Domain Theory ◽  
New Models ◽  
Different Types ◽  
Maximal Point ◽  
Order Structures ◽  
Maximal Points

In domain theory, by a poset model of a T1 topological space X we usually mean a poset P such that the subspace Max(P) of the Scott space of P consisting of all maximal points is homeomorphic to X. The poset models of T1 spaces have been extensively studied by many authors. In this paper we investigate another type of poset models: lower topology models. The lower topology ?(P) on a poset P is one of the fundamental intrinsic topologies on the poset, which is generated by the sets of the form P\?x, x ? P. A lower topology poset model (poset LT-model) of a topological space X is a poset P such that the space Max?(P) of maximal points of P equipped with the relative lower topology is homeomorphic to X. The studies of such new models reveal more links between general T1 spaces and order structures. The main results proved in this paper include (i) a T1 space is compact if and only if it has a bounded complete algebraic dcpo LT-model; (ii) a T1 space is second-countable if and only if it has an ?-algebraic poset LT-model; (iii) every T1 space has an algebraic dcpo LT-model; (iv) the category of all T1 space is equivalent to a category of bounded complete posets. We will also prove some new results on the lower topology of different types of posets.

scholarly journals Topologies on Z n that Are Not Homeomorphic to the n-Dimensional Khalimsky Topological Space

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1072 ◽  
Author(s):  
Sang-Eon Han ◽  
Saeid Jafari ◽  
Jeong Kang
Keyword(s):  
Applied Sciences ◽  
Topological Space ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Discrete Topology ◽  
Separation Axiom ◽  
Different Types

The present paper deals with two types of topologies on the set of integers, Z : a quasi-discrete topology and a topology satisfying the T 1 2 -separation axiom. Furthermore, for each n ∈ N , we develop countably many topologies on Z n which are not homeomorphic to the typical n-dimensional Khalimsky topological space. Based on these different types of new topological structures on Z n , many new mathematical approaches can be done in the fields of pure and applied sciences, such as fixed point theory, rough set theory, and so on.

scholarly journals Fuzzy Counterparts of Fischer Diagonal Condition in ⊤-Convergence Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 685
Author(s):  
Qiu Jin ◽  
Lingqiang Li ◽  
Jing Jiang
Keyword(s):  
Topological Space ◽  
Fuzzy Topology ◽  
Convergence Space ◽  
Convergence Spaces ◽  
Different Types ◽  
Diagonal Condition ◽  
Operator Convergence

Fischer diagonal condition plays an important role in convergence space since it precisely ensures a convergence space to be a topological space. Generally, Fischer diagonal condition can be represented equivalently both by Kowalsky compression operator and Gähler compression operator. ⊤-convergence spaces are fundamental fuzzy extensions of convergence spaces. Quite recently, by extending Gähler compression operator to fuzzy case, Fang and Yue proposed a fuzzy counterpart of Fischer diagonal condition, and proved that ⊤-convergence space with their Fischer diagonal condition just characterizes strong L-topology—a type of fuzzy topology. In this paper, by extending the Kowalsky compression operator, we present a fuzzy counterpart of Fischer diagonal condition, and verify that a ⊤-convergence space with our Fischer diagonal condition precisely characterizes topological generated L-topology—a type of fuzzy topology. Hence, although the crisp Fischer diagonal conditions based on the Kowalsky compression operator and the on Gähler compression operator are equivalent, their fuzzy counterparts are not equivalent since they describe different types of fuzzy topologies. This indicates that the fuzzy topology (convergence) is more complex and varied than the crisp topology (convergence).

scholarly journals Portfolio Selection Based on Distance between Fuzzy Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Weiyi Qian ◽  
Mingqiang Yin
Keyword(s):  
Mathematical Models ◽  
Portfolio Selection ◽  
Expected Value ◽  
Simple Method ◽  
Numerical Examples ◽  
Fuzzy Variables ◽  
Fuzzy Environment ◽  
Investment Return ◽  
New Models ◽  
Different Types

This paper researches portfolio selection problem in fuzzy environment. We introduce a new simple method in which the distance between fuzzy variables is used to measure the divergence of fuzzy investment return from a prior one. Firstly, two new mathematical models are proposed by expressing divergence as distance, investment return as expected value, and risk as variance and semivariance, respectively. Secondly, the crisp forms of the new models are also provided for different types of fuzzy variables. Finally, several numerical examples are given to illustrate the effectiveness of the proposed approach.

Disaggregate Economic Base Multipliers in Small Communities

1997 ◽  
Vol 29 (6) ◽  
pp. 955-974 ◽  
Author(s):  
A C Vias ◽  
G F Mulligan
Keyword(s):  
Economic Base ◽  
Input Output ◽  
Data Set ◽  
Small Communities ◽  
Considerable Evidence ◽  
Transfer Payments ◽  
New Models ◽  
Base Analysis ◽  
Different Types ◽  
Community Data

Economic base analysis is frequently used to describe employment profiles and to predict project-related impacts in small communities. Considerable evidence suggests, however, that economic base multipliers should be estimated from survey data and not from shortcut methods. In this paper two competing versions of the economic base model are developed and then these two models are estimated by use of the Arizona community data set. In both cases, marginal multiplier estimates, controlled for transfer payments, are generated for ten individual sectors in five different types of communities. Results from these two disaggregate economic base models are assessed and then compared with results provided earlier by more aggregate models. The better of these two new models closely resembles the popular input—output model.

Wear-Life Models for Angular Contact Spherical Plain Bearing under Different Load Types

2013 ◽  
Vol 344 ◽  
pp. 3-7
Author(s):  
Xiang Po Zhang ◽  
Jian Zhong Shang ◽  
Xun Chen ◽  
Chun Hua Zhang ◽  
Ya Shun Wang
Keyword(s):  
Empirical Models ◽  
Plain Bearing ◽  
Wear Life ◽  
New Models ◽  
Different Types ◽  
Wear Calculation ◽  
Specific Configuration ◽  
Load Types ◽  
And Function ◽  
Spherical Plain Bearing

To meet the demand of wear-life calculation of spherical plain bearing (SPB), the wear-life models for angular contact spherical plain bearing (ACSPB) under different types of load were created based on the joint wear calculation method (JWCM). By integrating the friction wear laws of materials, specific configuration & mating characteristics of the SPB, and function requirement, the new models were more theoretical and had a good applicability and pertinence compared to the empirical models used at present.

scholarly journals A new convergence inducing the SI-topology

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 6017-6029 ◽  
Author(s):  
Hadrian Andradi ◽  
Chong Shen ◽  
Weng Ho ◽  
Dongsheng Zhao
Keyword(s):  
Topological Space ◽  
Domain Theory ◽  
Scott Topology ◽  
Convergence Structure ◽  
Equivalent Conditions

In their attempt to develop domain theory in situ T0 spaces, Zhao and Ho introduced a new topology defined by irreducible sets of a resident topological space, called the SI-topology. Notably, the SI-topology of the Alexandroff topology of posets is exactly the Scott topology, and so the SI-topology can be seen as a generalisation of the Scott topology in the context of general T0 spaces. It is well known that the convergence structure that induces the Scott topology is the Scott-convergence - also known as lim-inf convergence by some authors. Till now, it is not known which convergence structure induces the SI-topology of a given T0 space. In this paper, we fill in this gap in the literature by providing a convergence structure, called the SI-convergence structure, that induces the SI-topology. Additionally, we introduce the notion of I-continuity that is closely related to the SI-convergence structure, but distinct from the existing notion of SI-continuity (introduced by Zhao and Ho earlier). For SI-continuity, we obtain here some equivalent conditions for it. Finally, we give some examples of non-Alexandroff SI-continuous spaces.

scholarly journals Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable—Part II: Extremal Points, Convexity, Periodicity

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 114 ◽  
Author(s):  
Luciano Stefanini ◽  
Laerte Sorini ◽  
Benedetta Amicizia
Keyword(s):  
Interval Analysis ◽  
General Setting ◽  
Real Variable ◽  
Partial Orders ◽  
Single Variable ◽  
Variable Part ◽  
Extremal Points ◽  
Different Types ◽  
Interval Valued ◽  
Maximal Points

We continue the presentation of new results in the calculus for interval-valued functions of a single real variable. We start here with the results presented in part I of this paper, namely, a general setting of partial orders in the space of compact intervals (in midpoint-radius representation) and basic results on convergence and limits, continuity, gH-differentiability, and monotonicity. We define different types of (local) minimal and maximal points and develop the basic theory for their characterization. We then consider some interesting connections with applied geometry of curves and the convexity of interval-valued functions is introduced and analyzed in detail. Further, the periodicity of interval-valued functions is described and analyzed. Several examples and pictures accompany the presentation.

New Design Approach to Handle Spatial Vagueness in Spatial OLAP Datacubes

2016 ◽  
pp. 1859-1880
Author(s):  
Elodie Edoh-Alove ◽  
Sandro Bimonte ◽  
François Pinet ◽  
Yvan Bédard
Keyword(s):  
Spatial Data ◽  
End Users ◽  
Environmental Data ◽  
Decision Makers ◽  
Multidimensional Analysis ◽  
Multidimensional Data ◽  
New Approach ◽  
New Models ◽  
Different Types ◽  
Spatial Vagueness

Spatial-OLAP (SOLAP) technologies are dedicated to multidimensional analysis of large volumes of (spatial) data. Spatial data are subject to different types of uncertainty, in particular spatial vagueness. Although several researches propose new models to cope with spatial vagueness, their integration in SOLAP systems is still in an embryonic state. Also, analyzing multidimensional data with metadata brought by the exploitation of the new models can be too complex and demanding for decision-makers. To help reduce spatial vagueness consequences on the exactness of SOLAP analysis queries, the authors present a new approach for designing SOLAP datacubes based on end-users' tolerance to the risks of misinterpretation of fact data. An experimentation of the new approach on agri-environmental data is also proposed.

А REGIONAL LINGUOCULTURAL COMPONENT OF TRAINING LANGUAGE TEACHER (CONTENTS, FORMS AND MEANS OF IMPLEMENTATION)

2018 ◽  
Vol 1 ◽  
pp. 405-422
Author(s):  
Tatiana Nikitina ◽  
Elena Rogaleva
Keyword(s):  
Language Teachers ◽  
Linguistic Competence ◽  
Optimal Structure ◽  
Research Projects ◽  
Language Teacher ◽  
Master's Degrees ◽  
New Models ◽  
Different Types ◽  
Cultural Linguistics

The article presents the author’s concept of forming the regional cultural linguistic competence of language teachers in the process of study in pursuit of Bachelor's and Master's degrees. It regards the optimal structure and contents of the regional cultural linguistic competence, the forms and means of the implementation of the regional linguocultural component of teachers’professionaltraining. It shows different types of students’ in- and out-of-class activities and research projects connected with studying regional cultural linguistics, new models of modern means of teaching – the author’s textbooks and educational dictionaries that provide the implementation of the concept. The results of the methodical experiment that prove the effectiveness of the author’s model of forming the regional cultural linguistic competence of language teachers are given.

On the distribution of points in a poisson dirichlet process

1988 ◽  
Vol 25 (2) ◽  
pp. 336-345 ◽  
Author(s):  
R. C. Griffiths
Keyword(s):  
Population Genetics ◽  
Probability Density Function ◽  
Probability Density ◽  
Dirichlet Process ◽  
Computational Algorithm ◽  
Rational Polynomial ◽  
Maximal Point ◽  
Distribution Of Points ◽  
Expected Values ◽  
Maximal Points

A probability density function important in the Poisson Dirichlet process of population genetics is studied. An accurate computational algorithm is given for this density and for the marginal distributions of the points in the Poisson Dirichlet process. The distribution of the maximal point of the process is tabulated. Rational polynomial approximations in θ, the mutation parameter, are found for the expected values of the first three maximal points.

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