A STUDY ON FUZZY MONOTONICALLY NORMAL SPACE

2020 ◽  
Vol 9 (12) ◽  
pp. 10431-10436
Author(s):  
M. S. Jisha ◽  
R. Sreekumar
Keyword(s):  
Normal Space

On star Lindelöf spaces

2020 ◽  
Vol 57 (2) ◽  
pp. 139-146
Author(s):  
Wei-Feng Xuan ◽  
Yan-Kui Song
Keyword(s):  
Hausdorff Space ◽  
Normal Space ◽  
Star Countable

AbstractIn this paper, we prove that if X is a space with a regular Gδ-diagonal and X2 is star Lindelöf then the cardinality of X is at most 2c. We also prove that if X is a star Lindelöf space with a symmetric g-function such that {g2(n, x): n ∈ ω} = {x} for each x ∈ X then the cardinality of X is at most 2c. Moreover, we prove that if X is a star Lindelöf Hausdorff space satisfying Hψ(X) = κ then e(X) 22κ; and if X is Hausdorff and we(X) = Hψ(X) = κsubset of a space then e(X) 2κ. Finally, we prove that under V = L if X is a first countable DCCC normal space then X has countable extent; and under MA+¬CH there is an example of a first countable, DCCC and normal space which is not star countable extent. This gives an answer to the Question 3.10 in Spaces with property (DC(ω1)), Comment. Math. Univ. Carolin., 58(1) (2017), 131-135.

A Comprehensive Investigation of Ensembles of Gaussian-Based and Gradient-Based Transformed Reliability Analyses: When and How to Use Them

2016 ◽  
Author(s):  
Po Ting Lin ◽  
Wei-Hao Lu ◽  
Shu-Ping Lin
Keyword(s):  
Design Optimization ◽  
Design Space ◽  
Optimization Problems ◽  
Nonlinear Problems ◽  
Kernel Functions ◽  
Sensitivity Analyses ◽  
Normal Space ◽  
Highly Nonlinear ◽  
Standard Normal ◽  
Gradient Based

In the past few years, researchers have begun to investigate the existence of arbitrary uncertainties in the design optimization problems. Most traditional reliability-based design optimization (RBDO) methods transform the design space to the standard normal space for reliability analysis but may not work well when the random variables are arbitrarily distributed. It is because that the transformation to the standard normal space cannot be determined or the distribution type is unknown. The methods of Ensemble of Gaussian-based Reliability Analyses (EoGRA) and Ensemble of Gradient-based Transformed Reliability Analyses (EGTRA) have been developed to estimate the joint probability density function using the ensemble of kernel functions. EoGRA performs a series of Gaussian-based kernel reliability analyses and merged them together to compute the reliability of the design point. EGTRA transforms the design space to the single-variate design space toward the constraint gradient, where the kernel reliability analyses become much less costly. In this paper, a series of comprehensive investigations were performed to study the similarities and differences between EoGRA and EGTRA. The results showed that EGTRA performs accurate and effective reliability analyses for both linear and nonlinear problems. When the constraints are highly nonlinear, EGTRA may have little problem but still can be effective in terms of starting from deterministic optimal points. On the other hands, the sensitivity analyses of EoGRA may be ineffective when the random distribution is completely inside the feasible space or infeasible space. However, EoGRA can find acceptable design points when starting from deterministic optimal points. Moreover, EoGRA is capable of delivering estimated failure probability of each constraint during the optimization processes, which may be convenient for some applications.

scholarly journals The PCL Envelope Lack Sign (PELS) Is a Direct Arthroscopic Sign of Chronic Posterior Cruciate Ligament Insufficiency

2021 ◽  
Vol 11 (8) ◽  
pp. 3608
Author(s):  
Adrian Góralczyk ◽  
Marcin Mostowy ◽  
Michał Ebisz ◽  
Robert F. LaPrade ◽  
Aleksandra Sibilska ◽  
...  
Keyword(s):  
Soft Tissue ◽  
Predictive Value ◽  
Femoral Condyle ◽  
Cruciate Ligament ◽  
Normal Space ◽  
Control Group ◽  
Study Group ◽  
Post Injury ◽  
Diagnostic Characteristics ◽  
Posterior Knee

Purpose: To present the arthroscopic “PCL envelope lack sign” (PELS) and to calculate its diagnostic characteristics in chronic PCL insufficiency. Methods: Recordings of knee arthroscopies performed in a single clinic between April 2015 to March 2020 were retrospectively evaluated, searching for the “PCL envelope”. It was defined as a “soft tissue cuff coursing around the PCL tibial attachment, visible with the arthroscope positioned between the PCL, medial femoral condyle and posterior horn of the medial meniscus at the level of its shiny white fibers”. PELS was defined as “the PCL adhering to the proximal tibia adjacent to the medial meniscal posterior root attachment, inability to observe the normal space between the PCL and posterior tibia and no soft tissue cuff around the PCL tibial attachment”. Inclusion criteria were possibility to evaluate the PELS presence on recordings. Patients who underwent PCL reconstruction were assigned to the study group. The rest of the patients were controls. Criteria to operate on symptomatic PCL patients were at least 5 mm of posterior instability in physical examination and at least 6 months post-injury. Results: Out of 614 available recordings, 592 patients (205 females, 387 males; mean age 45.2 years, SD = 14.36, range 14–81) were included: 38 in the study group and 554 in the control group. In the study group, PELS was positive in 36 of 38 cases (94.7%). In the control group, PELS was negative in 554 PCL-efficient patients (100%). Calculated PELS sensitivity was 94.7%, specificity 100%, positive predictive value 100%, negative predictive value 99.6%. The PELS was present significantly more often in PCL-insufficient patients, p < 0.001. Conclusions: The PCL envelope lack sign was found to be a highly effective tool to arthroscopically confirm chronic PCL insufficiency, and should be considered a direct sign of chronic posterior knee instability.

scholarly journals Geometry and topology of the space of Kähler metrics on singular varieties

2018 ◽  
Vol 154 (8) ◽  
pp. 1593-1632 ◽  
Author(s):  
Eleonora Di Nezza ◽  
Vincent Guedj
Keyword(s):  
Einstein Metrics ◽  
Normal Space ◽  
Fano Varieties ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Metric Properties ◽  
Singular Varieties ◽  
Underlying Space ◽  
And Topology ◽  
Kähler Einstein Metrics

Let $Y$ be a compact Kähler normal space and let $\unicode[STIX]{x1D6FC}\in H_{\mathit{BC}}^{1,1}(Y)$ be a Kähler class. We study metric properties of the space ${\mathcal{H}}_{\unicode[STIX]{x1D6FC}}$ of Kähler metrics in $\unicode[STIX]{x1D6FC}$ using Mabuchi geodesics. We extend several results of Calabi, Chen, and Darvas, previously established when the underlying space is smooth. As an application, we analytically characterize the existence of Kähler–Einstein metrics on $\mathbb{Q}$-Fano varieties, generalizing a result of Tian, and illustrate these concepts in the case of toric varieties.

scholarly journals Intuitionistic Fuzzy Topological Spaces Model

2020 ◽  
Vol 55 (2) ◽  
Author(s):  
Hind Fadhil Abbas
Keyword(s):  
Hausdorff Space ◽  
Basic Structure ◽  
Normal Space ◽  
Regular Space ◽  
Topological Spaces ◽  
Intuitionistic Fuzzy ◽  
Separation Axioms ◽  
Fuzzy Ideal ◽  
Scientific Phenomenon ◽  
Fuzzy Topological Spaces

The fusion of technology and science is a very complex and scientific phenomenon that still carries mysteries that need to be understood. To unravel these phenomena, mathematical models are beneficial to treat different systems with unpredictable system elements. Here, the generalized intuitionistic fuzzy ideal is studied with topological space. These concepts are useful to analyze new generalized intuitionistic models. The basic structure is studied here with various relations between the generalized intuitionistic fuzzy ideals and the generalized intuitionistic fuzzy topologies. This study includes intuitionistic fuzzy topological spaces (IFS); the fundamental definitions of intuitionistic fuzzy Hausdorff space; intuitionistic fuzzy regular space; intuitionistic fuzzy normal space; intuitionistic fuzzy continuity; operations on IFS, the compactness and separation axioms.

On Certain Onto Maps

1962 ◽  
Vol 14 ◽  
pp. 461-466 ◽  
Author(s):  
Isaac Namioka
Keyword(s):  
Topological Space ◽  
Closed Subspace ◽  
Dimensional Space ◽  
Extension Theorem ◽  
Normal Space ◽  
Continuous Map ◽  
Image Position

Let Δn (n > 0) denote the subset of the Euclidean (n + 1)-dimensional space defined byA subset σ of Δn is called a face if there exists a sequence 0 ≤ i1 ≤ i2 ≤ … < im ≤ n such thatand the dimension of σ is defined to be (n — m). Let denote the union of all faces of Δn of dimensions less than n. A topological space Y is called solid if any continuous map on a closed subspace A of a normal space X into Y can be extended to a map on X into Y. By Tietz's extension theorem, each face of Δn is solid. The present paper is concerned with a generalization of the following theorem which seems well known.

A Mapping Problem and Jp-Index. I

1970 ◽  
Vol 22 (4) ◽  
pp. 705-712 ◽  
Author(s):  
Masami Wakae ◽  
Oma Hamara
Keyword(s):  
Cyclic Group ◽  
Prime Order ◽  
Transformation Group ◽  
Classical Group ◽  
Cohomology Ring ◽  
Transformation Groups ◽  
Normal Space ◽  
Mapping Problem ◽  
Countable Basis ◽  
Kakutani Theorem

Indices of normal spaces with countable basis for equivariant mappings have been investigated by Bourgin [4; 6] and by Wu [11; 12] in the case where the transformation groups are of prime order p. One of us has extended the concept to the case where the transformation group is a cyclic group of order pt and discussed its applications to the Kakutani Theorem (see [10]). In this paper we will define the Jp-index of a normal space with countable basis in the case where the transformation group is a cyclic group of order n, where n is divisible by p. We will decide, by means of the spectral sequence technique of Borel [1; 2], the Jp-index of SO(n) where n is an odd integer divisible by p. The method used in this paper can be applied to find the Jp-index of a classical group G whose cohomology ring over Jp has a system of universally transgressive generators of odd degrees.

scholarly journals Alternative configurations of quantile regression for estimating predictive uncertainty in water level forecasts for the upper Severn River: a comparison

2014 ◽  
Vol 18 (9) ◽  
pp. 3411-3428 ◽  
Author(s):  
P. López López ◽  
J. S. Verkade ◽  
A. H. Weerts ◽  
D. P. Solomatine
Keyword(s):  
Quantile Regression ◽  
Water Level ◽  
Skill Score ◽  
Water Levels ◽  
Normal Space ◽  
Numerical Verification ◽  
Relative Operating Characteristic ◽  
Hydrological Uncertainty ◽  
Quality Aspects ◽  
Normal Quantile Transformation

Abstract. The present study comprises an intercomparison of different configurations of a statistical post-processor that is used to estimate predictive hydrological uncertainty. It builds on earlier work by Weerts, Winsemius and Verkade (2011; hereafter referred to as WWV2011), who used the quantile regression technique to estimate predictive hydrological uncertainty using a deterministic water level forecast as a predictor. The various configurations are designed to address two issues with the WWV2011 implementation: (i) quantile crossing, which causes non-strictly rising cumulative predictive distributions, and (ii) the use of linear quantile models to describe joint distributions that may not be strictly linear. Thus, four configurations were built: (i) a ''classical" quantile regression, (ii) a configuration that implements a non-crossing quantile technique, (iii) a configuration where quantile models are built in normal space after application of the normal quantile transformation (NQT) (similar to the implementation used by WWV2011), and (iv) a configuration that builds quantile model separately on separate domains of the predictor. Using each configuration, four reforecasting series of water levels at 14 stations in the upper Severn River were established. The quality of these four series was intercompared using a set of graphical and numerical verification metrics. Intercomparison showed that reliability and sharpness vary across configurations, but in none of the configurations do these two forecast quality aspects improve simultaneously. Further analysis shows that skills in terms of the Brier skill score, mean continuous ranked probability skill score and relative operating characteristic score is very similar across the four configurations.

scholarly journals Third-Order Polynomial Normal Transform Applied to Multivariate Hydrologic Extremes

Water ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 490 ◽  
Author(s):  
Yeou-Koung Tung ◽  
Lingwan You ◽  
Chulsang Yoo
Keyword(s):  
Flood Control ◽  
Random Variables ◽  
Rainfall Data ◽  
Normal Space ◽  
Modeling Framework ◽  
Third Order ◽  
Maximum Rainfall ◽  
Normal Distributions ◽  
Order Polynomial ◽  
Hydrologic Extremes

Hydro-infrastructural systems (e.g., flood control dams, stormwater detention basins, and seawalls) are designed to protect the public against the adverse impacts of various hydrologic extremes (e.g., floods, droughts, and storm surges). In their design and safety evaluation, the characteristics of concerned hydrologic extremes affecting the hydrosystem performance often are described by several interrelated random variables—not just one—that need to be considered simultaneously. These multiple random variables, in practical problems, have a mixture of non-normal distributions of which the joint distribution function is difficult to establish. To tackle problems involving multivariate non-normal variables, one frequently adopted approach is to transform non-normal variables from their original domain to multivariate normal space under which a large wealth of established theories can be utilized. This study presents a framework for practical normal transform based on the third-order polynomial in the context of a multivariate setting. Especially, the study focuses on multivariate third-order polynomial normal transform (TPNT) with explicit consideration of sampling errors in sample L-moments and correlation coefficients. For illustration, the modeling framework is applied to establish an at-site rainfall intensity–duration-frequency (IDF) relationship. Annual maximum rainfall data analyzed contain seven durations (1–72 h) with 27 years of useable records. Numerical application shows that the proposed modeling framework can produce reasonable rainfall IDF relationships by simultaneously treating several correlated rainfall data series and is a viable tool in dealing with multivariate data with a mixture of non-normal distributions.

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