scholarly journals Some Properties of Regular and Normal Space on Topological Graph Space

2021 ◽  
Vol 1879 (2) ◽  
pp. 022106
Author(s):  
Rasha A Isewid ◽  
Nabila I Aziz ◽  
Samer R Yaseen ◽  
Mahera Rabee Qasem
Keyword(s):  
Normal Space ◽  
Topological Graph

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 Similar Vertices and Isomorphism Detection for Planar Kinematic Chains Based on Ameliorated Multi-Order Adjacent Vertex Assignment Sequence

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Liang Sun ◽  
Zhizheng Ye ◽  
Fuwei Lu ◽  
Rongjiang Cui ◽  
Chuanyu Wu
Keyword(s):  
Degree Of Freedom ◽  
Adjacent Vertex ◽  
Topological Graph ◽  
Innovative Design ◽  
Kinematic Chains ◽  
Effectiveness And Efficiency ◽  
Definition Of ◽  
Specific Definition

AbstractIsomorphism detection is fundamental to the synthesis and innovative design of kinematic chains (KCs). The detection can be performed accurately by using the similarity of KCs. However, there are very few works on isomorphism detection based on the properties of similar vertices. In this paper, an ameliorated multi-order adjacent vertex assignment sequence (AMAVS) method is proposed to seek out similar vertices and identify the isomorphism of the planar KCs. First, the specific definition of AMAVS is described. Through the calculation of the AMAVS, the adjacent vertex value sequence reflecting the uniqueness of the topology features is established. Based on the value sequence, all possible similar vertices, corresponding relations, and isomorphism discrimination can be realized. By checking the topological graph of KCs with a different number of links, the effectiveness and efficiency of the proposed method are verified. Finally, the method is employed to implement the similar vertices and isomorphism detection of all the 9-link 2-DOF(degree of freedom) planar KCs.

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 KVGCN: A KNN Searching and VLAD Combined Graph Convolutional Network for Point Cloud Segmentation

2021 ◽  
Vol 13 (5) ◽  
pp. 1003
Author(s):  
Nan Luo ◽  
Hongquan Yu ◽  
Zhenfeng Huo ◽  
Jinhui Liu ◽  
Quan Wang ◽  
...  
Keyword(s):  
Point Cloud ◽  
Nearest Neighbor ◽  
Semantic Segmentation ◽  
K Nearest Neighbor ◽  
Topological Graph ◽  
Convolutional Network ◽  
Cloud Data ◽  
Nearest Neighbor Searching ◽  
Point Cloud Segmentation ◽  
Local Feature Extraction

Semantic segmentation of the sensed point cloud data plays a significant role in scene understanding and reconstruction, robot navigation, etc. This work presents a Graph Convolutional Network integrating K-Nearest Neighbor searching (KNN) and Vector of Locally Aggregated Descriptors (VLAD). KNN searching is utilized to construct the topological graph of each point and its neighbors. Then, we perform convolution on the edges of constructed graph to extract representative local features by multiple Multilayer Perceptions (MLPs). Afterwards, a trainable VLAD layer, NetVLAD, is embedded in the feature encoder to aggregate the local and global contextual features. The designed feature encoder is repeated for multiple times, and the extracted features are concatenated in a jump-connection style to strengthen the distinctiveness of features and thereby improve the segmentation. Experimental results on two datasets show that the proposed work settles the shortcoming of insufficient local feature extraction and promotes the accuracy (mIoU 60.9% and oAcc 87.4% for S3DIS) of semantic segmentation comparing to existing models.

A Model for Mechanism Data Storage

1992 ◽  
Author(s):  
Wan Wang
Keyword(s):  
Data Storage ◽  
Data Model ◽  
Computer Time ◽  
Kinematic Structure ◽  
Topological Graph ◽  
Complete Set ◽  
Isomorphism Identification

Abstract A data model for kinematic structure of mechanisms and its coding principle are proposed, based on the topological graph and contract graph. In the model every basic chain is mapped by a code of 5 decimal digits and a mechanism is mapped by a set of code of basic chains. The model occupies minimal memory, and contains a complete set of useful primary parameters of structure, and significantly reduce computer time for isomorphism identification.

scholarly journals The multi-attribute topological graph method and its application on power flow analysis in closed planetary gear trains

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401879410 ◽  
Author(s):  
Yahui Cui ◽  
Jing Gao ◽  
Xiaomin Ji ◽  
Xintao Zhou ◽  
Haitao Yan
Keyword(s):  
Power Flow ◽  
Flow Analysis ◽  
Planetary Gear ◽  
Topological Graph ◽  
Template Model ◽  
Power Flow Analysis ◽  
Analysis Process ◽  
Planetary Gear Trains ◽  
Graphical View ◽  
Gear Trains

The concept of multi-attribute topological graph is proposed in this article to represent the characteristics of both structure and state for typical one-degree-of-freedom planar spur closed planetary gear trains. This method is well applied in power flow analysis and provides a graphical view for the types, values, directions, and transmission relationship of power flow, especially for the recirculation power representation. Furthermore, a template model of multi-attribute topological graph for closed planetary gear trains is also presented, which would be helpful to the multi-attribute topological graph generation for some certain types of closed planetary gear trains just by changing symbols in the template model. A corresponding software is also developed to make the analysis process more convenient. By inputting different parameters, the different visual results can be obtained automatically, thus benefiting engineers in conceptual design.

scholarly journals On the Graph of Divisibility of an Integral Domain

2015 ◽  
Vol 58 (3) ◽  
pp. 449-458 ◽  
Author(s):  
Jason Greene Boynton ◽  
Jim Coykendall
Keyword(s):  
Topological Space ◽  
Integral Domain ◽  
Point Of View ◽  
Current Understanding ◽  
Main Theme ◽  
Topological Graph ◽  
Integral Domains ◽  
Graph Theoretic ◽  
Theoretic Point ◽  
Group Of Divisibility

AbstractIt is well known that the factorization properties of a domain are reflected in the structure of its group of divisibility. The main theme of this paper is to introduce a topological/graph-theoretic point of view to the current understanding of factorization in integral domains. We also show that connectedness properties in the graph and topological space give rise to a generalization of atomicity.

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