Small loop spaces and covering theory of non-homotopically Hausdorff spaces

In this paper we devote to spaces that are not homotopically hausdorff and study their covering spaces. We introduce the notion of small covering and prove that every small covering of $X$ is the universal covering in categorical sense. Also, we introduce the notion of semi-locally small loop space which is the necessary and sufficient condition for existence of universal cover for non-homotopically hausdorff spaces, equivalently existence of small covering spaces. Also, we prove that for semi-locally small loop spaces, $X$ is a small loop space if and only if every cover of $X$ is trivial if and only if $\pi_1^{top}(X)$ is an indiscrete topological group.Comment: 7 page

Spanier spaces and covering theory of non-homotopically path Hausdorff spaces

H. Fischer et al. (Topology and its Application, 158 (2011) 397-408.) introduced the Spanier group of a based space $(X,x)$ which is denoted by \psp. By a Spanier space we mean a space $X$ such that \psp=\pi_1(X,x), for every $x\in X$. In this paper, first we give an example of Spanier spaces. Then we study the influence of the Spanier group on covering theory and introduce Spanier coverings which are universal coverings in the categorical sense. Second, we give a necessary and sufficient condition for the existence of Spanier coverings for non-homotopically path Hausdorff spaces. Finally, we study the topological properties of Spanier groups and find out a criteria for the Hausdorffness of topological fundamental groups.Comment: 14 pages, 2 figures. arXiv admin note: text overlap with arXiv:1102.0993 by other author

On locally 1-connectedness of quotient spaces and its applications to fundamental groups

Let $X$ be a locally 1-connected metric space and $A_1,A_2,...,A_n$ be connected, locally path connected and compact pairwise disjoint subspaces of $X$. In this paper, we show that the quotient space $X/(A_1,A_2,...,A_n)$ obtained from $X$ by collapsing each of the sets $A_i$'s to a point, is also locally 1-connected. Moreover, we prove that the induced continuous homomorphism of quasitopological fundamental groups is surjective. Finally, we give some applications to find out some properties of the fundamental group of the quotient space $X/(A_1,A_2,...,A_n)$.Comment: 11 page

Barriers to research activities of faculty members in Islamic Azad University

Background: The present study was conducted to determine the inhibiting factors of research activities among the faculty members of Islamic Azad University.  Methods: In the present cross-sectional study, conducted between 2009-2013, 300 faculty members of Islamic Azad University, Science and Research Branch, Tehran, were selected following stratified random sampling method. Data collection instrument was a questionnaire comprising 20 questions about their research activities and 22 questions about their unwillingness to perform research activities.  Results: A total of 254 faculty members participated in the present study. About 15% of the participants were female. The findings of the current study showed that a) lack of physical space for work, study, and research, b) unfamiliarity with the searching methods on the Internet, and c) lack of sufficient familiarity with research methods and Statistics were the most important obstacles for the participant to carry out research projects.  Conclusion: Supporting the researcher financially and spiritually, considering the priorities and research needs, honoring the social status of faculty members, creating a calm and active environment for them, and removing encumbering administrative rules and regulations can help faculty members become eager to join in scientific research projects.

Complexity Analysis Of Next-Generation VVC Encoding and Decoding

While the next generation video compression standard, Versatile Video Coding (VVC), provides a superior compression efficiency, its computational complexity dramatically increases. This paper thoroughly analyzes this complexity for both encoder and decoder of VVC Test Model 6, by quantifying the complexity break-down for each coding tool and measuring the complexity and memory requirements for VVC encoding/decoding. These extensive analyses are performed for six video sequences of 720p, 1080p, and 2160p, under Low-Delay (LD), Random-Access (RA), and All-Intra (AI) conditions (a total of 320 encoding/decoding). Results indicate that the VVC encoder and decoder are 5x and 1.5x more complex compared to HEVC in LD, and 31x and 1.8x in AI, respectively. Detailed analysis of coding tools reveals that in LD on average, motion estimation tools with 53%, transformation and quantization with 22%, and entropy coding with 7% dominate the encoding complexity. In decoding, loop filters with 30%, motion compensation with 20%, and entropy decoding with 16%, are the most complex modules. Moreover, the required memory bandwidth for VVC encoding/decoding are measured through memory profiling, which are 30x and 3x of HEVC. The reported results and insights are a guide for future research and implementations of energy-efficient VVC encoder/decoder.Comment: IEEE ICIP 202

PROCJENA HRAPAVOSTI POVRŠINE PRIRODNIH STIJENSKIH PUKOTINA TEMELJENA NA TEHNICI NENADZIRANOG PREPOZNAVANJA UZORAKA POMOĆU 2D PROFILA

The stability of a jointed rock mass is generally controlled by its shear strength that significantly depends on surface roughness. So far, different methods have been presented for determining surface roughness using 2D profiles. In this study, a new method based on the unsupervised pattern recognition technique using a combination of statistical, geostatistical, directional, and spectral methods for the quantification of the surface roughness will be proposed. To reach this goal, more than 10,000 profiles gathered from 92 surfaces of natural rock joints were scanned. The samples were collected from limestone cores of the Lar Dam located in the Mazandaran Province, Iran. After introducing a new spectral index, determined from the fast Fourier transform for measuring the unevenness of rough profiles, statistical, geostatistical, directional, and spectral features revealing waviness and unevenness of the 2D profiles were extracted, and a representative vector and profile for each surface were introduced through the weighted mean and median of the profile features. Principal component analysis (PCA) was utilized for finding the direction of the maximum variance of information. Then, clustering of the 92 samples was performed via K-means, and the silhouette measure was used in order to find the optimal number of clusters resulted in the creation of 13 clusters. To verify the procedure, a sample was selected in each cluster, and direct shear tests were performed on the samples. Comparing the experiments and the clustering results shows they are in good agreement. Thus, the method is an efficient tool for the quantitative recognition of surface roughness considering the waviness and unevenness of a surface.Stabilnost raspucane stijenske mase općenito se kontrolira posmičnom čvrstoćom koja značajno ovisi o hrapavosti površine. Do sada su prikazane različite metode za određivanje hrapavosti površine pomoću 2D profila. U ovom radu predlaže se nova metoda koja se temelji na tehnici nenadziranog prepoznavanja uzoraka kombinacijom statističkih, geostatističkih, usmjerenih i spektralnih metoda za kvantifikaciju hrapavosti površine. Kako bi se postigao taj cilj, skenirano je više od 10.000 profila prikupljenih s 92 površine prirodnih stijenskih pukotina. Uzorci su prikupljeni iz vapnenačkih jezgri brane Lar koja se nalazi u pokrajini Mazandaran u Iranu. Nakon uvođenja novog spektralnog indeksa, određenog Fourierovom transformacijom za mjerenje neravnina hrapavih profila, izvučene su statističke, geostatističke, usmjerene i spektralne značajke koje opisuju valovitost i neravnine 2D profila, a reprezentativni vektor i profil za svaku površinu uvedeni su kroz ponderiranu aritmetičku sredinu i medijan značajki profila. Analiza glavnih komponenti (PCA) korištena je za pronalaženje smjera najvećeg odstupanja informacija. Zatim je grupiranje 92 uzorka provedeno putem metode K-sredina, a mjera siluete korištena je kako bi se pronašao optimalan broj grupa, a to je rezultiralo stvaranjem 13 grupa. Za provjeru postupka odabran je uzorak u svakoj grupi, a na tim uzorcima provedena su ispitivanja izravnog smicanja. Usporedba rezultata ispitivanja i grupiranja pokazala je dobro slaganje, stoga je ova metoda učinkovit alat za kvantitativno utvrđivanje hrapavosti s obzirom na valovitost i neravnine površine