scholarly journals A characterization of alternating links in thickened surfaces

2021 ◽  
pp. 1-19
Author(s):  
Hans U. Boden ◽  
Homayun Karimi
Keyword(s):  
Opposite Sign ◽  
Bilinear Pairing ◽  
Compact Surface ◽  
Topological Characterization ◽  
Definite Form ◽  
Minimal Genus ◽  
Thickened Surface ◽  
Alternating Links ◽  
Closed Oriented Surface

We use an extension of Gordon–Litherland pairing to thickened surfaces to give a topological characterization of alternating links in thickened surfaces. If $\Sigma$ is a closed oriented surface and $F$ is a compact unoriented surface in $\Sigma \times I$ , then the Gordon–Litherland pairing defines a symmetric bilinear pairing on the first homology of $F$ . A compact surface in $\Sigma \times I$ is called definite if its Gordon–Litherland pairing is a definite form. We prove that a link $L$ in a thickened surface is non-split, alternating, and of minimal genus if and only if it bounds two definite surfaces of opposite sign.

Intersections of quotient rings and Prüfer v-multiplication domains

2016 ◽  
Vol 15 (08) ◽  
pp. 1650149 ◽  
Author(s):  
Said El Baghdadi ◽  
Marco Fontana ◽  
Muhammad Zafrullah
Keyword(s):  
Integral Domain ◽  
Algebraic Approach ◽  
Quotient Field ◽  
Topological Characterization ◽  
Locally Finite ◽  
Star Operation ◽  
Star Operations ◽  
Quotient Rings ◽  
Special Case

Let [Formula: see text] be an integral domain with quotient field [Formula: see text]. Call an overring [Formula: see text] of [Formula: see text] a subring of [Formula: see text] containing [Formula: see text] as a subring. A family [Formula: see text] of overrings of [Formula: see text] is called a defining family of [Formula: see text], if [Formula: see text]. Call an overring [Formula: see text] a sublocalization of [Formula: see text], if [Formula: see text] has a defining family consisting of rings of fractions of [Formula: see text]. Sublocalizations and their intersections exhibit interesting examples of semistar or star operations [D. D. Anderson, Star operations induced by overrings, Comm. Algebra 16 (1988) 2535–2553]. We show as a consequence of our work that domains that are locally finite intersections of Prüfer [Formula: see text]-multiplication (respectively, Mori) sublocalizations turn out to be Prüfer [Formula: see text]-multiplication domains (PvMDs) (respectively, Mori); in particular, for the Mori domain case, we reobtain a special case of Théorème 1 of [J. Querré, Intersections d’anneaux intègers, J. Algebra 43 (1976) 55–60] and Proposition 3.2 of [N. Dessagnes, Intersections d’anneaux de Mori — exemples, Port. Math. 44 (1987) 379–392]. We also show that, more than the finite character of the defining family, it is the finite character of the star operation induced by the defining family that causes the interesting results. As a particular case of this theory, we provide a purely algebraic approach for characterizing P vMDs as a subclass of the class of essential domains (see also Theorem 2.4 of [C. A. Finocchiaro and F. Tartarone, On a topological characterization of Prüfer [Formula: see text]-multiplication domains among essential domains, preprint (2014), arXiv:1410.4037]).

Polycrystalline Silicon Gettering Layers with Controlled Residual Stress

2013 ◽  
Vol 205-206 ◽  
pp. 284-289 ◽  
Author(s):  
David Lysáček ◽  
Petr Kostelník ◽  
Petr Pánek
Keyword(s):  
Residual Stress ◽  
Vapor Deposition ◽  
Polycrystalline Silicon ◽  
Opposite Sign ◽  
Chemical Vapor ◽  
Pressure Chemical ◽  
Novel Method ◽  
The Individual ◽  
Scanning Electron

We report on a novel method of low pressure chemical vapor deposition of polycrystalline silicon layers used for external gettering in silicon substrate for semiconductor applications. The proposed method allowed us to produce layers of polycrystalline silicon with pre-determined residual stress. The method is based on the deposition of a multilayer system formed by two layers. The first layer is intentionally designed to have tensile stress while the second layer has compressive stress. Opposite sign of the residual stresses of the individual layers enables to pre-determine the residual stress of the gettering stack. We used scanning electron microscopy for structural characterization of the layers and intentional contamination for demonstration of the gettering properties. Residual stress of the layers was calculated from the wafer curvature.

Topological characterization of dendrimer, benzenoid, and nanocone

2018 ◽  
Vol 74 (1-2) ◽  
pp. 35-43
Author(s):  
Wei Gao ◽  
Muhammad Kamran Siddiqui ◽  
Najma Abdul Rehman ◽  
Mehwish Hussain Muhammad
Keyword(s):  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Zagreb Index ◽  
Topological Characterization ◽  
Complex Molecules ◽  
Chemical Structures ◽  
Physico Chemical ◽  
Quantitative Structure Activity Relationships

Abstract Dendrimers are large and complex molecules with very well defined chemical structures. More importantly, dendrimers are highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core. Topological indices are numbers associated with molecular graphs for the purpose of allowing quantitative structure-activity relationships. These topological indices correlate certain physico-chemical properties such as the boiling point, stability, strain energy, and others, of chemical compounds. In this article, we determine hyper-Zagreb index, first multiple Zagreb index, second multiple Zagreb index, and Zagreb polynomials for hetrofunctional dendrimers, triangular benzenoids, and nanocones.

scholarly journals A Graphlet-Based Topological Characterization of the Resting-State Network in Healthy People

2021 ◽  
Vol 15 ◽  
Author(s):  
Paolo Finotelli ◽  
Carlo Piccardi ◽  
Edie Miglio ◽  
Paolo Dulio
Keyword(s):  
Resting State ◽  
Brain Regions ◽  
Brain Network ◽  
Induced Subgraphs ◽  
Topological Characterization ◽  
Network Information ◽  
The Subject ◽  
Euclidean Distances ◽  
The Brain

In this paper, we propose a graphlet-based topological algorithm for the investigation of the brain network at resting state (RS). To this aim, we model the brain as a graph, where (labeled) nodes correspond to specific cerebral areas and links are weighted connections determined by the intensity of the functional magnetic resonance imaging (fMRI). Then, we select a number of working graphlets, namely, connected and non-isomorphic induced subgraphs. We compute, for each labeled node, its Graphlet Degree Vector (GDV), which allows us to associate a GDV matrix to each one of the 133 subjects of the considered sample, reporting how many times each node of the atlas “touches” the independent orbits defined by the graphlet set. We focus on the 56 independent columns (i.e., non-redundant orbits) of the GDV matrices. By aggregating their count all over the 133 subjects and then by sorting each column independently, we obtain a sorted node table, whose top-level entries highlight the nodes (i.e., brain regions) most frequently touching each of the 56 independent graphlet orbits. Then, by pairwise comparing the columns of the sorted node table in the top-k entries for various values of k, we identify sets of nodes that are consistently involved with high frequency in the 56 independent graphlet orbits all over the 133 subjects. It turns out that these sets consist of labeled nodes directly belonging to the default mode network (DMN) or strongly interacting with it at the RS, indicating that graphlet analysis provides a viable tool for the topological characterization of such brain regions. We finally provide a validation of the graphlet approach by testing its power in catching network differences. To this aim, we encode in a Graphlet Correlation Matrix (GCM) the network information associated with each subject then construct a subject-to-subject Graphlet Correlation Distance (GCD) matrix based on the Euclidean distances between all possible pairs of GCM. The analysis of the clusters induced by the GCD matrix shows a clear separation of the subjects in two groups, whose relationship with the subject characteristics is investigated.

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