scholarly journals Icosahedral carboranes as scaffolds for congested regioselective polyaryl compounds: the distinct distance tuning of C–C and its antipodal B–B

2019 ◽  
Vol 55 (61) ◽  
pp. 8927-8930
Author(s):  
Zsolt Kelemen ◽  
Ariadna Pepiol ◽  
Marius Lupu ◽  
Reijo Sillanpää ◽  
Mikko M. Hänninen ◽  
...  
Keyword(s):  
Distinct Distance

Four-fold dense precisely defined patterns of substitution in o-carborane have been demonstrated by experimentation and computed.

scholarly journals Metric Dimension in fuzzy(neutrosophic) Graphs-VII

2021 ◽  
Author(s):  
Henry Garrett
Keyword(s):  
Graph Theory ◽  
Individual Case ◽  
Metric Dimension ◽  
Neutrosophic Graph ◽  
Distinct Distance ◽  
Optimal Set ◽  
Dimension Number

New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification(neutrosofication) of twin vertices but using crisp concept of antipodal vertices are another approaches of this study. Thus defining two notions concerning vertices which one of them is fuzzy(neutrosophic) titled twin and another is crisp titled antipodal to study the behaviors of cycles which are partitioned into even and odd, are concluded. Classes of cycles according to antipodal vertices are divided into two classes as even and odd. Parity of the number of edges in cycle causes to have two subsections under the section is entitled to antipodal vertices. In this study, the term dimension is introduced on fuzzy(neutrosophic) graphs. The locations of objects by a set of some junctions which have distinct distance from any couple of objects out of the set, are determined. Thus it’s possible to have the locations of objects outside of this set by assigning partial number to any objects. The classes of these specific graphs are chosen to obtain some results based on dimension. The types of crisp notions and fuzzy(neutrosophic) notions are used to make sense about the material of this study and the outline of this study uses some new notions which are crisp and fuzzy(neutrosophic). Some questions and problems are posed concerning ways to do further studies on this topic. Basic familiarities with fuzzy(neutrosophic) graph theory and graph theory are proposed for this article.

Intensive care

2016 ◽  
Keyword(s):  
Intensive Care ◽  
Clinical Practice ◽  
Evidence Base ◽  
Cutting Edge ◽  
Direct Impact ◽  
Independent Research ◽  
Everyday Clinical Practice ◽  
Distinct Distance ◽  
Short Space ◽  
The Uk

In the last two decades, intensive care has progressed significantly. The phenomenal developments clinically, academically, organizationally, and professionally during this relatively short space of time have all helped to define a specialty that has not only come of age, but also has established a distinct distance from its parent specialties. Intensive care in the UK now has an established Faculty and continues to forge ahead in expanding an independent research and evidence base. The field is rapidly changing, with cutting-edge ideas driving clinical progress. Through the papers considered in this chapter, various innovations are described that have had a direct impact on everyday clinical practice.

scholarly journals Aster migration determines the length scale of nuclear separation in the Drosophila syncytial embryo

2012 ◽  
Vol 197 (7) ◽  
pp. 887-895 ◽  
Author(s):  
Ivo A. Telley ◽  
Imre Gáspár ◽  
Anne Ephrussi ◽  
Thomas Surrey
Keyword(s):  
Early Embryo ◽  
Length Scale ◽  
Free System ◽  
Nuclear Separation ◽  
A Cell ◽  
Distinct Distance ◽  
Spindle Elongation ◽  
Insect Embryos ◽  
Microtubule Aster

In the early embryo of many species, comparatively small spindles are positioned near the cell center for subsequent cytokinesis. In most insects, however, rapid nuclear divisions occur in the absence of cytokinesis, and nuclei distribute rapidly throughout the large syncytial embryo. Even distribution and anchoring of nuclei at the embryo cortex are crucial for cellularization of the blastoderm embryo. The principles underlying nuclear dispersal in a syncytium are unclear. We established a cell-free system from individual Drosophila melanogaster embryos that supports successive nuclear division cycles with native characteristics. This allowed us to investigate nuclear separation in predefined volumes. Encapsulating nuclei in microchambers revealed that the early cytoplasm is programmed to separate nuclei a distinct distance. Laser microsurgery revealed an important role of microtubule aster migration through cytoplasmic space, which depended on F-actin and cooperated with anaphase spindle elongation. These activities define a characteristic separation length scale that appears to be a conserved property of developing insect embryos.

scholarly journals Spectra of products of digraphs

2020 ◽  
Vol 36 (36) ◽  
pp. 744-763
Author(s):  
Minerva Catral ◽  
Lorenzo Ciardo ◽  
Leslie Hogben ◽  
Carolyn Reinhart
Keyword(s):  
Directed Graphs ◽  
Distance Matrix ◽  
Kronecker Products ◽  
Unified Approach ◽  
Jordan Canonical Form ◽  
Cartesian Products ◽  
Signless Laplacian ◽  
Natural Extensions ◽  
Distinct Distance

A unified approach to the determination of eigenvalues and eigenvectors of specific matrices associated with directed graphs is presented. Matrices studied include the new distance matrix, with natural extensions to the distance Laplacian and distance signless Laplacian, in addition to the new adjacency matrix, with natural extensions to the Laplacian and signless Laplacian. Various sums of Kronecker products of nonnegative matrices are introduced to model the Cartesian and lexicographic products of digraphs. The Jordan canonical form is applied extensively to the analysis of spectra and eigenvectors. The analysis shows that Cartesian products provide a method for building infinite families of transmission regular digraphs with few distinct distance eigenvalues.

scholarly journals B2-sequences and the distinct distance constant

2000 ◽  
Vol 39 (11) ◽  
pp. 37-42
Author(s):  
G.S Yovanof ◽  
H Taylor
Keyword(s):  
Distance Constant ◽  
Distinct Distance

scholarly journals Distinct distance sets in a graph

1991 ◽  
Vol 93 (2-3) ◽  
pp. 155-165 ◽  
Author(s):  
Richard A. Gibbs ◽  
Peter J. Slater
Keyword(s):  
Distinct Distance ◽  
Distance Sets

scholarly journals On distinct distance sets in a graph

1997 ◽  
Vol 175 (1-3) ◽  
pp. 277-282
Author(s):  
Xiaohui Lin ◽  
Minghua Zhu ◽  
Zhengguo Yu ◽  
Chengxue Zhang ◽  
Yuansheng Yang
Keyword(s):  
Distinct Distance ◽  
Distance Sets

scholarly journals A note on distinct distance subsets

2013 ◽  
Vol 104 (3) ◽  
pp. 439-442 ◽  
Author(s):  
Marcos Charalambides
Keyword(s):  
Distinct Distance

scholarly journals Distinct Distance Estimates and Low Degree Polynomial Partitioning

2014 ◽  
Vol 53 (2) ◽  
pp. 428-444 ◽  
Author(s):  
Larry Guth
Keyword(s):  
Degree Polynomial ◽  
Polynomial Partitioning ◽  
Low Degree ◽  
Distinct Distance

Graphs with few distinct distance eigenvalues irrespective of the diameters

2015 ◽  
Vol 29 ◽  
pp. 194-205 ◽  
Author(s):  
Fouzul Atik ◽  
Pratima Panigrahi
Keyword(s):  
Distance Matrix ◽  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Arbitrary Graph ◽  
Distance Spectrum ◽  
Strong Product ◽  
Strongly Regular ◽  
Distinct Distance ◽  
Simple Connected Graph ◽  
Spectrum Of Graphs

The distance matrix of a simple connected graph $G$ is $D(G)=(d_{ij})$, where $d_{ij}$ is the distance between $i$th and $j$th vertices of $G$. The multiset of all eigenvalues of $D(G)$ is known as the distance spectrum of $G$. Lin et al.(On the distance spectrum of graphs. \newblock {\em Linear Algebra Appl.}, 439:1662-1669, 2013) asked for existence of graphs other than strongly regular graphs and some complete $k$-partite graphs having exactly three distinct distance eigenvalues. In this paper some classes of graphs with arbitrary diameter and satisfying this property is constructed. For each $k\in \{4,5,\ldots,11\}$ families of graphs that contain graphs of each diameter grater than $k-1$ is constructed with the property that the distance matrix of each graph in the families has exactly $k$ distinct eigenvalues. While making these constructions we have found the full distance spectrum of square of even cycles, square of hypercubes, corona of a transmission regular graph with $K_2$, and strong product of an arbitrary graph with $K_n$

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