scholarly journals An arc graph distance formula for the flip graph

2017 ◽  
Vol 145 (7) ◽  
pp. 3179-3184
Author(s):  
Funda Gültepe ◽  
Christopher J. Leininger
Keyword(s):  
Graph Distance ◽  
Flip Graph ◽  
Distance Formula

A note on Steiner reciprocal degree distance

2020 ◽  
Vol 12 (04) ◽  
pp. 2050050
Author(s):  
D. Sarala ◽  
S. K. Ayyaswamy ◽  
S. Balachandran ◽  
K. Kannan
Keyword(s):  
Connected Graph ◽  
Natural Generalization ◽  
Bipartite Graphs ◽  
Graph Distance ◽  
Straightforward Method ◽  
Steiner Formula ◽  
Degree Distance ◽  
Complete Bipartite Graphs ◽  
Gutman Index ◽  
Distance Formula

The concept of reciprocal degree distance [Formula: see text] of a connected graph [Formula: see text] was introduced in 2012. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. The [Formula: see text]-center Steiner reciprocal degree distance defined as [Formula: see text], where [Formula: see text] is the Steiner [Formula: see text]-distance of [Formula: see text] and [Formula: see text] is the degree of the vertex [Formula: see text] in [Formula: see text]. Motivated from Zhang’s paper [X. Zhang, Reciprocal Steiner degree distance, Utilitas Math., accepted for publication], we find the expression for [Formula: see text] of complete bipartite graphs. Also, we give a straightforward method to compute Steiner Gutman index and Steiner degree distance of path.

scholarly journals Best Simultaneous Approximation in Orlicz Spaces

2007 ◽  
Vol 2007 ◽  
pp. 1-7 ◽  
Author(s):  
M. Khandaqji ◽  
Sh. Al-Sharif
Keyword(s):  
Banach Space ◽  
Simultaneous Approximation ◽  
Closed Subspace ◽  
Orlicz Spaces ◽  
Unit Interval ◽  
Luxemburg Norm ◽  
Integrable Functions ◽  
Best Simultaneous Approximation ◽  
Distance Formula

LetXbe a Banach space and letLΦ(I,X)denote the space of OrliczX-valued integrable functions on the unit intervalIequipped with the Luxemburg norm. In this paper, we present a distance formula dist(f1,f2,LΦ(I,G))Φ, whereGis a closed subspace ofX, andf1,f2∈LΦ(I,X). Moreover, some related results concerning best simultaneous approximation inLΦ(I,X)are presented.

A note on the Gordian complexes of some local moves on knots

2018 ◽  
Vol 27 (09) ◽  
pp. 1842002
Author(s):  
Kai Zhang ◽  
Zhiqing Yang
Keyword(s):  
Infinite Family ◽  
Distance Formula

In this paper, the [Formula: see text]-move is defined. We show that for any knot [Formula: see text], there exists an infinite family of knots [Formula: see text] such that the Gordian distance [Formula: see text] and pass-move-Gordian distance [Formula: see text] for any [Formula: see text]. We also show that there is another infinite family of knots [Formula: see text] (where [Formula: see text]) such that the [Formula: see text]-move-Gordian distance [Formula: see text] and [Formula: see text]-Gordian distance [Formula: see text] for any [Formula: see text] and all [Formula: see text].

scholarly journals Movement of a railway car rolling down a classification hump with a tailwind

2018 ◽  
Vol 216 ◽  
pp. 02027 ◽  
Author(s):  
Khabibulla Turanov ◽  
Andrey Gordienko
Keyword(s):  
Frost Resistance ◽  
Gravitational Force ◽  
Frictional Resistance ◽  
Resistance Force ◽  
Kinematic Parameters ◽  
Wind Resistance ◽  
Acceleration Time ◽  
Research Results ◽  
D’Alembert Principle ◽  
Distance Formula

The purpose of this paper is to calculate kinematic parameters of a railway car moving with a tailwind for designing a classification hump. The calculation of kinematic parameters is based on the d'Alembert principle, and the physical speed and distance formula for uniformly accelerated or uniformly decelerated motions of a body. By determining a difference between two components - gravitational force of a car and the resistance force of all kinds (frictional resistance, air and wind resistance, resistance from switches and curves, snow and frost resistance), which take place at different sections of a hump profile, the authors calculated the car acceleration at various types of car resistance, as well as time and speed of its movement. Acceleration, time and speed were plotted as a function of the length of a hump profile section. The research results suggest that permissible impact velocities of cars can be achieved by changing profiles of projected hump sections or by using additional hump retarders.

scholarly journals A whole-brain and cross-diagnostic perspective on functional brain network dysfunction

2018 ◽  
Author(s):  
Marjolein Spronk ◽  
Kaustubh Kulkarni ◽  
Jie Lisa Ji ◽  
Brian P. Keane ◽  
Alan Anticevic ◽  
...  
Keyword(s):  
Mental Illness ◽  
Resting State ◽  
Brain Network ◽  
Functional Network ◽  
Graph Distance ◽  
Network Organization ◽  
Whole Brain ◽  
Functional Brain ◽  
Functional Brain Network ◽  
Mental Diseases

AbstractA wide variety of mental disorders have been associated with resting-state functional network alterations, which are thought to contribute to the cognitive changes underlying mental illness. These observations have seemed to support various theories postulating large-scale disruptions of brain systems in mental illness. However, existing approaches isolate differences in network organization without putting those differences in broad, whole-brain perspective. Using a graph distance measure – connectome-wide correlation – we found that whole-brain resting-state functional network organization in humans is highly similar across a variety of mental diseases and healthy controls. This similarity was observed across autism spectrum disorder, attention-deficit hyperactivity disorder, and schizophrenia. Nonetheless, subtle differences in network graph distance were predictive of diagnosis, suggesting that while functional connectomes differ little across health and disease those differences are informative. Such small network alterations may reflect the fact that most psychiatric patients maintain overall cognitive abilities similar to those of healthy individuals (relative to, e.g., the most severe schizophrenia cases), such that whole-brain functional network organization is expected to differ only subtly even for mental diseases with devastating effects on everyday life. These results suggest a need to reevaluate neurocognitive theories of mental illness, with a role for subtle functional brain network changes in the production of an array of mental diseases.

Sign in / Sign up

Export Citation Format

Share Document