scholarly journals Square root stress-sum index for graphs

2021 ◽  
Author(s):  
K. B. Mahesh ◽  
R. Rajendra ◽  
P. Siva Kota Reddy
Keyword(s):  
Topological Index ◽  
Shortest Paths ◽  
Square Root ◽  
Node Centrality ◽  
Centrality Index ◽  
Root Stress

The stress of a vertex is a node centrality index, which has been introduced by Shimbel (1953). The stress of a vertex in a graph is the number of geodesics (shortest paths) passing through it. In this paper, we introduce a new topological index for graphs called square root stress sum index using stresses of vertices. Further, we establish some inequalities, prove some results and compute stress-sum index for some standard graphs.

A Theory of Fracture Based Upon an Extension of Continuum Mechanics to the Nanoscale

2005 ◽  
Vol 73 (5) ◽  
pp. 792-798 ◽  
Author(s):  
Eun-Suok Oh ◽  
Jay R. Walton ◽  
John C. Slattery
Keyword(s):  
Numerical Simulation ◽  
Long Range ◽  
Continuum Mechanics ◽  
Bulk Material ◽  
Stress Singularity ◽  
Intermolecular Forces ◽  
Square Root ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Root Stress

A theory of fracture is presented that is based upon an extension of continuum mechanics to the nanoscale through the incorporation of long-range intermolecular forces which correct bulk material descriptions near interfaces. The surface energy on crack surfaces, which is given in terms of the long-range intermolecular forces, plays an important role in an expression for the stress distribution near the crack tip. It is observed through numerical simulation that the incorporation of these long-range intermolecular forces removes the square-root stress singularity predicted by classical linear elastic fracture mechanics.

Node centrality in weighted networks: Generalizing degree and shortest paths

2010 ◽  
Vol 32 (3) ◽  
pp. 245-251 ◽  
Author(s):  
Tore Opsahl ◽  
Filip Agneessens ◽  
John Skvoretz
Keyword(s):  
Shortest Paths ◽  
Weighted Networks ◽  
Node Centrality

Fatigure and Reliability Analysis on Tether of Submerged Floating Tunnel under Vortex-Induced Vibration

2012 ◽  
Vol 170-173 ◽  
pp. 1669-1672 ◽  
Author(s):  
Xiao Jun Zhou ◽  
Gang Luo
Keyword(s):  
Reliability Index ◽  
Probability Model ◽  
Water Current ◽  
Square Root ◽  
Mean Square ◽  
Euler Beam ◽  
Submerged Floating Tunnel ◽  
Energy Equilibrium ◽  
The Mean ◽  
Root Stress

The tether used to balance a submersed floating tunnel under water current is definitely subject to greater pre-tension, and is simplified as a Bernoulli-Euler beam. The fatigure characteristics of vortex-induced multi-modal resonance of tether under traverse shear flow are analyzed. In terms of the principle of energy equilibrium, both the mean square root displacement and mean square root stress of the dynamic response of tether is derived.The reliability index of tether is obtained in combination with S-N curve and fatigure probability model.

About the Complexity of Square Root Extraction Algorithms in Finite Fields and Residue Rings

Vestnik MEI ◽  
2018 ◽  
Vol 5 (5) ◽  
pp. 79-88
Author(s):  
Sergey B. Gashkov ◽  
◽  
Aleksandr B. Frolov ◽  
Elizaveta Р. Popova ◽  
◽  
...  
Keyword(s):  
Finite Fields ◽  
Square Root ◽  
Root Extraction

The digital function filters – algorithms and applications

2013 ◽  
Vol 61 (2) ◽  
pp. 371-377
Author(s):  
M. Siwczyński ◽  
A. Drwal ◽  
S. Żaba
Keyword(s):  
Digital Filters ◽  
Phase Shifters ◽  
Square Root ◽  
Real Power ◽  
The Real ◽  
Distributed Parameters ◽  
Digital Modeling ◽  
Analysis And Synthesis ◽  
Basic Functions ◽  
Recursive Formulas

Abstract The simple digital filters are not sufficient for digital modeling of systems with distributed parameters. It is necessary to apply more complex digital filters. In this work, a set of filters, called the digital function filters, is proposed. It consists of digital filters, which are obtained from causal and stable filters through some function transformation. In this paper, for several basic functions: exponential, logarithm, square root and the real power of input filter, the recursive algorithms of the digital function filters have been determined The digital function filters of exponential type can be obtained from direct recursive formulas. Whereas, the other function filters, such as the logarithm, the square root and the real power, require using the implicit recursive formulas. Some applications of the digital function filters for the analysis and synthesis of systems with lumped and distributed parameters (a long line, phase shifters, infinite ladder circuits) are given as well.

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