A simple proof of the unimodular property for the basic loop matrix

1967 ◽  
Vol 55 (4) ◽  
pp. 564-565
Author(s):  
R.S. Wilkov
Keyword(s):  
Simple Proof ◽  
Loop Matrix ◽  
Basic Loop

Valve-Shut off Scheme and Affected Zone Analysis of Multi-Sources Looped-Pipe Network Based on ARCGIS

2015 ◽  
Vol 713-715 ◽  
pp. 178-181
Author(s):  
Fang Wei
Keyword(s):  
Data Model ◽  
Functional Method ◽  
Calculation Model ◽  
Heat Sources ◽  
Pipe Network ◽  
Heat Network ◽  
Hydraulic Regime ◽  
Pipe Bursting ◽  
Loop Matrix ◽  
Basic Loop

Based on ArcGIS,Multi-heat sources and multi-loops complex heating network is Modeled and simulated ,and a functional method is put forward, by using Geodatabase data model,it can creat relating matrix and basic loop matrix of heat network quickly,and calculate Hydraulic Regime of heating Network with the Basic Circuit.When pipe-bursting accident occur in heating Network,along with changes in the logical network model.also the entire calculation model is changed.This method is applied to the Study of Valve-shut off scheme after tube-burst accident ,the heating Influence of the accident can be quantitative analyzed , also the degree of influence is compared when tube-burst accident happen at different place.

scholarly journals A simple proof of Andrews’s 5 F 4 evaluation

2013 ◽  
Vol 36 (1-2) ◽  
pp. 165-170 ◽  
Author(s):  
Ira M. Gessel
Keyword(s):  
Simple Proof

A simple proof of existence of weak and statistical solutions of Navier–Stokes equations

1992 ◽  
Vol 436 (1896) ◽  
pp. 1-11 ◽  
Keyword(s):  
Weak Solution ◽  
Initial Data ◽  
Natural Number ◽  
Simple Proof ◽  
Stokes Equations ◽  
Galerkin Approximation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Existence Proofs ◽  
Statistical Solutions

The Galerkin approximation to the Navier–Stokes equations in dimension N , where N is an infinite non-standard natural number, is shown to have standard part that is a weak solution. This construction is uniform with respect to non-standard representation of the initial data, and provides easy existence proofs for statistical solutions.

scholarly journals A representation theorem for the linear quasi-differential equation(py′)′+qy=0

2000 ◽  
Vol 23 (8) ◽  
pp. 579-584
Author(s):  
J. G. O'Hara
Keyword(s):  
Differential Equation ◽  
Comparison Theorem ◽  
Simple Proof ◽  
Representation Theorem ◽  
Second Order ◽  
Order Linear

We establish a representation forqin the second-order linear quasi-differential equation(py′)′+qy=0. We give a number of applications, including a simple proof of Sturm's comparison theorem.

A simple proof of the kinematic formula

1988 ◽  
Vol 105 (4) ◽  
pp. 279-285 ◽  
Author(s):  
P. Mani-Levitska
Keyword(s):  
Simple Proof ◽  
Kinematic Formula

An argument of a function in H1/2

2012 ◽  
Vol 55 (2) ◽  
pp. 507-511
Author(s):  
Takahiko Nakazi ◽  
Takanori Yamamoto
Keyword(s):  
Hardy Space ◽  
Simple Proof ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc

AbstractLet H1/2 be the Hardy space on the open unit disc. For two non-zero functions f and g in H1/2, we study the relation between f and g when f/g ≥ 0 a.e. on ∂D. Then we generalize a theorem of Neuwirth and Newman and Helson and Sarason with a simple proof.

A Simple Proof that ζ(2) =  $$\frac{\pi^{2}}{6}$$

2011 ◽  
Vol 33 (3) ◽  
pp. 81-82 ◽  
Author(s):  
Michael D. Hirschhorn
Keyword(s):  
Simple Proof
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