scholarly journals A PROOF OF ISBELL’S ZIGZAG THEOREM

2008 ◽  
Vol 84 (2) ◽  
pp. 229-232 ◽  
Author(s):  
PIOTR HOFFMAN
Keyword(s):  
Intuitive Proof

AbstractWe provide a short, intuitive proof of Isbell’s zigzag theorem.

scholarly journals A linear-optical proof that the permanent is # P -hard

2011 ◽  
Vol 467 (2136) ◽  
pp. 3393-3405 ◽  
Author(s):  
Scott Aaronson
Keyword(s):  
Quantum Computing ◽  
Complexity Theory ◽  
Universality Theorem ◽  
Linear Optical ◽  
Intuitive Proof

One of the crown jewels of complexity theory is Valiant's theorem that computing the permanent of an n × n matrix is # P -hard. Here we show that, by using the model of linear-optical quantum computing —and in particular, a universality theorem owing to Knill, Laflamme and Milburn—one can give a different and arguably more intuitive proof of this theorem.

On the asymptotic distribution of the size of a stochastic epidemic

1983 ◽  
Vol 20 (2) ◽  
pp. 390-394 ◽  
Author(s):  
Thomas Sellke
Keyword(s):  
Population Size ◽  
Asymptotic Distribution ◽  
Epidemic Process ◽  
Stochastic Epidemic ◽  
Original Number ◽  
Intuitive Proof

For a stochastic epidemic of the type considered by Bailey [1] and Kendall [3], Daniels [2] showed that ‘when the threshold is large but the population size is much larger, the distribution of the number remaining uninfected in a large epidemic has approximately the Poisson form.' A simple, intuitive proof is given for this result without use of Daniels's assumption that the original number of infectives is ‘small'. The proof is based on a construction of the epidemic process which is more explicit than the usual description.

scholarly journals A Historical Note On The Proof Of The Area Of A Circle

2011 ◽  
Vol 8 (3) ◽  
Author(s):  
Yonah Wilamowsky ◽  
Sheldon Epstein ◽  
Bernard Dickman
Keyword(s):  
Twelfth Century ◽  
Historical Note ◽  
Mathematics Majors ◽  
Mathematical Literature ◽  
Intuitive Proof ◽  
Infinite Sequences

Proofs that the area of a circle is ?r2 can be found in mathematical literature dating as far back as the time of the Greeks. The early proofs, e.g. Archimedes, involved dividing the circle into wedges and then fitting the wedges together in a way to approximate a rectangle. Later more sophisticated proofs relied on arguments involving infinite sequences and calculus. Generally speaking, both of these approaches are difficult to explain to unsophisticated non-mathematics majors. This paper presents a less known but interesting and intuitive proof that was introduced in the twelfth century. It discusses challenges that were made to the proof and offers simple rebuttals to those challenges.

scholarly journals An Intuitive Proof of Brouwer's Theorem in $\mathbb{R}^2$

1984 ◽  
Vol 0010 ◽  
pp. 53-60
Author(s):  
C. C. Morrison ◽  
M. Stynes
Keyword(s):  
Intuitive Proof

scholarly journals Managing Queues with Heterogeneous Servers

2011 ◽  
Vol 48 (2) ◽  
pp. 435-452 ◽  
Author(s):  
Jung Hyun Kim ◽  
Hyun-Soo Ahn ◽  
Rhonda Righter
Keyword(s):  
Waiting Time ◽  
Waiting Times ◽  
Structural Result ◽  
Batch Arrivals ◽  
Optimal Thresholds ◽  
Mean Waiting Time ◽  
Server Problem ◽  
The Mean ◽  
The Impact ◽  
Intuitive Proof

We consider several versions of the job assignment problem for an M/M/m queue with servers of different speeds. When there are two classes of customers, primary and secondary, the number of secondary customers is infinite, and idling is not permitted, we develop an intuitive proof that the optimal policy that minimizes the mean waiting time has a threshold structure. That is, for each server, there is a server-dependent threshold such that a primary customer will be assigned to that server if and only if the queue length of primary customers meets or exceeds the threshold. Our key argument can be generalized to extend the structural result to models with impatient customers, discounted waiting time, batch arrivals and services, geometrically distributed service times, and a random environment. We show how to compute the optimal thresholds, and study the impact of heterogeneity in server speeds on mean waiting times. We also apply the same machinery to the classical slow-server problem without secondary customers, and obtain more general results for the two-server case and strengthen existing results for more than two servers.

scholarly journals NEAR-ISOMETRIES BETWEEN $C(K)$-SPACES

2005 ◽  
Vol 48 (3) ◽  
pp. 585-594
Author(s):  
N. J. Cutland ◽  
G. B. Zimmer
Keyword(s):  
Linear Operator ◽  
Representation Theorem ◽  
Hausdorff Spaces ◽  
Standard Analysis ◽  
Invertible Linear Operator ◽  
Non Standard Analysis ◽  
Intuitive Proof

AbstractLet $X$, $Y$ be compact Hausdorff spaces and let $T:C(X,\mathbb{R})\to C(Y,\mathbb{R})$ be an invertible linear operator. Non-standard analysis is used to give a new intuitive proof of the Amir–Cambern result that if $\|T\|\hskip1pt\|T^{-1}\|\lt2$, then there is a homeomorphism $\psi:Y\to X$. The approach provides a proof of the following representation theorem for such near-isometries:$$ Tf=(T1_X)(f\circ\psi)+Sf, $$with $\|S\|\leq2(\|T\|-(1/\|T^{-1}\|))$, so $\|S\|\lt\|T\|$. If $\|T\|\hskip1pt\|T^{-1}\|=1$, then $S=0$, giving the well-known representation for isometries.

Sign in / Sign up

Export Citation Format

Share Document