@article{goodman:singleuser:1996,
author = “David J. Goodman and P. Krishnan and Binay Sugla”,
title = “Minimizing Queuing Delays and Number of Messages in Mobile Phone Location”,
journal = “Mobile Networks and Applications”,
volume = “1″,
number = “1″,
pages = “39-48″,
year = “1996″,
url = “citeseer.ist.psu.edu/20574.html” }

Minimizing Queuing Delays and Number of Messages in Mobile Phone Location

In this paper, Goodman et. al made two contributations.

First, they established a model of paging a single mobile user in $N$ cells within $D$ rounds. They assume $p_1=\ldots=p_N=\frac{1}{N}$ and paging strategy is to arbitrarily partition the cells into equal-sized subsets. The also assumes the calls arrives at Poisson distribution and the bottle neck of the paging process is at the radio channels. They construct the $M/M/1$ model, that is, multiple calls arrives at multiple users, while only a single user sent by a single call can be paged at a time. Through analysis, they established the distribution of the queue length in while calls are waiting to page.

Second, they designed an algorithm, of complexity $\Theta(N^2 D)$, using dynamical program, such that a paging strategy can be generated through the $p_i$s and the expected number of paged cells is minimized.

@article{2318447,
author = {Martin Davis},
title = {Hilbert’s Tenth Problem is Unsolvable},
journal = {Am. Math. Monthly},
volume = {80},
number = {3},
year = {1973},
pages = {233–269},
publisher = {Mathematical Association of America},
address = {Washington, DC, USA},
}

Hilbert’s Tenth Problem Is Unsolvable

This is a comprehensible proof to the intractability to the Hilbert’s 10th Problem

Hilbert 10th problem – decide if there is an integer solution to a Diophantine equation.

Unsolvable.

@article{135397,
author = {James P. Jones and Yuri V. Matijasevi\v{c}},
title = {Proof or recursive unsolvability of Hilbert’s tenth problem},
journal = {Am. Math. Monthly},
volume = {98},
number = {10},
year = {1991},
issn = {0002-9890},
pages = {689–709},
publisher = {Mathematical Association of America},
address = {Washington, DC, USA},
}

Proof of Recursive Unsolvability of Hilbert’s Tenth Problem

The USSR version of Hilbert Tenth Problem.

Hilbert 10th problem – decide whether there is a integer solution to an Diophantine equation.

This is a short proof showing the problem is unsolvable.