2019 Newsletter: 58/61 — PreviousNext — (Attach.)

Sydney Harbour

Hello and Welcome,

Meetings This Week:

Tuesday Forum - Tuesday Nov 19th - 9:30 am (10:00 am meeting start) - 12 noon

We can discuss the recent monthly Windows updates plus the new Windows 10 1909 updates. Then the usual Q&A and other discussions.

Digital Photography - Friday Nov 22nd - 9:30 am (10:00 am meeting start) - 12 noon

Hear about all the newest digital photography topics.

And, of course, there will be the usual Q&A and other discussions.

Meeting Next Week:

Main Meeting - Tuesday Nov 26th - 5:30 pm (6:00 pm meeting start) - 8:00 pm

Current & Upcoming Meetings:

79 2019/11/02 - 14:00-17:00 - 02 Nov, Saturday - Penrith Group
80 2019/11/08 - 09:30-12:30 - 08 Nov, Friday - Friday Forum
81 2019/11/08 - 12:30-15:30 - 08 Nov, Friday - Communications
82 2019/11/12 - 17:30-20:30 - 12 Nov, Tuesday - Programming
83 2019/11/16 - 13:30-16:30 - 16 Nov, Saturday - Web Design
84 2019/11/19 - 09:30-12:30 - 19 Nov, Tuesday - Tuesday Forum
85 2019/11/22 - 09:30-12:30 - 22 Nov, Friday - Digital Photography
86 2019/11/26 - 17:30-20:30 - 26 Nov, Tuesday - Main Meeting

87 2019/12/07 - 14:00-17:00 - 07 Dec, Saturday - Penrith Group
88 2019/12/10 - 17:30-20:30 - 10 Dec, Tuesday - Programming + after-SIG visit to the StarBar
89 2019/12/13 - 09:30-12:30 - 13 Dec, Friday - Friday Forum + lunchtime visit to the StarBar
90 2019/12/13 - 12:30-15:30 - 13 Dec, Friday - Communications
91 2019/12/17 - 09:30-12:30 - 17 Dec, Tuesday - Tuesday Forum + lunchtime visit to the StarBar


Tech News:

“What's New in Windows 10's November 2019 Update, Available Now”:

See the How-To Geek article by CHRIS HOFFMAN | @chrisbhoffman | UPDATED NOVEMBER 13, 2019, 11:36AM EDT.

Microsoft released Windows 10's November 2019 Update, codenamed 19H2, on November 12. Also known as Windows 10 version 1909, this is the smallest, quickest Windows 10 Update yet. It's practically just a service pack.

To install the update, head to Settings > Update & Security > Windows Update. Click "Check for Updates." You'll see a message saying the update is available. Click "Download and install now" to get it.

A "Less Disruptive Update" With Fewer Changes

Microsoft's John Cable explains that this update "will be a scoped set of features for select performance improvements, enterprise features, and quality enhancements." In other words, expect a select set of bug fixes, performance tweaks, and a handful of business features.

If you're sick of big Windows 10 updates every six months, Windows 10's November 2019 Update (19H2) is the update for you! Installing this update will be more like installing a standard cumulative update like the updates that arrive on Patch Tuesday. It should be a small download with a fast installation process — no long reboot and purging of old Windows installations necessary.

Computers with the May 2019 Update (also known as 19H1) installed will get a small patch via Windows Update and quickly update themselves to the November 2019 Update (19H2.) This will likely arrive sometime in November 2019, as the name suggests.

With Windows 7's end of life looming on January 14, 2020, Microsoft clearly wants to avoid a repeat of last year's buggy October 2018 Update.

It's already out there and being tested. As of September 5, Microsoft says every Windows Insider in the "Release Preview" ring has been offered Windows 10 version 1909. A year ago, Windows 10's October 2018 Update was released without any testing in the Release Preview ring at all. On October 10, Microsoft said Windows Insiders in the Release Preview ring already had what Microsoft expects is the final build.

Online Search in File Explorer

File Explorer has a new search experience. When you type in the search box, you'll see a dropdown menu with a list of suggested files. It will also search for files in your OneDrive account online — not just files on your local PC. You can also right-click one of the search results here to open the file's location.

You can still access the more powerful, classic search experience by pressing Enter. This will allow you to search non-indexed locations, for example.

This feature was initially added to Windows 10's 20H1 update but was moved to the 19H2 update.

Read more »

“Australia releases advice to counter 'foreign interference' after university cyber attacks”:

See the Cyber Security Online article by Liam Tung (CSO Online) on 15 November, 2019 04:16.

The Australian Government has published the "Guidelines to counter foreign interference in the Australian university sector" in response to recent targeted cyberattacks aimed at stealing research and intellectual property.

Minister for Education, Dan Tehan, and Minister for Home Affairs, Peter Dutton, announced the new guidelines for universities on Thursday.

The guidance is the result of the University Foreign Interference Taskforce launched in August over concerns that state-backed foreign organizations were attempting to interfere with the research agendas of Australian universities through funding deals and cyber attacks.

Universities are to use the 44-page guidance document to mitigate the risks of foreign interference when collaborating with foreign entities. It defines foreign interference as efforts to alter a university's research agenda, applying economic pressure, recruiting researchers, and hacking.

"The Director-General of ASIO says foreign interference against Australia's interests is at an unprecedented level that includes universities and the research sector," Dutton said.

Duncan Lewis, the now former head of ASIO, in September warned that espionage and foreign interference was "by far and away the most serious issue going forward" for Australia, ahead of terrorism.

The Australian National University, based in Canberra, detailed a massive data breach that occurred in November 2018 after a senior staff member opened a spearphishing email loaded with malware. The breach was not detected until April 2019 and potentially exposed a database with 19 years worth of research records as well as personal information on staff.

According to ANU's post-mortem of the incident, the attackers used custom-built malware and zero-day vulnerabilities to breach ANU's Enterprise Systems Domain (ESD) network.

China appears to be viewed as the major cyber threat to Australian universities, however Iran-based hackers have also been accused of hacking Australian research bodies and universities.

Read more »

Fun Facts:

“Paul Erdös and Egyptian Fractions”:

Egyptian fractions are fractions which have 1 in the numerator, like 1/2, 1/3 or 1/97 etc.

In fact, the Ancient Egyptians liked to express ordinary fractions, like 10/73 as sums of fractions using 1 as the numerator. [ We don't really know why. ] And they especially liked finding these sums with distinct denominators.

"One of the great mathematician Paul Erdös' earliest mathematical interests was the study of so-called Egyptian fractions, that is, finite sums of distinct fractions having numerator 1."

"The Rhind Papyrus of Ahmes is one of the oldest known mathematical manuscripts, dating from around 1650 B.C. It contains among other things, a list of expansions of fractions of the form 2/n into sums of distinct unit fractions, that is, fractions with numerator 1.

Examples of such expansions are 2/35 = 1/30 + 1/42 and 2/63 = 1/56 + 1/72 .

We can also consider expansions of more general rational numbers into sums of unit fractions with distinct denominators such as:

10/73 = 1/11 + 1/22 + 1/1606 and 67/2012 = 1/31 + 1/960 + 1/2138469 + 1/10670447077440."

Here, we will just consider one of Erdös' (unsolved) conjectures about these interesting fractions.

The Greedy Algorithm

To find any of these sums, we can subtract the largest unit fraction from the given fraction and continue until the whole sum is revealed.

For example, try 10/73. Take the reciprocal, i.e. 73/10 giving 7.3, so we round the number up to 8 and subtract 1/8 from the given fraction (being the largest that we can use without going negative). If we use 1/7, that is too big and we end up with 10/73 - 1/7 = -3/511.

Using 1/8 leads to 10/73 - 1/8 = 7/584. Repeating, we calculate 584/7 = 83.428... so the next unit fraction that we use is 1/84. This leads to 7/584 - 1/84 = 1/12264. As soon as we get a unit fraction we can stop.

So, we end up with the "Greedy" sum: 10/73 = 1/8 + 1/84 + 1/12264.

You can see the progression of numerators in this algorithm (starting with 10, next was 7 and finally 1). It can be proved that this sequence is strictly decreasing, showing that the algorithm must stop eventually and does not turn into an infinite sequence of terms.

Ubasic and the n//m syntax

A few years ago, I came across the program Ubasic which uses multi-precision integers to do calculations. It is a very handy program to calculate with large numbers and primes among other things.

To calculate with Egyptian fractions, one amazing syntax is to use a double slash to indicate that the calculations should be done exactly, keeping the numerator and denominator as whole numbers.

For example, to add the three fractions 23/56, 91/370 and 123/256, we just say "print 23//56 + 91//370 + 123//256" and this produces the fraction 376981//331520 rather than the unhelpful decimal number 1.1371289816602316601....

So, you can easily write a Ubasic program to take a fraction and find its Greedy sum.

That unsolved Erdös problem

What Erdös wanted to find out was "Can the fraction 4/n always be split into only three Egyptian fractions?" Four are obviously sufficient as the solution 1/n + 1/n + 1/n + 1/n shows.

For example, 4/409 = 1/103 + 1/14043 + 1/295794731 + 1/174989045478929991 using the Greedy algorithm.

Four fractions are needed here, but that's no good.

Try again: Here's one that does work with just three unit fractions: 4/409 = 1/105 + 1/3906 + 1/7987770.

But, can we prove it can work for all values of n? [ We can easily prove that we only have to use prime denominators because if the number n was equal to p*q and we had a solution for 4/p we could just multiply through by 1/q for each fraction and we get a solution for 4/(p*q). ]

Erdös worked on Egyptian fractions in 1932, 1950 and later, and we're still working on this "simple" problem!

Of course, the sensible thing would be to solve infinitely many of these numbers at once by resorting to some algebra:

Start with the expression: (120t + 80) / (30t + 20) = 4 = (120t + 73 + 5 + 2) / (30t + 20)

Then 4 = (120t + 73) / (30t + 20) + 1 / (6t + 4) + 1/ (15t + 10)

Or: 4 / (120t + 73) = 1 / (30t + 20) + 1 / (120t + 73)*(6t + 4) + 1 / (120t + 73)*(15t + 10)

Setting t = 0, 1, 2 ... gives the first few examples:

4 / 73 = 1/20 + 1/(73*4) + 1/(73*10) = 1/20 + 1/292 + 1/730
4 / 193 = 1/50 + 1/(193*10) + 1/(193*25) = 1/50 + 1/1930 + 1/4825
4 / 313 = 1/80 + 1/(313*16) + 1/(313*40) = 1/80 + 1/5008 + 1/12520
+ infinitely many other solutions

That takes care of all numbers of the form (120t + 73). Unfortunately, there don't appear to be simple algebraic solutions for all possible numbers.

For example, numbers of the form (120t + 1) seem to be rather tricky. Can you find such a formula?

Here is a link to the 1989 - 2000 UBASIC package:

UBASIC for IBM-PC version 8.8f

UBASIC is a BASIC interpreter with multiprecision arithmetic,
UBASIC is a free software written by Yuji KIDA at Rikkyo University
in Japan(kida@rkmath.rikkyo.ac.jp),
If the line is very thin and hard to download via FTP, send me
an file list selected below.

haber zip b 31150 961014 Tutorial by Seymour Haber
ubmalm zip b 34303 940623 number theory programs by D.Malm
ubiapl96 zip b 124896 970504 applications until 1996
ubgraph zip b 82654 970504 graphic applications
ubhelp zip b 58345 970524 help files
ub16i88f zip b 107959 001007 main exec file(16bit)
ub32i88f zip b 108448 001007 main exec file(32bit)
ubc88f zip b 106719 001007 main exec file(CGA)
ppmpx36e zip b 74913 991224 integer factorization on DOS-window


Bob Backstrom
~ Newsletter Editor ~

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