## Saturday, August 29, 2009

### Stamp - Singapore and Philippines 40 Years of Diplomatic Relations (Bridges)

Miniature sheet of the joint stamp issue with the theme ''Bridges''
Top-left: ''Bamban Bridge'' - (Philippines)
Top-right: "Cavenagh Bridge'' - (Singapore)
Bottom-left: ''Henderson Waves" and "Alexandra Arch" - (Singapore)
Bottom-right: ''Marcelo Fernan Bridge'' - (Philippines)

The joint stamp issue with the theme ''Bridges''

Date of Issue: 28 August 2009
Denominations: 1st local, 65¢, 80¢ & $1. 10 Stamp Size: 40.8mm x 29.85mm Miniature Sheet: 120mm x 75mm Perforation: 13 Paper: Unwatermarked Printing Process: Offset Lithography Printer: Secura (Singapore) Pte Ltd Sheet Content: 10 stamps per sheet Designer: Victorino Z. Serevo Graphic Designer: Chan Willie From https://shop.vpost.com.sg/vPOSTMall/execute/viewCatalog?catalog=CSK09 and https://shop.vpost.com.sg/vPOSTMall/images/philatelic/CSK09.pdf First Day Cover of the joint stamp issue with the theme ''Bridges'' (large) First Day Cover of the miniature sheet joint stamp issue with the theme ''Bridges'' (large) ''Henderson Waves" and "Alexandra Arch" - (Singapore) Picture (large) is obtained from http://heathergarratt.files.wordpress.com/2009/01/p1030202.jpg Presentation pack front cover (large) - Singapore and Philippines 40 Years of Diplomatic Relations (Bridges) Extracted from the stamp leaflet accompanying the stamps. This year marks the 40th Anniversary of the establishment of diplomatic relations between Singapore and the Philippines. To commemorate this anniversary, Singapore and the Philippines will be releasing this joint stamp issue with the theme ''Bridges'', which aims to illustrate the close and multifaceted ties between both countries. Chosen bridges include Henderson Waves & Alexandra Arch and Cavenagh Bridge from Singapore, as well as Bamban Bridge and Marcelo Fernan Bridge from the Philippines. ''Henderson Waves" and "Alexandra Arch" - (Singapore) Picture is obtained from http://farm3.static.flickr.com/2374/2504216647_3b4c890b44.jpg ''Henderson Waves" and "Alexandra Arch" , both found along the Southern Ridges, were opened May 2008. Presently Singapore's highest pedestrian bridge, standing 36m above Henderson Road. ''Henderson Waves" and "Alexandra Arch" - (Singapore) Picture is obtained from Henderson Waves connects Mount Faber park to Telok Blangah Hill Park, while the smaller bridge Alexandra Arch, connects Kent Ridge Park to Telok Blangah Hill Park via the Flora Walk. ''Henderson Waves" and "Alexandra Arch" - (Singapore) Picture is obtained from http://ymsim.files.wordpress.com/2009/01/p10904782.jpg (medium) From Presentation pack - the joint stamp issue with the theme ''Bridges'' Top-right: "Cavenagh Bridge'' - (Singapore) "Cavenagh Bridge'', built in 1868, is the oldest bridge on the Singapore River. Built to commemorate the 50th Anniversary of the founding of the Crown Colony of the Straits Settlement, it was converted to a pedestrian bridge. Now, with lighting added in the 1990s to accentuate its architectural features at nightfall, it provides the most convenient pedestrian link between the cultural district at the north bank and the commercial district to the south of the Singapore River. Picture is obtained from Top-left: ''Bamban Bridge'' - (Philippines) ''Bamban Bridge'', crossing the Sacobia-Bamban River system, along the MacArthur Highway between Mabalacat, Pampanga and Bamban. Tarlac, is one of the modern and sleek-looking bridges in The Philippines. The bridge's arch has a span of 174 metres and contains 1,400 tons of steel. It is one of the longest bridges of its type in the world and was completed sometime around 1998. Picture is obtained from https://shop.vpost.com.sg/vPOSTMall/execute/viewDetail?itemSku=CSK09@^CSK09AST Note: Orientation is slightly different Top-right: ''Marcelo Fernan Bridge'' - (Philippines) ''Marcelo Fernan Bridge'' is an extradosed cable-stayed bridge located in Metro Cebu, Cebu in the Philippines. It spans across Mactan Channel connecting Cebu Island to Mactan Island. Opened in August 1999 to decongest the traffic from the older Mactan-Mandaue Bridge, the bridge has a total length of 1237 metres with a centre span of 185 metres. This bridge is one of the widest and longest bridge span in the Philippines, and is named after Senator Marcelo Fernan from Cebu City. From Presentation pack - the joint stamp issue with the theme ''Bridges'' (large) Extracted from the text behind the envelope of the first day cover. The Philippines and Singapore enjoy a warm bilateral relationship. Both countries also work closely together in ASEAN as well as various international and regional fora. On the economic front, the Philippines is also one of Singapore's major trading partners within ASEAN. Issued against the backdrop of the 40th Anniversary of the establishment of diplomatic relations between Singapore and the Philippines, this set of stamps commemorates the warm relationship between both countries. ''Henderson Waves" and "Alexandra Arch" - (Singapore) Picture is obtained from First Day Cover (without stamps): S$0.25*
Pre-cancelled First Day Cover affixed with stamps or miniature sheet: S$3.65* each Presentation Pack: S$4.60*
Pre-cancelled Commemorative Cover affixed with Singapore and Philippines stamps: S\$4.55*

• Obtainable from any Post Office and Singapore Philatelic Museum.
• * Prices inclusive of 7% GST for purchases within Singapore.
• 1st Local stamps can be used to make up the postage for overseas mail.
• The designs in the leaflet were reproduced from rough, visuals.
• Details may be subject to changes.

''Henderson Waves" and "Alexandra Arch" by night - (Singapore)
Picture is obtained from http://neatorama.cachefly.net/images/2008-08/henderson-wave-bridge.jpg

Reference

## Sunday, August 23, 2009

### Chocolate may cut heart attacks

GOOD news for heart attack survivors:
Those who eat chocolate two or more times per week cut their risk of dying from heart disease about threefold, compared to those who never touch the stuff, scientists have reported.

Extracted from MY PAPER MONDAY AUGUST 17, 2009, A14 MY LIFESTYLE
(My Lifestyle Moment)
From http://myepaper.mypaper.sg/ebook/web_php/fvbrowserjsback.php?urljs=http://myepaper.mypaper.sg/ecreator/sphopf/ep170809cnd_opf_files/ep170809cnd.js&ver=Gen
by AGENCE FRANCE-PRESSE

A new study, led by Dr Imre Janszky of the Karolinska Institute in Stockholm, is the first to demonstrate that consuming chocolate can help ward off the grim reaper if one has suffered an acute heart attack.

It seems that antioxidants in cocoa are a likely candidate” for explaining the life-saving properties, said Dr Kenneth Mukamal, a co-author of the study.

Antioxidants are compounds that protect against so-called free radicals, molecules which accumulate in the body over time, that can damage cells and are thought to play a role in heart disease, cancer and the ageing process.

In the study, Dr Janszky and colleagues tracked 1,169 non-diabetic men and women, 45 to 70 years old, in Stockholm County during the early 1990s, from the time they were hospitalised with their first heart attack.

Picture is obtained from http://www.abc.net.au/reslib/200706/r153151_548938.jpg

The participants were queried before they left hospital on their food consumption habits over the previous year, including how much chocolate they ate on a regular basis. They underwent a health examination three months after discharge and were monitored for eight years after that.

The incidence of fatal heart attacks correlated inversely with the amount of chocolate consumed.

The researchers caution that clinical trials are needed to back up the findings of their study.

In the meantime, however, a bit of chocolate may not be amiss, they suggest.

by AGENCE FRANCE-PRESSE

Reference

## Saturday, August 22, 2009

### Mathematics - Matrices (Part 1)

The question:
Write the matrix equation representing the following simultaneous equations and hence solve the equation 5y = 39 - 2x and 11x = 1 + 3y using matrices.

Solution:
(Explanation can be obtained from the Properties of Matrices, presented after the answer).

Rewriting the simultaneous equations,
2x + 5y = 39
11x - 3 y = 1

The simultaneous equations may be represented by the matrix equation

Therefore x = 2, y = 7 (Answer).

Picture is obtained from http://www.philipmantione.com/matrix1.jpg

Properties of Matrices

From:
http://www.sosmath.com/matrix/matrix0/matrix0.html - Introduction and Basic Operations (Author: M.A. Khamsi)

• Matrices involved in the addition operation must have the same size

The following are obtained from
Additional Mathematics, 8th Edition, by The Keng Seng, Loh Cheng Yee, Consultant: Dr. Yeap Ban Har, Shinglee Publishers Pte Ltd, Chapter 8 - “Matrix and its Applications”, Page 215 to 229.

Multiplication of Matrices:
• A matrix of the order m x n multiplied by a matrix of order n x p will result in a matrix of order m x p.

Given that

The order of matrix A is 1 x 2 (1 row by 2 columns), of matrix B is 2 x 1 and of matrix C is 2 x 2.

For the matrix product AB to exist, the number of columns of matrix A must be equal to the number of rows of matrix B. The order of AB will be given by the number of rows of A and the number of columns of B.

The Inverse Matrix
In the real number system, there exists an additive identity, 0, such that a + 0 = 0 + a = a.

For matrix there also exists an additive identity which is the null matrix, 0, such that A + 0 = 0 + A = A.

A Null matrix is a matrix in which all the elements are equal to 0.

considering only 2 x 2 matrices, we have:

In the real number system, there exists an multiplicative identity, 1, such that a x 1 = 1 x a = a.

Similarly there exists for matrices, the multiplicative identity, I, such that AI = IA = A.

In the number system, for every number a, there is an additive inverse, -a, such that a + (-a) = 0;
and a multiplicative inverse
,

The additive inverse of a matrix can be found easily.

The multiplicative inverses of matrices are the following.

In general, if A and B are two matrices and AB = BA = I, then B is said to be the inverse of A, denoted by and A is said to be the inverse of B, denoted by

When the inverse of a matrix is mentioned, it generally refers to its multiplicative inverse.

If A is the inverse of B, then the order of A and B are the same, eg. 2 x 2.

where the difference of the product of the elements on the leading diagonal and the product of the elements of the other diagonal is 2.

Pre-multiplying A by B, i.e. BA,

Post-multiplying A by B, i.e. AB, we have,

The difference of the products of the elements in the leading diagonal and the other diagonal in A is 2, and the product AB is twice the unit matrix.

General Cases:
Consider the general 2 x 2 matrix

Using the multiplicative inverse matrix rule above, let

In general,

The expression ad - bc is known as the determinant of the matrix A and is denoted by

If det A = 0, then the inverse of A is not defined because

is not defined.

In such a case, A does not have an inverse.
Where a matrix does not possess an inverse, it is known as a singular matrix.

References