Tuesday, July 8, 2008

Trip to Paris, France (July 2008)

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Photo Caption: Location map of the Laboratoire d'Informatique, University of Paris 6 in Paris, France -- venue of the ONCO-MEDIA project meeting starting on July 11, 2008.


On Thursday morning (10 July 2008)
I will leave Manila and go to Paris, France for a scheduled research meeting (ONCO-Media Project, http://www.onco-media.com) via KLM flight KL 0804, departing from the Ninoy Aquino International Airport at 10:45 a.m. and arriving in Paris (via Amsterdam) at 9:20 p.m. on the same day.

This will be my third time to visit Paris, France. My first time was in August 1997 when I joined the XII World Youth Day Celebration. My second time was in September 2002 when I made a side trip to Paris (from Spain) on my way to Copenhagen (Denmark).

Our research meeting is scheduled to start on July 11 in the Laboratoire d'Informatique, University of Paris 6 ( http://www.lip6.fr/en/index.html ) in Passy, Paris, France. Our host is Dr. Patrick Brezillon.

I will attend this research meeting in my capacity as Co-Principal Investigator (for Ateneo de Manila University) of the ONCO-MEDIA project.

For more more information about ONCO-MEDIA, visit the website:
http://www.onco-media.com



Raffy 7/8/08

Congratulations to Dr. Rafael Guerrero, NAST Awardee

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From the Ateneo Blueboard:


The School of Science and Engineering of Ateneo de Manila University proudly announces that Dr. Rafael A. Guerrero, Assistant Professor of the Department of Physics, was selected as awardee of the 2008 National Academy of Science and Technology (NAST) Talent Search for Young Scientists in the field of Physics.

Dr. Guerrero, along with two other scientists from the University of Santo Tomas and the University of the Philippines-Los Banos (UPLB), had to present his paper before a panel of judges last April before being chosen as the grand winner.

Dr. Guerrero presented his paper on volume holographic storage which introduces bigger data storage for computers and a new way of producing images.

It will be recalled that he also won the Outstanding Scholarly Work Awards for Science and Engineering in 2006. He has been active in research in the area of photonics.

The awarding ceremonies will be held on July 10, 2008 at the Manila Hotel.

Congratulations, Dr. Guerrero. We are proud of you!

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Monday, July 7, 2008

Celebrator or Celebrant? Happy Birthday Jocelyn, Butch and Carlo (PSHS Alumni Association)

. Photo Caption: Shown in photo are some of the PSHS Alumni Association Board of Directors who were present during its monthly meeting held on 8 7 July 2008 in Kabisera Restaurant, Fort Bonifacio, Taguig City. From the photo collection of Raffy Saldaña (http://raffysaldana.blogspot.com/).

Yesterday (7 July 2008) the Philippine Science High School Alumni Association Board of Directors met at Kabisera Restaurant, Fort Bonifacio, Taguig City for its monthly Board of Directors meeting.

Thanks to Jocelyn (Sanchez-Mendoza), Butch (Zaldarriaga) and Carlo (Subido) for the wonderful Filipino dinner treat. (Jocelyn, Butch and Carlo are the birthday celebrators for the month of July).

HAPPY BIRTHDAY Jocelyn, Butch and Carlo! We wish you many happy returns... Goodluck, Good health, and God Bless!

Note: One of the pre-meeting discussions focused (OR focussed) on the difference between a celebrant and a celebrator :) . One English expert in the group pointed out that the proper usage should be "birthday celebrator" and not "birthday celebrant."

Today I searched Google and this is what I found:

"The American Heritage dictionary says: cel·e·brant (sµl“…-br…nt) n. 1. a. A person who participates in a religious ceremony or rite. b. The priest officiating at the celebration of the Eucharist. 2. A participant in a celebration.

USAGE NOTE: Strictly speaking, celebrant should be reserved for an official participant in a religious ceremony or rite. In an earlier survey, however, a majority of the Usage Panel accepted the use of celebrant to mean “a participant in a celebration” (as in New Year's Eve celebrants). In this more general sense, celebrator is an undisputed alternative.
"

The following PSHS (Pisay) Board Members and Alumni Guests were present at the meeting yesterday (7/7/08):

1. Pio Esguerra (Batch 2003)
2. Joyce Simpas (Batch '92)
3. Raffy Saldaña (Batch '77)
4. Tina Jardiolin (Batch '84)
5. Carlo Subido (Batch '82)
6. Jun Sabug (Batch '69)
7. Jocelyn Sanchez-Mendoza (Batch '78)
8. Susan Warren-Mercado (Batch '78)
9. Jeff Jubilado (Batch '93)
10. Butch Zaldarriaga (Batch '80)
11. Gladys Barrer (Batch '83)
12. Elena Dacanay (Batch '98)
13. Karen P. Jubilado (Batch '93)
14. Jun Bucayan (Batch '80)
Also present was Kris Llavera (PSHS AA office assistant).
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The meeting agenda include the following:
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1. Updates on the on-going projects:
a. Preparation for the PSHS Alumni Homecoming (c/o Gladys)
b. Pisay Cup (Golf Tournament c/o Carlo)
c. Pisay Concert (c/o Susan)
d. PSHS AA/ NAA merger (c/o Jocelyn and Jun)
e. Gawad Lagablab (c/o Butch)
f. PSHS Career Orientation Day (c/o Raffy)
2. Other Matters
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Click on the link below to see more photos of the event:

Cheers,

Raffy
8 July 2008
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Saturday, July 5, 2008

Call For Papers and Entries: 4th East Asia SIAM Conference/ EASIAM Student Paper Prize

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The NIMS 2008 Conference & The 4th East Asia SIAM Conference
October 10-12 2008

National Institute for Mathematical Sciences (NIMS)
Daejon, Korea

Website: http://www.math.hkbu.edu.hk/easiamconf08/


Scientific Committee:

Zhong-Ci Shi (Chair)
Chinese Academy of Sciences (CAS), China

Pham Ky Anh
Vietnam National University

Raymond Chan
The Chinese University of Hong Kong

I-Liang Chern
National Taiwan University

Victor D. Didenko
Universitii Brunei Darussalam

Roger Hosking
Universitii Brunei Darussalam

Nguyen Van Huu
Hanoi University of Science

Xiao-qing Jin
University of Macau

Hyung-Chun Lee
Ajou University

Ping Lin
National University of Singapore

Tom Mitsui
Nagoya University

Michael Ng
Hong Kong Baptist University

Hisashi Okamoto
Kyoto University

Mohd Omar
University of Malaysia

Abdul Rahni
Universiti Sains Malaysia

Rafael P. Saldana
Ateneo de Manila University

Dongwoo Sheen
Seoul National University

Zuowei Shen
National University of Singapore

Haiwei Sun
University of Macau

Tao Tang
Hong Kong Baptist University

Organizers:

Taeyoung Ha
NIMS, Korea

Chi-Ok Hwang
NIMS, Korea

Hyung-Chun Lee
NIMS and Ajou University, Korea

Zhong-Ci Shi
Chinese Academy of Sciences, China

Tao Tang
Hong Kong Baptist University

Registration, Accommodation and Visa:
will be posted soon

Paper Submission:

Please submit your abstract online. The deadline of the submission is 15 August 2008.

EASIAM Student Paper Prize:

Principal Guidelines

The EASIAM Student Paper Prizes are awarded every year to the student author(s) of the most outstanding paper(s) submitted to the EASIAM Student Paper Competition. This award is based solely on the merit and content of the student's contribution to the submitted paper.

The purpose of the Student Paper Prizes is to recognize outstanding scholarship by students in applied mathematics or computing.

Requirements for Submission

To enter the competition, each student author must study in East or Southeast Asia, and submit:
a short vitae including his/her list of publications (at most two pages).
the complete paper.

The student's advisor must submit a letter that: describes and evaluates the paper's contribution to the literature and the student's role in the scholarship; verifies that the student meets the conditions of eligibility for the award and state the study period of the student.

Notification of Prize Winners

The EASIAM president will notify the recipient(s) at least six weeks before the award date.
Each recipient is required to present his or her paper at the EASIAM meeting where the prizes are awarded.

Description of the Award

Each recipient of the EASIAM Student Paper Prize shall receive acertificate and reimbursement of up to US$250 toward travel expenses. Up to four awards will be made each year.
Please direct your submission and any questions you have to Tang Tao (The Chairman of EASIAM), email: ttang@hkbu.edu.hk.
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Friday, July 4, 2008

Talk on Soliton Theory

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ANNOUNCEMENT

What: Special Lecture on SOLITON THEORY

When: Monday, 14 July 2008, 4:30 - 6:00 p.m.

Where: Ateneo de Manila University
(Room TBA)

Guest Speaker: Prof. Mikhail Kovalyov
Professor of Mathematics
University of Alberta
Canada

Abstract:

Prof. Mikhail Kovalyov will talk about some work in Soliton Theory. Solitons are stable formations of nonlinear systems some of which might be described by PDEs, integral equations, graphs, etc. Many "soliton equations" describe motions of fluids and find a great deal of applications in the description of water waves and atmospheric waves e.g. tsunami and rogue waves.Prof. Mikhail Kovalyov is a professor of Mathematics at the University of Alberta, Canada. He obtained his PhD in Mathematics from the Courant Institute of Mathematical Sciences at New York University. He was in Ateneo, as a visiting professor, in 1993-1994. And it was at this time when he started working on the theory of solitons.
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Call For Papers: PSHS Global Forum on the Environment

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PSHS GLOBAL FORUM ON THE ENVIRONMENT

Mission:

The Global Forum's mission is to raise awareness among the target audience on the importance of environmental stewardship through the use of alternative energy and alternative fuels.

Website: http://www.pshsglobalforum.com/


Call for Papers

The Philippine Science High School (PSHS) Global Forum on the Environment intends to raise awareness, interest, and participation among global scientists and researchers on advances in science and technology which can be applied in the Philippines to aid in environmental remediation, or even better, to contribute in stopping the vicious cycle of environmental degradation. We are providing a forum that allows interaction between government, academe, and industry scientists around the world at very low cost and very broad reach using advanced Internet conferencing. Scientists and technologists are invited to submit presentations on the following topics of interest.

1) The First Virtual Conference topic is Solar and Geothermal Energy. The use of Renewable Energy has become an increasingly important environmental initiative around the world. The Philippines is in a unique global position to significantly contribute to and apply emerging technology in this field. It has a vast array of indigenous renewable energy resources, including geothermal, wind, solar, biomass, hydro, tidal and wave power, which most countries around the world do not have.

2) The Second Virtual Conference covers Alternative Fuels, Climate, and People. Oil dependence, Air Quality, and impact on People are inter-related studies being addressed by projects at many levels of government and academic research.

Important dates

First Virtual Conference: Aug 10 US, Aug 11 RP
Submission deadline: July 20, 2008
Notification of acceptance: July 27, 2008

Second Virtual Conference: Sept 27 US
Submission deadline: Aug 30, 2008
Notification of acceptance: Sept 6, 2008

Submission Guidelines

All papers accepted for publication by the PSHS Global Forum on the Environment will be available to the public, at very low cost, via the Global Forum website.

Submit your 2-4 page technical papers in Adobe PDF or Microsoft Word format. Upon notification of acceptance, please prepare a 12 minute presentation in Microsoft Powerpoint or similar format.

You will be asked to go through a dry run of your presentation via Web Meeting with one of our staffers. For the August conference, three papers will be accepted for presentation. For September, six presentations will be accepted.

Because of the electronic nature of our Virtual Conferences, and our desire to save trees, we do not encourage submissions by regular mail or courier. Please send in your submissions electronically through joseph@pshs83.org

Presentations via Virtual Conference

The Virtual Conference is held as a Web Meeting wherein every participant attends via their computer linked to the Internet. Presenters can share their screen and display their slides to the web meeting participants. Presentations are limited to 15 minutes, followed by 10 minutes of Q&A. A session with 3 presentations is expected to take 1.5 – 2 hours. Please prepare and allot your time accordingly.

For more information, contact:

Ruth Alegre Buchanan
Chief Marketing Officer
PSHS Global Forum on the Environment
E-mail: ruth@pshs83.org
Website: http://www.pshsglobalforum.com/
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Ma 20 (Calculus): Congratulations to 'A' Students (Exam 1)

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Note: Last Tuesday, 1 July 2008, I gave the 1st Long Exam to my Ma 20 (Calculus) class. I started giving the results of the exam on 2 July (Wednesday) until 4 July (Friday).

Out of the 28 students in my class, three students got a grade of 'A' in the first exam. Their raw scores are as follows (perfect score is 100 pts.):

1. Miguel Antonio ROJAS : 96

2. Ann Jillian ADONA : 93

3. Jose Isaac MONJE: 92

CONGRATULATIONS!
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Congratulations to the Ateneo Environmental Management Coalition Team

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From the Ateneo Blueboard:

The Ateneo Environmental Management Coalition (AEMC) team, composed of Mr. Herwin Jerome P. Unidad (V BS Physics with Material Science Engineering), Mr. David T. So (V, BS Physics with Material Science Engineering), Ms. Vivienne Erica M. Zerrudo (IV, BS Environmental Science), and Ms. Abigail Favis (Coach and faculty of the Environmental Science Department), was proclaimed National Winner (first place) at the ASEAN DuPont Green Vision Case Challenge held at the DuPont Far East Office in Makati last 2 July 2008.

Their winning entry is entitled "Waste to Resource Conversion at the Loyola Schools, Ateneo de Manila University". They will represent the Philippines at the ASEAN Green Vision Sustainability Forum to be held at the Singapore Management University on 16 July 2008.

Congratulations to the AEMC!
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Thursday, July 3, 2008

Ateneo de Manila University and the Europe-Asia Grid Computing Infrastructure (EUAsiaGrid) Project

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Photo Caption: (L-R) Ms. Ines Loge (Cultural Attache, Embassy of France to the Philippines), Dr. Fabian Dayrit (Dean, School of Science), Dr. Rafael Saldaña (Associate Professor, Mathematics Department), and Dr. Bernard Mely (Director, CNRS Southeast-Asia Burea) are shown with Ateneo's MedGrid Cluster in the background. Photo taken on April 23, 2008.

The School of Science and Engineering of Ateneo de Manila University is now part of a European Commission funded project on grid computing. Called “EUAsiaGrid - Towards a Common e-Science Infrastructure for the European and Asian Grids,” the project is an international research collaboration involving 15 institutions from Europe, Asia and Australia.

The EUAsiaGrid project contributes to the aims of the EU Research Infrastructure FP7 Program by promoting international interoperation between similar infrastructures with the aim of reinforcing the global relevance and impact of European e-Infrastructure.

The project's main goal is to pave the way towards an Asian e-Science Grid Infrastructure, in synergy with the other European Grid initiatives in Asia, namely EGEE-III via its Asia Federation, and both the EUChinaGRID and EU-IndiaGRID projects and their eventual follow on efforts.

Taking advantage of the existing global Grid technologies, with the specific emphasis on the European experience with the gLite middleware and applications running on top of it, the project plans to to encourage federating approaches across scientific disciplines and communities.

EUAsiaGrid will act as a support action, aiming to define and implement a policy to promote the gLite middleware developed within the EU EGEE project across Asian countries. Its main actions will be to spread dissemination, provide training, support scientific applications and monitor the results.

Aside from Ateneo de Manila University, the project consortium includes the following institutions:

1. Instituto Nazionale di Fisica Nucleare (Italy)
2. CESNET, z.s.p.p. (Czhech Republic)
3. University of Manchester (United Kingdom)
4. HEALTHGRID (France)
5. The Australian National University (Australia)
6. Academica Sinica (Taiwan)
7. Advanced Science and Technology Institute (Philippines)
8. Hydro and Agro Informatics Institute (Thailand)
9. Infocomm Development Authority (Singapore)
10. Ho Chi Minh City Institute of Information Technology (Vietnam)
11. Institute of Technology of Bandung (Indonesia)
12. National Electronics and Computer Technology Center (Thailand)
13. Universiti Putra Malaysia (Malaysia)
14. MIMOS Berhard (Malaysia)


The over-all project leader for EUASiaGrid is Dr. Marco Paganoni of the Instituto Nazional di Fisica Nucleare, Milan, Italy while the project leader for Ateneo de Manila University is Dr. Rafael Saldaña, Associate professor in the Mathematics Department.


Dr. Saldaña together with Mr. Allan Espinosa, faculty (on-leave) of the Electronics, Communications and Computer Engineering (ECCE) Department attended the EUAsiaGrid Project Launch and the International Symposium on Grid Computing on September 7 - 11, 2008 in Academia Sinica, Taipei, Taiwan.

Ateneo's Role in the Project

Ateneo de Manila University (AdMU) will be involved and contribute in WP3 (Support of Scientific Applications) and WP5 (Training). The Ateneo de Manila University partners will be involved in the subtasks: (1) Computational Chemistry/Bioinformatics and (2) Mitigation of Natural Disasters.

The Philippines is rich in natural products. There are active researchers in AdMU who are conducting molecular dynamics (MD) simulation of natural products such as carrageenan and indigenous plants with potential medicinal uses. AdMU's researchers intend to use grid computing technology to enhance the studies (MD simulations and bioinformatics aspects) of natural products.

The Philippines is also abundant in natural disasters: earthquakes, floods, volcano eruptions, landslides, etc. There are researchers in AdMU engaged in landslide modeling and simulation, climate change studies, and mitigation of natural disasters such as landslides, lahar flow, and volcano eruptions. Using grid computing technology our researchers intend to establish international collaborations towards building data grids on natural disaster mitigation and to utilize grid computing technology for modeling and simulation of natural disasters.

The Grid and High-Performance Computing Group of AdMU led by Dr. Rafael Saldaña has conducted training programs in the past in the area of high performance computing and computational science. AdMU will be involved in the Training subtask (WP5) and is aiming to conduct a national workshop on the benefits of and best practices in the usage of Grid Computing Technology, particularly in the fields of biomedical computing/bioinformatics/computational chemistry and mitigation of natural disasters, as part of the promotion of the proposed EU-Asia Grid infrastructure.

In addition to the EUAsiaGrid project, the School of Science and Engineering is also involved in ONCO-MEDIA (an international project funded by the ICT Asia Regional Program of the French government) and the Philippine e-Science Grid project of the Department of Science and Technology Advanced Science and Technology Institute (DOST-ASTI).

For more information about the EUAsiaGrid project visit the website http://www.euasiagrid.org/ or contact Dr. Saldaña at raffysaldana@gmail.com
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Wednesday, July 2, 2008

Is This Dementia? (A Funny Thing Happened To Me On My Way To The Forum)

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This is not about the broadway play nor the film, "A Funny Thing Happened on the Way to the Forum."

I just want to have a "catchy" subtitle for this blog entry...

Earlier today ( 2 July 2008) I went to Leong Hall (the new Social Science building in campus) to attend the Environmental Leadership Forum. When I reached the hall I was surprised to see a different event going on, not a forum. I thought that perhaps I went to the wrong venue. Later, when I rechecked my invitation (I did not bring it along with me earlier), I realized that the forum was scheduled on July 3 and not July 2. I was correct about the venue but I was wrong about the date.

When I reflected on what happened I began to have a scary thought. Am I having a case of "dementia"?

Or is this just a case of watching too much "Dr. House" on tv?

I am not a medical doctor but I deal with biomedical-related research, particularly in computing and medical informatics.

My first instinct was to look into an online encyclopedia like Wikipedia and search for introductory information.

Here are some information that I gathered from a Wikipedia article on dementia:

"
1. Dementia (from Latin de- "apart, away" + mens (genitive mentis) "mind") is the progressive decline in cognitive function due to damage or disease in the brain beyond what might be expected from normal aging.

2. Although dementia is far more common in the
geriatric population, it may occur in any stage of adulthood. This age cutoff is defining, as similar sets of symptoms due to organic brain dysfunction are given different names in populations younger than adulthood (see, for instance, developmental disorders).

3. Dementia is a non-specific illness
syndrome (set of symptoms) in which affected areas of cognition may be memory, attention, language, and problem solving. Higher mental functions are affected first in the process. Especially in the later stages of the condition, affected persons may be disoriented in time (not knowing what day of the week, day of the month, month, or even what year it is), in place (not knowing where they are), and in person (not knowing who they are).

4. Symptoms of dementia can be classified as either reversible or irreversible, depending upon the
etiology of the disease. Less than 10 percent of cases of dementia are due to causes which may presently be reversed with treatment. Causes include many different specific disease processes, in the same way that symptoms of organ dysfunction such as shortness of breath, jaundice, or pain are attributable to many etiologies. Without careful assessment of history, the short-term syndrome of delirium can easily be confused with dementia, because they have many symptoms in common. Some mental illnesses, including depression and psychosis, may also produce symptoms which must be differentiated from both delirium and dementia [1].

Reference: [1]
American Family Physician, March 1, 2003

"
Of course, the best way to confirm my speculation is for me to undergo medical examination and consult experts in the field.

So, am I just overreacting? Should I accept that the fact I am "aging" now and will soon enter another phase of life? Or is this just a case of "brain overload" (too much information processing)?

I know that it is an overreaction on my part but I'm just "thinking out loud."

And besides, I want to introduce the topic dementia in my blog :)

One thing I know for sure -- dementia is not funny.

Cheers,

Raffy
7/2/08

Reminder: July 7, 2008 is Alternative Class Program Day in Ateneo de Manila University

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TO THE ATENEO LOYOLA SCHOOLS COMMUNITY:

Please be reminded of the Alternative Class Program/INAF Day on July
7, 2008. A copy of memo from the Vice President for the Loyola Schools
is pasted below for your reference.

Thank you very much,

Evelyn Q.


21 June 2008

MEMO TO: The Loyola Schools Community

FROM: Ma. Assunta C. Cuyegkeng
Vice President

SUBJECT: Alternative Class Program/INAF Day
-----------------------------------------------------------------------------

The Ateneo Debate Society (ADS) is hosting the Australasian
Intervarsity Debate Championship. To assist ADS in their need to
provide venues for 150 matches for Monday, 7 July 2008, we have agreed
to hold the Alternative Class Program/INAF
Day on the same day.

First year students will be given the opportunity to observe the
debates and prepare for the annual Horacio de la Costa Cup, a debate
tournament among first year English classes. Further announcements
will be made by the Sanggunian ng mga Mag-aaral ng Ateneo, in
cooperation with the English Department.

The National Service Training Program-Plus (NSTP+), the Junior
EngagEment Program (JEEP), and the Pabaon will hold their plenary
sessions for all second, third, and fourth year students,
respectively. Details will be announced by the respective Program
Coordinators.

Please be reminded that these three programs are part of the LS
Integrated Non-Academic Formation Program (INAF). Since INAF is
integral to Ateneo education, completion of the programs is needed to
be cleared for graduation.

The Alternative Class Program/INAF Day will replace regular
undergraduate classes from 7:30 a.m. to 6:00 p.m. Regular
undergraduate classes will resume at 6:00 p.m. Graduate classes will
proceed, as scheduled, for the whole day.

Thank you very much.

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Tuesday, July 1, 2008

A Twitter, A Blogger, A Multiplier

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Remember the phrase, "The butcher, the baker, the candlestick maker" from a nursery rhyme?

Well, I have a modern version of that phrase..."A Twitter, A Blogger, A Multiplier."

Twitter refers to the social networking software that is freely available on the Web/Internet or a person who has a Twitter account.

Blogger refers to someone who writes a blog (like me) using a blogging software like Blogspot (or Blogger).

Multiplier is my term for someone who uses the social networking software Multiply -- which is reportedly very popular among Filipinos.

Well, I am a Twitter, a Blogger, and a Multiplier.I also subscribe to other social networking softwares such as Facebook, LinkedIn, Plaxo Pulse, WYAN, MySpace, Friendster, etc...

Why do I subscribe to these free softwares?

One reason is curiosity.

I'm curious about the features of these software, their functionalities, design, appearance, usability, and other software engineering aspects. Many of my colleagues in computing/computer science also subscribe to several social networking softwares for the same reason that I mentioned.

Of course, it also helps to connect to family members, friends, former classmates, colleagues and other people (even strangers) through these various softwares.

And most of all, they are free.

Raffy
7/2/08

Activities, 1 July 2008

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Some of my activities today, 1 July 2008. Note: Click on the image to see a larger view.
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7/1/08

Laboratory Exercise No. 4 (Ma195a15, Numerical Analysis): Mathematica and Bisection Method

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For my class in Ma 195a15 (Seminar on Numerical Analysis) today (1 July 2008) I discussed the Secant Method and later I taught my students how to write a Mathematica loop construct using the While[] function. The example I gave is the Mathematica implementation of the Bisection Method. See figure above. (Note: Click on the image to see a larger view).

Use of Technology in Math: Plot of f(x), Limit of f(x)

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Given the function f(x) = ( Absolute Value of (3x -1) )/(x -1), shown above is the graph of f(x) using the Mathematica command Plot[ ]. Notice that f(x) is undefined when x = 1 and the line x = 1 is a vertical asymptote. (Note: Click on the image to see a larger view.)

As x approaches 1 from the left, f(x) approaches negative infinity.

As x approaches 1 from the right, f(x) approaches positive infinity.

For a limit to exist, the limit from the left must be equal to the limit from the right.

Therefore, we can say that the limit of f(x) as x approaches 1 does not exist (DNE) .

Note: I gave a similar item to my Ma 20 (Calculus) class in their first long exam today (1 July 2008). The students do not have an access to a computer or a graphing calculator during the exam. But they have access to a scientific calculator. So the students have to plot f(x) by producing an x y table where y = f(x). For example, when x = 0, y = -1. This item is worth 10 points in the exam. There were 10 items with a total of 100 points.

(P.S. Thanks for the feedback/correction I received from Dr. Pablo Manastas.)