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31.5.12

The Good, The Bad, and The Ugly Aspects of Cholesterol

The Good, The Bad, and The Ugly Aspects of Cholesterol
From:  http://www.yourmodernliving.com/the-good-the-bad-and-the-ugly-aspects-of-cholesterol/


Although we generally think of cholesterol in a negative way we cannot survive without some cholesterol in our system. It is produced by our liver and is needed to:
  • Produce Vitamin D
  • Help in making certain hormones
  • Build cell walls
  • Create bile salts(help digest fat)·
Besides our body producing its’ own cholesterol we also get it from certain foods that we eat. Our body does produce enough cholesterol on its own, so any extra that we take in through our diet may not always be a good thing. Avoiding food that is high in bad cholesterol can be a challenge in this fast paced society that we live in.
There are two types of cholesterol. There is the good cholesterol which we refer to as HDL and then there is the bad cholesterol which we know as LDL(low density lipoprotein).
Cholesterol needs a way to get to all the cells in your body and the way they do that is through our bloodstream. Proteins first form a shell around the cholesterol and then release it into our blood system allowing it to travel where it is needed.
Any extra cholesterol is just let go into the bloodstream where it keeps circulating and building up. This buildup can eventually clog the blood vessels which will increase the chances for heart disease and stroke.
Keeping these levels of cholesterol or our LDL in check is vital for a healthy life.
The other type of cholesterol found in our system is referred to as HDL or High Density Lipoproteins. This good cholesterol can help prevent atheroma forming. Atheroma is fatty deposits in the arteries which can lead to various cardiovascular diseases. The way HDL helps to prevent these fatty deposits from forming is by taking the extra unwanted cholesterol back to the liver.
In order to maintain a healthy body we need to keep these two types in balance. We need to have a low count for the LDL’s and a high count for the HDL’s.
We can lower our LDL’s through diet. We need to avoid foods high in cholesterol. Many foods that are high in cholesterol are also high in fat content. So a rule of thumb would be that by avoiding fatty foods you are avoiding food high in cholesterol.
Our focus when it comes to cholesterol seems to be on lowering the bad cholesterol or the LDL and not on increasing the HDL’s. A popular opinion as to why that is has to do with the drug companies that produce the medication to help a person lower their cholesterol. Their medications all seem to deal with lowering LDL’s as they have not found an effective way to raise HDL’s through medication.
Two things that you can do to raise your HDL’s is to lose weight and quit smoking. Both of these will help you in your fight against cardiovascular disease.


29.5.12

How they voted

How the senators voted on CJ Corona's impeachment trial


"This impeachment breaks new ground...I find the respondent guilty." -Senator Edgardo Angara...



Verdict: Not guilty. "This is not justice, political or legal. certainly not the law..it is only naked power, as it was in 1972." -Senator Joker Arroyo...


Verdict: Guilty. "Hindi ko po matanggap ang interpretasyon ng pinakamataas na hukom ng bansa." -Senator Alan Peter Cayetano...


Verdict: Guilty. "The failure to declare $2.4 million and P80 million is not minor." -Sen. Pia Cayetano...


Verdict: Not guilty. "Does SALN omission amount to an impeachable offense? NO! SALN carries light penalty, allows correction." and added, as she addressed her colleagues " I am insulted by the way your minds run." -Senator Miriam Defensor-Santiago...


Verdict: Guilty. "He has lost his moral fitness as leader." -Senator Franklin Drilon...


Verdict: Guilty. "Ikinalulungkot ko na di ko po masasang-ayunan ang posisyong ito ni Chief Justice Corona. . Para sa akin, maliwanag ang mga batas natin at di ito nagbabanggaan. Ang pinagbabawalan ng FCDU law na mag-release ng impormasyon ukol sa dollar deposits ay ANG MGA BANKO AT DI ANG DEPOSITOR. " -Senator Francis Escudero...


Verdict: Guilty "I pray that as we conclude this defining moment, we can unite again as a nation, as a society." -Senator Jinggoy Estrada...


Verdict: Guilty. ""Ang nasasakdal na punong mahistrado ay hindi na, hindi na po karapat-dapat sa pagtitiwala ng sambayanang Pilipino." -Senator TG Guingona...


Verdict: Guilty. "He is no longer fit to preside in highest court in the land. May duda na sa kakayahan ng ating punong hukom. " -Senator Gringo Honasan...


Verdict: Guilty. "Guilty as charged under Art II on the Articles of impeachment." -Senator Panfilo Lacson...


Verdict: Guilty: "Sa akin ay malinaw na malinaw na si chief justice ay lumabag sa batas." -Senator Lito Lapid...

Verdict: Guilty. "My chief concern is the credibility and the trust of our people in the most important institution of the land." -Senator Loren Legarda...


Verdict: Not guilty. "When the furor has died down and this political storm has subsided, I know that like the lady Justice we shall find solace in the fact that this decision, though maybe not popular, was fair, impartial and just." -Senator Bongbong Marcos...


Verdict: Guilty. "There is more reason to apply the law when the assets in question amount to P180 million." -Senator Sergio Osmena III...


Verdict: Guilty. "The Chief Justice displayed a disturbing pattern of dishonesty." -Senator Kiko Pangilinan...


Verdict: Guilty. "Ang batas para kay Juan, ay batas rin para kay Renato." -Senator Koko Pimentel...


Verdict: Guilty. "It is easy to impeach one man. What is hard is to impeach hunger, joblessness, poverty." -Senator Ralph Recto...


Verdict: "Napakahirap man, alang-alang sa pagkakaisa at paghilom ng ating bayan. alang-alang sa pagpapatibay ng institusyon ng ating pamahalaan at nang darating pang henerasyon. I found Chief Justice Renato Corona guilty." -Senator Bong Revilla...


Verdict: Guilty. "Ang tunay na hukom sa paglilitis na ito ay ang taong bayan." -Senator Tito Sotto...


Verdict: Guilty. "From now on, no one is untouchable." -Senator Antonio Trillanes...


Verdict: Guilty -Senator Manuel Villar


"This court means serious business and would not succumb or to allow underhanded tactics and gimmickry to deter this court from our tasks."... - Senate President Juan Ponce Enrile

Chief Justice Renato Corona: Guilty as charged

Chief Justice Renato Corona: Guilty as charged
From:  http://ph.news.yahoo.com/verdict-is-out.html


After 43 trial days and hundreds of grueling hours of hearing, the Senate sitting as impeachment court have declared Chief Justice Renato Corona guilty.




An overwhelming majority of Senators, 20-3, voted for the removal of Corona from office, most of them noting that the top magistrate no longer deserves his post. This makes Corona the first government official to be convicted by an impeachment court.



Senators Edgardo Angara, Alan Peter Cayetano and Pia Cayetano, Franklin Drilon, Francis Escudero, Jose "Jinggoy" Estrada, TG Guingona, Gringo Honasan, Panfilo Lacson, Lito Lapid, Loren Legarda, Sergio Osmena III, Kiko Pangilinan, and Koko Pimentel, Ralph Recto, Bong Revilla, Tito Sotto, and Antonio Trillanes, Manny Villar, and presiding officer Juan Ponce Enrile all have voted for Corona's conviction.



Senators Joker Arroyo, Miriam Santiago, Ferdinand "Bongbong" Marcos Jr., meanwhile voted for Corona's acquittal.



"The Senate, sitting as an impeachment court, having tried Chief Justice Renato Corona, upon three articles of impeachment charged against him by the House of Representatives, by a guilty vote of 20 senators, has found him guilty of the charge under Article II.



"Now therefore, be it adjudged that Renato Corona, is hereby convicted of the charge against him in Article II of the Articles of impeachment, so ordered," Enrile added.



Enrile also said as he explained his vote, "there is deliberate act of excluding substantial assets."



"This is not justice, political or legal. Certainly not the law..it is only naked power, as it was in 1972," however said Arroyo as he defended his vote.



Each senator was given two minutes to explain their votes while as presiding officer, Senate President Juan Ponce Enrile was last to vote.



Corona was impeached by the House of Representatives in December after 188 congressmen signed the impeachment complaint.



From the original eight, the prosecution team reduced its complaint to three articles of impeachment.



Article II: Non-inclusion of assets in SALN



Deemed as the prosecution’s strongest case, Article II of the impeachment complaint accuses Corona of inaccurately declaring his assets, including peso and dollar deposits and real estate properties.



In his 2010 statement of assets, liabilities and net worth, Corona declared "cash and investments" amounting to P3.5 million.



The prosecution team presented bank managers of the Bank of Philippine Islands and Philippine Savings Bank who testified that Corona has at least P31 million peso deposits.



The defense team, on the other hand, presented Ombudsman Conchita Carpio-Morales as hostile witness who accused the chief justice of having $10-million deposits, citing transaction records from the Anti-Money Laundering Council report.



But Corona refuted these and claimed that he has a combined peso and dollar accounts only worth P185 million.



He said he did not declare his dollar deposits worth $2.4 million or around P105 million because of the confidentiality guaranteed by the banking secrecy and foreign currency deposit units laws.



As for the P80-million peso accounts, Corona said they are commingled funds that he does not solely own. These accounts contain the expropriation proceeds of the sale of the lot owned by his wife’s company, Basa Guidote Enterprises Inc., the common funds from his late mother, and some savings of his children.



Meanwhile, Corona declared five real properties in his SALN including a house and lot in Quezon City and four condominium units.



The chief justice, however, allegedly owns various properties under the name of his children, who, the prosecution said, have questionable capacity to acquire posh properties.



Article III: Flip-flopping decision



In Article 3, the prosecution panel intended to cast doubt on Corona's competence, integrity, probity, and independence as a chief justice following the Supreme Court's flip-flopping decision in the case between the Flight Attendants and Stewards Association of the Philippines (FASAP) and the Philippine Airlines (PAL).



The prosecution presented FASAP President Roberto Anduiza to testify that then Associate Justice Corona was responsible for the recall of the SC ruling in favor of the alleged illegally retrenched 1,400 PAL flight attendants.



PAL Vice President for Sales Exequiel Javier also took the witness stand to expose the alleged perks and special privileges that Corona received, including a platinum card that gave him unlimited top class courtesy travel, which the prosecutors believe motivated Corona to rule in favor of PAL.



However, Senate President Juan Ponce Enrile stopped the prosecution from presenting Javier as he pointed out that the prosecution never accused the chief justice of receiving favors and gifts in the articles of impeachment.



Meanwhile, the defense was not able to present evidence to refute the allegations due to time constraint.



Corona said he was supposed to explain the issue in his narrative testimony but his poor health prevented him from doing so.



Article VII: The Corona-Arroyo affair



Article VII emphasizes Corona's ties to former president Gloria Macapagal-Arroyo, who named him chief justice in May 2010.



The prosecution presented Justice Secretary Leila De Lima to prove that Corona played a special role to allow the Arroyo couple to escape electoral sabotage charges.



The SC issued a temporary restraining order on a government-issued travel ban against Arroyo, who said was leaving the country to seek medical treatment, but the Department of Justice ordered airport authorities to defy the SC order. The former president now Pampanga representative is now under hospital arrest.



De Lima cited incidents mentioned in the dissenting opinion of Associate Justice Maria Lourdes Sereno which the justice secretary said clearly showed that Corona was acting in favor of Arroyo.



The impeachment court, however, ruled De Lima’s testimonies as hearsay since she was not present during the SC’s discussion of the TRO and merely reading Sereno’s dissenting opinion.



The prosecution wanted Sereno to testify but the Senate refused to issue a subpoena.



Corona said his explanation on this accusation was also part of his testimony but he was forced to cut it short as he was not feeling well.



Closing arguments



While the senator-judges will decide on three articles of impeachment, the prosecution and defense teams decided to focus their closing statements on Article II of the impeachment complaint.



The prosecutors said they have strongly proved that Corona is “morally unfit” to remain as chief justice since he lied about his SALN to conceal his wealth.



The defense, on the other hand, insisted that the non-disclosure of some of Corona’s accounts does not constitute an impeachable offense as he did it in “good faith.”





.

.

12.4.12

Sorli's Conjecture, April 2012

If N = {q^k}{n^2} is an odd perfect number with Euler prime q,
then Sorli's conjecture predicts that k = 1.

From previous posts, we have the implication "n < q ---> k = 1".

Here, we show other statements that imply n < q.

Claim #1:  If q = sigma(n), then n < q.

Proof of Claim #1:
Suppose that q = sigma(n).  Then

sigma(n)/q = 1 < sigma(n)/n = q/n < sigma(q)/n

From previous posts, sigma(n)/q < sigma(q)/n ---> n < q.


Claim #2:  If sigma(q) = sigma(n), 
then n < q.

Proof of Claim #2:
Suppose that sigma(q) = sigma(n).  Then

sigma(n)/q = sigma(q)/q < sigma(n)/n = sigma(q)/n

From previous posts, sigma(n)/q < sigma(q)/n ---> n < q.

29.3.12

Society of Actuaries - Grade Slip - Jose Arnaldo Dris

Sorli's Conjecture, March 2012 (Part II)

If N = {q^k}{n^2} is an odd perfect number given in Eulerian
form, then Sorli's conjecture predicts that k = 1.

We will be needing the following theorem from the author's
M. Sc. thesis:

[Dris, 2008]  If N = {q^k}{n^2} is an odd perfect number given in
Eulerian form, then q^k < n^2.

It follows that, if n < q, then k = 1.

Here, we prove the following result:

If sigma(n) < sigma(q), then n < q 
if and only if sigma(n)/q < sigma(q)/n.


Suppose sigma(n) < sigma(q).


If n < q, then 1/q < 1/n.  It follows that sigma(n)/q < sigma(q)/n.


If sigma(n)/q < sigma(q)/n, then since sigma(q)/q < sigma(n)/n,
it follows that n < q.


QED.


In fact, we have the following result:


If sigma(n) < sigma(q), then n < q.

Since sigma(n) < sigma(q), 1 < sigma(q)/sigma(n).

But sigma(q)/q < sigma(n)/n, which implies that

sigma(q)/sigma(n) < q/n.

It follows that n < q.

QED.


As a bonus, we have:

If sigma(n)/q < sigma(q)/n, then n < q.


Now, in order to show that:


If n < q, then sigma(n) < sigma(q).


we need to rule out Case 2:  n < q < sigma(q) < sigma(n), which is
equivalent to sigma(q)/sigma(n) < 1 < q/n.

Sorli's Conjecture, March 2012

If N = {q^k}{n^2} is an odd perfect number given in Eulerian form
(i.e. q == k == 1 (mod 4) and gcd(q, n) = 1), then

I(q) = sigma(q)/q <= 6/5 < sqrt(5/3) < I(n) = sigma(n)/n.

This implies that:

sigma(q)/sigma(n) < q/n

There are three cases to consider:

Case 1: sigma(q)/sigma(n) < q/n < 1

This is equivalent to the case q < sigma(q) < n < sigma(n)
alluded to before.

Multiplying through by sigma(n):

sigma(q) < q*I(n) < sigma(n)

Dividing through by q:

I(q) < I(n) < sigma(n)/q

Considering the reciprocals:

1 < n/q < sigma(n)/sigma(q)

Multiplying through by sigma(q):

sigma(q) < n*I(q) < sigma(n)

Dividing through by n:

sigma(q)/n < I(q) < I(n)

Hence:  sigma(q)/n < I(q) < I(n) < sigma(n)/q.

But: q < sigma(q) < n < sigma(n)

Therefore: sigma(q)/n < 1 < I(q) < I(n) < sigma(n)/q.

Case 2: sigma(q)/sigma(n) < 1 < q/n


This is equivalent to the case n < q < sigma(q) < sigma(n)
alluded to before.


Multiplying through by sigma(n):


sigma(q) < sigma(n) < q*I(n)


Dividing through by q:


I(q) < sigma(n)/q < I(n)

Considering the reciprocals:

n/q < 1 < sigma(n)/sigma(q)

Multiplying through by sigma(q):

n*I(q) < sigma(q) < sigma(n)

Dividing through by n:

I(q) < sigma(q)/n < I(n)

Therefore:

1 < I(q) < sigma(q)/n < I(n) < 2
1 < I(q) < sigma(n)/q < I(n) < 2

Case A:
If sigma(q)/n < sigma(n)/q, then since
sigma(q)/q < sigma(n)/n, it follows that:

sigma(q)(1/n + 1/q) < sigma(n)(1/q + 1/n)

Therefore:  sigma(q) < sigma(n).
(No contradictions under Case 2 so far.)

Case B:
If sigma(n)/q < sigma(q)/n, then since
sigma(q)/q < sigma(n)/n, it follows that:

(1/q)(sigma(n) + sigma(q)) < (1/n)(sigma(q) + sigma(n))

Therefore:  n < q.
(No contradictions under Case 2 so far.)

Case 3:  1 < sigma(q)/sigma(n) < q/n

This is equivalent to the case n < sigma(n) <= q < sigma(q)
alluded to before.

Multiplying through by sigma(n):

sigma(n) < sigma(q) < q*I(n)

Dividing through by q:

sigma(n)/q < I(q) < I(n)

Considering the reciprocals:

n/q < sigma(n)/sigma(q) < 1

Multiplying through by sigma(q):

n*I(q) < sigma(n) < sigma(q)

Dividing through by n:

I(q) < I(n) < sigma(q)/n

Hence: sigma(n)/q < I(q) < I(n) < sigma(q)/n.

But: n < sigma(n) <= q < sigma(q)

Therefore: sigma(n)/q <= 1 < I(q) < I(n) < sigma(q)/n.