Free VIN check

Auto check is basically free if we use the following website and put the VIN after "&vin=" .

http://mydealerbiz.com/inventory/autocheck_car_report.php?sid=5052057&vin=

A college math problem

Is there a positive and twice differentiable function f defned on [0,∞) such
that f(x)f’’(x) ≤ -1 on [0,∞) ? Why or why not???

The answer is NO:

Suppose the statement is true. Then $f(x)>0, f''(x)<0 $ for all [tex] x>0 [/tex]. Moreover, $\lim_{x\rightarrow +\infty} f''(x)<0 $ if it exists. Let [tex] f(0)>0, f'(x) [/tex] is monotonically decreasing, then [tex]\lim_{x\rightarrow +\infty} f'(x) [/tex] is either [tex] -\infty [/tex] or a constant.

If [tex]\lim_{x\rightarrow +\infty} f'(x)=-\infty [/tex], then [tex]f [/tex] is monotonically decreasing on [tex] [T,\,+\infty)[/tex] for some [tex]T [/tex] large enough and [tex]\lim_{x\rightarrow+\infty} f(x) [/tex] must be negative. Otherwise, [tex]\lim_{x\rightarrow+\infty} f(x)=c_0\geq 0 [/tex] and there exists a unbounded sequence [tex]\{x_n\}[/tex] so that [tex]\lim_{n\rightarrow +\infty} f'(x_n)=0 [/tex]. Contradiction;

if [tex]\lim_{x\rightarrow +\infty} f'(x)=c [/tex], where [tex]c[/tex] is a constant, then there exists a unbounded sequence [tex]\{x_n\}[/tex] so that [tex]\lim_{n\rightarrow +\infty} f''(x_n)=0 [/tex], but we already have [tex]\lim_{n\rightarrow +\infty} f''(x_n)<0 [/tex]. Contradiction. P. S. Note that the assumption is [tex]f(x)\cdot f''(x)\leq -1 [/tex] on [tex][0,\,+\infty)[/tex]. If we change it into [tex]f(x)\cdot f''(x)<0 [/tex], then we cannot have [tex]\lim_{x\rightarrow +\infty} f''(x)<0 [/tex] and in this case the statement is true: e.g.: Let [tex]f(x)=\ln (x+2)[/tex]. Then we have [LEFT] [tex]\begin{align*} f'(x)&=1/(x+2),\\ f''(x)&=-1/(x+2)^2. \end{align*}[/tex] [/LEFT] Therefore, for all [tex]x\geq 0[/tex], we have [LEFT][tex]\begin{align*}f(x)\cdot f''(x)&=-\frac{\ln (x+2)}{(2+x)^2}<0 \\ \intertext{and} f(x)&>0.
\end{align*}[/tex][/LEFT][/QUOTE]

A very nice personal website

http://www.deminy.net/blog/

Beer Suggestions in Canada

1. Alexander Reiths (Brewed in Nova Scotia, Canada)




2. Rickard's Red (Montreal, Canada)




3. Hoegaarden (Belgium)



4. Stella Artois (Belgium)



5. Corona (Mexico)



6. Guinness (Ireland)

Garmin nuvi comparsion chart

Chinese Restaurants in London, Ontario

1. Mandarin Restaurant: 387 Wellington Road, N6C 4P9 (519) 680-5000‎;

2. Harmony Grand Buffet: 304 Talbot Street, (519) 433-8000 (the east side neighbor of the Greyhound Bus terminal of London);

3. 边城：Ben Thanh Restaurant, 57 York Street, to the west side of the Greyhound Bus terminal of London, Tel.: 519-438-4888;

4. 满江红 （川味, Sichuan cuisine）New Kung Fu House - london, 689 Oxford Street West ( Capulet Walk and Oxford Street, near Wonderland St. ), 519-472-3120;

5. 红萍 （粤式, Cantonese cuisine）Hong Ping Restaurant, 339 Horton Street East, N6B 1L6, 519 -858-3074 (at the southeast corner of Horton Street and waterloo street)；

6. 金碧 Kambie Restaurant， 375 Horton St. 519-434-8787；

7. 六福 （Cantonese dim sum） Ken's Restaurant, 699 Wilkins Street, (near Wellington St.) 519-668-1133;

8. 人力车夫 Rickshaw Chinese ‎Restaurant, 768 Dundas Street, London, ON N5W 2Z7‎ - (519) 642-3502‎.

Cannot vs. can not -- by Alex O'Neal

There is a grammatical misunderstanding common to many U.S. Americans, largely because we learned about grammar in the either/or terms of right vs. wrong. Here's the misunderstanding: can not or cannot? My public school teachers said can not was the correct form, and that cannot was a corruption. A friend of mine from a previous generation was taught the opposite. Her son, much better at using the language than either of us, said both were right, but usage depended on context.

Here's the explanation: If I can not do something, then I can also do it. I can not write these words if I choose (and you may think I shouldn't), but I also can, and am, writing them. What I cannot do is know who will read them, or what they will think. I can imagine such things, but I'm limited by my experience and perceptions. So this is the rule: if you either could or could not do something, then you use two words, because you can leave out the second word if you so choose. If you could not do something no matter how much you desired or tried, then you use one word, cannot. There is no other option.

Sometimes both are true. Witness:

I cannot change the world.

I can not change the world.

It's true, I cannot change the world. What I mean, and what many mean when they say or think this to themselves, is that the world's problems are too big for any one person, or group of people, to take on. Poverty, sickness, hatred, love, weather, earthquakes, political and religious differences—these are inevitable conditions. Even Jesus said, "the poor you will have with you always," and, "Let the dead bury the dead."

It's also true that I can change the world. I, and every other person on the planet, can make a difference. We can give to the poor, and try to cure ourselves of the sickness of wealth (more on that later). We can be courteous, we can provide emotional (listening) or physical (assisting) or financial (donating) help to others, we can feed and help and forgive each other. (More about forgiveness later, too.) We can take in an abandoned dog or cat and give it love. We can plant a garden. We can put in a day's work and know we earned our pay, and someone, hopefully, was the better for it. We can not cut off someone in traffic. We can dedicate our lives to healing. We can dedicate our lives to loving our family and community. We can respect the differences of others. In other words, what we can do, we can do.

Grammar is the tool we use to communicate and should be taught as such. Our bodies, our minds, and our voices are the tools we have to interact with our universe. We must use them while we live; we cannot evade using them except through death or dire injury. In this sense we cannot not change the world. And now, while the world suffers on every level, from the sky to the deeps of the sea, from humans to tiny coral polyps, we can make what time we have count.

Don't berate yourself for previous behavior. Don't congratulate yourself, either. Just take the next opportunity to make a difference to the next person, and help make what we cannot change bearable.

Cited from http://alexfiles.com/cannot.shtml

Old pictures of China

If you are interested in old pictures of China, the following blog at www.sina.com.cn would be a good place to go.

http://blog.sina.com.cn/lzhp

Learning English-5

come down

When did you come down from Oxford?

Do you think Sir Run Run Shaw will come down again when our school needs more money?

Shylock came down on Antonio for the pound of flesh.

The court will come down heavily on hardened criminals

The enemy came down on the town during the night.

The chairman will have to come down on one side or the other soon.

When we come down to details, the plan seems possible.

The whole matter comes down to a power struggle between President Musharraf and Benazir Bhutto.

The former world weightlifting champion came down to picking odds and ends from refuse heaps.

All this talk about ideas is getting us nowhere, let’s come down to brass tacks.

I’m glad you have come down to earth and stopped dreaming of getting a windfall.

come for

I saw the robber coming for me.

come forward

The police have asked witnesses of the accident to come forward.

come home

At last the real difficulty has come home to me.

come in

This week came in very windy.

If your party comes in at the next election, what will you do about taxes?

Cited from http://lghbe.blog.sohu.com/

Learning English-4

come at

I wanted to reply to your letter, but I can’t come at it anywhere.

It is always difficult to come at the truth.

The shrew came at her husband with a rolling-pin.

come away

Come away! The door’s open!

come back

Is Wang Fei expected to come back?

Long skirts are starting to come back.

I didn’t hear you, could you come back?

The soprano sang beautifully, her name will come back to me soon.

Can I come back to you on the project tomorrow?

Our Tokyo correspondent came back at the chief cabinet secretary with some sharp questions.

come before

Your application came before the board of directors yesterday, but I haven’t heard the result.

come between

It’s dangerous to come between two fighting bulls.

Qian Zhongshu, a true scholar, never lets anything come between himself and his work.

come by

Why don’t you come by some afternoon and have tea with me?

come by

How did you come by that beautiful picture?

How did you come by that wound on your arm?

come clean

The prisoner came clean and admitted to stealing two Picasso paintings from the museum.

Cite from http://lghbe.blog.sohu.com

Learning English-3

come it

Don't try to come it!

come next

The military government refused to allow the people their right to vote; what came next was violence and lawlessness.

come of

The chief engineer promised to help, but I don't think anything will come of it, since he himself is to be sent to the turkey farm soon.

I don't know what will come of the boy if he keeps failing his exams.

Che Guevara comes of a rich family, yet he fights for the poor.

In China, a young person comes of age on his or her 18^th birthday.

come off

The open-air party came off in spite of the heavy rain.

“House of flying Daggers” didn't come off as well as one had hoped.

He always comes off badly in debates.

come off

I've heard that $1000 per square meter is coming off the price of the house.

Come off it, tell the truth!

come on

I can feel a cold coming on.

The night nurse doesn't come on till midnight.

come on

Fear came on the Ghoul as he stood in the empty coffin chamber.

Suddenly it came on me where I had seen her before.

Cited from http://lghbe.blog.sohu.com/

Learning English-2

come in

Long hair for men is coming in these days.

Strawberries will be coming in soon.

Number three well came in last night.。

Which horse came in first?

This is where you come in; we want you to help us get a bank loan.

Can I come in on your plan?

I heard you talking about sharing out the money, but where do I come in?

President Bush's Iraq policies have come in for much criticism in the newspapers.

I don't like a garden party with crowds of people coming in on me.

Suddenly it came in on me that I had left the key behind.

Don't throw that empty box away, it might come in handy another time.

When my ship comes in, I'll send my children abroad.

It's often to one's advantage to come in on the ground floor.

come into

Athina came into a huge fortune when her mother died.

The trade bureau has asked all the shop owners to come into line with the price regulations.

It's a good thing that the mayor's wrong doing has at last come into the open.

The scientific study of dreams has not yet come into its own.

Who knows what factors come into play when these decisions are made?


From http://lghbe.blog.sohu.com/

Learning English-1

1. It is not like that.

2. Good thing+.......

3. There is nothing good playing/There is nothing good on TV.

4. I have gotten carried away.

5. I am glad you are bringing this up.

I don't believe you are bringing this up.

6. There is no other way of saying it.

7. She is coming on to you.

8. He was being polite.

9. Don't stand me up.

10. So that explains everything.

11. I can't help but wonder.

12. We have something/nothing in common.

13. What have you got to lose?

14. You shouldn't be so hard on yourself.

15. Don't get me started on it.

16. Let him off.

17. I will get down to it.

18. I think you are thinking someone else.



Cited from http://club.backchina.com/

Customize a windows cleaner

Open the notepad and input the following lines. Then save it with the file name "trash-cleaning.bat". Then you can double click this file to execute the cleaning process.

@echo off echo is cleaning the trash files, please wait......　　　　
del /f /s /q %systemdrive%\*.tmp　　　　
del /f /s /q %systemdrive%\*._mp　　　　
del /f /s /q %systemdrive%\*.log　　　　
del /f /s /q %systemdrive%\*.gid　　　　
del /f /s /q %systemdrive%\*.chk　　　　
del /f /s /q %systemdrive%\*.old　　　　
del /f /s /q %systemdrive%\recycled\*.*　　　　
del /f /s /q %windir%\*.bak　　　　
del /f /s /q %windir%\prefetch\*.*　　　　
del /f /s /q %windir%\temp\*.*　　　　
del /f /q %userprofile%\cookies\*.*　　　　
del /f /q %userprofile%\recent\*.*　　　　
del /f /s /q "%userprofile%\Local Settings\Temporary Internet Files\*.*"　　　　
del /f /s /q "%userprofile%\Local Settings\Temp\*.*"　　　　
del /f /s /q "%userprofile%\recent\*.*" 　　　　
echo Trash cleaning is done!　　　　
echo. & pause