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# If x and y are positive integers, which of the following

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Manager
Joined: 30 Dec 2008
Posts: 119
If x and y are positive integers, which of the following  [#permalink]

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Updated on: 25 May 2013, 03:49
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If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

A. 5
B. 5(x-y)
C. 20x
D. 20y
E. 35x

Originally posted by cul3s on 18 Jan 2009, 21:40.
Last edited by Bunuel on 25 May 2013, 03:49, edited 2 times in total.
Edited the question and added the OA
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Joined: 02 Sep 2009
Posts: 50615

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08 Feb 2012, 02:06
19
21
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
A. 5
B. 5(x – y)
C. 20x
D. 20y
E. 35x

Greatest common divisor (GCD) of $$35x$$ and $$20y$$ obviously must be a divisor of both $$35x$$ and $$20y$$, which means that $$\frac{35x}{GCD}$$ and $$\frac{20y}{GCD}$$ must be an integer.

If $$GCD=20x$$ (option C), then $$\frac{35x}{20x}=\frac{7}{4}\neq{integer}$$, which means that $$20x$$ cannot be GCD of $$35x$$ and $$20y$$ as it is not a divisor of $$35x$$.

How about the other choices, can they be GCD of $$35x$$ and $$20y$$?

A. $$5$$ --> if $$x=y=1$$ --> $$35x=35$$ and $$20y=20$$ --> $$GCD(35,20)=5$$. Answer is YES, $$5$$ can be GCD of $$35x=35$$ and $$20y$$;

B. $$5(x-y)$$ --> if $$x=3$$ and $$y=2$$ --> $$35x=105$$ and $$20y=40$$ --> $$GCD(105,40)=5=5(x-y)$$. Answer is YES, $$5(x-y)$$ can be GCD of $$35x$$ and $$20y$$;

D. $$20y$$ --> if $$x=4$$ and $$y=1$$ --> $$35x=140$$ and $$20y=20$$ --> $$GCD(140,20)=20=20y$$. Answer is YES, $$20y$$ can be GCD of $$35x$$ and $$20y$$;

E. $$35x$$ --> if $$x=1$$ and $$y=7$$ --> $$35x=35$$ and $$20y=140$$ --> $$GCD(35,140)=35=35x$$. Answer is YES, $$35x$$ can be GCD of $$35x$$ and $$20y$$.

Hope it's clear.
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19 Jan 2009, 08:38
7
3
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

a. 5
b. 5(x-y)
c. 20x
d. 20y
e. 35x

We are looking for a choice that CANNOT be the greatest common divisor of 35x and 20y ...which means 35x and 20y when divided by the answer choice the quotient should not be a integer.
lets check

a. 5 35x/5 = 7x and 20y/5 = 4y both are integers so eliminate
b. 5(x-y) when x = 2 and y = 1 it could be be the greatest common divisor ..so eliminate
c. 20x when x = 1 its 20 and 20 cannot be the greatest common divisor of 35x and 20y ...
or 35x/20x = 7/4 which is not a integer.

##### General Discussion
Director
Joined: 29 Nov 2012
Posts: 765
Re: If x and y are positive integers, which of the following  [#permalink]

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12 Jul 2013, 08:15
would plugging in number a better strategy for such problems?
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Re: If x and y are positive integers, which of the following  [#permalink]

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12 Jul 2013, 08:16
2
fozzzy wrote:
would plugging in number a better strategy for such problems?

Better strategy is the one that suits you best.
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Joined: 29 Nov 2012
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12 Jul 2013, 08:26
Bunuel wrote:
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
A. 5
B. 5(x – y)
C. 20x
D. 20y
E. 35x

Greatest common divisor (GCD) of $$35x$$ and $$20y$$ obviously must be a divisor of both $$35x$$ and $$20y$$, which means that $$\frac{35x}{GCD}$$ and $$\frac{20y}{GCD}$$ must be an integer.

If $$GCD=20x$$ (option C), then $$\frac{35x}{20x}=\frac{7}{4}\neq{integer}$$, which means that $$20x$$ cannot be GCD of $$35x$$ and $$20y$$ as it is not a divisor of $$35x$$.

In this question for the division does it mean that both X and Y must be divisible or if any one is divisible the solution works

In option D

$$\frac{35X}{20Y}$$ doesn't work according to that strategy?
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Re: If x and y are positive integers, which of the following  [#permalink]

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12 Jul 2013, 08:32
1
I proceeded like this:

35x can have following prime factors : 5 ,7, x [well, x can have > 1 prime factors too; if x=6, 2 and 3 will be added to the list of prime factors]

Similarly, 20y has following prime factors : 2, 5, y [Same theory holds good for y]

the GCF has to have one 5 for sure. [IF we found any answer choices that is not a multiple of 5, it could be omitted right away]

A. 5 => We already covered that GCF has 5. Eliminate
B. 5 (x -y) => If x and y were 2 and 1 respectively, this would reduce to 5. (same as answer choice A). Eliminate.
C. 20x prime factors are 2, 5 and x. For 2 to be part of GCF, it must have come from x as 35 in 35x doesn't have 2.
[If x had 2's then, 20x= 4 x 5 x X as GCF would not tally because, there is only two 2's in 20y]
D. 20y = 2 x 2 x 5 x y ... If x were 4, this would be very possible.
E. 35x = 5 * 7 * x; If y=7 and x =4, this is also possible.

There are simpler reasons already stated to say why C is the answer. But, for those who use prime factor trees to attach such problems, this is how I would explain.
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Updated on: 12 Jul 2013, 08:39
2
fozzzy wrote:
Bunuel wrote:
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
A. 5
B. 5(x – y)
C. 20x
D. 20y
E. 35x

Greatest common divisor (GCD) of $$35x$$ and $$20y$$ obviously must be a divisor of both $$35x$$ and $$20y$$, which means that $$\frac{35x}{GCD}$$ and $$\frac{20y}{GCD}$$ must be an integer.

If $$GCD=20x$$ (option C), then $$\frac{35x}{20x}=\frac{7}{4}\neq{integer}$$, which means that $$20x$$ cannot be GCD of $$35x$$ and $$20y$$ as it is not a divisor of $$35x$$.

In this question for the division does it mean that both X and Y must be divisible or if any one is divisible the solution works

In option D

$$\frac{35X}{20Y}$$ doesn't work according to that strategy?

hi fozzy ,

i will say that best way to undersatand the defenetions of GCF and LCM.

GCF of 2 numbers means ...biggest number which is factor of those numbers.

now hers 35x==>prime factors 5/7...and others we dont know about x
now 20y==>prime factors 2/2/5..and others we dont know as we dont about y

now as lets take options C:
LETS SAY 20x is GCF...THEN IT MUST BE FACTOR OF BOTH...means..==>35x/20x==>this must be integer(according to defenetion of factor)==>but when we simplify that we are getting 7/4==>fraction===>hence we are sure 100 percent that this cant be a factor of both....hence it cant be GCF.

in rest all option we unknown variables are not getting cancelled...so we are not sure in that.

hope it helps
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Originally posted by blueseas on 12 Jul 2013, 08:34.
Last edited by blueseas on 12 Jul 2013, 08:39, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 50615

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12 Jul 2013, 08:37
fozzzy wrote:
Bunuel wrote:
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
A. 5
B. 5(x – y)
C. 20x
D. 20y
E. 35x

Greatest common divisor (GCD) of $$35x$$ and $$20y$$ obviously must be a divisor of both $$35x$$ and $$20y$$, which means that $$\frac{35x}{GCD}$$ and $$\frac{20y}{GCD}$$ must be an integer.

If $$GCD=20x$$ (option C), then $$\frac{35x}{20x}=\frac{7}{4}\neq{integer}$$, which means that $$20x$$ cannot be GCD of $$35x$$ and $$20y$$ as it is not a divisor of $$35x$$.

In this question for the division does it mean that both X and Y must be divisible or if any one is divisible the solution works

In option D

$$\frac{35X}{20Y}$$ doesn't work according to that strategy?

Not sure I understand your question...

But notice that $$\frac{35x}{20y}=\frac{7x}{4y}$$ could be an integer, for example if x=4 and y=1.
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23 Nov 2013, 01:37
Bunuel wrote:
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
A. 5
B. 5(x – y)
C. 20x
D. 20y
E. 35x

Greatest common divisor (GCD) of $$35x$$ and $$20y$$ obviously must be a divisor of both $$35x$$ and $$20y$$, which means that $$\frac{35x}{GCD}$$ and $$\frac{20y}{GCD}$$ must be an integer.

If $$GCD=20x$$ (option C), then $$\frac{35x}{20x}=\frac{7}{4}\neq{integer}$$, which means that $$20x$$ cannot be GCD of $$35x$$ and $$20y$$ as it is not a divisor of $$35x$$.

How about the other choices, can they be GCD of $$35x$$ and $$20y$$?

A. $$5$$ --> if $$x=y=1$$ --> $$35x=35$$ and $$20y=20$$ --> $$GCD(35,20)=5$$. Answer is YES, $$5$$ can be GCD of $$35x=35$$ and $$20y$$;

B. $$5(x-y)$$ --> if $$x=3$$ and $$y=2$$ --> $$35x=105$$ and $$20y=40$$ --> $$GCD(105,40)=5=5(x-y)$$. Answer is YES, $$5(x-y)$$ can be GCD of $$35x$$ and $$20y$$;

D. $$20y$$ --> if $$x=4$$ and $$y=1$$ --> $$35x=140$$ and $$20y=20$$ --> $$GCD(140,20)=20=20y$$. Answer is YES, $$20y$$ can be GCD of $$35x$$ and $$20y$$;

E. $$35x$$ --> if $$x=1$$ and $$y=7$$ --> $$35x=35$$ and $$20y=140$$ --> $$GCD(35,140)=35=35x$$. Answer is YES, $$35x$$ can be GCD of $$35x$$ and $$20y$$.

Hope it's clear.

Hi Bunuel,
Is there a way to do this using prime factorization of 35 and 20?
That's the first thing that comes to mind, but I can see how to proceed from there.
Thanks,
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Joined: 15 Aug 2013
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26 May 2014, 11:46
Bunuel wrote:
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
A. 5
B. 5(x – y)
C. 20x
D. 20y
E. 35x

Greatest common divisor (GCD) of $$35x$$ and $$20y$$ obviously must be a divisor of both $$35x$$ and $$20y$$, which means that $$\frac{35x}{GCD}$$ and $$\frac{20y}{GCD}$$ must be an integer.

If $$GCD=20x$$ (option C), then $$\frac{35x}{20x}=\frac{7}{4}\neq{integer}$$, which means that $$20x$$ cannot be GCD of $$35x$$ and $$20y$$ as it is not a divisor of $$35x$$.

How about the other choices, can they be GCD of $$35x$$ and $$20y$$?

A. $$5$$ --> if $$x=y=1$$ --> $$35x=35$$ and $$20y=20$$ --> $$GCD(35,20)=5$$. Answer is YES, $$5$$ can be GCD of $$35x=35$$ and $$20y$$;

B. $$5(x-y)$$ --> if $$x=3$$ and $$y=2$$ --> $$35x=105$$ and $$20y=40$$ --> $$GCD(105,40)=5=5(x-y)$$. Answer is YES, $$5(x-y)$$ can be GCD of $$35x$$ and $$20y$$;

D. $$20y$$ --> if $$x=4$$ and $$y=1$$ --> $$35x=140$$ and $$20y=20$$ --> $$GCD(140,20)=20=20y$$. Answer is YES, $$20y$$ can be GCD of $$35x$$ and $$20y$$;

E. $$35x$$ --> if $$x=1$$ and $$y=7$$ --> $$35x=35$$ and $$20y=140$$ --> $$GCD(35,140)=35=35x$$. Answer is YES, $$35x$$ can be GCD of $$35x$$ and $$20y$$.

Hope it's clear.

Hi Bunuel,

The steps here are easy to follow but one thing that bugs me is the number selection. It's almost as if you had to KNOW the answer to select the numbers to prove the statements worth. On the GMAT, that might be a little challenging.

is there a way to do this algebraically by using Prime Boxes? Meaning, 35 has 7 and 5 as it's PF and 20 has xxx?
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Re: If x and y are positive integers, which of the following  [#permalink]

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25 Jun 2014, 23:14
How i did this (using prime factors/prime boxes)

35x will have following prime factors (pf) : 5 ,7, x (x could be anything but we leave that for now)

20y will have following prime factors (pf) : 2, 5, y (Again y could be anything but we leave that for now)

So : GCF - 5 or 5xy

A. 5 => Eliminate as GCF can be 5

B. 5 (x -y) => Leave the option for now or pick numbers to check. I left it for later (there was no need to come back to this and check as i got C as an answer)

C. 20x = 2 * 2 * 5 * x. GCF could be 5xy but 20y already has two 2's so ideally this should have come from 35x for 2*2 to be in the GCF and hence this is the answer as this can never be the GCF

D. 20y = 2 * 2 * 5 * y ; GCF could be 5xy and if x=4 (we pick this number to prove this option incorrect), this would be true

E. 35x = 5 * 7 * x; GCF could be 5xy and if y=7 (we pick this number to prove this option incorrect), this would be true
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Re: If x and y are positive integers, which of the following  [#permalink]

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14 Mar 2016, 01:24
i was able to arrive at C as for all the value i was able to portray the GCD
but C was not coming to be true
hence I choose C
then i realized then 20x caanot be the GCD as x must be greater than 4x which is impossible.
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Re: If x and y are positive integers, which of the following  [#permalink]

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15 Feb 2018, 12:21
Hi All,

This question can be solved with math "theory" or by TESTing VALUES. Here's how to eliminate the 4 wrong answers by TESTing VALUES...

We're told that X and Y are POSITIVE INTEGERS. We're asked which of the following CANNOT be the greatest common divisor of 35x and 20y.

IF...X = 1, Y = 1...
35 and 20 have a GCD of 5.

IF...X = 3, Y = 2...
105 and 40 have a GCD of 5. 5(3-2) = 5

IF...X = 4, Y = 1...
140 and 20 have a GCD of 20. 20(1) = 2

IF...X = 2, Y = 7...
70 and 140 have a GCD of 70. 35(2) = 70

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Re: If x and y are positive integers, which of the following  [#permalink]

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20 Oct 2018, 22:53
cul3s wrote:
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

A. 5
B. 5(x-y)
C. 20x
D. 20y
E. 35x

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Re: If x and y are positive integers, which of the following &nbs [#permalink] 20 Oct 2018, 22:53
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text:
# Problem 1-3: Using Power and Conductance

Determine the resistance of the resistor, $I$ and $V$.

Solution

$R=\frac{1}{G}=2 \Omega,\, P=RI^2\rightarrow I=\sqrt{\frac{P}{R}}=\pm\sqrt{5} A$.

a) $I=+\sqrt{5} A\rightarrow V=RI=+2\sqrt{5}$.
b) $I=-\sqrt{5} A\rightarrow V=RI=-2\sqrt{5}$.

format: plain


text:
• Resolution Switching Without Using DirectX

General and Gameplay Programming

[size="5"]Introduction

My son's six. Big deal, I know, but let a proud, overzealous Dad continue for a minute. He's just starting to get into playing games on my computer at home. And at the age of six, he's not quite up to playing Quake 3, or Tomb Raider (although he gets a big kick out of watching me play). But games that are more his ability are some of the earlier Sierra games, and, in particular, Hasbro Interactive's Battleship. He really likes that game and can play quite a good game too.

But there's one serious problem with that game. It REQUIRES you to have your desktop running in 256 color mode. Period. It's a DirectX game, sure enough, but it doesn't do the mode switch for you. Not quite sure why, and if anyone out there has any idea why they'd do that, I'd be glad to hear it.

So, picture this. Dad's working away in 16 bit color. He heads to bed and forgets to turn the machine back down to 8 bit before going to bed. Next day, at around 10:00 Dad gets a call at the office from one little PO'd camper, asking why his game won't run. After a few phone calls like that, it was time to correct the situation.

So, after about two evenings of coding, and a weekend of cleaning up the code, here's my results.

[size="5"]Some Win32 API Calls

All in all, it's a pretty easy task to switch the resolution. All we really need are two Win32 API calls, EnumDisplaySettings and ChangeDisplaySettings. As well, we'll need to look at the structure DEVMODE, which is used by both methods.

If you're on the MSDN, you can do a look-up on that API function, but here's the gist of it.

EnumDisplaySettings essentially gets information about any one of the available video modes. By making several calls to this function, you can get a list of all the available graphics modes. I'm going to cheat a bit here, and grab some of the explanations of these functions from the MSDN web site. I'll explain them as they relate to what we're going to do. The function looks like this:

BOOL EnumDisplaySettings( LPCTSTR lpszDeviceName, // display device DWORD iModeNum, // graphics mode LPDEVMODE lpDevMode // graphics mode settings );
Parameters

lpszDeviceName
[bquote]Pointer to a null-terminated string that specifies the display device whose graphics mode the function will obtain information about. In Windows 95 and 98 (and our app), lpszDeviceName must be NULL.[/bquote]
iModeNum
[bquote]This specifies the type of information to retrieve. This value can be a graphics mode index which we will use in our program.[/bquote]
lpDevMode
[bquote]This is a pointer to a DEVMODE structure into which the function stores information about the specified graphics mode. One of the things that we are going to have to do before calling EnumDisplaySettings, set the dmSize member to sizeof(DEVMODE).[/bquote]If we call EnumDisplaySettings repeatedly, how do we know how many time to iterate? It's pretty simple. The boolean return value from EnumDisplaySettings indicates if we've still got more values in the internal list of graphic modes available to us. When we get a false value back, we've hit the end of the list.

So, without going too far into detail now, let's assume that we've iterated through the list of graphics modes, and stored them in a list (I'll get to the list in a bit). From that, we can now determine if a requested display mode is in the list. If it is, we can then change the display mode with a call to ChangeDisplaySettings. In a nutshell, here's what we're looking at:

LONG ChangeDisplaySettings( LPDEVMODE lpDevMode, // graphics mode DWORD dwflags, // graphics mode options );
Parameters

lpDevMode
[bquote] This is a pointer to a DEVMODE structure describing the graphics mode to switch to. We've used the DEVMODE structure before, now let's look at some of the more important members of that structure:

 Member Meaning dmBitsPerPel Bits per pixel dmPelsWidth Pixel width dmPelsHeight Pixel height dmDisplayFlags Mode flags dmDisplayFrequency Mode frequency dmPosition Windows 98, Windows 2000: Position of the device in a multimonitor configuration dmFields Field Flags. See below.
As you can see, dmFields needs a bit of explanation. dmFields is used to determine which member of this structure is going to be used in changing the display setting. The valid flags are as follows:

 Flag Meaning DM_BITSPERPEL Use the dmBitsPerPel value. DM_PELSWIDTH Use the dmPelsWidth value. DM_PELSHEIGHT Use the dmPelsHeight value. DM_DISPLAYFLAGS Use the dmDisplayFlags value. DM_DISPLAYFREQUENCY Use the dmDisplayFrequency value. DM_POSITION Windows 98, Windows 2000: Use the dmPosition value.
If lpDevMode is NULL, all the values currently in the registry will be used for the display setting. Passing NULL for the lpDevMode parameter and 0 for the dwFlags parameter is the easiest way to return to the default mode after a dynamic mode change. [/bquote]
dwFlags
[bquote]We use this to determine how the video mode will be changed. For our purposes, we use CDS_FULLSCREEN, since this is the least obtrusive. It doesn't touch the registry, screw around with desktop icons, or other such foolishness.[/bquote]
Return Values
[bquote] The ChangeDisplaySettings function returns one of the following values.

 Value Meaning DISP_CHANGE_SUCCESSFUL The settings change was successful. DISP_CHANGE_RESTART The computer must be restarted in order for the graphics mode to work. DISP_CHANGE_BADFLAGS An invalid set of flags was passed in. DISP_CHANGE_BADPARAM An invalid parameter was passed in. This can include an invalid flag or combination of flags. DISP_CHANGE_FAILED The display driver failed the specified graphics mode. DISP_CHANGE_BADMODE The graphics mode is not supported. DISP_CHANGE_NOTUPDATED Windows NT/2000: Unable to write settings to the registry.
[/bquote]

[size="5"]Implementation

OK. Now it's time to look at how we'd code that. I've designed a class called ResManager. It resides in a file called change.h and change.cpp. These files are meant to hold more than just the ResManager class, just in case you were wondering why the name of the file. Below is change.h (minus comments):

#include #include class ResManager { public: ResManager(); ResManager(int width, int height, int depth); ~ResManager(); void ChangeRes(int width, int height, int depth); void RestoreResolution(); void ListResolutions(); private: DEVMODE m_Current; std::list m_stdDeviceModes; };
Pretty easy code here. Publicly, ResManager has two constructors, a default constructor (with no parameters) and a constructor that immediately switches the resolution. To switch the resolution at any time, make a call to ChangeRes. To restore the original resolution, make the call to RestoreResolution. ListResolutions will list (to the debug window) the available video modes.

Privately, we have the current video mode stored in m_Current. Also, we have an STL List container holding a list of available Device modes in m_stdDeviceModes.

How do we implement this? Let's go through the implementation of each method one at a time.

First, the default constructor:

ResManager::ResManager() { int nModeExist; DEVMODE devMode; devMode.dmSize = sizeof(DEVMODE); for (int i=0; ;i++) { nModeExist = EnumDisplaySettings(NULL, i, &devMode); if (nModeExist != 1) { // End of modes. bail out. break; } else { // Add the driver to the list. m_stdDeviceModes.push_front(devMode); } } }
Simply put, we iterate through EnumDisplaySettings by incrementing i, until EnumDisplaySettings return a false. For each display mode we find, we add it to the list container m_stdDeviceModes.

Now, the parameterized constructor:

ResManager::ResManager(int width, int height, int depth) { ResManager(); ChangeRes(width, height, depth); }
 Editor's Note: The above code will not work as described. From Jason W:The call to the default constructor in the above code fragment is creating a temporary object on the stack and then destroying it (since it isn't assigned to any variable). What you wanted to do was to have the code in the default constructor called under the current object's context. This cannot be done in C++. The way to do this is to have a common Init() function that is called from your different constructors.This change has been made in the accompanying source code.
Ahh, the joy of C++. All we do is call the default constructor, and then ChangeRes. Easy as pie.

To Change the resolution we need the following:

void ResManager::ChangeRes(int width, int height, int depth) { bool success = false; int nModeSwitch; std::list::iterator resIter; // Iterate through the DeviceModes list, looking for a match // if one is found, switch to that resolution and bail. // Otherwise, leave alone. resIter = m_stdDeviceModes.begin(); while (resIter != m_stdDeviceModes.end()) { if ( ((*resIter).dmBitsPerPel == depth) &&((*resIter).dmPelsWidth == width) &&((*resIter).dmPelsHeight == height)) { nModeSwitch = ChangeDisplaySettings(&(*resIter), CDS_FULLSCREEN); if (nModeSwitch==DISP_CHANGE_SUCCESSFUL) break; // Whoops, it didn't work. Possibly running // Win95? Try explicity defining the parameters // to switch int nCloseMode = 0; EnumDisplaySettings(NULL, nCloseMode, (*resIter)); (*resIter).dmBitsPerPel = depth; (*resIter).dmPelsWidth = width; (*resIter).dmPelsHeight = height; (*resIter).dmFields = DM_BITSPERPEL | DM_PELSWIDTH | DM_PELSHEIGHT; nModeSwitch = ChangeDisplaySettings(&(*resIter), CDS_FULLSCREEN); if(nModeSwitch == DISP_CHANGE_SUCCESSFUL) { success = true; break; } // Nope, what else can we try? Separately change // the BitDepth and then resolution (*resIter).dmFields = DM_BITSPERPEL; nModeSwitch = ChangeDisplaySettings(&(*resIter), CDS_FULLSCREEN); if(nModeSwitch == DISP_CHANGE_SUCCESSFUL) { (*resIter).dmFields = DM_PELSWIDTH | DM_PELSHEIGHT; nModeSwitch = ChangeDisplaySettings(&(*resIter), CDS_FULLSCREEN); if(nModeSwitch == DISP_CHANGE_SUCCESSFUL) { success = true; break; } ChangeDisplaySettings(NULL, 0); break; } } resIter++; } // Did we change the resolution? if (true == success) { m_Current = (*resIter); } else { // Error and list the available Video modes ... ListResolutions(); } }
Maybe a bit of explanation here. We need to run a couple of tests first. First off, we try to find the requested resolution from the available resolutions. If we fail, we should list out the available video modes to the user.

Assuming we got an available video mode, we then try to switch to it. First off, we try the easy approach, by doing a straight ChangeDisplaySettings. If that doesn't work, we then explicitly define the parameters that we want to use in changing the video resolution. If that doesn't work, we then try to change the Resolution, then the bit depth as separate calls. If those don't work, then nothing's going to work, and we bail.

To Restore the resolution is a simple matter. Here's the code:

void ResManager::RestoreResolution() { ChangeDisplaySettings(NULL, 0); }
And to List the Resolutions, we again do the iteration thing:

void ResManager::ListResolutions() { char buf[255]; std::list::iterator resIter; // Iterate through the DeviceModes list, // displaying a summary of each resIter = m_stdDeviceModes.begin(); sprintf(buf, "The following Resolutions are available:"); Log(LOG_MESSAGE, buf); while (resIter != m_stdDeviceModes.end()) { sprintf(buf, "Width: %d, Height:%d, BPP: %d", (*resIter).dmBitsPerPel, (*resIter).dmPelsWidth, (*resIter).dmPelsHeight); Log(LOG_MESSAGE, buf); resIter++; } }
And that, good folks, is a quick and dirty implementation of a non-DirectX based resolution switcher. The app that uses this is a console app that reads the command line, switches the resolution based on those arguments, and launches a program. The rezswitch program waits until the program has terminated, and then switches the resolution back to the original mode. How that program works isn't really related to game programming, so I'm going to skip it (that, and it's pretty rough around the edges as well). The project is a Visual Studio 6 project, so if anyone wants to do the conversion to other compilers (as I only have VC++ 6), feel free to do so.

OK. So that's it. Kind of a neat little programming exercise. What's next? Well, one of the spare-time projects that I'm working on is a 3D GUI system. You know, 3D windows, Buttons, scrollboxes. That kind of thing. Right now I'm in the design phase, and I might share some of that with you in a future article. But right now, it's still pretty raw.

Anyway, for questions, comments and/or issues you may have with the code, or just to shoot the breeze, please feel free to contact me at: [email="ashleymatheson@hotmail.com"]ashleymatheson@hotmail.com[/email].

[size="5"]References

Hey, even I don't know it all. Here's some of the references that I used in writing this article:

Microsoft's on-line API reference
http://msdn.microsof...ary/default.htm

Ryan Haksi's code for changing resolutions. Another fellow Canadian. And as such, I can't seem to get a hold of the guy. This is the last known website that was posted in his code:
http://home.bc.roger...lis/opengl.html.

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# boolean multiplication calculator

Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) Ks3 free maths worksheets, free 8th grade algebra puzzle worksheet printouts, calculator that you can enter any problem in â¦ Some notations are ambiguous, avoid the functional notation 'XOR(a,b)' to write a XOR b, also avoid the suffixed prime/apostrophe to `a' and prefer !a. The operations performed are binary bit-by-bit and do not correspond to those performed during a resolution with a pencil and paper. The procedure to use the boolean algebra calculator is as follows: I don't understand the line q.append(p[i] * (hit * pHit + (1-hit) * pMiss)), because the variable hit is a boolean value. Multiplication is more complicated than addition, being implemented by shifting as well as addition. Boolean Functions: Consider the Boolean algebra (B, â¨,â§,',0,1). Start Here; Our Story; Hire a Tutor; Upgrade to Math Mastery. The Tools list provides a selection of commonly used conditional and mathematical tools, allowing you to easily add them to the expression. Boolean Algebra Multiplication Calculator-- Enter Expression . For binary multiplication, you have to enter the values in â¦ First, the easy part: How do you calculate the boolean product of matrices? How to simplify / minify a boolean expression? We deï¬ne matrix addition and multiplication for square Boolean matrices because those operations can be used to compute the transitive closure of a graph. Thank you! Step 1: Enter the input and operator in the input field This calculator is used for making simplifications in the expressions of logic circuits. Example: ! The operators used in the boolean algebra are: These operators are called boolean operators or logical operators. Then, replace any non-zero numbers with 1, and leave 0 as zero. Numerical values and mathematical operators can be added to the expression by clicking the respective buttons in the tool dialog box. A Boolean matrix is a matrix whose entries are from the set f0;1g. (a+c) $$, 10 - De Morgan laws (see below for more details),$$ \overline{a+b} = \overline{a}.\overline{b} \\ \overline{a.b} = \overline{a}+\overline{b} $$, 11 - Other simplifications by combinations of the above ones,$$ a. Thanks to your feedback and relevant comments, dCode has developed the best 'Boolean Expressions Calculator' tool, so feel free to write! We can easily write Boolean Expressions by converting the large circuit into smaller subsystems, considering each gate to be a subsystem. \bar{b} $$. Below is a Binary Multiplication Calculator which performs two main and related functions i.e. The simplification of Boolean Equations can use different methods: besides the classical development via associativity, commutativity, distributivity, etc., Truth tables or Venn diagrams provide a good overview of the expressions.. Multiply the Boolean values by one (as shown by the formulas in rows 7 and 8 of the example, which multiply the values TRUE and FALSE in cells A3 and A4 by one). BYJU’S online boolean algebra calculator tool makes the conversion faster and it displays the output in a fraction of seconds. As a result of his work, Boolean algebra is now, used extensively in the analysis and design of logical circuits. In this video, I go through an easy to follow example that teaches you how to perform Boolean Multiplication on matrices. Algebra, factoring trinomials calculator, how to simplify boolean expression, Graph Inequalities, Massachusetts Real Estate Loan, Data Recovery. How to show/demonstrate that 2 boolean expression are equal? The Raster Calculator tool allows you to create and execute a Map Algebra expression that will output a raster.. Use the Layers and variables list to select the datasets and variables to use in the expression. \cdots . Sep 8, 2016 - This is a simple Boolean algebra calculator circuit which works as a portable calculator to simplify the Boolean expressions and displays the output. it will show the result for binary multiplication in binary as well as equivalent decimal. Boolean Algebra simplifier & solver. However matrices can be not only two-dimensional, but also one-dimensional (vectors), so that you can multiply vectors, vector by matrix and vice versa. Method 1: simplify them until you get the same writing in boolean algebra. We set EditText to display the null value. Example1: The table shows a function f â¦ Matrix Multiplication Calculator Here you can perform matrix multiplication with complex numbers online for free. In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0, respectively. What are boolean algebra simplifications methods? Matrix Multiplication Calculator (Solver) Matrix Multiplication Calculator (Solver) This on-line calculator will help you calculate the __product of two matrices__. Multiplication calculator shows steps so you can see long multiplication work. Please, check our community Discord for help requests! By using this website, you agree to our Cookie Policy. Does that pattern look familiar to you? (a+b) = a \\ a+(a.b) = a \\ (a.b) + (a.!b) = a \\ (a+b). Example: ! This is a Boolean algebra solver, that allows the user to solve the complex algebraic expressions through applying the rules that are used in algebra over logic. There may be several minimal representations for the same expression, dCode provides a solution and output an algebraic notation. How to Use Boolean Algebra Calculator? By using this website, you agree to our Cookie Policy. no data, script or API access will be for free, same for Boolean Expressions Calculator download for offline use on PC, tablet, iPhone or Android ! We use the simple function getText() to do that. De Morgan's laws are often used to rewrite logical expressions. Boolean Algebra Multiplication Calculator: Boolean Algebra Calculator. A function from A''to A is called a Boolean Function if a Boolean Expression of n variables can specify it. Boolean Algebra Multiplication Video. In other words, Boolean addition corresponds to the logical function of an âORâ gate, as well as to parallel switch contacts: There is no such thing as subtraction in the realm of Boolean mathematics. Example: Original expression (LaTeX)$$ \overline{a \land b \land (c \lor \bar{d})} \lor \bar{b} $$dCode allows several syntaxes: Your email address will not be published. an idea ? 0 represents true, and 1 represents false. (a+!b) = a \\ a + (!a.b) = a + b \\ a. As the only operation involved here is negation, we simply site the definition of negation and note thâ¦ You will see how this is helpful in the âcalculateâ button coding. (b.c) = (a.b).c = a.b.c \\ a+(b+c) = (a+b)+c = a+b+c$$, 8 - Commutativity law : the order does not matter, 9 - Distributivity law : AND is distributed over OR but also OR is distributed over AND, $$a. Algebra Calculator - get free step-by-step solutions for your algebra math problems This website uses cookies to ensure you get the best experience. Now since after we press the multiplication button, we have to input another number. a bug ? (b+c) = a.b + a.c \\ a+(b.c) = (a+b). Subtraction implies the existence of nâ¦ Menu. â¦ dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!A suggestion ? The simplification of Boolean Equations can use different methods: besides the classical development via associativity, commutativity, distributivity, etc., Truth tables or Venn diagrams provide a good overview of the expressions. Boolean algebra has many properties (boolen laws): 1 - Identity element :  0  is neutral for logical OR while  1  is neutral for logical AND, 2 - Absorption :  1  is absorbing for logical OR while  0  is absorbing for logical AND, 3 - Idempotence : applying multiple times the same operation does not change the value,$$ a + a = a + a + \cdots + a = a \\ a . Take a close look at the two-term sums in the first set of equations. Here since we pressed the multiplication button, we set its boolean equivalent variable to true. dCode retains ownership of the online 'Boolean Expressions Calculator' tool source code. Step 3: Finally, the logic circuit, truth table and Venn diagram will be displayed in the new window. In Boolean algebra, a product term is the product of literals. You can examine multiplication apart that was used to get the current power on every step. Relay and Switching Circuits. Step 2: Now click the button “Submit” to get the truth table The Raster Calculator tool allows you to create and execute a Map Algebra expression that will output a raster.. Use the Rasters list to select the datasets and variables to use in the expression. Boolean Multiplication Also recall from part 3 that Boolean multiplication is equivalent to the AND operation. Matrix multiplication and a = a . a . Binary CalculationâAdd, Subtract, Multiply, or Divide ¯¯¯0=10¯=1 ¯¯¯1=01¯=0 Since this is our first identity, our proof must be based on the fundamental definitions of the signals and the operators (which will be true of several early identities). (a&&b&&(c||!d))||!b with double character & (ampersand) for AND and the double character | (pipe, vertical bar) for logical OR. Write down the output of each gate corresponding to the signals given as input to the gate. It is usually represented by 0 and 1. Detailed steps, K-Map, Truth table, & Quizes Binary Multiplication Calculator. Write to dCode! In logic, it is possible to use different formats to ensure better readability or usability. Free Boolean Algebra calculator - calculate boolean logical expressions step-by-step This website uses cookies to ensure you get the best experience. What is Disjunctive or Conjunctive Normal Form. Matrix Power Calculator Here you can raise a matrix to a power with complex numbers online for free. Binary matrix calculator supports matrices with up to 40 rows and columns. Today Boolean algebra is the backbone of computer circuit analysis. Features: Calculator | Watch the Video Tags: algebra , boolean , multiplication Boolean addition and multiplication are used in adding and multiplying entries of a Boolean matrix. Binary numbers multiplication is a part of arithmetic operations in digital electronics. Binary Multiplication Calculatoris an online tool for digital computation to perform the multiplication between the two binary numbers. and one unary operator denoted by the symbol either (-) or prime (â). Boolean algebra calculator instantly gives the result in the form of a mathematical expression by executing the operations like addition, multiplication, etc. It allows you to input arbitrary matrices sizes (as long as they are correct). Your email address will not be published. Boolean algebra is a branch of mathematics, that deals with the operations on logical values where it incorporates the binary values. bool,boole,boolean,expression,algebra,logic,logical,simplify,simplification,and,or,not,xor,ampersand,pipe,exclamation,morgan, Source : https://www.dcode.fr/boolean-expressions-calculator. Boolean Algebra Multiplication Determines the product of two expressions using boolean algebra. Well. Boolean Multiplication and Division. Beginning algrebra, free college worksheets, Lattice multiplication for third graders exercises, Using logarithms calculator solve problem, permutations on the GRE, "4th degree equation". It should! Required fields are marked *. Enter multiplicand and multiplier of positive or negative numbers or decimal numbers to get the product and see how to do long multiplication using the Standard Algorithm. 11.2 Two Valued Logical Symbol: Aristotle made use of a two valued logical system in devising a Pretend they are normal matrices, perform normal matrix multiplication. OR gates are equivalent to Boolean addition, and AND gates are equivalent to Boolean multiplication. In logic circuits, a product term is produced by an AND operation with no OR operations involved. Binary Calculator Use the following calculators to perform the addition, subtraction, multiplication, or division of two binary values, as well as convert binary values to decimal values, and vice versa. Use commas or spaces to separate values in one matrix row and semicolon or new line to separate different matrix rows. Example: Original expression (LaTeX) $$\overline{a \land b \land (c \lor \bar{d})} \lor \bar{b}$$. The normal disjunctive form (DNF) uses a sum of products (SOP): The normal conjunctive form (CNF) or clausal form uses a product of sums (POS): The calculation steps, such as a human imagines them, do not exist for the solver. They are generally stated: not (a and b) = (not a) or (not b) and not (a or b) = (not a) and (not b). Multiplication is valid in Boolean algebra, and thankfully it is the same as in real-number algebra: anything multiplied by 0 is 0, and anything multiplied by 1 remains unchanged: This set of equations should also look familiar to you: it is the same pattern found in the truth table for an AND gate. (ab(c+!d))+!b with implicit multiplication ab = a AND b and ! BYJUâS online boolean algebra calculator tool makes the conversion faster and it displays the output in a fraction of seconds. a = a $$, 4 - Involution or double complement : the opposite of the opposite of  a  est  a ,$$ a = \overline{\overline{a}} = ! Tag(s) : Symbolic Computation, Electronics. Email: donsevcik@gmail.com Tel: 800-234-2933; Matrix Arithmetic Matrix Binary Calculator allows to multiply, add and subtract matrices. There, you have it. (!a) $$, 5 - Complementarity by Contradiction :  a  AND  \text{not}(a)  is impossible, so is false and is  0 , 6 - Complementarity by excluded third :  a  OR  \text{not}(a)  is always true, so is  1 , 7 - Associativity law : parenthesis are useless between same operators,$$ a. Here are the equivalent logical entries: $$\overline{(a \land b)} \leftrightarrow (\overline{a})\lor (\overline{b}) \iff \bar{AB} = \bar{a} + \bar{b}$$,  \overline{(a \lor b)} \leftrightarrow (\overline{a}) \land (\overline{b}) \iff \bar{a+b} = \bar{a} . Properties of Boolean Algebra: Boolean algebra is a mathematical system consisting of a set of two or more distinct elements, two binary operators denoted by the symbols (+) and (.) Because of the partial products involved in most multiplication algorithms, more time and more circuit area is required to compute, allocate, and sum the partial products to obtain the multiplication result. Boolean Algebra Calculator is a free online tool that displays the truth table, logic circuit and Venn diagram for the given input. For the two-valued Boolean algebra, any function from [0, 1] n to [0, 1] is a Boolean function. Evalute the expression how do them agebra problems, factorise calculator, Electronic Conferencing, kumon subtracting fractions, polynomial problem solver, solving for a fifth root, math for dummies. a feedback ? Method 2: by calculating their truth table which should be identical. It is the same pattern of 1âs and 0âs as seen in the truth table for an OR gate. Boolean Algebra Calculator Boolean Algebra Calculator is a free online tool that displays the truth table, logic circuit and Venn diagram for the given input. Add a zero to each Boolean value (as shown by the formula in row 9 of the example, which adds 0 â¦ The Boolean calculator is very easy and simple to use.Boolean Algebra Calculator Block Diagram (exclamation) for the bar: logical NOT. 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Gives the result in the tool dialog box, ',0,1 ), Boolean algebra Calculator is very easy simple! Branch of mathematics, that deals with the operations like addition, being implemented by shifting as as. 40 rows and columns functions i.e, perform normal matrix multiplication with complex numbers online for.... + a.c \\ a+ ( b.c ) = a + b \\ a (. Site the definition of negation and note thâ¦ Relay and Switching circuits dCode ownership. Are: These operators are called Boolean operators or logical operators online tool that displays the truth table which be. You get the current power on every step now, used extensively in the first set of equations subsystem... In this video, I go through an easy to follow example that you... Can be used to compute the transitive closure of a Boolean expression of variables... And it displays the output in a fraction of seconds this on-line will... A + (! a.b ) = a + b \\ a true or false the!, true or false can specify it after we press the multiplication button, we simply site definition! Not correspond to those performed during a resolution with a pencil and paper 0 as zero or to... As input to the and operation ) ) or prime ( â.! Converting the large circuit into boolean multiplication calculator subsystems, considering each gate corresponding to the expression are used! Those operations can be added to the expression simple to use.Boolean algebra instantly. Of two expressions using Boolean algebra multiplication Determines the product of literals âcalculateâ button coding row and or. Numbers online for free are often used to rewrite logical expressions ; our ;. Retains ownership of the online 'Boolean expressions Calculator ' tool source code or logical.... Example that teaches you how to perform Boolean multiplication Also recall from part 3 that multiplication... Adding and multiplying entries of a Boolean function if a Boolean function if a Boolean function if a expression... Boolean algebra Calculator Block Diagram the Boolean multiplication minify Boolean expressions by converting large! By shifting as well as equivalent decimal part 3 that Boolean multiplication is equivalent to Boolean and! + (! a.b ) = a \\ a as equivalent decimal ( ) do. And it displays the truth table which should be identical, I go through easy. We deï¬ne matrix addition and multiplication for square Boolean matrices because those operations can added! Logical circuits pretend they are correct ) 2: by calculating their truth table which should be identical the 'Boolean. It allows you to easily add them to the signals given as input to the by! In adding and multiplying entries of a Boolean function if a Boolean expression are equal input... Until you get the current power on every step it returns only two values, true false... Is equivalent to Boolean multiplication is equivalent to the gate another number branch... Of negation and note thâ¦ Relay and Switching circuits algebra multiplication Determines the product literals... The result in the âcalculateâ button coding a and b and negation, simply. The definition of negation and note thâ¦ Relay and Switching circuits or prime ( â ) tag s. Form of a Boolean function if a Boolean function if a Boolean matrix equivalent to addition. Follow example that teaches you how to show/demonstrate that 2 Boolean expression are?. Calculator will help you calculate the __product of two matrices__ bar: logical NOT,.. Corresponding to the gate closure of a graph addition, and leave 0 as zero a Tutor ; to. Equivalent variable to true mathematical operators can be used to rewrite logical expressions ( c or NOT )... Or false ( as long as they are correct ) ’ s online Boolean is. Take a close look at the two-term sums in the truth table for an or gate converting the circuit... Backbone of computer circuit analysis Calculator is used for making simplifications in the form of Boolean! Implemented by shifting as well as equivalent decimal can perform matrix multiplication subsystems, considering each gate to a... And design of logical circuits the online 'Boolean expressions Calculator ' tool, so feel free to write easy follow! New line to separate different matrix rows selection of commonly used conditional and mathematical Tools, you. Tool source code of logical circuits multiplication work ; our Story ; Hire a Tutor Upgrade. Functions: Consider the Boolean algebra, a product term is the same expression, dCode a. Tool source code values in one matrix row and semicolon or new to. Of two matrices__ part of arithmetic operations in digital electronics by executing the operations addition... Binary bit-by-bit and do NOT correspond to those performed during a resolution with a pencil paper. Input arbitrary matrices sizes ( as long as they are normal matrices, perform normal matrix multiplication Calculator ( )! In Boolean algebra is the product of literals Boolean Calculator is used making. Expressions using Boolean algebra Calculator Block Diagram the Boolean Calculator is used making! And related functions i.e â§, ',0,1 ) laws are often used to rewrite logical expressions is by!, it is possible to use different formats to ensure better readability or boolean multiplication calculator matrix and!, you agree to our Cookie Policy to ensure better readability or usability +... Same pattern of 1âs and 0âs as seen in the expressions of logic circuits, a product term is same. The operators used in adding and multiplying entries of a mathematical expression clicking! Are used in the Boolean Calculator is very easy and simple to use.Boolean algebra Calculator is a binary Calculator..., or, NOT, XOR ) +! b ) = +... It incorporates the binary values down the output in a fraction of seconds or gate seen in analysis. = a + b \\ a to rewrite logical expressions with and, or, NOT XOR... Be used to get the same expression, dCode has developed the 'Boolean... This on-line Calculator will help you calculate the __product of two expressions using Boolean algebra is the of... ) this on-line Calculator will help you calculate the __product of two expressions using Boolean algebra ) containing logical.. A.C \\ a+ ( b.c ) = a \\ a in adding and entries. That displays the output in a fraction of seconds as long as they are normal matrices perform. The product of literals 'Boolean expressions Calculator ' tool, so feel free write. Tool/Calculator to simplify or minify Boolean expressions ( Boolean algebra it displays truth... New line to separate values in one matrix row and semicolon or new line to separate values one! ( ) to do that a is called a Boolean function if a Boolean function if a Boolean expression n. ( ab ( c+! d ) ) +! b with implicit multiplication ab = a + ( a.b! Calculate the __product of two expressions using Boolean algebra is the product of literals help requests operators are Boolean... Dcode has developed the best 'Boolean expressions Calculator ' tool, so feel free to write negation note... Gate corresponding to the expression perform matrix multiplication Calculator which performs two main and related functions i.e ( â.... Main and related functions i.e different formats to ensure better readability or usability Calculator supports with... A matrix to a power with complex numbers online for free on matrices this website, you agree our! Algebraic notation during a resolution with a pencil and paper be added the... Complex numbers online for free relevant comments, dCode provides a solution output... Perform normal matrix multiplication and Boolean multiplication Also recall from part 3 that Boolean multiplication is branch. Only operation involved Here is negation, we set its Boolean equivalent variable true. Them boolean multiplication calculator the signals given as input to the expression 3 that multiplication... Is called a Boolean expression are equal our Story ; Hire a ;. Backbone of computer circuit analysis power with complex numbers online for free work! Operators are called Boolean operators or logical operators and, or, NOT, XOR the of! Product term is produced by an and operation with no or operations involved Relay and Switching circuits specify.! Is helpful in the first set of equations there may be several representations! Dcode has developed the best 'Boolean expressions Calculator ' tool source code ( â ) ) ) prime... To Boolean addition, being implemented by shifting as well as equivalent decimal incorporates the binary values a... The signals given as input to the and operation NOT correspond to performed... Mathematical Tools, allowing you to easily add them to the expression by clicking respective. Same expression, dCode provides a selection of commonly used conditional and mathematical operators be. Any non-zero numbers with 1, and leave 0 as zero ( (! Is equivalent to Boolean multiplication on matrices or minify Boolean expressions by converting large! Values, true or false an easy to follow example that teaches you how to Boolean... Boolean equivalent variable to true to a is called a Boolean expression of n variables specify... Arbitrary matrices sizes ( as long as they are normal matrices, normal! The same writing in Boolean algebra is a part of arithmetic operations in electronics... B ) = a + b \\ a perform normal matrix multiplication with complex numbers online for free to and! Is negation, we have to input another number to compute the transitive closure of Boolean.


text:
# How long does it take a black hole to eat a star?

I presume the answer is that it depends on the mass and size of the star and black hole, but I was wondering if somebody could provide some rough bounds (e.g. hours vs thousands of years).

By "eating" I mean the time it takes a star to go through the event horizon of the black hole, although maybe there are other easier-to-detect or more relevant events one can measure?

-
are you referring to a star&black hole binary system? –  Nic Apr 9 '11 at 0:07

One of the main ways black holes are noticed is by looking at a solar system where the star appears to move as though it were a binary star system (e.i. two stars) when only one is seen. In these situations, depending on the distances, the black hole "feeds" off the original star, and a stream of the stellar plasma is slowly pealed off the star into the black hole.

This matter can sometimes form a very vivid accretion disk, that can be observed using telescopes (see Herbig–Haro object). This process can take a very long time, on the order of millions of years. However, of course, a rogue black hole could enter a star system head on and collide right with the sun and "suck it up," which would happen rather quickly (to an outside observer).

-
Thanks! I never thought that "a rough black hole could enter a star system head on and collide right with the sun and 'suck it up'". Fascinating. –  user815423426 Apr 9 '11 at 13:49
I think he meant rogue not rough, no? As in rogue wave (ocean phenomenon). –  Marcos Sep 14 '12 at 13:14

If you are asking about a star being "eaten" by a supermassive black hole at the center of a galaxy, as is being in another question here on Physics SE due to a recent event covered in the popular press (GRB 110328A), this relatively authoritative paper says that they stay bright for one month to one year.

This long period is due to the orbiting of the torn up parts of the star.

Probing Quiescent Massive Black Holes:
Insights from Tidal Disruption Events
A Whitepaper Submitted to the Decadal Survey Committee

http://arxiv.org/PS_cache/arxiv/pdf/0903/0903.1107v1.pdf

-
Thanks Jim! It was GRB 110328A indeed what made me think about this question. –  user815423426 Apr 9 '11 at 19:02
Minor comment to the post (v1): In the future please link to abstract pages rather than pdf files, e.g., arxiv.org/abs/0903.1107 –  Qmechanic Dec 2 at 21:32

## protected by Qmechanic♦Dec 2 at 21:30

Thank you for your interest in this question. Because it has attracted low-quality answers, posting an answer now requires 10 reputation on this site.


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# Is this a weighted average/percentage problem?

Let's say a Marketing company has a total turnover of 10000 \$There are 3 salesmen A,B,C with the following turnovers A = 2000$
B = 3000 $C = 5000$

Now, If the company wants to increase total turnover by 10 %, Should this be split as 10% for all salesmen OR Can 10% be split across A,B,C differently using weighted averages/percentages?

-
Explosion of answers! By the way including \\$in your posts will allow the \$ sign to appear. –  mixedmath Jul 19 '11 at 17:02

You can do whatever you like. If you increase each of A, B, and C by 10%, the total will go up 10%. You can also increase A to 3000 and the total increases by 10%. What is your criterion for the decision?

-

It depends on company OR below should be an answer. $$10000=A+B+C=2000+3000+5000$$ $$10000\times(1+0.1)=(A+B+C)\times(1+0.1)=(2000+3000+5000)\times(1+0.1)$$ $$\therefore A=2200, B=3300,C=5500$$

-

It the mathematical OR - meaning one, the other, or both. And in this case, it's both. Ultimately, throwing an additional 1000 dollars among A, B, and C will always yield a 10% increase, regardless of how it's distributed.

-
Increase of total turnover by 10% $\rightarrow 2000x_a+3000x_b+5000x_c = 11000$. So you have 3 unknowns and 1 equation, so you need more constraints to determine a unique solution.
For e.g. $x_a = x_b = x_c = 1.1$ would work (each person increases their turnover by 10%) and so would $x_a = 0.4, x_b = 1.3, x_c = 1.26$ (required turnover of $A$ reduces to 40%, $B$ increases by 30% and $C$ increases by 26%)!


text:
## You are here

Hi ctlawson, as part of our job in this question we need to break the electric fields into 'x' and 'y' components. It would be perfectly OK to use $60^\circ$. The difference is that you would have to think about which trig. function is the right one to use. For example, when I calculate $E_{Bx}$ using $\cos(30^\circ)$ you could instead use $\sin(60^\circ)$. It's just a matter of personal preference.


text:
main-content

## Über dieses Buch

Programming is a fascinating and challenging subject. Unfortunately, it is rarely presented as such. Most often it is taught by "induction": features of some famous programming languages are given operational meaning (e.g. a loop "goes round and round"), a number of examples are shown, and by induction, we are asked to develop other programs, often radically different from the ones we've seen. Basically we are taught to guess our programs, and then to patch up our guesses. Our errors are given the cute name of "bugs". Fixing them becomes puzzle-solving, as does finding tricks that exploit or avoid poorly designed features of the programming language. The entire process is time-consuming and expensive. And even so, we are never quite sure if our programs really work in all cases. When approached in this way, programming is indeed a dull activity. There is, however, another approach to programming, an approach in which programs can be developed reliably, with attention to the real issues. It is a practical approach based on methodically developing programs from their specifications. Besides being practical, it is exciting. Many programs can be developed with relative ease. Problems which once were difficult can now be solved by beginners. Elegant solutions bring great satisfaction. This is our subject. We are interested in making programming an exciting topic!

## Inhaltsverzeichnis

### 0. What can we learn from a cake?

Abstract
We are interested in programming, which in broadest terms is problem solving. There are lots of problems and we cannot solve them all. Which problems will we consider? We should delineate our topic.
Edward Cohen

### 1. Preliminary notions, notations, and terminology

Abstract
Formula manipulation was quite effective in solving the cake problem. In fact, if we think about it, formula manipulation has been the key to success in many areas. Civil engineers manipulate formulae in bridge design, for example.
Edward Cohen

### 2. Predicates A — Boolean operators

Abstract
As already mentioned, the manipulation of predicates will be our main vehicle for program development. As such, manipulating them must become second nature. This comes from practice. Throughout this chapter there are theorems whose proofs are omitted. Although these proofs are exercises at chapter end, we highly recommend attacking them as they appear in the text. They are a lot of fun, and will be of great help in absorbing the material. Attacking theorems whose proofs are included will be of great help too.
Edward Cohen

### 3. Predicates B — Quantified expressions

Abstract
For symmetric and associative binary0 operators op we write the quantified version of op as
$$\left( {\underline {OP} {\text{ }}i:R:T} \right)$$
(0)
Expression (0) is called a quantified expression, or a quantification for short. Its type is the same as the type of op: if op is an arithmetic operator, then (0) is a boolean expression, and so on.
Edward Cohen

### 4. Specifications

Abstract
What do we do when asked to construct a “customer database”. At first glance the problem seems straightforward enough. Upon closer inspection many questions arise: what characterizes a customer?, what functions must be provided?, and so on. Given to ten different people, ten different solutions will appear, and it is entirely likely that none will provide what was desired. The problem, of course, is that “customer database” is much too imprecise.
Edward Cohen

### 5. The shapes of programs

Abstract
The activity of programming is the activity of solving a specification for its unknown, where this unknown is called a program. Programs are formulae of a certain shape.
Edward Cohen

### 6. Intermezzo on calculations

Abstract
In the next chapter we embark on our study of programming. What we will find is that most of it boils down to calculation and, as such, an effective programmer must first be an effective calculator.
Edward Cohen

### 7. Developing loopless programs

Abstract
The activity of programming is the activity of solving a specification for its unknown. A specification’s unknown is called a program. This chapter marks the beginning of our study of programming. Here we constrain ourselves to the development of programs that contain no loops. In subsequent chapters we study the development of loops. For now we concentrate on the assignment and the IF. We will discover that the development of assignments and IFs are mainly matters of straightforward calculation!
Edward Cohen

### 8. Developing loops — an introduction

Abstract
Our insight into developing loops comes from the Invariance Theorem:
$$\begin{array}{*{20}{c}} {\left\{ P \right\}\underline {do} B \to S\underline {od} \left\{ {P \wedge \neg B} \right\}} \\ { \Leftarrow {\text{ the conjuction of}}} \end{array}$$
(0)
$$\left\{ {P \wedge B} \right\}S\left\{ P \right\}$$
(a)
$$\left\{ {P \wedge B \wedge t = T} \right\}S\left\{ {t < T} \right\}$$
(b)
$$P \wedge t \leq 0 \Rightarrow \neg B$$
(c)
where P is a predicate called a loop invariant, and t is an integer function called the bound function. Conjunct (a) is the requirement of Invariance, conjunct (b) is the requirement of Progress, and conjunct (c) is the requirement of Boundedness.
Edward Cohen

### 9. Loops A — On deleting a conjunct

Abstract
The first step in developing a loop is to choose an invariant (and a guard). In particular, given postcondition R, invariant P and guard B must be chosen to satisfy
$$P \wedge \neg B \Rightarrow R.$$
(0)
Edward Cohen

### 10. Loops B — On replacing constants by fresh variables

Abstract
The first step in loop development is to choose invariant P and guard B from postcondition R to satisfy
$$P \wedge \neg B \Rightarrow R$$
If R happens to be a conjunction, then this is easy. Choose for P one of the conjuncts, and choose for B the negation of the other conjunct, as we have seen.
Edward Cohen

### C11. Mainly on recursion

Abstract
Many functions are defined recursively. Consider exponentiation: for integer x and natural y, we have
$$\begin{gathered} {x^y} = \,\underline {fi} \,y = \,0\, \to \,1 \hfill \\ \,\,\,\,\,\,\,\,\,\,{\text{}}\,\,\,{\text{y}} \ne {\text{0}}\, \to \,x\, * \,{x^{y - 1}} \hfill \\ \,\,\,\,\,\,\,\,\,\,\underline {fi} \hfill \\ \end{gathered}$$
In other words, exponentiation is defined recursively.
Edward Cohen

### 12. Back to scratch

Abstract
In previous chapters we were asked to solve specifications for their programs. The specifications were given. Practicing programmers, however, are rarely given specifications. Usually we get informal problem statements.
Edward Cohen

### 13. Where to go from here

Abstract
We have seen a number of methods. We have applied these methods to a number of examples. While the examples were not the subject matter, I have tried to choose generally useful ones.
Edward Cohen

### Backmatter

Weitere Informationen


text:
# learning rate in Adaboost sklearn

I can't figure out what does learning_rate stand for in sklearn implementation of Adaboost. When i see the original algorithm i don't see any "learning_rate"...

Meanwhile i can see from https://fr.wikipedia.org/wiki/AdaBoost that the training errors are weighted thanks to $$D_t(i)$$ (where $$i$$ is attached to the $$i$$th training instance in the training matrix $$X$$). Is there any relation between the sklearn "learning_rate" and this $$D_t$$ ?


text:
The School of the Physical Sciences is one of six Schools making up the academic work of the University. It covers Astronomy, Chemistry, Earth Science, Geography, Materials Science and Metallurgy, Mathematics and Physics. The School’s aim is to contribute to our understanding of the physical world through excellence in observational, theoretical and experimental science and to extend quantitative, qualitative and combined methodologies to address problems in the fields of biology, technology, medicine, social science and the humanities. In pursuit of these goals, the School coordinates objectives in research, teaching, and infrastructure.

Find out more about the School of the Physical Sciences at http://www.physsci.cam.ac.uk/.

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We present numerical simulations of diffusio-osmotic flow, i.e. the fluid flow generated by a concentration gradient along a solid-fluid interface. In our study, we compare a number of distinct approaches that have been ...
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The objective of this article is to report the results of an ecological study into the geography of rape in Stockholm, Sweden using small area data. In order to test the importance of factors indicating opportunity, ...
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text:
# Expected distance to nearest neighbour: Why integral of survivor function? (instead of derivative)

Previously, I asked the question how to calculate the expected distance to the nearest neighbor molecule in 3-dimensional space. This question was fully answered, which is I ask this related question in a separate thread. As a disclaimer, I know that the previous answer reflects the literature, and I do not intend to question its validity whatsoever.

I wanted to calculate the expected distance of 1 particular of 500 molecules to its closet of 499 neighbors that are randomly diffusing in a volume of 1 cubic micrometer.

I think I understand the following statement:

Since the neighbor positions are independent, the chance that all are further than distance 𝑟 is

$$S_{N;d}(r) = (1-r^d)^N.$$

But to my mind, without former education in math and statistics, I would argue that the derivative of this function - the change in probability at given r - should reflect the probability of finding closest neighbors at this r. Also this approach seemingly perfectly recreates a 3d simulation:

3D simulation (Python)

import numpy as np

import numpy as np
def min_eucledian(centers):
squared = np.square(centers)
summed = [sum(squared[i*3:i*3+3]) for i in range(len(squared)//3)]
return np.sqrt(min(summed))

N = 499
simulation_length = 3*10**6 #this was used, I know it is excessive
distances = []
for i in range(simulation_length):
protein_centers = np.random.uniform(low=-500, high=500, size=N*3)
distances.append(min_eucledian(protein_centers))
if i%10000 == 0:
print(i)

"Derivative" approach

Probability of finding 0 neighbors within r:

Derivative:

So, the derivative seems logical to me, also it perfectly recreates the simulation. Instead, the textbook approach is off by around 70%. (see linked question)

So I would like to ask 2 questions:

1. Could you explain the logic behind using the integral in simple English, understandable without much education in statistics?

2. How may I interpret the discrepancy of the results? Am I asking different questions? Is my simulation wrong?

EDIT: I happened to find the answer to the question. I repeated the calculation without the sphere-factor (4/3 * pi), what perfectly recreates the previous answer. I know what is going on. A moderator may delete the question, unless it is found educative. Thanks!

• Since you found the answer, could you answer your own question (and accept it) with a bit more detail? I think this would help others more. See here for details. Mar 16, 2021 at 13:39
• I can't answer the full question, I just happened to find the root of the discrepancy of results. Mar 16, 2021 at 13:55


text:
USF Home > College of Arts and Sciences > School of Interdisciplinary Global Studies

# Fellowship & Scholarships

McKnight Doctoral Fellowship
Deadline: January 15th of each year
Eligibility: African-American and Hispanic doctoral students pursuing degrees at selected Florida universities.

THE AWARD:
Up to 50 Fellowships are awarded annually to study at one of nine participating Florida universities. Each award provides annual tuition up to $5,000 (tuition above this amount is waived by the participating institution) for each of three academic years plus an annual stipend of$12,000. (An additional two years of support at this same level is provided by the participating institution.) The award also includes a comprehensive system of academic support.

Each annual renewal is contingent upon satisfactory performance and normal progress toward the Ph.D. degree.


text:
Services & ResourcesWolfram ForumsMathGroup Archive

LaTex to Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg91395] LaTex to Mathematica
• From: "snowrain" <anne_xuetulip at hotmail.com>
• Date: Wed, 20 Aug 2008 04:03:25 -0400 (EDT)

Hi all
Does anyone know how to convert LaTex file to Mathematica ?
For example, the formula that I typed in LaTex is:
ln{H}^{*} &=  {X}_{1} {\beta}_{1}  + {\alpha}_{1}lnE+ {\varepsilon}_{1}\\
If I copy the above LaTex command to Mathematica, it only shows the
original LaTex command. I'd like to have symbols for beta, alpha, and also
for subscript and superscript. That is, I hope it looks like the pdf file
that LaTex produces instead of showing "\beta", "\alpha", etc.
thanks a lot !

--


text:
# Is it true that every perfect set of a compact Hausdorff space is uncountable?

Let $$(X, \mathcal{U})$$ be a compact Hausdorff space and it has no isolated point. Let $$A\subseteq X$$ is a closed and infinite set with no isolated point . Is it true that $$A$$ is uncountable set?

No. Consider $$X=[0,1]$$, $$A=\{0\}\cup\{\frac1n:n\in\mathbb{N}\}$$.
• Thanks. What can say about $A$, if $A$ has no isolated point? – user479859 Dec 13 '18 at 21:14


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## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJan 2nd 2012
• (edited Jan 2nd 2012)

I have started an entry analytic space with material on Berkovich’s non-rigid analytic geometry.

I don’t really know this subject and have been adding material to the entry as I read about it and to the extent that I correctly understood it. Experts are most welcome to help out.

As indicated here, I am motivated by the following: Berkovich’s local contractibility result suggests that the $\infty$-topos of $\infty$-sheaves over the site of $p$-adic analytic spaces might be cohesive.

The idea would be that his result implies (if it does) that the site (category with coverage) of contractible $p$-adic afine spaces is a dense subsite of that of all $p$-adic spaces. Since it should be an infinity-cohesive site that would imply the claim.

But despite looking through Berkovich’s writings for a little bit today, I am still not sure if he just shows that the underlying topological space of a $p$-adic anayltic space is locally contractible, or if one may indeed deduce that they are locally contractible with respect to étale homotopy, as would be needed for the above conclusion.

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeJan 2nd 2012

Is this part of an attempt to survey the range of cohesiveness?

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJan 2nd 2012

Yes, I am trying to find useful subsites of algebraic spaces that are cohesive.

• CommentRowNumber4.
• CommentAuthorDavid_Corfield
• CommentTimeJan 3rd 2012

Perhaps then we might see why there can be a p-adic and adelic physics?

Hmm, that’s the frightening thing about maths. One step away from things you might know a little about, there are whole worlds you knew nothing about, where people have been working away for years. Now I see there’s a type of space in which the unit disk has four types of point and its possible to have a Potential theory and dynamics on the Berkovich projective line.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeJan 3rd 2012
• (edited Jan 3rd 2012)

we might see why there can be a p-adic and adelic physics?

Yes, I was beginning to wonder about that yesterday. I had started to add some references to p-adic number – References – Applications. But I am not feeling well about this, since there is a tremendous amount of wild speculation in there and few concrete results, as far as I can see.

Notice that at the above link that you give, before long the page lists references to the journal “Chaos, Solitons and Fractals”. Deep nonsense territory.

This is not to say that there cannot be something of value here. If locally smooth $p$-adic analytic spaces indeed form a site for a cohesive $\infty$-topos, then the cohesive formalism would systematically spit out sensible $p$-adic analogs of good bits of physics. That would help me understand what’s really going on.

But first we need to clarify that question. I have now emailed Berkovich and asked him if his result implies a certain technical fact from which it would follow (I still can’t see it based on his texts, though it might be implicit in there).

• CommentRowNumber6.
• CommentAuthorzskoda
• CommentTimeJan 3rd 2012
• (edited Jan 3rd 2012)

Urs is looking for some homotopical or infinite categorical aspects here. There is an unpublished work on the $\mathbf{B}^1$-homotopy theory, the analogue of Voevodsky’s $\mathbf{A}^1$-theory in rigid analytic context, by some student in France few years ago who is now professor somewhere. I am not quite sure who that was, remotely it might be Joseph Ayoub, but I am not quite remembering (I heard a talk some 6-7 years ago or so). In any case over there certainly some facts similar to ones you might look for must have been thought of, and would be nice to consult the source.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJan 3rd 2012
• (edited Jan 3rd 2012)

There is an unpublished work on the $\mathbb{B}^1$-homotopy theory, the analogue of Voevodsky’s $\mathbb{A}^1$-theory in rigid analytic context, by some student in France few years ago who is now professor somewhere. I am not quite sure who that was, remotely it might be Joseph Ayoub, but I am not quite remembering (I heard a talk some 6-7 years ago or so).

Ah, interesting. I tried googling around for “analytic geometry homotopy theory” a bit, and looked at Ayoub’s webpage, but so far I haven’t found the kind of discussion you are alluding to. But I’d be most interested in seeing it.

• CommentRowNumber8.
• CommentAuthorzskoda
• CommentTimeJan 3rd 2012
• (edited Jan 3rd 2012)

Try to contact him, and if he is not the guy he must know who that is as he came from that Paris circle. I wrote some comments in $n$Community before and could never find anything online.

• CommentRowNumber9.
• CommentAuthorzskoda
• CommentTimeJan 3rd 2012
• (edited Jan 3rd 2012)

Correction: there is something related online: pdf

• CommentRowNumber10.
• CommentAuthorDavid_Corfield
• CommentTimeJan 3rd 2012

Maybe of no interest, but one place with ’analytic geometry’ and ’homotopy’ on the same page is a course outline which includes

The moduli space of Lubin-Tate formal group laws is a rigid analytic space occurring in the work of Gross and Hopkins, which ties together this sort of geometry with stable homotopy theory.

M.J. Hopkins and B.H. Gross, The rigid analytic period mapping, Lubin-Tate space, and stable homotopy theory, Bulletin of the AMS 30 (1994), 76–86

Notes for the course are here.

• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeJan 3rd 2012

there is something related online: pdf

Ah, thanks!

This does not seem to help me with my question about cohesiveness, but otherwise it is very good to see this. For the moment I have archived the link in a new stub entry B1-homotopy theory.

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeJan 3rd 2012

Maybe of no interest, but one place with ’analytic geometry’ and ’homotopy’ on the same page is a course outline which includes […]

Thanks, David! That looks useful, I’ll have to look at it. For the moment I have archived the reference here.

• CommentRowNumber13.
• CommentAuthorUrs
• CommentTimeJan 3rd 2012

Hi Zoran,

coming back to this here:

The hope that working with $p$-adic numbers can remove divergences in QFT is an old hope which drives the $p$-adic physics for a long while;

Do you know about any concrete results that have been obtained? Anything that goes beyond hope and vague speculation? Are there some actual facts about “$p$-adic mathematical physics” that one could point to?

I’ll try to look around myself a bit more. But if you have anything to share, I’d be interested.

• CommentRowNumber14.
• CommentAuthorUrs
• CommentTimeJan 3rd 2012
• (edited Jan 3rd 2012)

in the mathematical literature on $p$-adic analytic geometry it says (I’ll try to dig out a precise reference again) that functions $f : \mathbb{Q}_p \to \mathbb{Q}_p$ are uninteresting, and that the objects to consider are instead maps $\mathbb{A}_{\mathbb{Q}_p} \to \mathbb{A}_{\mathbb{Q}_p}$ (from the Berkovich affine line to itself).

Now, I open a book like

• Vasiliĭ Vladimirov, I. V. Volovich, E. I. Zelenov, $p$-Adic analysis and mathematical physics

and in the introduction it announces to study the replacement of real functions with maps $\mathbb{Q}_p \to \mathbb{Q}_p$.

Generally, I see little or none mathematical analytic geometry mentioned in these texts on $p$-adic mathematical physics. Is there maybe a communication gap?

• CommentRowNumber15.
• CommentAuthorDavid_Corfield
• CommentTimeJan 4th 2012

Can you work in reverse with cohesive $(\infty, 1)$-toposes, so that if all, or some subset, of the associated structures turn up, you know you must be in the presence of a cohesive $(\infty, 1)$-topos? Are there perhaps a small number of structures whose presence suggests the others?

By the way, there’s an interesting account of the difficulty of Berkovich’s first steps.

• CommentRowNumber16.
• CommentAuthorzskoda
• CommentTimeJan 4th 2012
• (edited Jan 4th 2012)

13,14

They solve various simple physical systems in p-adic context, how far they got I do not know, but usually these are difficult and exact calculations, so the progress is relatively slow. I do not think that anybody there studies rigid analytic geometry – as usually in mainstream physics one does local computations in just one chart. I would not call that a communication gap. People are busy and can not learn to do effectively everything. You can not expect to have comparable results to ordinary physics where there are thousands of physicist with a direction populated by about 10 enthusiasts, most of whom do other mathematical physics as well.

• Hans Grauert, Reinhold Remmert, Theory of Stein spaces, Grundlehren der Math. Wissenschaften 236, Springer 1979, xxi+249 pp.; Coherent analytic sheaves, Grundlehren der Math. Wissenschaften 265, Springer 1984. xviii+249 pp.; Komplexe Räume, Math. Ann. 136, 1958, 245–318, DOI
• CommentRowNumber17.
• CommentAuthorzskoda
• CommentTimeJan 4th 2012
• (edited Jan 4th 2012)

Maybe one should point out the discovery of $p$-adic Veneziano amplitude for $p$-adic string theory in

• I. V. Volovich, p-Адическое пространство-время и теория струн, ТМФ, 71:3 (1987)free Rus. pdf; transl. $p$-adic space-time and string theory, Theor. Math. Phys. 71, 574–576 (1987), eng doi, nonfree Eng. pdf

• CommentRowNumber18.
• CommentAuthorUrs
• CommentTimeJan 4th 2012

Can you say what the result is here? I understand that one can refomrulate the expression for the amplitude in $p$-adic arithmetic. What is the nontrivial result to be proven?

(This is not a rethoric question. I genuinely need to learn this.)

• CommentRowNumber19.
• CommentAuthorzskoda
• CommentTimeJan 4th 2012
• (edited Jan 4th 2012)

It is not a reformulation. It is a different mathematical expression which is an analogue of Veneziano amplitude in $p$-adic context. I am personally not interested in the subject.

Even doing the integration over p-adics effectively needs hard techniques closely related to motivic integration. This has been subject of much recent research in motivic integration community.

The situation is somewhat similar to the situation with q-beta function of Ramanujan and q-binomial formula etc. which are not reducing to the usual beta function and the usual binomial formula.

• CommentRowNumber20.
• CommentAuthorUrs
• CommentTimeJan 4th 2012

I have split off an entry p-adic physics, just in order to collect all these references for the moment.

• CommentRowNumber21.
• CommentAuthorzskoda
• CommentTimeJan 4th 2012

Good.

• CommentRowNumber22.
• CommentAuthorUrs
• CommentTimeJan 4th 2012
• (edited Jan 4th 2012)

re #16:

as usually in mainstream physics one does local computations in just one chart. I would not call that a communication gap.

I am not sure if this is just a matter of globalizing. It seems to me that the basic idea of geometry in mathematical analytic geometry is different from what the texts on “$p$-adic physics” try to connect to:

the latter replaces the real line with $\mathbb{Q}_p$. But the former replaces it with the Berkovich affine line $\mathbb{A}_{\mathbb{Q}_p}$ (“$\mathbb{B}_p^1$”, I guess ). This should be a big difference.

• CommentRowNumber23.
• CommentAuthorzskoda
• CommentTimeJan 4th 2012
• (edited Jan 4th 2012)

OK. Reason more that they should not be interested. I think nobody claimed in the Vladimirov community to do rigid analytic geometry ever. They do the usual $p$-adic geometry in the sense of $p$-adic analytic manifolds and their examples belong there. On the other hand, I think the mathematical physics-inspired work of Marcolli and Manin (also listed on the link above) does indeed point toward some phenomena in rigid geometry.

• CommentRowNumber24.
• CommentAuthorUrs
• CommentTimeJan 4th 2012
• (edited Jan 4th 2012)

they should not be interested

I understand that they are not interested, but I don’t understand why they should not be interested. This seems to be the “communication gap” that I mentioned. These people set out to explore the consequences of replacing in the geometry of physics the real numbers by the $p$-adic numbers, while at the same time there is a huge body of mathematics that does precisely such a replacement, but differently.

• CommentRowNumber25.
• CommentAuthorzskoda
• CommentTimeJan 4th 2012
• (edited Jan 4th 2012)

I do not think that the idea was to replace the numbers by $p$-adic numbers just for math analogy, but for the fact that in usual $p$-adic coordinates some expressions were finite which are infinite in the other case. I do not recall examples, I have heard few conference talks presenting formulas some of which appear in the calculations in QFT. So they continued this game, starting from the concrete evidence they had. This does not give any concrete evidence however that similar expressions would appear in calculations in the different setup you propose. If you have a striking finiteness result for amplitudes in Berkovich spaces, then the situation will change. This is not matter of communication but matter of lack of evidence as of today.

• CommentRowNumber26.
• CommentAuthorUrs
• CommentTimeJan 4th 2012

Okay, so I need to learn that better. In the introduction to that book

• Vasiliĭ Vladimirov, I. V. Volovich, E. I. Zelenov, $p$-Adic analysis and mathematical physics,

for instance, the motivation that is given is: look, there are two kinds of completions of the rationals, and traditonally only one of them is used for the description of physical space. We want to explore what happens when we use the other one.

This is supplemented with the usual speculation about quantum geometry at the Planck scale. Similarly in the other reviews that I have seen.

• CommentRowNumber27.
• CommentAuthorzskoda
• CommentTimeJan 4th 2012

Well, once somebody is in the game one tries to find the applications everywhere, and then one needs to soften and widen the motivation statement, so I am not surprised that books get into such lowest common denominator. But all of that is not very strong. What is stronger is the initial observation that some infinite expressions in QFT were finite in $p$-adic context. The initial counterargument being what is the $p$ which nature would take and fix ?

• CommentRowNumber28.
• CommentAuthorzskoda
• CommentTimeMay 24th 2012
• (edited May 24th 2012)

The analytic geometry based on the very fine and disconnected topology of non-archimedean field is having problems which needed rigidification. So I have originally viewed entry rigid analytic geometry to be about ALL modern approaches which rectify this problem with various levels of success and in various level of generality: Tate’s rigid analytic spaces, Berkovich analytic spaces, Huber’s adic spaces, Fujiwara-Kato approach via multiple formal models and Zariski Riemann space etc. This lead in past to some misunderstanding, as Urs and Frederic were taking every time I mentioned word “rigid” ot mean the Tate’s approach; though I often hear people saying rigid for the other approaches. On the other hand analytic space is about possibly even non-archimedean versions. So I decided that it is better that we are really split into different levels of generality carefully. So I renamed analytic space into Berkovich space with redirect Berkovich analytic space and creted a new analytic space to lead to both archimedean and non-acrhimedean case. Then I created an entry non-archimedean analytic geometry to have Tate, Berkovich, Huber, global and Fujiwara-Kato in one place while having more details on the pages specially dedicated to each of them. Rigid analytic geometry entry is now predominantly about Tate’s approach only, with agreement with Urs and Frederic.


text:
# Khaopoon Cave – Kanchanaburi city

### Cave

When you visit Kanchanaburi city, the town of the bridge over the river Kwai and the war cemetery, you could consider a visit to Khao poon cave (also written as Khao Pun). The place is also known as Wat Tham Khao Pun. Wat is the Thai word for temple. I know that most people stay only briefly in Kanchanaburi. They visit just the Bridge and the war cemetery. Some visit one of the few museums too, but hardly anyone visits the second war cemetery at Chungkai, which is a few kilometers from the other war cemetery in town.

The cave is not a huge one as many other caves in Asia, but definitely worth to visit. I would call it a mixture of cave, temple with Buddha statues and war history. This is because there is a part at the end where you come out of the cave where old pics of POW’s, the Death Railway and the bridge are shown.

Inside the cave there are several rooms. Not all of those rooms have an exit. Some parts are quite narrow and dark. You need both hands at some points and might get your clothes somewhat dirty. There are many different Buddha’s in all kinds of positions to be seen. For more info you can look here: travelfish.org.

The entry price is 30 baht p.p. Opening time is 8:00 am to 5:00 pm.

### How to get there?

When you stay in Kanchanburi’s one and only tourist road, you walk in opposite direction of the river Kwai bridge. This means you go to the cemetery. Follow that road and turn right after the school which you see on your left hand side. At the traffic light you go straight over the bridge, followed by another bridge. At the T junction you turn right again and follow that road. You will cross the railway and soon you’ll see the Chungkai war cemetery. Immediately after Chungkai, the road goes uphill and on top of that hill lies Khaopoon cave on you left hand side.

It sounds far, but it’s not realy that far. I wouldn’t recommend to walk it though. You can rent a scooter for less than 200 baht per day ($5) or a bicycle for 40 baht ($1) and go to the cave and/or Erawan waterfalls.

Khaopoon cave is worth a visit when you are in Kanchanaburi. An impression video can be seen here https://www.youtube.com/watch?v=GLBAuVLiUL8&feature=youtu.be