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### My adventures in 3D printing: Golomb ruler

At work we’ve got a 3D printer. In this series of posts I’ll share some of the designs I’ve made.

At the start of the Summer we (I) bought a new 3D printer for the department, a FlashForge Dreamer. It’s got two extruder heads, so it can do two-colour prints.

To test that out, I designed this Golomb ruler. It’s a straightedge with marks at 0, 1, 4 and 6 cm. The idea is that you can measure 1, 2, 3, 4, 5 or 6 cm by lining up against different pairs of marks. I recently did a silly Twitter thread on this subject.

As you can see from the photo, two-colour printing isn’t quite as straightforwared as it could be. Because both nozzles need to stay hot, while one colour was printing the other just oozed out and made a mess. There are some settings on the printer you can change to try to reduce this, but I haven’t got the hang of it yet.

### My adventures in 3D printing: Wallis’ Sheldonian theatre roof

At work we’ve got a 3D printer. In this series of posts I’ll share some of the designs I’ve made.

The roof of the Sheldonian theatre in Oxford, built from 1664 to 1669, is constructed from timber beams which are unsupported apart from at the walls, and held together only by gravity.

### My adventures in 3D printing: Spherical pseudo-cuboctahedron

At work we’ve got a 3D printer. In this series of posts I’ll share some of the designs I’ve made.

This shape is a “spherical pseudo-cuboctahedron”, prompted by a request from Jim Propp on the math-fun mailing list.

It has 24 vertices, 12 edges and 14 faces. That doesn’t satisfy Euler’s formula $V – E + F = 2$, so it can’t be a proper polyhedron – hence “pseudo-cuboctahedron”.

However, if you push all the vertices onto the surface of a sphere, all the edges are spherical arcs, it sort of works.

While designing this object, I got fed up with OpenSCAD‘s awkward control syntax, and switched to Python. I wrote Python code to produce the coordinates of points along the edges, which the SolidPython library turned into something that OpenSCAD can cut out of a sphere.

### My adventures in 3D printing: Write Angles Cube

At work we’ve got a 3D printer. In this series of posts I’ll share some of the designs I’ve made.

This is one of the first ‘proper’ things I’ve designed – I wanted to have a go at making something based on an object I already had. A colleague asked if I could make some props to explain coordinate systems, and I was holding a whiteboard pen at the time, so I decided to make a set of orthogonal axes out of whiteboard pens.

### TeXnique: a LaTeX typesetting game

You know what’s fun? Typesetting mathematics! Glad you agree, because here’s a game that puts the fun in ‘underfilled hbox’.

In TeXnique, you’re shown a typeset bit of mathematical notation, and have to frantically type LaTeX to reproduce it. You get three minutes, and you’re awarded points when you produce something that’s a pixel-perfect replica of the original. Think Typing of the Dead crossed with The Art of Computer Programming.

When I first saw this I rolled my eyes, but now my high score is 68 and I don’t know why I keep going back to it.

The formulas are largely well-known snippets of notation, so you might find some of them coming out through muscle memory, but if a symbol shows up that you can’t remember the macro for, there’s always the brilliant Detexify tool.

Play: texnique.xyz by Akshay Ravikumar.

### I’m streaming digits of π for π day

It’s π eve, and I’ve had a silly idea: I’m going to take the ridiculous website I made to show all the digits of π, and stream it scrolling indefinitely through them over the internet.

Starting at midnight GMT on 2019-03-14, the stream below will start scrolling down through the digits of π:

I had this idea this morning, and it’s running on my desktop PC which I’ll be away from until 8am tomorrow, so I won’t be surprised if something goes wrong.

But if it doesn’t: hooray!


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# Why do atomic radii decrease across a period? [closed]

It's said that atomic size/radius decreases across a period, in spite of addition of electrons. But how does this actually work?

Atomic radius decreases across a period because electrons are being added to the same energy level and at the same time the nucleus is increasing in protons. The increase in nuclear charge $$Z_{eff}$$ attracts the electrons more strongly, (addition of one proton has a greater effect than addition of 1 electron) thus pulling electron closer to the nucleus and making atomic radius decrease.

format: plain


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## alex_smith55 Group Title how many pounds are there in 1 Newton? one year ago one year ago

• This Question is Open
1. Decart Group Title

N=Kg/m^2

2. Decart Group Title

The pound or pound-mass (abbreviations: lb, lbm, lbm, ℔[1]) is a unit of mass used in the imperial, United States customary and other systems of measurement. A number of different definitions have been used, the most common today being the international avoirdupois pound which is legally defined as exactly 0.45359237 kilograms.

3. NoelGreco Group Title

4. Shane_B Group Title

You can also just calculate it:$1kg = 2.20462lbs$$1N=\frac{2.20462lbs}{9.80655m/s^2}=0.22481...lb_f$

5. Algebraic! Group Title

1kg=2.20462lbs ...

6. UnkleRhaukus Group Title

$1[\text N]=0.22481[\text{lbf}]$


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# How to make help open local help automatically instead of asking to choose each time?

Each time, when asking for help using ?Command, I now find I have to click one extra time compared to version 11.3, in order to choose local help instead of the web help. Since I always want to look at the local help, this extra click each time is a little annoying. Here is an example

Compare to 11.3

One might argue than one extra click is not a big deal. But doing this 50 times per day, 30 times per month, 12 months per year, this becomes 18,000 extra clicks per year.

Is there an option in option inspector to make it automatically open local help for those of us who want this choice all the time? (I did not know what to search for) Or to make help display the lower panel at the same time, so one can click on local directly?

• You may already know about this, but my favorite way to open a doc page is to hit F1 when the cursor is within a symbol. If you are counting clicks that may help. Jun 14, 2019 at 2:18


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# basic blackjack game in C++ ...help?

This topic is 4880 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

EDIT: new code in a newer post below -------------------------- I have to make a blackjack game for my intro to C++ class, but I couldn't afford to buy a textbook, and I may have missed some class discussions that would have helped me out with this. I haven't started coding the main program yet, but I was hoping that one of you kind souls might be willing to look at my classes at least and tell me if I'm heading in the right direction. I know very little about C++, so any advice anyone has, especially about how to make a deal function, would be appreciated. -------
class Card
{
private:
char face;
char suit;
int value;
public:
Card();
void getcard(char face, char suit, int value);
void getvalue(int value);
bool ace(char face);
};

--------- this is my card class. teacher's instructions were: The Card class should have at least the following functions: · An appropriate constructor function. · A mutator function for setting the type of card (e.g., A, 2, …) · An accessor function that returns the integer value of the card. · A function that returns a Boolean value (true or false) depending on whether the current card object is an ace or not. -----
class Hand
{
private:
int handvalue;
int carsdealt;

public:
Hand();
void gethandvalue(int handvalue);
void deal();
void hit();
void display(int handvalue);
};

------ hand class. teacher's instructions: Develop a class that represents a “hand” of up to 5 cards. This class should maintain: · An integer variable representing the number of cards dealt to the hand. · Five Card objects, created from the Card class defined above. · An integer variable representing the value of the hand (i.e., the sum of the card values). The Hand class should have at least the following functions: · An appropriate constructor function. · An accessor function that returns the value of the hand. · A function that deals the first two cards. · A function that deals a single card when a “hit” is requested. · A function to display the hand to the user. Thanks in advance. [Edited by - pg043 on December 8, 2004 11:31:16 AM]

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Remove the semicolon after class Card;. Thats shouldn't be there, and wont compile.

Quote:
 A mutator function for setting the type of card (e.g., A, 2, …)

You dont seem to have this at all. Unless getcard(..) should be named setcard(..) (after all, it wouldn't make much sense to have a getcard function which you have to pass details of the card into).

Quote:
 An accessor function that returns the integer value of the card.void getvalue(int value);

So how exactly is this function going to return the value of the card? And what value are you going to be passing it?

Quote:
 A function that returns a Boolean value (true or false) depending on whether the current card object is an ace or not.bool ace(char face);

Why do you need to pass face into this function? Doesn't the card know what face it is?

This is all pretty basic stuff. If you cant afford a text book try the library, or a google search. Theres tons of introductory information available on the internet.

Alan

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OK - here goes:

Quote:
 An appropriate constructor function

You've got the basis of a constructor (ctor) function there; I just think you need to think about how to build it. When you create a new card, do you want to create a blank card and then use mutators to specify it's type? Or would you rather create the card and its data-members all in one go. If it's the second, then you need some parameters in the ctor function.

[qoute]
A mutator function for setting the type of card (e.g., A, 2, …)
[/quote]

I think this is what you're trying to do with your getvalue function. A mutator is normally called 'Set...', not 'Get...' (that's an accessor). There are a number of ways you could do this. You could do each data-member one at a time, or do all 3 at once. It looks like the way you're planning on doing this is all 3 at once; just need to write the function body now!

Quote:
 An accessor function that returns the integer value of the card.

Again, I assume this is your getvalue function. Quick question : why do you need 'int value' as a parameter to this function? What is it doing?

Quote:
 A function that returns a Boolean value (true or false) depending on whether the current card object is an ace or not

And this is your ace function, yeah? Again, I think you need to think about what the parameter is doing in the function call.

I'm going to help out a little bit here (although I'm not going to give you an exact answer). When you declare / define a function, you've got the following parts:

return-type function-name ( parm-type1 parm-name1, parm-type2 parm-name2 , ...)

I'm fairly sure you've got your head around the return-type for the function (your use of bool for the ace function suggests you have). The function-name is the obvious bit. The parameters (which are pairs of parm-type and parm-name) are pieces of information you are giving to the function to help it carry out that function's task. So, for example, when you're writing an accessor, we need to think about what task that function is performing. In the case of an accessor, all we want it to do is to provide a piece of information held inside the object. So - when you call that function, do you need to provide the function (and therefore the object, as it's a member function of that object) any more information?

The next step is providing some function bodies. Once you've done that, we can see if this is all going to work, and then see how to add extra functionality (like deal!).

As an overall comment, this appears to me to be a wierd way to do a blackjack game (not sure why you'd want mutators, for example - unless you're planning on cheating and making all your cards aces!).

Hope this helps somewhat, and isn't too confusing!
Jim.

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I just got done (a month or so ago) doing a text based blackjack game in Java. The two languages are pretty similar, and aside from the interface there's not much in there that couldn't be replicated into C++, so maybe you could get some ideas from that (though please don't plaigerise, this is for school, be honest :-) ).

http://www.aklabs.net/index.php?akp=development&cat=3

The source code and documentation for it are linked to from that page. Feel free to use whatever from that is useful. let me know if it helped you out.

I designed Card objects so that they were objects with a single index (from 0 to the maximum passed to the Deck class's constructor (usually 52), discussed later). This index has various calculations performed on it to return its face value (2, 3, 10, ace, etc), to return its actual index (0-maximum), or to return a string representation of it ("Ace of Hearts" for example).

The Deck was designed as an object containing a Stack object and an ArrayList object (a linked list with random access functions). The constructor was passed a single value, the number of cards you wanted to have in the deck (for the purpose of my game 52 was always passed). New cards from 0-max are created and put into the list; then they are drawn at random and added to the stack, in order to shuffle them, until the list is empty. The deck has functions for combining the pile and shuffling the deck, adding a player's discarded card to the pile, and dealing a new card from the top of the stack.

Hand objects were designed to be able to hold cards, discard cards, and take cards. The only real functions they needed were to take cards, discard cards, and return the values of their totals. I gave the handTotal() function a boolean argument for whether or not you wanted the actual total (e.g., player is showing his cards, or for interal game calculations of bust and such) or just the total of the cards he was showing. Then there was a function to fold the hand (discarding all cards to the pile).

GamePlayer and GameDealer objects are pretty self explanatory. They have a hand each, and they perform blackjack specific operations on those hands. The only difference between the two is that GameDealer doesn't bet or fold and has an AI routine.

The interface on mine is slightly complex and could've been made easier to read, but that class was being written to work, not to be read by others. Enjoy it if you can understand it. :-)

The main game loop, all it really needs to do is grab the input from the user, determine what they want to do, apply that to the rules of the game, and perform the required operations. Or, more appropriately, tell the appropriate objects - the deck, the player, or the dealer - what the player is trying to do, and let them handle it.

Hope this helped out. Good luck

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I can give you some tips since i have just completed a hi-lo game for a degree module. We had to program a full deck (without jokers) in a perfectly object oriented angle.

1. Dont worry about certain cards having certain face values, like AJQK. For now program everything in numbers. This makes it easier for comparison etc.

2. Classes u will need:

Card
Deck
Player
Dealer
Table
Game

3. For the deck created a static array of pointers to the Card class:

Card* pCards[52];

This means u can manage your cards on the heap and then as a dealer would move the cards from the deck to hand to table, u can effectively do the same, by just moving the pointer.

4. NO literals

int numberCards = 52; // BAD - What does 52 mean? what if you wanted to include jokers, u'd have to go thru the entire app changing all 52s to 54s or 56s.

do this:

const unsigned int NUMBER_OF_CARDS = 52;

unsigned int numberCards = NUMBER_OF_CARDS;

5. Might help to research a bit of UML to help get ur head around the class structure of the app.

6. A table class can do the conversion from 1 to Ace when u view the table.

7. In the Game class write a FSM (Finite State Machine). This simply means have a class that has a currentState, define some states and do a simple switch inside a game loop that runs certain parts of the app depending on what state its running in.
This makes it easier if u want to restart the game because u can create a restart state that handles everything for you.

8. For the card class u will need a default constructor with no params, but u could also have a constructor that accepts the parameters Value and Suit. This could mean that u can't create a card without setting the values.

9. In the game loop you should only ever be asking the Dealer, Player and the table to do anything. Like:

pDealer->DealCard();
pTable->DisplayTable();
pPlayer->TakeGo();

This opens up the whole idea of encapsulation/reusability and just OO in general.

This way makes the logic of the game incredibly easy to encode.

Hope this helps

ace

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Quote:
 6. A table class can do the conversion from 1 to Ace when u view the table.

Actually I disagree. Mainly in that you should be checking aces when totaling the player's hand for any reason - whether it's to check for 21/bust, or to compare for winners. Your comparison function needs to be smart enough to know how to use the Ace in the hand, too - using it as a 1 and an 11. I did this by keeping track of how many aces were in the hand while looping through the hand, and then calculating each ace depending on the current total, after I'd done all the other cards.

I also don't agree with using a global constant for setting the size of the deck; this should be passed to the deck as a constructor argument. This way, you can use your deck class again later no matter what game it's in (as some games use decks of different sizes), or at least extend its basic functionality into subclasses (RumDeck, GoFishDeck, etc etc etc). And you can do it without using a global to define a class member's size (which, in my opinion, goes against OO anyways).

I don't really see a need for a Table object, as much as for an interface class that will handle all your update calls generically - paint the screen, update it with the player's cards, etc etc. This'll take the junk of displaying out of your main loop and let it focus on the logic (rules) of the game. The only thing I found that I needed to keep track of related to the table was how many games the player had won at the current table.

If you're going to use a Card constructor with no parameters, then you should have a static variable inside the constructor that tells what card comes next in the logical progression. This way you won't break your code by accidentally not providing an argument. (This is a better method anyway, in my opinion - your deck constructor can just keep calling = new Card() on objects up until it reaches the size of the deck and you don't have to worry about your loop counting logic being wrong.)

With your Card class, what I would do is define a constant inside of that class (or global or something) that is an array of faces and values. That's what I did in my game; there were two arrays consisting of the face ("Two", "Three", "Ace", etc) and then the Suit. The modulo of the index by the faces array provides the char representation of the card's face, and index/faces.length provides the suit. This way you only have to store one copy of the faces/suits in memory, and you don't have to pass them to each card; you can have the cards handle their own descriptions and remove yourself from the equation, not to mention use less memory.

You shouldn't really need a function to return whether or not the card is an ace; this should be irrelevant, and if it is relevant it will be obvious if its value is 1 or if its value is 11 and its face is "Ace". (Though a simple distinction between 1 and 11, regardless of the face value, should be sufficient for whatever you're doing with it.) Tell your instructor I said he's overcomplicating things. :-)

Your hand class's requirements don't jive with me. Why does he want you to write two separate functions to do the same thing - take cards? Just write one hit function, and pass it a Card object. If you need to deal the initial two cards, just call it twice. Be sure to pass it a Card object from the Deck, otherwise you run the risk of duplicating cards (the game won't be very true if both players somehow wind up holding the Ace of Spades).

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Well, I did a lot of research and this is where I'm at with it so far.

//blackjack.cpp#include <iostream>using namespace std;#include <ctime>#include <cstdlib>#include "Card.h"#include "Hand.h"int main(){int menuChoice, handValue;Hand h;	h.deal();	handValue=h.getHandValue();	h.display();do	{	cout<<"\n\n\nWhat would you like to do?"		<<endl		<<"\t1. Hit"		<<endl		<<"\t2. Stay"		<<endl;	cin>>menuChoice;				switch(menuChoice)		{		case 1:			h.hit();		case 2:			h.results(handValue);				default:			cout<<"Invalid selection.\n\n";		}				}while(menuChoice > 0 && menuChoice < 3);	return 0;}

I know it doesn't have many options, but the real purpose of this project is just to create proper card and hand classes.

//Hand.hclass Hand{private:	int cardsDealt;	int handValue;	Card card[5];public:	Hand();		int deal();	int hit();	int getHandValue();	void display();	void results(int handValue);	};Hand::Hand(){	}Hand::deal(){	srand((unsigned)time(0));	card[0].value=rand() % 13;	card[1].value=rand() % 13;	cardsDealt=2;		return 0;}Hand::hit(){	int i=cardsDealt;		card.value=rand() % 13;	cardsDealt++;	return 0;}Hand::getHandValue(){	int handValue=card[0].value+card[1].value+card[2].value+card[3].value+card[4].value;	return handValue;}void display(){			cout<<"\n\nYour Hand is:  "    		<<card[0].face<<"  "         //this section is giving me errors		<<card[1].face<<"  "         //when i try to build it.		<<card[2].face<<"  "        //i'm not sure if this is proper		<<card[3].face<<"  "        //syntax, but i thought it would 		<<card[4].face;             //work because i was using                                            //card[1].value and it compiled OK}void results(){	Hand handValue;	cout<<"Your final hand is ";		}

This class, I know, is also not completely finished. I've not yet coded a way to record the dealer's score and all that.

//Card.hclass Card{private:			public:	Card();	int setCard(char face, int value);	int getValue();	int value;	char face;	};Card::Card(){	value=0;	face=0;}Card::setCard(char face, int value){	char J,Q,K,A;	int handValue;	switch(face, value)	{	case 0:		value=2;		face=2;	case 1:		value=3;		face=3;	case 2:		value=4;		face=4;	case 3:		value=5;		face=5;	case 4:		value=6;		face=6;	case 5: 		value=7;		face=7;	case 6:		value=8;		face=8;	case 7:		value=9;		face=9;	case 8:		value=10;		face=10;	case 9:		value=10;		face=J;	case 10:		value=10;		face=Q;	case 11:		value=10;		face=K;	case 12:		if(handValue<=21)			value=11;		else			value=1;		face=A;    }	return 0;}Card::getValue(){	return value;}

My main question is the comment I added in Hand.h, so if anyone could point out my mistake I would appreciate it. This is my first OO program, and I know that I'm probably going about it backwards. Thanks

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A brief tutorial on declarations, definitions and member & non-member functions:
class Class{	public:		returnType memberFunction(parameter)		{			// code		}};

This is a combined class and class member function definition. It contains the definition of the class and the definition of the class member function in one place.

class Class{	public:		returnType memberFunction(parameter);};returnType Class::memberFunction(parameter){	// code}

This is a class definition followed by a seperate class member function definition. The class definition contains only the declaration of the member function - the definition for the member function is given outside the class definition.

class Class{	public:		returnType memberFunction(parameter);};returnType memberFunction(parameter){	// code}

This is a class definition followed by a non-member function definition. The class definition contains only the declaration of the member function - the definition for the member function is not included in this code snippet. The function definition at the bottom of the code is a seperate function and has nothing to do with the class member function, despite sharing the same name and prototype.

Compare this to your definitions of Hand and its member functions.

Enigma

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Are you saying that my writing "Hand::getValue()" is the wrong syntax for a member function definition? Sorry to seem dull, I've just really never done OO and I don't know the proper syntax for sure.

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C++ can be a bit confusing at first.

First off, your class methods (functions inside the class) are jacked up. Specifically, the definitions do not match the declarations. Take the following code snippet:

class Hand{// data members snipped for brevitypublic:	Hand();		int deal();        //snip};Hand::Hand(){// snip}Hand::deal(){// snip}

See, your definition and declaration of the Hand constructor is good - it takes no arguments, is public and has no return type. So therefore
Hand::Hand()
is the proper way to begin the definition of the function (the definition being where the actual code lies). However, you've declared deal as a public function that returns an integer, and takes no arguments. However, you've got it defined as a public function of Hand that takes no arguments and returns nothing; this is no good. When the compiler reaches this function, it says "Hey wait a minute - the Hand class doesn't have a member function deal() that doesn't return anything. Let me schmack the programmer." There's other cases in your code where you've not only missed the return type, but you've also missed the argument list. Remember, your function definition needs to look exactly like the function declaration, with the exception of it including the class name and the access modifier. So the syntax is:
 <return type> <class name><access modifier><function name>(<argument list>)
where access modifier is : for private and :: for public. So your function definitions in the above snippet should've looked like this:

class Hand{// data members snipped for brevitypublic:	Hand();		int deal();        //snip};Hand::Hand(){// snip}int Hand::deal(){// snip}

There's numerous other errors in your source and violations of coding conventions :-), but this should be enough to get you started. I can send you corrected/commented source files if you want, just let me know.


text:
02-379 G. D. Raikov
Spectral Asymptotics for the Perturbed 2D Pauli Operator with Almost Periodic Magnetic Fields. I. Non-Zero Mean Value of the Magnetic Field (235K, ps.gz) Sep 13, 02
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We consider the Pauli operator \$H(b,V)\$ acting in \$L^2({\mathbb R}^2; {\mathbb C}^2)\$. We describe a class of admissible magnetic fields \$b\$ such that the ground state of the unperturbed operator \$H(b,0)\$ which coincides with the origin, is an isolated eigenvalue of infinite multiplicity. In particular, this class includes certain almost periodic functions of non-zero mean value. Under the assumption that the matrix-valued electric potential \$V\$ has a definite sign and decays at infinity, we invastigate the asymptotic distribution of the discrete spectrum of \$H(b,V)\$ accumulating to the origin. We obtain different asymptotic formulae valid respectively in the cases of power-like decay of \$V\$, exponential decay of \$V\$, or compact support of \$V\$.

Files: 02-379.src( 02-379.keywords , almost1.ps )


text:
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# Errata for Maximum Likelihood Estimation with Stata, Third Edition

The errata for Maximum Likelihood Estimation with Stata, Third Edition, are provided below. Click here for an explanation of how to read an erratum. Click here to learn how to determine the printing number of a book.

mysureg reported a model p-value greater than 1. This error has been fixed in the corresponding ado-files at the download site.

mylogit and myprobit produced incorrect model likelihood-ratio tests. This error has been fixed in the corresponding ado-files at the download site.

In myweibull, appendix C.4, line 4 from the bottom, ereturn local depvar time' should be suppressed. This error has been fixed in the corresponding ado-files at the download site.

 (1) Chapter 3, p. 62, alternative form of mynonlin_lf
  program mynonlin_lf version 9.1 args lnf theta1 theta2 theta3 theta4 quietly replace lnf' = /* */ ln(normalden($ML_y1-theta1'-theta2'*bp0^theta3')/theta4' - ln(theta4') end  program mynonlin_lf version 9.1 args lnf theta1 theta2 theta3 sigma quietly replace lnf' = /// ln(normalden($ML_y1,theta1'+theta2'*bp0^theta3',sigma')) end


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MathSciNet bibliographic data MR293942 81.46 Slawny, Joseph On factor representations and the \$C\sp{\ast} \$$C\sp{\ast}$-algebra of canonical commutation relations. Comm. Math. Phys. 24 (1972), 151–170. Article

For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.


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# Browse Dept. of Physics by Title

• (1994)
1/f resistance noise studies of the spin dynamics in two magnetic systems are described in this thesis. In chromium, 1 If noise was used as a probe to study spin density wave polarization dynamics. Measurements of the ...

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• (1986)
Properties of 1/f noise (low frequency resistance fluctuations) are analyzed using the results of a number of experiments, several of which are unique to our laboratory. Measurements of thermally activated noise spectral ...

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• (1984)
The nature of l/f noise in semiconductors and metals has been analyzed in light of the information provided by some unique, empirically determined parameters. Measurements of the instantaneous resistivity fluctuation ...

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• (1974)

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• (1969)
9Be , 1OB, 11B, 12c, 24Mg , 25Mg , 26Mg and 27Al targets have been bombarded with the 3He beam from the University of Illinois cyclotron. Elastic scattering angular distributions have been obtained in the approximate ...

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• (1984)
The 13C Nuclear Magnetic Resonance lines, spin-lattice relaxation times Tl and spin-spin relaxation times T2 of CO chemisorbed on the surface layer of small particles of Pt metal have been observed by the method of spin ...

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• (1984)
This thesis consists of two parts. The first part deals with the question of whether localized magnetic moments are present on the 3d atoms, Cr and Mn, when dilutely doped in Nb and V. The second part deals with the ...

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• (1969)
A study of the A2 meson has been made on data obtained from pi p interactions at 5 BeV/c in the 72"Alvarez liquid hydrogen bubble chamber. The p pi decay mode in the 4-constraint, p pi+ pi- pi- final state is treated ...

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Self-consistent unrestricted Hartree-Fock calculations are presented for the adsorption of atomic oxygen onto the nickel oxide (100) surface. The perfect surface is shown to be non-reactive, but enhanced binding is found ...

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• (1986)
In this thesis the use of the Unrestricted Hartree-Fock technique augmented by many body perturbation theory techniques and symmetry projection methods in the study of the energies of the excited states of atomic, molecular ...

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• (1996)
We have measured the absolute $\rm\sp2H(\gamma,p)n$ angular distribution using the Illinois LASA detector at the Saskatchewan Accelerator Laboratory's tagged photon facility. Using 40 to 90 MeV photons, we aimed to measure ...

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• (1996)
We have measured the absolute 2H( 1 ,p )n angular distribution using the Illinois LASA detector at the Saskatchewan Accelerator Laboratory's tagged photon facility. Using 40 to 90 MeV photons, we aimed to measure the ...

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• (1988)
This experiment measured the differential cross section for deuteron photodisintegration between photon energies of 63 and 71 MeV. The photon beam was produced by the bremsstrahlung of an 88.4 Me V CW electron beam, from ...

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• (1966)
Luminescent excitation spectra were measured for the F and M centers in KCl; in particular, for the F band, M band, and the M2 transition. In all 3 cases, the spectra were nearly double-Gaussian in shape, and the efficiency ...

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• (1966)

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• (1972)

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• (1978)
It is generally accepted that many pulsating X-ray sources are rotating magnetic neutron stars undergoing accretion. The text of this thesis provides a historical introduction to four studies, contained herein as appendices, ...

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• (2013-08-22)
Analysis of observations of the X-ray emission produced by accreting neutron stars with millisecond spin periods can provide important information about the masses M and radii R of neutron stars, thereby yielding uniquely ...

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HOSTING A TOTAL OF 318 FORMULAS WITH CALCULATORS

Dividends Per Share

Here,D=Dividends Paid, S=Number of Shares

$\frac{D}{S}$

The amount of dividend that a stockholder will receive for each share of stock held. It can be calculated by taking the total amount of dividends paid and dividing it by the total shares outstanding.

ENTER THE VARIABLES TO BE USED IN THE FORMULA

Similar formulas which you may find interesting.


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Monday, August 05, 2019

114 private jets gathered in Sicily to fight carbon emissions

Do their ends justify their means?

One week ago, sources including WUWT and Euronews have mentioned a secretive meeting of the self-described elite that wanted to save the climate.

The meeting took place in the Verdura Resort, Sicily. The participants paid for their transportation but the local expenses – with hotels from $900 a night – were paid by Google and its local counterpart, Cosa Nostra. Leonardo DiCaprio, Barack Obama, and Prince Harry were supposed to be stars of the meeting and others have arrived because they enjoy being seen as peers of these three morons – which they mostly are, indeed. As I said, the guests have paid for their own transportation. To show that they're important, many of them took their private jets and yachts. Just the number of private jets was reported to be 114 by the Italian press. A decade ago, we would make fun of Al Gore and his private jet – what a hypocrisy – or an actress who flew in the same way. Barbra Streisand recently sent a private jet just for her two puppies simply because she felt the urge to torture them and force them to listen to her delusions about the climate spoken in a distant country. Animal rights activists remained silent – just like the two doggy faces who can't clearly express how much they hate this babbling as well as the useless trips in jets. But these days, with the number such as 114, the hypocrisy has been turned into a mega industry. Euronews estimates that over 4 tons of CO2 are emitted on a New York to Palermo flight of a jet. Multiply such amounts by more than 100... they determined that the CO2 emissions from such 100 flights are comparable to the emissions from charging of phones 50 million times. It's basically the energy that the U.S. – a country – needs to charge their phones for a whole day. A bunch of 100 morons has created the same emissions just to meet and talk about the fight against emissions. Even after these years, it seems that they don't even understand what's strange about their flying private jets; and talking about the evil of the fossil fuels at the same moment. I think that most of them or all of them genuinely misunderstand what's shocking about the combination – they misunderstand it because they are really, really stupid. They have apologists who are not this stupid but, like the writer of the Euronews article, they still end up thinking that it's not bad or hypocritical for them to arrive in yachts and private jets because... But, with them all in one place, perhaps working together to achieve a common goal is worth it? Cool. So the ends justify the means. And, at the end, Euronews mentions that these folks are rich enough so that they may pay for the carbon indulgences. So the hugely higher energy prices aren't a problem for them – they can afford it – so everything is fine with their event. Is it? Well, first, it is unquestionable that all these people may afford to pay the 5 times more expensive fuel prices and energy, including some extra 500% increase that you might need for the carbon indulgences. But is it enough to conclude that the ends – it's so great when 100+ pompous morons meet at one place to talk anti-scientific nonsense about a dangerous climate change (BTW in Czechia, we've had a colder-than-normal week or two and we will have a much colder-than-normal weather soon) – justify the means? It's not OK at all and these stupid people overstate their wealth and importance, at least by four orders of magnitude. Let me show you the calculation. One must distinguish two activities: those are that made consensually, with all the participants acting according their will (but perhaps in an unusual way because they were paid to do so); and those that are done against someone's will, e.g. against the will of a huge part of mankind. So which activities are consensual, which are not, and how much money do you need to create a consensus? Now, according to the laws of the old world that we used to have, and we still have it to a large extent, it is perfectly legal to buy a private jet or a yacht and arrive to a meeting of 100 or 200 similar morons in Sicily with it. Also, it is perfectly legal to buy some indulgences from a postmodern replication of the medieval church – indulgences that are claimed to strip you of the guilt for the emissions that you have emitted but every sane person knows that this promise is a fabrication. What is not consensual is to prevent some 7 billion people from using cheap energy. You know, a significant fraction of mankind – almost certainly a majority – doesn't want to lose its access to affordable energy sources. So plans to regulate carbon emissions are clearly non-consensual according to status quo. How much money do you need to change the people's views and are the billionaire rich enough to achieve such an outcome? The answer is a resounding No. Some ten percent of the world GDP – and 10% of$100 trillion is about $10 trillion (per year) – is spent for energy in the same interval of time. The switch to carbon-free energy would make the energy approximately 5 times more expensive, so something like 50% of the current GDP or$50 trillion per year globally. Or some $5 quadrillion per lifetime. Now, the average billionaire at the Sicily meeting is worth less than$5 billion, and I am sure it's still an overestimate, so even if they paid their whole wealth to persuade mankind to abandon the cheap energy from fossil fuels, they would only collect some $500 billion – which is 4 orders of magnitude below the required expenses,$5 quadrillion per mankind and per the average lifetime. And I generously overlook the fact that most of them wouldn't be willing to pay their whole $5 billion: they were unwilling to pay even$900 for their hotel! ;-)

So cheap 100 morons, your importance is nowhere near to the ability to make similar changes to mankind and the way how it operates. You would need to be some 10,000 times wealthier – and pay everything you have
– for these plans to become realistic in a peaceful world. The only other option for your carbon-neutral fantasies is to change the world non-consensually.

But that won't work, either. If you, Leonardo, will really credibly threaten (or temporarily break) the access of billions of people in the world to cheap energy they need for the lives lived according to the standards that they're roughly used to, you will simply be killed. If your armies of aßlickers are telling you that you have good enough guards to protect your life after similar moves and the totally just and predictable dissatisfaction that would follow them, they are simply lying to you. You would die in a rather terrible death, like other climate alarmists who would put mankind's existential interests at risk. It would be the end of you while the access to energy would be restored. It's a matter of common sense.

It approximately boils down to the same number 10,000 because if you wanted to rob mankind of its access to fossil fuels, you would declare a war on mankind – or a huge portion of it. And because the motivation and the strength of the weapons may be considered proportional to the amount of wealth that is at risk, you – the collective of 100+ unjustifiably self-confident morons – would fight an army that is 10,000 times stronger than yours.

So enjoy your current position of hypocritical morons who are just brainless actors (this label applies to the likes of Barack Obama as well) who aren't taken seriously by anyone with his or her own brain – because if you became more than that, politically speaking, your life expectancy would shrink dramatically.

I wanted to say a few more words about the indulgences. When a billionaire pays the money for the carbon indulgences to another one, does it actually reduce the CO2 emissions by the promised amount? The answer is No. This answer is easy to see if you look at the evolution of the CO2 emissions in the years in which the carbon indulgences were traded. They just kept on increasing at more or less unchanged rate. Why is it so? Because it's much easier to fool the cap-and-trade system, move the emissions around, or persuade a friend in politics to loosen the caps – than it is to actually reduce the consumption of cheap energy – which is pretty much unavoidably tied to the quality of contemporary human lives.

The carbon indulgences have been a stupid game that couldn't work as a driver of global changes – it's at most a method to administratively relocate the CO2 emissions and to make a few green crooks rich.

One explanation why it's so may be linked to the same number 10,000 as before. Lots of money is already being circulated in the alarmist industry and the CO2 reductions – but it's only enough money to turn hundreds of green crooks into billionaires. But the actual price of genuine globally tangible reductions of CO2 emissions would be even greater – by orders of magnitude. If someone really wanted to go in this direction, he would spark the dissatisfaction that would indicate a huge war. Note that the French Yellow Vests started because of a few-percent extra tax on gasoline – which would only reduce the consumption of fuels in France, a not so decisive country, by less than a percent. To make a real difference, and to do so globally, you would create tension that would exceed the Yellow Vests by many orders of magnitude and the morons from the Sicily meeting should believe me that they wouldn't have a chance to withstand it.

So one may say that the counting indicating that "the purchase of the indulgences reduces someone's emissions" only works assuming that the total CO2 reductions are negligible – i.e. when you actually can't see the "benefits" of the CO2 reduction schemes on the global emissions. Any visible change would produce tensions that would challenge the billionaires' right to keep their money – or even their lives. There is a trade-off: the trading with carbon permits only has a chance to "hypothetically work" as long as it doesn't "really work".


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# Interpretation of coefficients

Recall that the fitted model for the poverty rate of U.S. counties as a function of high school graduation rate is:

$$\widehat{poverty} = 64.594 - 0.591 \cdot hs\_grad$$

Which of the following is the correct interpretation of the slope coefficient?


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## A community for students. Sign up today!

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## monroe17 one year ago Find the volume formed by rotating the region enclosed by: y=5sqrt(x) and y=x about the line x=26

• This Question is Closed
1. ByteMe

For this one, i'd prefer the shell method. The representative volume of each shell is: $$\large dV=2\pi x(5 \sqrt x - x)dx$$ just figure out your limits of integration...

2. ByteMe

oops.... that first x should be (26-x)

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Article

Bravyi-Kitaev Superfast simulation of fermions on a quantum computer

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Abstract

Present quantum computers often work with distinguishable qubits as their computational units. In order to simulate indistinguishable fermionic particles, it is first required to map the fermionic state to the state of the qubits. The Bravyi-Kitaev Superfast (BKSF) algorithm can be used to accomplish this mapping. The BKSF mapping has connections to quantum error correction and opens the door to new ways of understanding fermionic simulation in a topological context. Here, we present the first detailed exposition of BKSF algorithm for molecular simulation. We provide the BKSF transformed qubit operators and report on our implementation of the BKSF fermion-to-qubits transform in OpenFermion. In this initial study of the hydrogen molecule, we have compared BKSF, Jordan-Wigner and Bravyi-Kitaev transforms under the Trotter approximation. We considered different orderings of the exponentiated terms and found lower Trotter errors than previously reported for Jordan-Wigner and Bravyi-Kitaev algorithms. These results open the door to further study of the BKSF algorithm for quantum simulation.

No full-text available

... Generalization of the transformation to higher dimensions using lattice gauge fields have also been proposed [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Such exact bosonization mappings are also important form the quantum simulation perspective, for they address the possibility of simulating a quantum many-body fermionic systems using a bosonic quantum computer [21][22][23][24][25][26]. Symmetries, however, may not remain manifest under the transformation. ...
... The ηχ approach is inspired by earlier works provid-ing lattice bosonization recipes through the introduction of Majorana fermions [7,8,23]. It is also closely related to the approach developed in Refs. ...
Preprint
Full-text available
We discuss a scheme for performing Jordan-Wigner transformation for various lattice fermion systems in two and three dimensions which keeps internal and spatial symmetries manifest. The correspondence between fermionic and bosonic operators is established with the help of auxiliary Majorana fermions. The current construction is applicable to general lattices with even coordination number and an arbitrary number of fermion flavors. The approach is demonstrated on the single-orbital square, triangular and cubic lattices for spin-1/2 fermions. We also discuss the relation to some quantum spin liquid models.
... However, there is a mapping with which locally-interacting Fermion and qubit lattices can be related: the Verstraete-Cirac transform (VCT) [23] also known as Auxiliary Fermion Mapping [24][25][26], can be regarded as a manipulation of the Jordan-Wigner transform, in which additional auxiliary particles are added, hence the name. Other works on Fermion-to-qubit mappings [25,[27][28][29] are based on two transforms proposed by Bravyi and Kitaev in [30]. Firstly, there is what is commonly known as the Bravyi-Kitaev transform, that, compared to the Jordan-Wigner transform, exhibits an up to exponential improvement on the number of qubits that each fermionic interaction term acts on. ...
... So far, we still have not left the even-parity subspace, but we might have systems to solve that are populated by odd numbers of Fermions. In [29], it is suggested to add another mode to the system that is however not coupled to any other term in the Hamiltonian. From the original concept of the BKSF it is however not clear how this mode is brought into the system, since all qubits correspond to couplings of modes in the Hamiltonian, which here do not exist. ...
Preprint
Full-text available
Quantum simulation of fermionic systems is a promising application of quantum computers, but in order to program them, we need to map fermionic states and operators to qubit states and quantum gates. While quantum processors may be build as two-dimensional qubit networks with couplings between nearest neighbors, standard Fermion-to-qubit mappings do not account for that kind of connectivity. In this work we concatenate the (one-dimensional) Jordan-Wigner transform with specific quantum codes defined under the addition of a certain number of auxiliary qubits. This yields a novel class of mappings with which any fermionic system can be embedded in a two-dimensional qubit setup, fostering scalable quantum simulation. Our technique is demonstrated on the two-dimensional Fermi-Hubbard model, that we transform into a local Hamiltonian. What is more, we adapt the Verstraete-Cirac transform and Bravyi-Kitaev Superfast simulation to the square lattice connectivity and compare them to our mappings. An advantage of our approach in this comparison is that it allows us to encode and decode a logical state with a simple unitary quantum circuit.
... Constructing all generators directly in their fermionic representation, will result in automatic gradient evaluation schemes independent of the underlying qubit encoding, allowing flexible adaption of new encodings [44,45] and improved compiling strategies into quantum gates [46]. In analogy to the qubit construction in Eq. (29) the nullspace projector of a general single, double or n-fold fermionic excitation (5) can be constructed as ...
Preprint
We develop computationally affordable and encoding independent gradient evaluation procedures for unitary coupled-cluster type operators, applicable on quantum computers. We show that, within our framework, the gradient of an expectation value with respect to a parameterized n-fold fermionic excitation can be evaluated by four expectation values of similar form and size, whereas most standard approaches based on the direct application of the parameter-shift-rule come with an associated cost of O(2^(2n)) expectation values. For real wavefunctions, this cost can be further reduced to two expectation values. Our strategies are implemented within the open-source package tequila and allow blackboard style construction of differentiable objective functions. We illustrate initial applications for electronic ground and excited states.
Article
Full-text available
Trotter–Suzuki decompositions are frequently used in the quantum simulation of quantum chemistry. They transform the evolution operator into a form implementable on a quantum device, while incurring an error—the Trotter error. The Trotter error can be made arbitrarily small by increasing the Trotter number. However, this increases the length of the quantum circuits required, which may be impractical. It is therefore desirable to find methods of reducing the Trotter error through alternate means. The Trotter error is dependent on the order in which individual term unitaries are applied. Due to the factorial growth in the number of possible orderings with respect to the number of terms, finding an optimal strategy for ordering Trotter sequences is difficult. In this paper, we propose three ordering strategies, and assess their impact on the Trotter error incurred. Initially, we exhaustively examine the possible orderings for molecular hydrogen in a STO-3G basis. We demonstrate how the optimal ordering scheme depends on the compatibility graph of the Hamiltonian, and show how it varies with increasing bond length. We then use 44 molecular Hamiltonians to evaluate two strategies based on coloring their incompatibility graphs, while considering the properties of the obtained colorings. We find that the Trotter error for most systems involving heavy atoms, using a reference magnitude ordering, is less than 1 kcal/mol. Relative to this, the difference between ordering schemes can be substantial, being approximately on the order of millihartrees. The coloring-based ordering schemes are reasonably promising—particularly for systems involving heavy atoms—however further work is required to increase dependence on the magnitude of terms. Finally, we consider ordering strategies based on the norm of the Trotter error operator, including an iterative method for generating the new error operator terms added upon insertion of a term into an ordered Hamiltonian.
Article
Full-text available
We present a quantum algorithm for simulating quantum chemistry with gate complexity $$\tilde {\cal{O}}(N^{1/3}\eta ^{8/3})$$ where η is the number of electrons and N is the number of plane wave orbitals. In comparison, the most efficient prior algorithms for simulating electronic structure using plane waves (which are at least as efficient as algorithms using any other basis) have complexity $$\tilde {\cal{O}}(N^{8/3}{\mathrm{/}}\eta ^{2/3})$$. We achieve our scaling in first quantization by performing simulation in the rotating frame of the kinetic operator using interaction picture techniques. Our algorithm is far more efficient than all prior approaches when N ≫ η, as is needed to suppress discretization error when representing molecules in the plane wave basis, or when simulating without the Born-Oppenheimer approximation.
Article
Full-text available
Current implementations of the Variational Quantum Eigensolver (VQE) technique for solving the electronic structure problem involve splitting the system qubit Hamiltonian into parts whose elements commute within their single qubit subspaces. The number of such parts rapidly grows with the size of the molecule. This increases the computational cost and can increase uncertainty in the measurement of the energy expectation value because elements from different parts need to be measured independently. To address this problem we introduce a more efficient partitioning of the qubit Hamiltonian using fewer parts that need to be measured separately. The new partitioning scheme is based on two ideas: 1) grouping terms into parts whose eigenstates have a single-qubit product structure, and 2) devising multi-qubit unitary transformations for the Hamiltonian or its parts to produce less entangled operators. The first condition allows the new parts to be measured in the number of involved qubit consequential one-particle measurements. Advantages of the new partitioning scheme resulting in severalfold reduction of separately measured terms are illustrated on the H2 and LiH problems.
Article
The ability to perform classically intractable electronic structure calculations is often cited as one of the principal applications of quantum computing. A great deal of theoretical algorithmic development has been performed in support of this goal. Most techniques require a scheme for mapping electronic states and operations to states of and operations upon qubits. The two most commonly used techniques for this are the Jordan-Wigner transformation and the Bravyi-Kitaev transformation. However, comparisons of these schemes have previously been limited to individual small molecules. In this paper we discuss resource implications for the use of the Bravyi-Kitaev mapping scheme, specifically with regard to the number of quantum gates required for simulation. We consider both small systems which may be simulatable on near-future quantum devices, and systems sufficiently large for classical simulation to be intractable. We use 86 molecular systems to demonstrate that the use of the Bravyi-Kitaev transformation is typically at least approximately as efficient as the canonical Jordan-Wigner transformation, and results in substantially reduced gate count estimates when performing limited circuit optimisations.
Article
Full-text available
We present three techniques for reducing the cost of preparing fermionic Hamiltonian eigenstates using phase estimation. First, we report a polylogarithmic-depth quantum algorithm for antisymmetrizing the initial states required for simulation of fermions in first quantization. This is an exponential improvement over the previous state-of-the-art. Next, we show how to reduce the overhead due to repeated state preparation in phase estimation when the goal is to prepare the ground state to high precision and one has knowledge of an upper bound on the ground state energy that is less than the excited state energy (often the case in quantum chemistry). Finally, we explain how one can perform the time evolution necessary for the phase estimation based preparation of Hamiltonian eigenstates with exactly zero error by using the recently introduced qubitization procedure.
Article
Quantum computers can be used to address electronic-structure problems and problems in materials science and condensed matter physics that can be formulated as interacting fermionic problems, problems which stretch the limits of existing high-performance computers. Finding exact solutions to such problems numerically has a computational cost that scales exponentially with the size of the system, and Monte Carlo methods are unsuitable owing to the fermionic sign problem. These limitations of classical computational methods have made solving even few-atom electronic-structure problems interesting for implementation using medium-sized quantum computers. Yet experimental implementations have so far been restricted to molecules involving only hydrogen and helium. Here we demonstrate the experimental optimization of Hamiltonian problems with up to six qubits and more than one hundred Pauli terms, determining the ground-state energy for molecules of increasing size, up to BeH2. We achieve this result by using a variational quantum eigenvalue solver (eigensolver) with efficiently prepared trial states that are tailored specifically to the interactions that are available in our quantum processor, combined with a compact encoding of fermionic Hamiltonians and a robust stochastic optimization routine. We demonstrate the flexibility of our approach by applying it to a problem of quantum magnetism, an antiferromagnetic Heisenberg model in an external magnetic field. In all cases, we find agreement between our experiments and numerical simulations using a model of the device with noise. Our results help to elucidate the requirements for scaling the method to larger systems and for bridging the gap between key problems in high-performance computing and their implementation on quantum hardware.
Article
It is shown that an arbitrary fermion hopping Hamiltonian can be mapped into a system with no fermion fields, generalizing an earlier model of Levin and Wen. All operators in the Hamiltonian of the resulting description commute (rather than anticommute) when acting at different sites, despite the system having excitations obeying Fermi statistics. While extra conserved degrees of freedom are introduced, they are all locally identified in the representation obtained. The same methods apply to Majorana (half) fermions, which for Cartesian lattices mitigate the fermion doubling problem. The generality of these results suggests that the observation of Fermion excitations in nature does not demand that anticommuting Fermion fields be fundamental.
Article
INTRODUCTION E-commerce and e-business on the Internet with worldwide round-the-clock operation require enterprises to be operational 24 hours per day, 7 days per week. Outages are very expensive for these enterprises, with accompanying loss of revenue and reputation, and with disgruntled customers. Table I gives the estimates of the financial losses [1] due to downtime for different types of enterprises. With an increasing demand for 24 7 operation, and with downtime being unacceptable and prohibitive in cost, enterprises must have fault tolerance to survive in today's marketplace. # Correspondence to: P. Narasimhan, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A. + E-mail: priya@cs.cmu.edu Contract/grant sponsor: Defense Advanced Research Projects Agency in conjunction with the office of Naval Research and the Air Force Research Laboratory; contract/grant number: N00174-95-K-0083, F3602-97-1-0248. Copyright # 2002 John Wiley & Sons, Ltd.
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# Math Help - Fluid Flows - Flow Mapping Theorem (not for the faint hearted!!)

1. ## Fluid Flows - Flow Mapping Theorem (not for the faint hearted!!)

How do I do this question:

Hi Guys

Since I last posted this question, I have figured out how to calculate part (i) and (ii). However, I am stuck on part (iii).

I think I need to use the formula (Inverse Function Rule), f '(z)=1/1-1/(f(z))^2). However, when I input the values of f(z) into the equation, i dont get the function as stated in part (iii). Am I missing something? Do i need to use parts (i) and (ii) of the answer? If so, for part (ii) I got z+4/z-16/z^3....


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Do black holes have infinite areas and volumes?

How to calculate the area / volume of a black hole? Is there a corresponding mathematical function such as rotating $1/x$ around the $x$-axis or likewise to find the volume?

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Presumably the area and volumes are that of and inside the event horizon. –  namehere Dec 5 '12 at 3:55
How much do you know about integrating over forms? Also, the volume of a black hole is coordinate dependent. –  Jerry Schirmer Dec 5 '12 at 4:11

The event horizon is a lightlike surface, and so its area is coordinate-invariant. For a Schwarzschild black hole, $$ds^2 = -\left(1-\frac{2m}{r}\right)dt^2 + \left(1-\frac{2m}{r}\right)^{-1}dr^2 + r^2(d\theta^2+\sin^2\theta\,d\phi^2)$$ The horizon suface is at $r = 2m$ of Schwarzschild radial coordinate, and so at any particular Schwarzschild time ($dt = 0$) has the metric $$dS^2 = (2m)^2(d\theta^2 + \sin^2\theta\,d\phi^2),$$ which is just the metric on a standard 2-sphere of radius $2m$. You can find the square area element explicitly as the determinant of the metric, $dA^2 = (2m)^4\sin^2\theta\,d\theta^2d\phi^2$, and integrating: $$A = 16\pi m^2 = \frac{16\pi G^2}{c^4}m^2.$$

The volume of the black hole is not invariant, as Jerry Schirmer says. If you try to apply anything the above Schwarzschild coordinates above, then since the coefficients of $dt^2$ and $dr^2$ switch signs across the horizon, $t$ is spacelike and $r$ is timelike. Therefore, since the black hole is eternal, it could be said to have infinite volume (classically, but a real astrophysical black hole would have a finite but still extraordinarily high lifetime), as you'll be integrating $dt$ across its lifetime.

Technically, the above argument is a bit flawed, because the Schwarzschild coordinate chart is not defined across the event horizon, so one should be more careful how they're continued across the horizon (e.g., with Kruskal-Szekeres coordinates). But this can be made more rigorous.

In another coordinate chart, e.g., the Gullstrand-Painlevé coordinates adapted to a family of freely falling observers, $$ds^2 = -\left(1-\frac{2m}{r}\right)dt^2-2\sqrt{\frac{2m}{r}}\,dt\,dr + \underbrace{dr^2 + r^2(d\theta^2 + \sin^2\theta\,d\phi^2)}_{\text{Euclidean in spherical coord.}},$$ at any instant of time ($dt = 0$), space is precisely Euclidean; since the horizon is still $r = 2m$ in these coordinates, "the" volume is $$V_{\text{GP}} = \frac{4}{3}\pi(2m)^3.$$

If you pick yet another coordinate chart, you may get a yet different answer.

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A better answer than mine! +1 –  John Rennie Dec 5 '12 at 9:11

If you are a Schwarzschild observer the radial co-ordinate $r$ is defined as the circumference of a circle around the black hole divided by $2\pi$. Also the event horizon is at a Schwarzschild radius of $2M$ (in geometrised units), so for a Schwarzschild observer the area of the event horizon is simply $16\pi M^2$.

But this is a somewhat trivial answer as in effect I'm just saying "well that's how we define $r$". I get the impression you're looking for a deeper answer than this, but you'll need to expand on your question a bit.

Later:

I've just noticed Is a black hole's surface area invariant for distant intertial observers? that states the area of the event horizon is an invarient. This means all observers will measure the area to be $16\pi M^2$.

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I am trying to compute the calibration of an FX market volatility surface, and especially I want to retrieve the strikes from the deltas quoted.

I don't have any trouble reverse-engineering the formulas for non premium-adjusted deltas. However, for many currency pairs, the convention is to use premium-adjusted deltas, which are not monotonic in strike. For example, for a premium-adjusted forward delta (Source: Clark - FX Option Pricing - Chap3 p47): $$\Delta_{F;\%} = \omega\frac{K}{F_{0,T}}N(\omega d_{2})$$

Following this source, p14:

One common solution to this problem is to search for strikes corresponding to deltas which are on the right hand side of the delta maximum.

What is the argument or the intuition behind this statement?

• I guess the intuition behind this is that the market tends to quote out-of-the-money options. For calls, these are on the upside and thus right of the max. delta strike. – LocalVolatility Dec 19 '16 at 17:53


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# Tag Info

2

Here is some code that should serve as a starting point. This uses datatool package. I have added a column with a short key for center in addition to your columns. center,RollNo,Subject,Venue Bangalore,022701,Sociology,Deptt. of Physics Bangalore,022702,Sociology,Deptt. of Physics Bangalore,022704,Sociology,Deptt. of Physics ...

1

One possibility; for this example I used the following simple file diffecorrenti.txt: 1 2 3 -3 4 5 6 7 and suppressed parts of the original code that were not relevant to the question and to the solution. For the first requirement, you can use the axis cs coordinate system to place a \node with some predefined style at the desired location at one ...

3

You can set anything inside an equation, including a \parbox (or other textual components like a minipage or tabular). Here's an example: \documentclass{article} \usepackage{lipsum,amsmath} \begin{document} This is a displayed quote. \tag{A}\label{eq:A} \parbox{\dimexpr\linewidth-4em}{% \strut \lipsum*[1]% \strut } ...

5

Actually, tikz nodes have text inside and labels outside: \documentclass{standalone} \usepackage{tikz} \begin{document} \begin{tikzpicture}[scale=0.8,every node/.style={draw=black,circle}] \node[label={\small 1/16}] (a) at (0,0) {a}; \node (b) at (2,0) {b}; \draw[->] (a) to (b); \end{tikzpicture} \end{document}

1

A PSTricks solution using the pst-node (for the drawing itself) and expl3 packages (for the bounding box and the label distance): \documentclass{article} \usepackage{pst-node} \usepackage{expl3} \ExplSyntaxOn \cs_new_eq:NN \calc \fp_eval:n \ExplSyntaxOff \def\labelSep{\calc{28.75*\radius+3.375}} % found by experimenting % parameters ...

3

The displaymath environment does not provide an equation number: \begin{displaymath} \label{somelabel} will use the last counter being used in the \refstepcounter call and this is certainly not what is wanted here. To get the labels it is necessary to use a numbering math environment, e.g. equation or align and then use the \begin{cases}...\end{cases} ...

1

I've come across similar package showlabels that solved the issue. It has a number of options to show specified labels on the left or right margins of the page as well as in an inline mode.

2

The caption package provides the \captionsetup macro to modify a great many aspects of the output of the \caption macro (and, just for completeness, of the \captionof macro). The following code illustrates how to modify two such aspects: the font that's used for the label, and the separator between the label and the captioning text itself. (I've commented ...

8

In my point of view, it's sufficient to set a \hypertarget{destname}{} and use the destname as argument to the evince --named-dest option. This works at least in my evince version (3.6.1, very old, I believe) It works with Acrobat Reader as well, the calling syntax is slightly different, however: acroread /a "nameddest=pos2" nameddestexample.pdf to ...

2

You can use scaled x ticks=false, xticklabel style={/pgf/number format/.cd,fixed,precision=2}, to format the xticklabels automatically. Additionally the order of the colors in the color list and the order of the plots could be changed to use the cycle list color list for the plots. \documentclass{scrreprt} \usepackage{pgfplots} ...

4

I can't compile that thing so I'm summoning my crystal ball and guess that you need to add scaled x ticks=false option to the first plot axis options. pgfplots loads TikZ. TikZ loads pgfkeys and xcolor. So you only need the first for those four packages.

2

You should have no space in the comma separated list of values in the optional argument: \documentclass[preprint,12pt]{elsarticle} \begin{document} \begin{frontmatter} \title{My title} \author[affiliation1,affiliation2]{Author1} \author[affiliation3,affiliation5]{Author2} \author[affiliation2]{Author3} ...

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