The actual principle behind the C type declarations is "declaration follows use". Let me explain what this means. Take this declaration
int *pi;
Means that when I dereference the variable pi, I get an int. This also explains why
int *pi, i;
declares `pi` as a pointer to `int` and `i` as an `int`. From this point of view it makes sense stylistically to put * near the variable.
Declaration of array types is similar. For example,
int arr[10];
means that when I take an element of `arr`, I obtain an `int`. Hence, `arr` is an array of ints.
Pointers to functions work the same way. For example,
int (*f)(char, double);
means that if I dereference the variable `f` and I evaluate it on a `char` and on a `double`, then I get an `int`. Hence, the type of `f` is "pointer to function which takes as arguments a char and a double and returns an int".
You can compute this integral as follows. First, you remember that sinc(x) = sin(x)/x is the Fourier transform of 1/2 * indicator function of [-1, 1]. In general you have:
Next, replace the sinc functions by their Fourier representation, change the order of integration and use the formula
\int_{-\infty}^\infty d x e^{i a x} = 2 pi \delta(a),
where \delta(a) is the Dirac delta. You are left with an integral of a delta function over a product of intervals. What remains to be done is just some tedious computation.
\int_{-1}^1 d t_0 \dots \int_{-1/(2 k + 1)}^{1/(2 k + 1)} d t_k 1/2 \dots (2 k + 1)/2 2 \pi \delta(t_1 + \dots + t_k).
Next, the question is whether t_1 + \dots + t_k = 0 has a solution for t's in the integration domain. This holds until k = 7. To see this, compute
I didn't read the article but, in case you don't know quantum mechanics, I should tell you that the vast majority of people who study such things think that Bohm's theory is plain wrong.
I should also say that it is not taught in schools, papers about it are not published in serious journals and the field is just not an active field of research. It's quite likely that all the people trying to develop this idea are crackpots.
I tried to find an example that contradicts what you said, but I can't find any. Here's an online example which can be compiled as both C and C++ and I obtain exactly the same assembly using both clang and gcc. Maybe somebody can tweak this example to force the C compiler not to perform the optimization.
See my reply to the parent poster for an example where RVO applies in C++ but not C, leading to better code in the C++ case. The key is to let the address of the objects involved escape: otherwise "as if" will let C (and C++ even without RVO) optimize away the copies anyways, since they are not observable in that case.
No, she most certainly did not discover the DNA. The DNA (which was not named like that) had been around since Friedrich Miescher's work in the 19th century.
Your statement is at least[#] as ignorant as saying that J.J. Thompson discovered electricity since he discovered the electron. Of course, the electricity had been discovered long before that.
[#] What I have in mind here is that even the statement that she discovered the molecular structure of the DNA is not strictly speaking accurate.
I see they are adding an analog of the C++ iostreams, but I don't see a discussion of how to disambiguate between `sin' as in stream-in and `sin' as in the mathematical function.
Really, they should introduce some kind of modules or namespaces. Of course, C++ already has namespaces and will have modules sooner or later...
I don't know if you're going to see this, but I feel the need to defend myself. Sorry about going on a tangent here, but I have no other way of doing this.
Here's what happened. Somebody posted a link to a PhD thesis in mathematics which was not at all written in the style in which math PhD these are written. Somebody else commented that this is great all math PhD these should be written like that. Then, I pointed out that the author of this thesis (a black woman), wrote a piece on a blog of the American Mathematical Society website saying that all the white male in the math departments in the USA are the problem, she wants them out and they should all resign.
Then various people started down-voting and attacking me. I replied to their attacks and defended myself. This amounted to "ideological war" according to some moderator. Also, since I did not use this account for making lots of comments, it appeared to the moderator that this account was created to primarily to start flamewars. The people who attacked me in a very nasty and personal way did not suffer any consequences since they had more comments hence their accounts looked more legitimate.
So yes, I feel like I've been the victim of an injustice.
> the fact that many sexist anti-STEM cues are given to children at a much earlier stage, way before careers are even on the horizon
It doesn't look like you read the article. It clearly stated that in countries like Finland and Sweden, where such cues are less likely to be given, there is a larger inequality in STEM. Meanwhile, in Iran there are more women in STEM. Do you think that in Iran young girls are more or less likely to be subjected to "harmful gender stereotypes" than in Sweden or Finland?
> Cues can be as subtle as a wide-eyed look while reacting ...
This was precisely addressed in the article. It goes by the name of micro-aggression. Go back and read about it.
>This was precisely addressed in the article. It goes by the name of micro-aggression.
No. As I said above to another person who also made the same mistake:
They only describe it in the context of the workplace and in degree-granting institutions, not in earlier schools or in the home where minds are in their formative stages. It’s microagression for sure, but they are overlooking the more powerful instances of it.
Your intuition is correct and the question of the speed of gravitational waves is pretty complicated. The usual treatment of gravitational waves is done by linearization of some non-linear equations. This is a very good approximation for the propagation of gravitational waves since they disturb the space-time only very slightly (for example, the mirrors in the interferometry experiment at LIGO get displaced by a tenth of a nucleus of a hydrogen atom, during the passage of a gravitational wave).
In this linear approximation the gravitational waves are governed by the same wave equation as for electromagnetism (only the spin part is different since the spins of the gravitons and photons are different). Since in the linear approximation we recover the Lorentz symmetry, then the linearized wave equation has to be Lorentz invariant. Then, one can apply results from the representation theory of the Lorentz or Poincare groups; there are two major types of representations: massless and massive. They differ in striking ways when it comes to spin and when it comes to propagation, for example massless particles travel at the speed of light. If you want to have a massive graviton then you need to get the mass somehow from your theory. Einstein's theory predicts a massless graviton, which by the argument above has to travel at the speed of light. We still don't know experimentally if the graviton is massless (but last time I looked at the Particle Data Book there was an upper bound on the mass which was very small).
Now, coming back to why your question is complicated. Remember that in Einstein's theory space-time itself is dynamical. Now suppose you follow the propagation of a gravitational wave. Since this takes some time, we need to take into account the fact that the shape of the space-time itself has changed in the meantime. In such dynamical situations it becomes complicated to even define what the speed of propagation between two points is. One way this becomes important is in cosmological situations. For example, the expansion of the universe stretches the distances and this allows us for example to see further that the distance you obtain multiplying the speed of light by the age of the universe. This being said, you can define the speed locally by studying propagation for very short distances and times and this will be a constant. However, you need to remember that the global situation is more complicated.
Please, please, please, don't take MathML away from us. Even though we are few in number, we want to be able to put mathematics on the Web. I'm sad Chrome and IE chose not to implement support for MathML.
Declaration of array types is similar. For example,
means that when I take an element of `arr`, I obtain an `int`. Hence, `arr` is an array of ints.Pointers to functions work the same way. For example,
means that if I dereference the variable `f` and I evaluate it on a `char` and on a `double`, then I get an `int`. Hence, the type of `f` is "pointer to function which takes as arguments a char and a double and returns an int".