Argument Definition and 388 Threads

I am trying to compute the amount of energy received by the Earth from the sun, by integrating over the Earth's surface. I keep reading that the formula should be: E = e-max * cos @ * area e-max is the solar insolation, @ is the angle between the sun and the perpendicular to the land...

The following is a paraphrase of an argument for the discreteness of spacetime, made by Smolin in his popular-level book Three Roads to Quantum Gravity. The Bekenstein bound says there's a limit on how much information can be stored within a given region of space. If spacetime could be described...

Hello everyone, I'm having a bit of trouble with using the argument function with DeMoivres formula. I have the question: z8= 16 and am meant to find the solution using DeMoivre's formula (zn=rn(cosn(Θ) +isinn(Θ)) ). The problem is, I have no idea what an argument function is or how to find...

When given a complex number z=x+iy and transforming this into its mod-arg form giving rcis\theta where r=\sqrt{(x^2+y^2)} and \theta=arctan(y/x), we are assuming that -\pi/2<\theta<\pi/2. What if however a student is asked to convert the complex number -1-i into mod-arg form? If they just start...

String theory requires 9 spatial dimensions, M-theory 10. One followup to Verlinde's paper is this: http://arxiv.org/abs/1002.0488 Hidden symmetries for thermodynamics and emergence of relativity Liu Zhao (Submitted on 2 Feb 2010) Verlinde recently proposed an idea about the thermodynamic...

Can anyone provide an elementary argument for why the zero mass of the photon means that it can't be longitudinally polarized? I know of at least one non-elementary argument, which is that if you write down the Proca equation, it only has longitudinally polarized solutions if the mass is...

Homework Statement Find the minimum value of arg(z) where z satisfies the inequality |z + 3 -2i| </_ 2 Homework Equations Is this working correct? Thank you for help in advance The Attempt at a Solution Z lies on a circle with radius 2 and centre -3,2 arg(z)min = pi - 2...

I've argued in other threads in this and other forums against strict determinism (non probabilistic) on philosophical grounds. The probabilistic formulation of quantum mechanics is still the standard view, but it seems to irritate some who post in PF. They would seek a fully deterministic theory...

Homework Statement I have a function y where y = 3x+2 I made x as a vector in matlab: for i=1:10 x(i) = 4*i but when i do a plot, i don't want to plot y against the vector x but against x as an argumetn of the function. In general if i have any function...how do i plot it against its...

VectorPlot[{D[x[t], t] == x[t] (4 - y[t] - x[t]^2), D[y[t], t] == y[t] (-1 + x[t])}, {x, -10, 10}, {y, -10, 10}, {t, -10, 10}] I'm trying to graph the phase plane of these equations. I get an error, what's wrong with my command?

This is an excerpt from a manuscript by William James Sidis published in 1920 called "The Animate and the Inanimate": But there is one outstanding objection to this theory that the stellar universe is infinite. There may be supposed to be no reason why the average brightness of...

Homework Statement Is mathematical induction a deductive or inductive argument? Would appreciate the help. Thanks. Jeremy Homework Equations The Attempt at a Solution Its name suggests that the process is inductive, yet I know all of mathematics depends on deductive reasoning...

A Lorentz boost along the x-axis conserves area in the x-t plane. Can anyone think of an argument to prove this fact that's simpler than the one below? I don't want to assume the form of the Lorentz transformation, because I want to use the conservation of area as part of a derivation of the...

There is a logical argument I'd like to have some comments on. I read it in a book, and I am not sure about it. "An instructor teaches a class five days a week, Monday through Friday. She tells her class that she will give one more quiz during the final week of classes, but that the students...

The situation is this: A truck is moving at 70mph with a ramp leading into it at the back. A car with front-wheel drive is behind it doing 75mph. The car goes up the ramp and into the truck. Here is where the dispute starts. My theory: Once the front wheels of the car are on the ramp the...

My friend and I disagree on this problem: A spaceship of proper length 200m moves with respect to us at 0.6c. There are two clocks on the ship, at the bow and stern, that have been synchronized with each other in their rest frame. We, also have a number of clocks synchronized in our frame...

I had a physics test last week. When I got the results, there were some correction mistakes in my opinion, so now it's being revised. I had a small disagreement with my professor over one of the theoric exercises, and tomorrow i'll probably be having the same argument again, so I thought of...

There is an argument to account for the Casimir effect based on cardinalities: that inside the two plates only (virtual) photons with wavelengths corresponding to the harmonic series can exist, hence countable infinity, whereas photons of all wavelengths can exist in the space around it, hence...

Homework Statement Objects are composed of atoms. Atoms are nucleii surrounded by electrons. The electrons are tiny in comparison to the gaps between each other, and between electrons and the nucleus. This means that there are significant gaps between atoms in objects. Homework Equations...

This is pretty much like the twin paradox question: if person A and person B were moving with a velocity v relative to each other and away from each other, then person B would observe a time dilation in person A's reference frame while person A would observe a time dilation in person B's...

Hi, Want to show: a<=r However I ended up with such an argument: For each eps>0, a<r+eps. Does this statement imply a<=r?

-1-(under root)3 i here we find that r=2(hypotenuse) a=-1(base) b=-(under root)3 when i take sin theat= p/h=-(under root)3 / 2 theat from sin is -60 when i take cos theta = b/h =-1 / 2 which gives 120 now one is -60 and other is 120, which is the angel , i have to follow and what...

I've watched the Dateline NBC episode on Vincent Brothers, and was disturbed that the evidence used to convict him was exactly the kind that UFO crackpots like to use. Here's a pretty good summary of the show, even though it's from an unreliable-looking website...

Homework Statement Give an argument for there being a connection between scale length and frequency Homework Equations scale length = (wave length) / (Length)The Attempt at a Solution So from only my physical intuition I'm coming up with the longer the scale length the longer the wave length...

Hello, a couple decades ago, an argument was introduced in a notable physics journal of some kind, but I cannot recall the name of this argument, or the journal. I believe it might have been associated with Cambridge, but can't remember. The argument is a logical theory as to why the...

I just need to make sure that I've got this analysis right: The argument S = 1 - 1 + 1 - 1 + 1 - ... then S = (1 - 1) + (1 -1) + (1 -1) + ... = 0 is invalid because it ignores all sum Sn for n not congruent modulo 2 (not even). The argument S = 1 - 1 + 1 - 1 + 1 - ... then S = 1 - (1 -1) - (1...

can we really give a definition of \delta (x-a-ib) a,b real and 'i' means the square root of -1 if i try it in the sense of generalized function for any x a and b i get the result oo unless b is zero

the question is if we suppose that a function f(n) can take only two values +1 and -1 both with equal probability and define the summatory \sum_{n=0}^{x}f(n) =A(x) how can one prove that A(x)= O(x^{1/2+e}) ?? if we set A(n)=M(n) the Mertens function and since...

Homework Statement Evaluate (1/2ipi)* contour integral of [z^(n-1)] / [(3z^n) - 1 ] dz Homework Equations I would assume you would have to use the Argument Theorem since this problem comes after the proof of the argument theorem in my book. The Attempt at a Solution z^(n-1)...

According to Caratheodory, the first law of thermodynamics (dE=dQ-dW) could be derived from the definition of heat (dQ=dE-dW), whether this form a circular argument or tautology ? How to clarify the confusion between the first law of thermodynamics and the definition of heat，and capture the true...

I was in a discussion with a man. I've read a study about reading habits. The study shows a low average of read books for some countries and told to a man "most of people doesn't read books" because the average was 6 books a year for a sample taken from a population of 100 millions of people...

Hi everyone, I have a couple questions that have been gnawing at my head for some time: Why is it that on wikipedia for the example logarithms and residue at infinity, (on the methods of conour integration link) that the integral is not zero? there are no isolated singularities inside the...

i was wondering whether it was possible to have a class say Vec4(i,j,,k,n) and then being able to assign it as an int eg/ Vec4 A(i,j,k,1) = 1; does this make any sense?

I am confused with the coordinates when using the symmetry argument for this graph. Is Mx=0 using the symmetry argument ?

sorry for starting yet another one of these threads :p As far as I know, cantor's diagonal argument merely says- if you have a list of n real numbers, then you can always find a real number not belonging to the list. But this just means that you can't set up a 1-1 between the reals, and...

It's an old joke, and an old sketch, but some here may not have seen it before, and you can imagine this is how many forum debates end up: http://www.youtube.com/watch?v=teMlv3ripSM&fmt=22

Homework Statement Suppose that a sequence {p}->p, and {q}->q. Show that if p_n < q_n for infinitely many n, then p<q. Homework Equations The Attempt at a Solution I'm sure I know why this is true intuitively. The convergence guarantees that all but a finite number of p_n are within some...

What allows us to do the construction found in Cantor's diagonal argument? Is there an axiom we must adopt to allow for such infinite constructions?

PHP - "Wrong datatype for second argument" So I build this class in my library file (assume that I have all the PHP tags and stuff)... class errorchecker { var $error; function errorsearch($error) { if (in_array($error, $pb)){ echo '<div class="error">'.$error.'</div>'; } }...

Homework Statement Find the modulus and argument of z=1-cos(a)-i*sin(a) Homework Equations mod(z)=sqrt(a^2+b^2) The Attempt at a Solution mod(z)=sqrt((1-cos(a))^2+(-sin(a))^2) =sqrt(2-2cos(a)) arg(z)=arctan((-sin(a))/(1-cos(a))) This is as far as I can get, I have asked my math...

Hey, in my Schaum' Outline Calculus it says Dx(ex) = ex Let y = ex. Then ln(y) = x. By implicit differentiation, \frac{1}{y}y' = 1 therefor y' = y = exFor a more rigorous argument, let f(x) = ln(x) and f-1(y) = ey. Note that f'(x) = \frac{1}{x}. By Theorem 10.2(b). (f-1)'(y) =...

Hello. I am having an argument with two of my friends. They went to Harvard and MIT and are making fun of me for saying you would experience weightlessness in a free falling elevator. They say you would be stuck to the ground and unable to lift your legs since the faster you fall the harder...

Homework Statement By a combinatorial argument, prove that for r \leq n and r \leq m, (^{n+m}_{r}) = (^{m}_{0})(^{n}_{r}) + (^{m}_{1})(^{n}_{r-1}) + ... + (^{m}_{r})(^{n}_{0}) Homework Equations The Attempt at a Solution I need some direction on how to start this problem. It is...

Homework Statement Hi all. When finding the argument of a complex number using tan(\theta) = y/x (where z = x + iy), sometimes I do not get the correct answer. I assume this is because tangent is only defined for -pi/2 to pi/2 (and from this it is periodic). So is it a good idea always...

Given a lagrangian L[\phi], where \phi is a generic label for all the fields of the system, a transformation \phi(x) \rightarrow \phi(x) + \epsilon \delta \phi(x) that leaves the lagrangian invariant corresponds to a conserved current by the following argument. If we were to send \phi(x)...

If z is a complex number, isn't the derivative of arctan(z) just 1/(1+z^2) ? That's what I would think, but my CAS does not agree with me.

Homework Statement Find the argument of (-2+i)(1+2i). 2. The attempt at a solution z=(-2+i)(1+2i)=-4-3i. I've read on the Internet that I can write z=\rho (\cos \theta +i\sin \theta) where \rho is the modulo of z. I've calculated the modulo of z which is 5. So I have that -4=5\cos \theta...

I had a brief conversation with a professor of mine and he presented, in short an argument against the existence of black holes. I'm sure you've heard it or a variation of it. It goes something like this: An advisor and his student are near a black hole. They are both wearing a watch, the...

We're just learning special relativity in class and my lecturer uses the light clock argument (two moving clocks - one parallel and one perpendicular) to explain length contraction. I didn't quite get one thing about it. My notes say the light beam reflects at different times (i.e. they have...

My daughter and I don't agree on pronunciation of the delicious Thai dish, "phad thai." Is it "pod tie" or "pad tie"?