Consider the following linear functional operator:
$$Q_w[f(x)] = \lim_{h\rightarrow w} \lbrace \frac{f(x + h) - f(x)}{h} \rbrace $$
How does one solve the equation
$$a_0(x)Q_0[f(x)] = a_1(x)Q_1[f(x)]$$
Spelt out that is:
$$a_0(x)*f'(x) = a_1(x)(f(x+1) - f(x))$$
For the case of constant...
out of curiosity what level of linear algebra is this? Because I just finished my course and we never covered this haha. Though we did talk about eigenvectors
Suppose that an amateur mathematician finds a solution to a major unsolved problem and they have written their full proof and would now like to publish it somewhere or at least have it critiqued by the professional community. What steps should they take?
Additionally, let's say that the...
Well it turns out if you do an iterated Newton method the number works. To speed things up i broke up the function into separate segments defined as linear. The function appeared out of the context of being given a discrete function how do you make a contonuous analog
ehhh not exactly from a class (sorry), and I don't have any sample problems for this thing either. It just kind of came up. My best guess is to use Newton's formula.
I mean Newton's method
Would Newton's method or some other method work? Consider the following problem:
find the zeroes of the function: y = 40sin(2x) - floor(40sin(2x))
where Y,X \in R
I don't exactly know how to handle this problem. My best insight so far is that it is only equal to zero whenever 40sin(2x)...
Forgive ne if this sounds stupid but does GR take into account angular momentum, torsion, and other effects of rotation? The stress energy tensor doeznt appear to have any terns that are meant two accommodate angular momentum abd rotational stress.
See, if one just considers the outer layer of the sphere; then, yes it is gaining momentum (ie becoming heavier) due to the lorentz factor, but at the same time as the volume expands this mass gets distributed around so the sphere is definitely becoming "heavier". Relativity says it has to. I...
suppose I have a 10 kg sphere with homogenous distribution of mass (aka density is same everywhere) that is 10 m^3. Now suppose I rapidly increased its radius at a speed of 1/2c m^3 (and because its homogenous the volume increased correspondingly). Now my question is whether that would cause the...
So basically here's the deal:
I believe there exists a P(x) defined on [-2π, 2π]
such that over that interval P(x) = \sum^{\infty}_{n=0}[sin(πnx)]
Its weird but I have a feeling that this might converge to a function such as tangent
Suppose we lived in significantly hotter conditions that what we live in right now (or lower pressure)... could organisms composed of Tin or Lead as opposed to carbon, Bismuth/Antimony as opposed to Nitrogen, Selenium and Tellurium as opposed to oxygen and sulfur respectively, and substances...