All Questions
2
votes
3answers
25 views
Deducing a result about entire functions [duplicate]
We need to show that for an entire function $f$ on $\mathbb{C}$, there are constants $a_1,...,a_n$ such that $\int^{2 \pi}_{0}|f(re^{i \theta})|^2 d\theta=2\pi\sum_{n=0}^{\infty}|a_n|^2r^{2n}$.
...
0
votes
2answers
25 views
Existence theorem for Laplace's equation.
Regarding Laplace's equations, the following two are my questions:
1) If Dirichlet boundary conditions are specified on the surfaces, is it guaranteed that a solution will exist? Or is there some ...
2
votes
1answer
29 views
Books on computational complexity
Can anyone recommend a good book on the subjects of computability and computational complexity? What are the de facto standard texts (say, for graduate students) in this area?
I've heard a thing or ...
0
votes
0answers
17 views
A qestion about almost split squences.
On page 124 of the book Elements of representation theory of associative algebras, volume 1, Proposition 3.11, I have a question about the proof. On Line 8 of the proof, it is said that if $u: R \to ...
0
votes
1answer
32 views
Inequality for embedding in Sobolev space
For $\Omega=(0,1). $Prove that there exists $M>0$ such that
$$||u||_{C^0(\overline{\Omega})}\le M||u||_{H^1(\Omega)}$$
for all $u\in H^1(\Omega).$
1
vote
1answer
20 views
What are interesting properties of totally bounded uniform spaces?
I work on reloids, a generalization of uniform spaces.
As such I am interested about properties of totally bounded uniform spaces.
My question: What are interesting properties of totally bounded ...
1
vote
0answers
22 views
Universal bundle and induced bundle.
Let be $G$ a compact Lie group and $\pi: EG \rightarrow BG$ the associated universal bundle. If $X$ is a compact Hausdorff space there is a one-to-one corrispondence between the equivalence classes of ...
1
vote
0answers
20 views
Convergence in distribution and convergence of expectation.
Let $\{X_n\}_{n\geq1}$ and $\{Y_n\}_{n\geq1}$ be two sequences of uniformly integrable iid random variables with distributions $F_n(x)$ and $G_n(x)$, respectively. If
$$|F_n(x)-G_n(x)|\leq ...
1
vote
0answers
22 views
Absolute summable sequence in normed space [duplicate]
I have studied that for a sequence of real numbers absolute summability implies summability. What can we say about the sequences $\{x_k\}$ in a normed space . If it is not true in general could ...
0
votes
1answer
21 views
Shortcut in calculating examples of elements of a given order?
My question is:
Find all possible orders of elements of the group of units $G_{31}$. Give an example of an elememt of each possible order.
I did the question, but I felt I did it a long way. As ...
2
votes
2answers
53 views
why is an annulus close to it's boundary when it's boundary curves are close?
This is the motivating question for the rather vague question here: when is the region bounded by a Jordan curve "skinny"?
Suppose we are given two Jordan curves in the plane, one inside ...
10
votes
6answers
372 views
Submit papers: arxiv or vixra?
If I submit a paper at other place (for example vixra) first, can I (modify it and) submit it to arxiv again?
Is it valuable to publish a paper at the vixra?
Except arxiv and vixra, does any other ...
2
votes
2answers
38 views
Listing subgroups of a group
I made a program to list all the subgroups of any group and I came up with satisfactory result for $\operatorname{Symmetric Group}[3]$ as
...
2
votes
2answers
67 views
0
votes
0answers
11 views
Self-intersection number of a complex curve in complex projective space
I'm currently trying to get a grip on actually calculating some differential-geometric definitions. I'm looking at the following map from $\mathbb{CP}^{1}$ to $\mathbb{CP}^2$ :
...
3
votes
3answers
32 views
Subrings and homomorphisms of unitary rings
Let $(R,+,\cdot)$ be a ring (in the definition i use multiplication is associative operation and it's not assumed that there is unity in the ring).
I've seen two definitons of subring.
1) non-empty ...
-1
votes
1answer
34 views
How find this $(8\sqrt{6}-12\sqrt{2})\left(t_{2}+160e^{-\frac{1}{160}t_{2}}-1\right)=15$ [closed]
someone can help me?
use MATLAB find $$(8\sqrt{6}-12\sqrt{2})\left(t_{1}+120e^{-\frac{1}{120}t_{1}}-1\right)=20$$
and
$$(8\sqrt{6}-12\sqrt{2})\left(t_{2}+160e^{-\frac{1}{160}t_{2}}-1\right)=15$$
I ...
1
vote
1answer
21 views
Approximation of beam
Assume that there is a simply supported beam subjected to concentrated moments $M_0$ at each end. The governing equation is
$$EI\frac{d^2y}{dx^2}-M(x)=0$$
with the boundary conditions $y(0)=0$ and ...
2
votes
2answers
27 views
Forest graphs $F_1$ and $F_2$ with same vertices but different edges. Prove there is an edge where $F_1$ with it is still a forest
I am having quite a hard-time with this question, been thinking about it for a few hours and have not got a clue on how to even start proving this, because it is trivial but proving it has been hard ...
1
vote
1answer
19 views
Points contained in the diagonal of the product of schemes
Let $X,Y$ schemes over $S$, and $f,g$ two $S$-morphisms of schemes, $h:X \to Y\times_{S} Y$ the morphism obtained from $f$ and $g$ and $\Delta:Y \to Y \times_{S} Y$ the diagonal morphism.
I tried to ...
1
vote
0answers
16 views
In the case of the Ricci flow, the symmetries of the flow are scalings and diffeomorphisms
Can anyone help me and prove that in the case of the Ricci flow, the symmetries of the flow are scalings and diffeomorphisms?
Thanks for your time.
3
votes
1answer
36 views
Several graph theory proofs
Let $G=(V,E)$ be a graph with $|V|=n$. Prove that $G$ is connected if $d(v)\geq \frac{n-1}{2}$ for all $v\in V$.
Let $G=(V,E)$ be a graph with $|V|=n$ and $|E|=m$. Prove that $\min\limits_{u\in V} ...
-3
votes
0answers
30 views
What are other definitions can be further learnt in real analysis beside analytic definition [closed]
Any other modern definitions in real analysis are the starting points
$$f'(x) > 0$$
which books are for these
I would like to further expand in all new roads
3
votes
1answer
29 views
Is it true that bounded metric can never be induced by norm.
Let $(X, d)$ be a metric space where, $d$ is metric on $X$.
We know that metric space $X$ is called bounded if there exists some number $r$, such that $d(x,y) ≤ r$ for all $x$and $y$ in $X$.
I want ...
1
vote
4answers
84 views
How is “n+n/2+n/4…1” equal to “2n-1” using the formula for geometric series?
I never knew not having good knowledge of basic maths will be so crippling!! So please help me out this time. I'll be working on my maths from today on.
I was discussing about complexity of an ...
1
vote
0answers
12 views
Fourier transforms and Gaussian elimination
The solution of the complex linear system $Ax = b$ of $n$ equations can be computed using
Gaussian elimination with $O(n^3)$ complex multiplications.
However, how can we show that if ...
3
votes
3answers
56 views
when is the region bounded by a Jordan curve “skinny”?
How can I formalize and prove the following intuition?:
Picture a very skinny rectangle, one with base length 1 and sides length $\epsilon$. Or imagine a very flattened ellipse. The interiors of ...
1
vote
0answers
23 views
Diagonalizing/eigenvalues of a particular infinite dimensional matrix
I have trying to show that the continuum limit of n quantum harmonic oscillators gives rise the the klein-gordon field. However, instead of a usual finite string, I want to do it on a ring.
Assume $n ...
1
vote
0answers
66 views
Hilbert space proof
$X$ is a separable Hilbert space and $ A\in L(X,X)$ and compact.
I need to prove that $A$ is approximately of finite dimension.
0
votes
0answers
20 views
Eliminating the constant from a summation
Suppose I have the following two equations:
$$
x=\sum\limits_{t=1}^N [C\cdot(1-g)^t - 1]\cdot k^t,\qquad
y=\sum\limits_{t=1}^N [C\cdot(1+h)^t -1]\cdot k^t
$$
I want to calculate $x/y$, and in the ...
1
vote
3answers
34 views
Show that $\left( \frac{q}{p} \right) \equiv q^{(p-1) / 2} \mod p$, where $\left( \frac{q}{p} \right)$ is the Legendre Symbol
Show that if $p$ is any odd prime then
$$\left( \frac{q}{p} \right) \equiv q^{\frac{p-1}{2}} \mod p.$$
stating any theory that you use. In particular, you may assume the existence of a ...
1
vote
1answer
28 views
Absolute convergance of function series
The question is for which values of $x\in \mathbb R$, the following series absolute/conditionally converge: $$\sum_{n=1}^{\infty}\frac{x^n}{(1+x)(1+x^2)...(1+x^n)}$$ I have no idea how to solev it ...
2
votes
0answers
27 views
Find the eigenvalues and eigenvectors of an integral equation
I need to find the eigenvalues e eigenvectors of this integral.
A)
$$\int_{0}^{1}(cos^2(x+y)+1/2)\phi (y)dy$$
B)
$$\int_{0}^{1} K(x,y)\phi (y)dy,$$
where
$K(x,y)=x(1-y),\; 0 \le x\le y \le 1$
...
5
votes
0answers
29 views
Prove by Hilbert deduction: $\vdash _{HFOL} \forall x (\neg(A \to \bar{B}))\to \neg(\forall xA \to \neg(\forall xB))$
I'd really like your help proving:
$\vdash_{HFOL} \forall x (\neg(A \to \bar{B}))\to \neg(\forall xA \to \neg(\forall xB))$
Where $HFOL$ is the proof system which contains the Hilbert relevant ...
1
vote
2answers
44 views
Counterexample to Leibniz alternating series test
The alternating series test is a sufficient condition for the convergence of a numerical series. I am searching for a counterexample: i.e. a series (alternating, of course) which converges, but for ...
2
votes
1answer
27 views
Volume of revolution around a line
Find the volume of revoulution of the region enclosed by $y = x^3, x = 0, x = 1$ and $y=-1$ around the axis $y = -1$.
This question is most easily done via the disk method, however, I tried ...
0
votes
0answers
18 views
Solve integral equation of second kind using Fredholm method
I need to solve this integral equation
$$\phi (x)=(x^2-x^4)+ \lambda \int_{-1}^{1}(x^4+5x^3y)\phi (x)dy$$
Using the Fredholm theory of the intergalactic equations of second king.
I really don't ...
1
vote
3answers
38 views
Uniform convergance for $f_n(x)=x^n-x^{2n}$
the function $f_n(x)=x^n-x^{2n}$ converge to $f(x)=0$ in $(-1,1]$. Intuativly the function does not converge uniformally in (-1,1]. How can I prove it?
I tried using the definition $\lim ...
1
vote
1answer
34 views
What will be the count of “4cardstraight” in a Poker Game
Let's modify the poker hand(fake): "4cardstraight" -- i.e. a straight, but with only 4 cards in a row instead of 5.
Rules of the game:
A hand is counted as a "4cardstraight" if it includes 4 ...
0
votes
1answer
37 views
Problem with lowercase versus uppercase.
I often attack problems on two levels, a verbal level and a visual level. At a visual level, I try to imagine how everything is related - I arrange the ingredients of the problem into a two (or ...
0
votes
1answer
35 views
Prime divisibility in a prime square bandtwidth
I am seeking your support for proving (or fail) formally the following homework:
Let $p_j\in\Bbb P$ a prime, then any $q\in\Bbb N$ within the interval $p_j<q<p_j^2$ is prime, if and only if ...
3
votes
0answers
32 views
Units of the quotient of an order
Let $n$ be a positive integer and $R$ be an order in a imaginary quadratic number field such that $disc(R)$ is prime to $n$. Further suppose that for every prime $p$ dividing $n$, $p$ is inert in $R$. ...
2
votes
1answer
35 views
Finding eccentricity of an ellipse from latus rectum
The latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is the same as latus rectum of a parabola $y^2=4cx$ . Find eccentricity of the ellipse .
0
votes
0answers
24 views
Does reachability belong to P?
Reachability is defined as follows:
a digraph $G = (V, E)$ and two vertices $v,w \in V$. Is there a directed path from $v$ to $w$ in $G$?
Does it belong to P (the class of polynomial running time ...
1
vote
2answers
26 views
Given a spanning set, what is the span of the 'transpose' of the set?
Given $$sp\left \{
\begin{pmatrix}
a_1\\
a_2\\
a_3
\end{pmatrix}
,\begin{pmatrix}
b_1\\
b_2\\
b_3
\end{pmatrix}
,\begin{pmatrix}
c_1\\
c_2\\
c_3
\end{pmatrix}
\right \} = \mathbb{R}^3$$
What ...
6
votes
1answer
63 views
Topology on Integers such that set of all Primes is open
In my topology homework we are asked to describe a topology on the Integers such that:
set of all Primes is open.
for each $x\in\mathbb Z$, the set $\{x\}$ is not open.
$\forall x,y \in\mathbb Z$ ...
1
vote
1answer
36 views
What is the difference between a surface and the graph of a function?
When I was studying a book, Elementary classical analysis (Jerrold.E.Marsden), there was a confusing sentence.
"The unit sphere $x^2+y^2+z^2=1$ in $\mathbb R^3$ is a surface of the form $F(x,y,z)=c$ ...
0
votes
1answer
25 views
Simple Expect Value Exercise
Question: We have $9$ coins, $1$ of them is false (lighter). We divide them up in pairs (with one left) and weigh them (that is taking two in a balance and seeing if one of them is lighter). What is ...
0
votes
1answer
33 views
the area principle of biholomorphic mapping
If $f=\frac 1z +\sum_{i=0}^\infty a_nz^n $ is a biholomorphic mapping on $B(0,1)\setminus${0},then prove that:
$$\sum_{i=1}^\infty n|a_n|^2\le1$$
I have known that when ...
0
votes
4answers
35 views
Is a set of prime numbers open in Furstenberg's topology?
I was reading Furstenberg's Proof of Infinitude of Primes and I wonder if a set of prime numbers is open in this topology.
Thanks!
