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I am a scientist writing my first manuscript with a substantial amount of mathematical methodological documentation.
I am using LaTeX, but this is not my question.
I would like to find a list of usage rules similar to Strunk and White. I can follow the practices that I see in my field, but it would be helpful to know ... |
This post is related to a previous SE post If a 1 meter rope …. concerning average length of a smallest segment.
A rope of 1m is divided into three pieces by two random points. Find the average length of the largest segment.
My answer is 11/18. Here is how I do it:
Here we have two independent random variables $X,... |
Is there a way to (efficiently) enumerate all simple graphs with a given number of vertices up to isomorphism? That is, I don't care about the degeneracy of a graph, only the set of isomorphically unique ones of a given size.
|
What is the rate of growth of the partial sums of the reciprocals of the odd numbers?
|
How does a technical and theoretical study of a project of implementing an algorithm on a specific hardware architecture?
Function example:
%Expresion 1:
y1 = exp (- (const1 + x) ^ 2 / ((conts2 ^ 2)),
y2 = y1 * const3
Where x is the input variable,
y2 is the output and const1, const3 const2 and are constant.
I need to... |
Suppose $g:\mathbb{R} \rightarrow [0,\infty)$ is a strictly increasing function such that $\lim g(x) = \infty$ as $x \rightarrow \infty$.
Suppose $h:\mathbb{R} \rightarrow [0,\infty)$ is a strictly decreasing function such that $\lim h(x) = 0$ as $x \rightarrow \infty$.
Consider the product function $f(x)=g(x)h(x)$. Is... |
I will be using relativistic terminology for pseudo-Riemannian manifolds as in the book by Barret O' Neil.
If one can show that the chronal future and the chronal past of some set are disjoint then why is this enough for showing that the set is achronal?
I mean one can have a set such that there is precisely one tim... |
I'm trying to get familiar with the Newton-iteration over here but I got stuck at the proof of the error estimate.
Let $f: [a,b] \rightarrow \mathbb{R}$ be continuously differentiable twice, concave or convex and $f' \neq 0 \;\; \forall x \in [a,b]$. Let $\xi$ be the root of $f$. We define the Newton-iteration for $k \... |
Every finitely generated free group is a subgroup of $F_2$, the free group on two generators. This is an elementary fact, as is the fact that $G$, finitely presented, is the quotient of $F(|S|)$ the free group on some set of generators $S$ for $G$.
My question is whether $F_3$, and hence any finitely presented group... |
I am interested in learning (and implementing) an alternative to polynomial interpolation.
However, I am having trouble finding a good description of how these methods work, how they relate, and how they compare.
I would appreciate your input on the pros/cons/conditions under which these methods or alternatives would ... |
I found a contradiction I couldn't resolve by my self.
It's about a "Uniform White Noise".
Let ${x}_{t}$ be a "White Noise" i.i.d. Random Process:
$ \forall t \in \mathbb{R}, \ {x}_{t} \sim U[-1, \ 1] $
If we chose to go by the PSD definition of "White Noise" (Constant all over the Frequencies) we get:
$ {R}_{xx... |
I'm confused about the concept of pivoting a Matrix element. This operation seems to be a fundamental operation which is used as part of more complex operations such as inverting a matrix.
However, the definition of pivoting, and what it entails, seems to vary depending on the context.
In the context of inverting a ma... |
Let's say, we have an array/matrix $n \times m$ and we need to find, how many ways can we fill this array with numbers from $\{ 1, \ldots , m\cdot n \}$, but:
1) every number can be used only 1 time
2) every column and every row should be sorted in increasing order
For example, if we have $n = m = 3$, there are 42 diff... |
A module $M_{R}$ is called semi-artinian if every nonzero image of $M$ contains a simple submodule. Given $m\in M$ and $a_1,a_2,...$ in J(R). Why $ma_1a_2...a_{n-1}a_n=0$ for some $n\geq 1$.
(Edit by KennyTM: The above is OP's original question. The latest, completely changed question follows:)
if $R$ is regular what ... |
I was rather confused about this proof I came across in Rudin Chapter 7. The premise is: If K is a compact metric space, if $f_n \in C(K)$ for $n = 1, 2, 3, ...,$ ($C(K)$ being a set of complex-valued, continuous and bounded functions), and if $\{f_n\}$ converges uniformly on $K$, then $\{f_n\}$ is equicontinuous on ... |
The question asks me to determine if $4\mathbb{Z}$ and $5\mathbb{Z}$ (with standard addition) are isomorphic and if so to give the isomorphism.
My attempts:
What I am having difficulty with is showing a mapping that preserves the operation. i.e., $\phi(a+b) = \phi(a) + \phi(b)$.
What I have so far is:
$\phi(a+b) = ... |
I was reading over this in my notes, but it doesnt make any sense to me:
However, suppose we fix an alphabet for
writing our programs (e.g. 8- bit
ASCII). Since each individual program
is finite in length, we can put all
possible programs into a (very long)
ordered list. For any fixed character
length k, ther... |
Alright, so this is how I am doing it:
float xrot = 0;
float yrot = 0;
float zrot = 0;
Quaternion q = new Quaternion().fromRotationMatrix(player.model.getRotation());
if(q.getW() > 1){
q.normalizeLocal();
}
float angle = (float) (2 * Math.a... |
Justin needs to pick 17 toy animals to
give to children at a party. The
animals come in 5 kinds: dogs,
dinosaurs, cows, lizards, and fish. How
many different ways can he choose his
set of toys
Ok the answer for this is 21 choose 4. However, I dont understand how they arrived at this answer. If there are 17 sl... |
I tried to prove this, but was unsuccessful for a long time..
Any ideas?
Prove that $(\exp(x))^y=\exp(xy)$ using the identities,
$$\exp(x)=\sum_{n\geq0} \frac{x^n}{n!}, \quad (1+x)^\alpha=\sum_{n\geq0} {\alpha \choose n} x^n$$
|
I've been studying the finite-dimensional representations of the lie algebra sl(2,C). I've read that these representations are related to the harmonic oscillator and the associated raising and lowering operators, but I'm not really sure how they are related. I've read you can generate a new energy state from an old one... |
A two dimensional space (eg. $\mathbb{R}^2$ ) could be a flat or it could be the surface of sphere (or of any shape) in a 3-dimensional space. How do we distinguish between such spaces without invoking higher dimensions.(here I am using the term 'space' in a general term and not strictly in a manner used in mathematics... |
Let $X$ be a subspace of $\ell_1^4$ (i.e. $\mathbb{R}^4$ equipped with the $\ell^1$ norm). Can one always extend a linear operator $l:X\rightarrow \ell_1^4$
to $L:\ell_1^4\rightarrow \ell_1^4$ such that $L$ has the same operator norm as $l$?
Thanks!
|
There are Artin $L$-series and Dirichlet $L$-series, and zeta functions for varieties and for number fields; there are a slew of objects named after Hecke... There are also various kinds of characters in these areas.
I've always had a hard time keeping all of them straight. I would be very grateful if someone could put... |
Are all groups of order $156$ solvable?
|
I have an epimorphism $f:B_4\longrightarrow S_4$, from the braid group on 4 strands onto the symmetric group on 4 elements. Is it possible the kernel is not isomorphic to $P_4$, the pure braid group on 4 strands?
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I want to construct a nowhere dense set of positive measure by using the Smith-Volterra-Cantor method but subtracting closed sets intead of open sets.
Suppose we start with the open interval (0,1). Let $\alpha=1/2$. Now remove $U_1=[1/2-\alpha/4,1/2+\alpha/4]$. The measure $\mu(U_1)=\alpha/2$. For each of the two r... |
How to check if two multiplications are equal to each other or greater or lesser without actually multiplying them?
For example, compare (254)(847) and (383)(536)
EDIT:
While trying to find a rule i got one
(5)(11) < (6)(10)
or
(x)(y) < (x+1)(y-1) when y > x > 0
and another rule is that if adding and subtracting 1 equ... |
Recall the following relevant definitions. We say that
$b$ is divisible by $a$ in $R$, or $a\mid b$ in $R$, if $b = r a$ for some $r\in R$.
$a$ and $b$ are associates in $R$ if $a\mid b$ and $b\mid a$, (or, equivalently, if $aR = bR$).
$u\in R$ is a unit if it has a multiplicative inverse (a $v\in R$ such that $uv=vu... |
Let $f, g$ be two paths in a space such that their concatenation $f * g$ is nullhomotopic. Prove that $f$ is homotopic to $g$ rel $\{0,1\}$.
|
I'm trying to prove an identity involving the digamma function $\psi(z)$, but I can't seem to figure out a way to do it. Can anyone help me out? The identity is
$$\psi\left(\frac{m}{2} + iy\right) + \psi\left(\frac{m}{2} - iy\right) = \psi\left(\frac{n}{2} + iy\right) + \psi\left(\frac{n}{2} - iy\right)$$
where $m$ an... |
Let $a$ and $b$ be elements of the polynomial ring $\mathbb{Z}/n\mathbb{Z}[x]$. If $a$ and $b$ generate the same ideal, must they be associates? If $n$ is prime, then it is easy to see that the answer is "yes". But what if $n$ is not prime?
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Is the functor from the category of projective varieties over a field $k$ to the category of pure motives over $k$, faithful? (Perhaps it is not full).
Ditto:
Is the functor from the category of affine varieties over a field $k$ to the category of mixed motives over $k$, faithful? (Perhaps it is not full).
|
Let $$\psi_{j,k}(t)=\begin{cases} 2^{j/2}, & 2^{-j}k < t < 2^{-j}(k+1/2)\\-2^{j/2} ,& 2^{-j}(k+1/2) < t < 2^{-j}(k+1) \\ 0, & \textrm{otherwise.} \end{cases}$$ How to prove that it is orthogonal? In other words how to prove that $\langle \psi_{j_1,k_1}(t), \psi_{j_2, k_2}(t) \rangle = 0$, $j_1<j_2$ and $k_1<k_2$. I h... |
Say $M := \begin{pmatrix} A & B\\ C & D \end{pmatrix}$ is a block matrix with $A, D$ being square matrices and this $B$ and $C^T$ having the same shape. Is there any norm characterizing the collection of $B$ and $C$ that is invariant under all block diagonal similarity transformations $M\to S M S^{-1}$ with $S=\begin{p... |
Let $G \in \mathbf{Grp}$, $H \leq G$, $G/H := \lbrace gH: g \in G \rbrace$. We can then introduce group operation on $G/H$ as $(xH)*(yH) := (x*y)H$, so that $G/H$ becomes a quotient group when $H$ is a normal subgroup.
But why do we only work with quotient groups by normal subgroups? If we introduce the notion of left ... |
Update: There is an answer on same question I posted on Stack Overflow.
I'm working on a data structure for the graph cut algorithm. The problem is to make different cuts on the shortest paths. I made a data structure for which I'm not sure about properties.
The input is a directed graph of shortest paths, which is a b... |
We are talking about Non-uniform rational B-spline. We have some simple 3 dimensional array like
{1,1,1}
{1,2,3}
{1,3,3}
{2,4,5}
{2,5,6}
{4,4,4}
Which are points from a plane created by some B-spline
How to find control points of spline that created that plane? (I know its a hard task because of weights that need to ... |
I need to understend how black box optimizer work. I need a real life example of how it hlps. So what I need: What was the task, what were parameters, what was the function to minimize and how it all worked toogether. I need deteiled info on this topic, please - wiki does not give lot of help...
|
I'm developing a computer program, and need an algorithm to solve the following problem:
How to select the optimum combination of numbers from a random list that add to up to a certain total (or as close to as possible).
Example:
List of random numbers:
1.0,
2.1,
5.3
Required number = 6.5
Here the answer would be 6.3 (... |
I came across this problem in the context of spectroscopy today. Because of it's simplicity, I'm sure it's a question that's been posed by some mathematician ages ago, I just can't figure out how to formulate it mathematically:
Suppose you have a mirror that forms a perfect ring and has an aperture in it with width $\... |
You are allowed to roll a die up to six times. Anytime you stop, you get the dollar amount of the face value of your last roll.
Question: What is the best strategy?
According to my calculation, for the strategy 6,5,5,4,4, the expected value is $142/27\approx 5.26$, which I consider quite high. So this might be the best... |
We solve the pell equation using the continued fraction for square root of 2. What equations can we solve using the continued fraction of cube roots (and other numbers too)?
|
I have to prove Simpson's rule including the error with the help of the integral remainder. However, I have practically no idea how to start.
Let $f: [a,b] \rightarrow \mathbb{R}$ be continuously differentiable four times. Let $n \in 2\mathbb{N}$ and $h = (b-a)/n$. Let $y_k = f(a+kh)$ for $0 \leq k \leq n$. Show:
$$\le... |
Can a CFG over large alphabet describe a language, where each terminal appears even number of times?
If yes, would the Chomsky Normal Form be polynomial in |Σ| ?
EDIT: What about a language where each terminal appears 0 or 2 times?
EDIT: Solving this may give interesting extension to "Restricted read twice BDDs and c... |
Let $R$ be a ring, $A$ is an ideal of $R$, and assume that $A\subseteq J(R)$.
Let $r\longmapsto \overline{r}$ denote the coset map $R\rightarrow \overline{R}=R/A$. The following are equivalent:
(1) $A$ is lifting.
(2) If $\overline{R}=\overline{K_1}\oplus...\oplus \overline{K_n}$ where the $\overline{K_i}$ are left id... |
It is known that, for $n \geq 5$, it is possible to partition the integers $\{1, 2, \ldots, n\}$ into two disjoint subsets such that the product of the elements in one set equals the sum of the elements in the other. One solution is the following:
Let $N = \{1, 2, \ldots, n\}$.
If $n$ is even, take $P = \{1, \frac{n-... |
If i have a graph in this form (adjacency matrix):
0 0 1 0 0 0 1
0 0 0 1 0 1 0
1 0 0 1 0 0 0
0 1 1 0 0 0 0
0 0 0 0 0 1 1
0 1 0 0 1 0 0
1 0 0 0 1 0 0
This is a 2-regular graph with 7 vertices. What are examples of vertex invariants? Usually i would look at the degrees of each vertex, but they are all the same in this c... |
Consider the game described here, but for a sequence $X_1,\ldots,X_n$ of i.i.d. uniform rv's on $\lbrace 1,\ldots,n \rbrace$ (in the original game $n=6$). Using the original notation, let $a_n$ denote the first element in the best strategy $a_n,\ldots,a_2$. We saw that for $n=6$, $a_n = n$. Can you provide a heuristic ... |
A Laskerian ring is a ring in which every ideal has a primary decomposition. The Lasker-Noether theorem states that every commutative Noetherian ring is a Laskerian ring (as an easy consequence of the ascending chain condition).
And I've found the statement that there are non-Noetherian Laskerian rings, but I can't f... |
I am truly lost as to what this problem is asking. I did post this on another forum and received what my have been wonderful advice. However, even after multiple hours and many "Google" searches I am still confused. Please anyone....
The problem states:
If $\sigma$ is a permutation of a set $A$, we say that $\sigma$... |
I have a triangle ABC in the x-y coordinate plane.
Corners A and B lie on x-axis. Length of AB is known. Angles A and B are also known.
Question: Find (x,y) coordinates of corner C.
|
Question:
(a) Determine sign$(\tau)$ for $$\left( \begin{array}{ccccccc} 1&2&3&4&5&6&7 \\ 2&3&5&7&1&6&4 \end{array} \right )$$.
(b) Let $A_{n} = \{\tau \in S_{n} | \mbox{sign}(\tau) = 1\}$. Show that $A_{n}$ is a sub group of $S_{n}$ and calculate the number of elements (Tip: Show that for any transposition $\tau$, $S_... |
Can anyone give a nonlinear regular function from C^2 to C^2 with a constant nonzero Jacobian? It seems to me that the only such functions are linear.
According to the Jacobian conjecture, a function from C^2 to C^2 with a constant nonzero Jacobian must have an inverse.
|
Twin, cousin, and sexy primes are of the forms $(p,p+2)$, $(p,p+4)$, $(p,p+6)$ respectively, for $p$ a prime.
The Wikipedia article on cousin primes says that,
"It follows from the first Hardy–Littlewood conjecture that cousin primes have the same asymptotic density as twin primes," but the analogous article on sexy pr... |
I've just been thinking about for what values of n we can place n points in the plane so that any three of those points define an isosceles triangle. A triangle, square and pentagon work for 3,4 and 5, and to get 6 just place a point in the centre of the pentagon.
The question is can we do this for 7 points in the plan... |
I am in graduate school for chemical engineering and the method of characteristics appears in many journal articles. Does anyone have a good reference: either online or a book that provides a good explanation with examples of the method of characteristics.
|
Let $G$ be a $n \times n$ matrix with real entries and let $\Lambda = \{x^n \colon \exists i^n \in \mathbb{Z}^n \text{ such that } x^n = G \cdot i^n\}$ define a lattice. I am interested in projecting the lattice points onto a $k$-dimensional subspace $U$ with $k < n$. Let $A$ be a $n \times k$ matrix of vectors that sp... |
The problem is stated-
Do the following two sets of points have the same cardinality and if so, establish a bijection:
A line segment of length four and half of the circumference of radius one (including both endpoints).
My reasoning is they do have the same cardinality and my bijection is a picture in which I drew a h... |
Given a multi-undirected graph, how can I find the number of different paths from Node A to B using every node in the graph (means shortest path algorithms are useless)
In some cases there may be no way to achieve this. I am looking for the number of available different paths.
Note: You have to use every node and use t... |
Given $R$ is a ring, and $b$ is some positive integer such that $x + x^{2b + 1} = x^{2b} + x^{10b + 1}$ for all $x \in R$, prove that $R$ is Boolean, i.e. $x =x^2$ for all $x$ in $R$.
I am not sure where to begin with the problem, and what avenue of approach I should take such that my methodology is inclusive to all $... |
So, we have a function
$$f(x) = \frac{3\sin(x)}{2 + \cos(x)} $$
and we fix a point $$ x_0 \in \left(0, \frac{2\pi}{3}\right] $$ and define a sequence by setting $$ x_{n+1} = f(x_n) $$
Now I need to show that $$ \lim_{n\to\infty} n^{1/4}x_n = 45^{1/4}$$
I am pretty sure this has something to do with Cesàro means. In ... |
I'm trying to solve the following problem:
The probability $p_{i}$ that a given cell contains exactly i balls is given by the binomial distribution $p_{i}=\displaystyle \frac{\binom{r}{i}(n-1)^{r-i}}{n^{r}}$. Prove that the most probable number is the integer $v$ such that $\displaystyle \frac{(r-n+1)}{n}< v \leq \dis... |
Suppose that every open interval in $\mathbb{R}$ is a connected set. Does this implies the least upper bound axiom? (i.e every non-empty subset of $\mathbb{R}$ which is bounded above has a least upper bound) Is this true? in such case, how would you prove this?
|
I am a bit confused on how to go about this problem:
Let G be a finite group and $p$ the smallest prime dividing its order. Assume $P$ is a $p$-Sylow subgroup which is cyclic. Show $P$ is contained in the center of its normalizer.
|
Here's what I recall of the question from CNML Grade 11, 2010/2011 Contest #3, Question 7:
There are 2010 points on a circle,
evenly spaced. Ford Prefect will*
randomly choose three points on the
circle. He will* connect these points
to form a shape. What is the
probability that the resulting shape
will* f... |
I was talking with a friend and we were discussing a math problem disguised as a social situation:
If the chance that someone to accept your request to go out with them was 1% and you asked 1 person only, then the probability they would say yes is .01
If you were to ask 100 people, then your chances are still .01 accor... |
I have the following overdetermined linear equation system:
$$Ax=b$$
where $A$ is a matrix of $n \times k$, $x$ is of $k \times 1$,$b$ is of $n \times 1$, where $n>k$.
We all know this is an overdetermined linear equation system.
The question is how to check whether the solve for $x$, and check that the vector is cons... |
just a quick question dealing with probability. The annual returns on stocks and treasury bonds over the next 12 months are uncertain. Suppose that these returns can be described by normal distributions with stocks having a mean of 15% and a standard deviation of 20%, and bonds having a mean of 6% and a standard devia... |
I was asked to compute the Fourier series for $\sin^2(x)$ on $[0,\pi]$. Now this is what I did and I'd like to know if I'm right. $\sin^2(x)=\frac12-\frac12\cos(2x)$ . I got the right hand side using trig identities. I'm wondering If I can do this without using the formulas. Thanks.
|
I am using math as a tool and for entertainment, I am not a pro, I do not understand most of the posts here but I am glad such site exists.
Anyway, a friend asked me a question the other day, and I was able to redefine it in terms of a directed graph where all nodes in and out degree equal to 1. I know that If if each ... |
It is referred to in An invariant form for the prior probability in estimation problems (Jeffreys).
|
I was watching this TED talk, which suggested that on average your friends tend to individually have more friends than you do. To define this more formally, we are comparing the average number of friends with:
average over each person p of:
friend popularity, defined as:
average over each friend f of p:
... |
It's possible, that count of unique algebras (up to isomorphism) with one unary operation on set with $n$ elements is $2^n-1$?
For $n=1,2,3,4$ is this hypothesis true (I still have not verified it on the computer). Is there any counterexample, or idea for proof?
Thanks.
|
I was trying to expand $\displaystyle \left(1+x\right)^{y}$ as a power series in terms of $y$ using the Generalized Binomial Theorem,
$\displaystyle \left(1+x\right)^{y}=\sum_{k=0}^{\infty}\binom{y}{k}x^{k}$
Assume $x,y \in \mathbb{R}$ and $\left | x \right | < 1$. With this in mind I would get something like
$\disp... |
It is well known that any conformal mapping of the unit disk onto itself extends to the unit cirle.
However, is there an homeomorphism of the unit disk onto itself which does not extend to a continuous function on the closed unit disk?
If yes, can you give an explicit one?
Thank you,
Malik
|
Let $\Omega$ be a domain of the complex plane. The Hardy space $H^p(\Omega)$ is defined, for $1 \leq p<\infty$, as the class of functions $f$ that are holomorphic on $\Omega$ such that $|f|^p$ has a harmonic majorant on $\Omega$, i.e. there is a function $u$ harmonic on $\Omega$ such that
$$|f(z)|^p \leq u(z) $$
for a... |
Can this sum be simplified: $\sum \limits_{k=0}^{n} \binom{n}{k} 2^{\sqrt{k}}$
Or at least is there a simple fairly tight upperbound?
EDIT
So I think this sum is more easily bounded than I previously thought:
Clearly, $$\sum_{k=0}^{n} \binom{n}{k} 2^{\sqrt{k}} \cdot \leq 2^{\sqrt{n}} \sum_{k=0}^{n} \binom{n}{k} = 2^{n+... |
I know there are some encrypting algorithm that once the text (the message) is encrypted there is no way to decrypt it.
I can think one way of doing this: using as encryption key the current date at the encryption moment. But there is one problem wiht that: Each time you encrypt the same message the result will be diff... |
I am studing for exams and am stuck on this problem.
Suppose $f$ is an entire function s.t. $f(z) =f(z+1)$ and $|f(z)| < e^{|z|}$.
Show $f$ is constant.
I've deduced so far that:
a) $f$ is bounded on every horizontal strip
b) for every bounded horizontal strip of length greater than 1 a maximum modulus must occur... |
My motivation for asking this question is that a classmate of mine asked me some kind of question that made me think of this one. I can't recall his exact question because he is kind of messy (both when talking about math and when thinking about math).
I'm kind of stuck though. I feel like the set $A^{\mathbb{N}} = \{... |
It's pretty easy to construct an ($R$-$S$) bi-module $M$ and a left $S$-module $N$ such that neither $M_S$ nor $N$ is a projective $S$-module, but the tensor product $M_S \otimes N$ is a non-zero projective $R$-module.
However, taking $R=S= \mathbb{Z}$ defies my zoo of examples. Here projective=free is closed under di... |
this question may be shameful, but nevertheless I can't help myself.
Let $U \subset \mathbb R^n$ be arbitrary, in particular not the whole of the space itself. I wonder about the dual of the space $W^{1,p}(U)$, for $p < \infty$.
For $U = \mathbb R^n$, we have $(W^{1,p})' = (W^{1,p'})$ with $p' = \frac{p}{p-1}$. How abo... |
Prove that if $\kappa$ is an inaccessible cardinal, then $V_{\kappa}$ satisfies all the axioms of ZFC.
How is this done for the axiom of choice and for regularity?
|
I'm trying to understand this:
Working in $\mathbb{Z}_p[x]$, $(x-c)^p \equiv x-c \pmod{x^p-x}$.
From Fermat Little theorem we know that $(x-c)^p \equiv (x-c) \pmod{p}$ but I don't see a connection. Actually, I'm not sure if I'm mixing things up because $\mathbb{Z}_p[x]$ is a polynomial ring.
Also I tried to show it fr... |
Given four coordinates that define the corners of an irregular quadrilateral and a point defined by its coordinates, what is the simplest way to determine if the point is within or outside of the quadrilateral?
|
While I tagged this question homework, it's not really homework. I'm really studying for a test and don't understand how to do something. I have the answer to the question, so the important part is for my to understand how to get there.
X has distribution Gamma(2,4)
X = Y-3 Find: P(Y>11|Y>7) Which I know is equals to:
... |
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be strictly monotonically increasing.
(i) Is $f$ not continuous at $p \in \mathbb{R}$, there exists a non-empty, open interval $(a_p, b_p) \subset \mathbb{R}$ such that $f(x)\leq a_p$ for all $x < p$ and $f(x) \geq b_p$ for all $x > p$.
(ii) The set of discontinuity points $$ ... |
Is there a closed form expression for the number of terms in a monomial symmetric polynomial in a given number of variables for a particular partition of exponents, in terms of which/how many exponents are distinct?
I feel the answer should be straightforward, and it's probably just a contrived statement of a more elem... |
In Hatcher's "Algebraic Topology" in the Poincaré Duality section he introduces the subject by doing orientable surfaces. He shows that there is a dual cell structure to each cell structure and it's easy to see that the first structure gives the cellular chain complex, while the other gives the cellular cochain comple... |
Let $R$ be a ring and assume that for every left $R$-module ${}_RM$, if $M$ has a projective cover, then $M$ is projective.
Can someone help me prove that in that case, $J(R)=0$?
|
I have already taken up to Multivariable Calculus, Linear Algebra and Diff Eq.
I want to learn Calculus on Manifolds by myself, could you recommend a good introductory book on this subject?
Should I look at other things first, like topology, to get a better background?
|
Any hints about how to prove
$$!n = n!- \sum_{i=1}^{n} {{n} \choose {i}}\,!(n-i)$$
from
Wikipedia's article on derangements?
Here, $!n$ is the number of derangements of a set with $n$ elements.
I am not looking for proofs, just nudges in the right direction.
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I have a question about Hatcher's proof that the fundamental group of a circle is Z. Specifically, halfway through, ( http://www.math.cornell.edu/~hatcher/AT/ATch1.pdf , page 30), he proves an important a lemma stated rather generally:
Given a map $Y\times I\rightarrow S^1$ (Y is any space, and I is an interval), there... |
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Different methods to compute $\sum_{n=1}^\infty \frac{1}{n^2}$.
I just got the "New and Revised" edition of "Mathematics: The New Golden Age", by Keith Devlin. On p. 64 it says the sum is $\pi^2/6$, but that's way off. $\pi^2/6 \approx 1.64493406685$ whereas the sum in question is $\approx 1.2912... |
we are a group of three, and we've got this question in an assignment (the question is originally in French, so bear with me) :
Let $X_1 \dots X_4$ be a random sample drawn from a population of average $\mu$ and variance $\sigma^2$. We define the following estimators:
$$\hat{\mu}_1=\frac{X_1+2X_2-2X_3+5X_4}{6} \qquad ... |
This is from one of the exercises in "Concrete Mathematics", and is something I'm doing privately, not homework.
This is a variant on the classic towers of Hanoi, where all moves must be made clockwise only. The recursive solution is to consider $Q_n$ to be the number of moves to move a tower size $n$ one step across (... |
I am trying to work through Boothby's An Introduction to Differentiable Manifolds on my own and, embarassingly, have got stuck at the very first chapter. At the end of section 4, chapter 1 (called: Further examples of manifolds: cutting and pasting), there's this question:
Prove that adding a handle to a 2-manifolds ... |
Let's say I have a list of points( in 2D coordinates!) with the vertex $V$, how to find all the triangular faces $F$ ( which has three edges $E$) that covers all of the points? In other words, I'm looking for a mesh that connects all the points together with well behaved triangles.
The conditions are that the faces mus... |
How can I construct a CW complex A with $H_0(A) = \mathbb{Z}$, $H_2(A) = \mathbb{Z}/4\mathbb{Z}$, $H_4(A) =
\mathbb{Z}\oplus\mathbb{Z}$ and all other homology groups trivial?
Any idea?
Thanks!
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