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I'm stuck on this example in Boto v. Querenburgs "Mengentheoretische Topologie" and I would really appreciate some insight from our more topologically savvy friends on here. =)
Let $I$ be an ordered set, and let $(X_j, \mathcal T_j)_{j \in I}$ be a family of topological spaces, such that for $j<k$, $j,k \in I$ we have:... |
As I'm constantly running across higher categories these days, I'm wondering what is a good starting point to get into the theory?
While I am aware of nLab
and the n-Category Café, I am having a real hard time getting into the material provided. One reason for this is: afaik there is no generally favored way of definin... |
I'm taking a course on differential geometry, and up until now I'd always thought that the definition of a geodesic is (loosely speaking) a curve on a surface with the minimal length between its endpoints. My professor, taking his lead from do Carmo, however, defines it as any curve whose geodesic curvature $\kappa_g=0... |
I am building a photo challenge website. To get the winning ratio, I am using the following equation
ratio = number of win (number of win / number of lose) * 100
the problem is, I get the same winning ratio for the following photos
photo a: 1 win 1 lose
photo b: 2 win 2 lose
so now I changed my equation to
number of pl... |
Consider the following expression:
$x\cdot a\cdot b$
In programming you could define a function $f(x,a,b)$ to assign values to all the variables. However, since I cannot remember seeing such notation being used in purely mathematical context, I am somewhat unsure whether I can do this in my math paper.
Hence, I have tw... |
So I'm seeing a Dirichlet form written as
$$\mathscr{E}(f,f) = \frac{1}{2} \sum_{x,y} |f(x)-f(y)|^2 K(x,y)\pi(x)$$
where $K(x,y)$ is the probability of taking a step to state $y$ from $x$.
And the conventional way of writing it seems to be
$$\mathscr{E}(f) = \int \left|\triangledown f\right|^2 d\mu. $$
How come the two... |
Just started studying tensor products. Let $A$ be a commutative ring with unity and let $M$ be an $A$-module. Now let $k$ be a field, I know that a $k$-module is precisely a $k$-vector space.
My question is the following:
Why $k \otimes_{A} M$ is also a $k$-vector space? here $\otimes$ denotes the tensor product with r... |
As I understand it, the mean value theorem is where $${f}'(c)=\frac{f(b)-f(a)}{b-a}$$ if $f$ is continuous on the open interval (a, b) and differentiable on the closed interval [a,b].
A problem in the current homework set on WebAssign has me confused. Given $f(x)=x^{7}$ on the closed interval [0, 1], determine wheth... |
I've poked about in some other questions, and I'm no sure how to deal with my problem and my knowledge of statistics has atrophied. Particularly that I'm trying to choose a sample size for a population that I don't know the size of (potentially infinite, but it could be 10,000's or 100,000's or more). How do I choose a... |
MathWorld gives the root linear coefficient theorem as
The sum of the reciprocals of roots of an equation equals the negative coefficient of the linear term in the Maclaurin series.
The theorem appears to me to be false as stated. For example, the equation $e^x = 0$ has no roots, yet (taking the Maclaurin series of ... |
Let $f$ be an analytic function from $\{z; -1 < \Re(z) < 1, -1 < \Im(z) < 1\}$ to $\{z; |z| < 1\}$. If $f(0)=0$ and $f$ is one-one and onto, should $f(i\ z)=i\ f(z)$ for each $z$? I tried to show that $f(i\ z)-i\ f(z)$ is a constant, but it seems that I could not use Liouville Theorem.
Thank you very much.
|
A paper I'm reading claims that the smallest class of monoids which contains $\mathbb{Z}$ and is closed under finite direct product and block product only contains solvable monoids. I think that a proof that solvability of groups is closed under wreath product would be of great help to understand why this is true. Wo... |
I'm having a discussion with a co-worker over the number of permutations in a bin packing problems as follows.
There are two bins each of which can hold 6 cu ft. A package can be from 1 - 6 cu feet, there can be from 1 - 12 packages. How many permutations are possible?
It's been a great many years since either of us ... |
The Hermite-Gauss functions appear commonly in physics. These functions are formed from the product of a Hermite polynomial and a Gaussian:
$$ u_n(x) = \left(\frac{2}{\pi w_0^2}\right)^{1/4} \frac{1}{\sqrt{n! 2^n}} H_n\left(\frac{\sqrt{2}x}{w_0}\right)\exp\left\{-\left(\frac{x}{w_0}\right)^2\right\}$$
and are orthonor... |
Question: What can you conclude about a tempered distribution $G\ \in\ S'(R^n)$ that is concentrated in some k-dimensional manifold $M\ \subset\ R^n$ (for k < n)? More specifically, is there a result analogous to the following n=1 result?
$n=1$ result (hope I remember it correctly):
Let $\ S(R)\ $ be the set of Schwar... |
I'm programming a learning software. It works with question-/answercards. I´m searching for a algorithm that gives me a higher probability for cards that the user has answered wrong.
My actual idea (edit: Inverse transform sampling) is that each card has an integer which indicates how often the user has answerd the que... |
Any hint on how to prove the following please:
Let $K$ be a convex cone, and $K^*$ its dual cone. Prove that $K^{**}$ is the closure of $K$.
Thanks!
|
I've recently started learning Category theory- and I have a pondering- wondering if anyone can help.
Is it possible for two categories to satisfy two different set-axiom system. Namely- is it possible for two distinct categories $SetZFC$ and $SetZF\neg C$ to exists? One satisfying AC and the other negating it?
And fi... |
I have a rectangle and a circular sector in a Cartesian plane. What is the easiest way (algorithmically) to tell if they intersect?
Edit:
I'm looking to see if the areas intersect, not just the perimeters.
Also, the rectangle is guaranteed to be of the form $a \leq x \leq b$, $c \leq y < d$ i.e. it will not have any ... |
Repeating for the sake of TeX rendering:
Does the functional equation $f(1/r) = rf(r)$ have any nontrivial solutions besides $f(r) = 1/\sqrt{r}$?
|
$\langle u + v, w \rangle = \langle u, w \rangle + \langle v, w \rangle$ ; $u = (3, -2), v = (4, 5), w = (-1, 6)$
$\langle u, v \rangle = 4u_1v_1 + 5u_2v_2 $
When I tried to do this I got:
$\langle u + v, w \rangle = \langle(48, -50), (-1, 6)\rangle = -348$ (probably the wrong answer)
Looking at it, it appears that:
... |
Can someone explain this solution to me? The question was find E[W1 | X(t) = 2] where W1 is the time until the first event occurs and X(t) is a Poisson process. V1 represents the smallest of the uniform variables that are a part of this theorem. I understand the first line but I am unsure why they proceed to P(V1>s) an... |
If response is defined as $Res=\sum_{i=1}^{4} r_i x_i$ and $x=(x_1;x_2;x_3;x_4)$. $y$ is constant.
And
$$\frac{d}{dt} x = P(y) \cdot x + Q(y)$$
Then, how can we pick $r_i$'s such that the steady state Response is independent of $y$?
I have no idea how to even begin on this question. Note: $P$ and $Q$ are 4x4 and 4x... |
$X \sim \mathcal{N}(0,1)$, then to show that for $x > 0$,
$$
\mathbb{P}(X>x) \leq \frac{\exp(-x^2/2)}{x \sqrt{2 \pi}} \>.
$$
|
Eg: In a list of three items ("1", "2", "3") the user is asked which item is higher, 1 or 2. They select 1. They are then asked which is higher, 2 or 3. They select 3. The system then reasons: "1 is higher than 2. If 3 is lower than 2 it must logically be lower than 1 also." etc.
(So that you can sort a list of items ... |
Let $X(T)$ be a Poisson process. What is
$$
\mathbb{P}(X(t) - X(s) = 1 \mid X(t) = 4) \,?
$$
I split this up into $\mathbb{P}(X(s) = 3, X(t) - X(s) = 1)$ and found the answer. However, it did not work out to be the solution which is
$$
\frac{4(t-s) s^3}{t^4} \,.
$$
I am unsure why I am not able to match the sol... |
Aside from the power, gamma, exponential functions are there any other very fast growing functions in (semi-) regular use?
|
This is Exercise 5.4.5 in Introduction to Stochastic Modeling (4th edition) page 257:
Customers arrive at a certain facility according to a Poisson process of rate lambda. Suppose that it is known that five customers arrived in the first hour. Each customer spends a time in the store that is a random variable, exponen... |
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\/
_
With the numbers 1-10, use each number once so that any number is equal to the absolute value of the difference of the upper two numbers. any ideas?
|
I have a finite summation series of identical fractions e.g $ \frac{1}{3} + \frac{1}{3} + \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = \frac{5}{3}$. Now lets say I add one to the denominator for the first two values of the series. I now have $ \frac{1}{4} + \frac{1}{4} + \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = \frac{3}{... |
How can the eigenvector corresponding to zero eigenvalue be found out? I was trying with the following simple matrix in Matlab:
$$A=\left[\begin{array}{ccc}1 & -2 & 3 \\ 2 & -3 & 4 \\ 3 & -4 & 5 \end{array}\right] \; .$$
In matlab computations, the matrix seemed nearly singular with one of the eigenvalues very close ... |
Suppose that $f(x_1,\dots,x_n)$ is a polynomial in variables $x_1,\dots, x_n$. Does there always exist an injective homomorphism
$$\phi:\mathbb{Z}[x_1,\dots,x_n]/(f)\to\mathbb{Z}[y_1,\dots,y_m]$$
for some $m$?
If not, are there sufficient conditions one can put on $f$ to ensure that $\phi$ exists?
If $\phi$ exists, is... |
Let $X_1, X_2, ..., X_n$ be a random sample from a distribution with p.d.f.,
$$f(x;\theta)=\theta^2xe^{-x\theta} ; 0<x<\infty, \theta>0$$ Obtain minimum variance unbiased estimator of $\theta$ and examine whether it is attained?
MY WORK:
Using MLE i have found the estimator for $\theta=\frac{2}{\bar{x}}$
Or as $$X\sim ... |
Let $A$ be a commutative ring with $1$ and let $M,N$ be $A$-modules. Let $I$ be an ideal of $A$.
How do we show the following isomorphism?
$(M \otimes_{A} N)/(I \cdot (M \otimes_{A} N)) \cong M/(IM) \otimes_{A/I} N/(IN)$
What confuses me is how to pass from tensoring with respect $A$ to tensoring with respect $A/I$.
|
Let $f$ and $g$ be locally integrable, say on $R^n$ (for arbitrary open domains, just extend trivially). Suppose
$\forall \phi \in C_c^\infty : \int f \phi dx = \int g \phi dx$.
Let $K = supp(\phi)$. If $f,g \in L^2(K)$, we see by Hilbert space theory $f = g$ almost everywhere, as the $C_c^\infty(K)$ is dense in $L^2(K... |
I am missing some knowledge about torsion and torsion-free groups that I need to understand an example (let's say I have not seen these expression before). We have the exact sequence of abelian groups:
$$0 \to H_2(\mathbb{R} P^2) \to \mathbb{Z} \stackrel{2}{\to} H_1(\mathbb{R} P^1) \stackrel{i_*}{\to} H_1(\mathbb{R} P^... |
Everyone:
I am reading a paper that makes reference to this "natural surjection" between
Mg ; the mapping-lass group of the genus-g surface, and Sp(2g,Z), the group of
2gx2g -symplectic matrices over Z.
Does anyone know what this surjection is? . I know that the kernel is the
Torelli group ( and, of... |
Let $X$ be a set. Let $\mathrm{Over}(X)$ be the category of sets $A$ with a map $A\to X$; the morphisms are equivariant maps, that is, maps which make the obvious triangle commute.
A map of sets $f\colon X\to Y$ induces a functor $f_*\colon\mathrm{Over}(X)\to\mathrm{Over}(Y)$ by postcomposition. This shows that $\mathr... |
Is it possible to express $(1+x+x^2+\cdots+x^m)^n$ as a power series?
|
I want to know how to express $a$ in terms of $x$, $y$ and $z$ in the following system (i.e., I want to find the function $a(x,y,z)$). And how to investigate (and to play with the equations) to know whether a variable can expressed in terms of $x, y, z$ or not in similar situations?
$$\begin{cases}
x + 2y -z = 2\\
2x... |
I am looking for examples of a flat but not projective module, and of a projective but not free module.
|
in one physics problem, there is a cube. A computationally expensive function can be calculated inside the cube. But one needs to do the calculation faster and to know for a given point inside the cube, an approxmated value, which depends on the 8 vertices. For that I tried linear interpolation in 3D and it works more ... |
Definition: Let $X$ be a compact metric space and let $\mu$ be a Borel probability measure on $X$, then we say that the sequence $(x_n)$ of elements of $X$ is equidistributed with respect to $\mu$ if we have that for any $f \in C(X)$
$$\frac1n \sum_{m = 1}^n f(x_m) \to \int_X f(x) \, d\mu(x).$$
Now, I want to find ... |
The curvature equation for implicit functions, level sets is usually given in two forms: one is the divergence of the gradient of the unit normal:
$\kappa = \bigtriangledown \cdot \frac{\bigtriangledown \phi}{|\bigtriangledown \phi|}$
and the other is
$\kappa = \frac{\phi_{xx}\phi_y^2 - 2\phi_x\phi_y\phi_{xy} + \phi_{y... |
This is a problem in Frank Jones's Lebesgue integration on Euclidean space (p.57),
$$\mathbb{R}^n = N \cup \bigcup_{k=1}^\infty \overline{B}_k$$
where $\lambda(N)=0$, and the closed balls are disjoint.
could any one give some hints?
|
In answering this question we have used the following result.
Lemma If a measurable function $f \colon \mathbb{R}^n \to \mathbb{R}$ is such that, for every (compact) rectangle $R$,
$$\int_R f(x)\,dx=0,$$
then $f=0$ almost everywhere.
I'm pretty much sure this is true, both for recalling having read about it somewhere a... |
This question arises because of a problem I was doing (Bartle 3rd edition, section 9.4 problem 3). It was like this. Given $a_n$ a decreasing sequence of positive numbers and suppose that $$\sum_{n=0}^{\infty}{a_n \sin{(nx)}}$$ Converge uniformly (It doesn't specify the domain, so I guess is for every x). Prove that $n... |
I am thinking in a mathematical problem that probably is already formulated and even solved. It is about big integers and someting else.
Let n be an integer positive number.
For n := 1,000 we have written words to name it: “thousand” in English, “mil” in Spanish, “mille” in French, “Tausend” in German, and “sen” or “... |
Given:
$$ \Sigma = \{ a, b, c \}. $$
I am trying to give the inductive definitions of both the set of strings $\Sigma^*$ and $\Sigma^+$.
Thank you.
|
Least common multiple of $A$ and $B$ that is greater than $C$.
Is there any algorithm to find it without prime factorization?
|
I recently saw a conjecture that a modular form is a congruence modular form if and only if it has bounded denominators. I wonder if one direction or the other is already known to be true?
EDIT: For completeness, here is the answer I received at Math Overflow when I asked a while back.
https://mathoverflow.net/question... |
[EDITED] (Changed the question)
Hello, now I'm making tables to review it, but it's slow... Xor with product in Z/(2^n) are a ring?
I have a "linear" system like this (we know $a,b,c,d,e,f,g,h$, we want to know $x_1,x_2,x_3,x_4$):
$
\begin{array}{ccccccccl}
a\cdot x_1 & \oplus & b\cdot x_2 & \oplus & 0 & \oplus & 0 &... |
This problem has a picture to explain what I'm talking about:
I'm just a little confused how to set this up. I know that I need to differentiate to minimize the distance from A to B, but I get a little confused on how 4 mi/hour factors into the equation.
Any assistance on how to set this problem up would be greatly a... |
I'm curious about the following:
Given a countable index set $I$, is it ever true that $\Omega^n(\bigvee_I X)\simeq\bigvee_I\Omega^n X$? What would we have to assume about $X$ (if possible) to make it true?
My motivation (wishful thinking) is that this would allow the following computation: $\pi_n\bigvee_I X\cong\pi_1\... |
Let $F$ be a field, and let $K_1$, $K_2$ be two splitting fields over $F$ (Suppose they are contained in a larger field $K$). Is $K_1\cap K_2$ necessarily a splitting field over $F$?
The statement is true if $K_1$ and $K_2$ are finite extensions of $F$, however I'm not sure how to prove (or disprove) the statement in t... |
Find a basis $\alpha = \{ \vec\alpha_1, \vec\alpha_2, \vec\alpha_3 \}$ of $P_2(R)$, such that $[2 + 5x + 4x^2]_\alpha =\left(\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}\right)$
I have approached the problem the following way:
$$\begin{align*}
\vec v &= 2 + 5x + 4x^2\\
s &= \{1, x, x^2\}\\
[\vec v]_s &= \left(\begin{matr... |
Why there is no compact symplectic submanifold with dimension greater than 2 in $\mathbb{R}^{2n}$ ?
|
I am currently studying network flow algorithms and one of its application is supposed to be "Project Selection". A (more) complete description is given here, but the problem basically is this:
There is a graph $G$ with a number of projects $P$ as nodes. Projects have a revenue $p_i$ and a dependency from project $j$ o... |
I'm not sure that this will make a lot of sense, but I guess that I'm trying to decide which course of study or action to persue.
I have a system of equations that seems to be linear, if the complex numbers are treated as scalars.
In other words, I have a system of equations with complex coefficients. I'm wondering ho... |
I defined a function in Mathematica. It is a function of n, so f[n_]:=, but in the definition, I used a sum, $\sum_{k=0}^n$. So, the $k$ is just an index variable for the sum and no $k$ shows up in the final answer. As I was using this function I tried evaluating f[k-1] and got a weird answer, 0. I finally figured ... |
I was looking at the proof of Lemma 2.17 in Narkiewicz Elementary and Analytic Theory of Algebraic Numbers but don't understand a step.
Let $p$ be a rational prime, $a$ be an algebraic integer of degree $n$, $K = \mathbb{Q}(a)$, and $R_K$ be the ring of integers of $K$. Assume the minimal polynomial of $a$ is Eisenste... |
Does anyone know how to prove that $f(x)=e^x$ is Riemann integrable using right or left hand Riemann sums?
|
I'm not sure whether this question suits this website, however, I don't know where else I could ask it. It is no mathematical problem or something similar, still I hope it won't be closed.
A few weeks ago, our assistant professor in physics told us a story about Maxwell when we came to speak about Maxwell's equations. ... |
Suppose that $S$ is a well-ordered set; how can we prove that the following is a total order on the power set of $S$?
$$A\prec B\Longleftrightarrow \min(A\triangle B)\in A.$$
|
How does one convert a recurrence relation to a non-recursive function?
I am not sure about the substitution, recursion tree, and master method. Is there an easy way to do this?
|
Would you please explain the importance of Hecke operators on modular forms? I am studying modular forms mostly on my own and I have a pretty good understanding up to Hecke operators. So, I just wonder why we care about them.
|
A chemical solution contains $N$ molecules of type $\mathrm{A}$ and $M$ molecules of type $\mathrm{B}$. An irreversible reaction occurs between type $\mathrm{A}$ and type $\mathrm{B}$ molecules in which they bond to form a new compound $\mathrm{AB}$. Suppose that in any small time interval of length $h$, any particula... |
What is the average number of times it would it take to roll a fair $6$-sided die and get all numbers on the die? The order in which the numbers appear does not matter.
I had this questions explained to me by a professor (not math professor), but it was not clear in the explanation. We were given the answer $(1-(\fra... |
This is Exercise III.2.20 of Bourbaki's Set Theory.
(Von Neumann ordinals are actually called "pseudo-ordinals" by Bourbaki, but I simply call them ordinals here)
Let $X$ be a transitive set, and suppose that each $x\in X$ is an ordinal. Then $X$ is an ordinal (Hint: for each $x\in X$, $x\cup\{x\}$ is an ordinal conta... |
I am having difficulty (and my textbook is of no help!) figuring out when to treat a problem as a linear death process with death parameters $\mu n$h vs. a pure death process with death parameter $\mu$h. Is there anything we need to look out for in questions to signify which one to use? Thanks for the help!
|
Consider the product $b_1, b_2,..., b_{\phi(m)}$ where $\phi(m)$ is the number of coprimes that are less than or equal to $m$. When is this product congruent to $-1$ (mod $m$) and when is this congruent to $1$ (mod $m$)?
Let $b_1, b_2, \cdots, b_{\phi(m)}$ be the integers between $1$ and $m$ that are relatively prim... |
Using the limit comparison test how do I find the test the convergence of the sum of $$\frac{1+2^{(n+1)}}{1+3^{(n+1)}}?$$
|
Hi does anyone have any suggestions on how to solve this problem?
To construct a circuit a student needs, among others, 12 chips of a certain type.
The student knows that 4% of these chips are defective.
How many chips have to be provided so that, with a probability of not less than 0.9, the student has a sufficient n... |
I've come across another exact sequence, where (I guess) I need to deduce the result using some properties of torsion.
I am calculating the homology of the Klein bottle using attaching maps.
I start by defining $\Phi:I \times I \to K$ as the natural map and denote $\partial(I \times I)$ as the boundary, then let $f=\Ph... |
I've been looking a bit into differential geometry and have gotten stuck on a question:
Given a function $f,$ is there a way to find the explicit space curve which has $f$ as both it's curvature and torsion?
I've been able to find a formula for a plane curve with curvature $k(s),$ but extending to what seems to be th... |
I've seen many variations of this problem but I can't find a good, thorough explanation on how to solve it. I'm not just looking for a solution, but a step-by-step explanation on how to derive the solution.
So the problem at hand is:
You have m balls and n bins. Consider throwing each ball into a bin uniformly and at ... |
I am just double checking to see if my solutions are correct for these two questions. Assume that for both customers arrive at rate lambda. I am unsure about the second one so confirmation would be great. Thanks!
1) Amy is the first customer to arrive after 12 NOON and Frank is the second. What is the expected amount o... |
Can you help me find the following:
$$E [W_1 \mid X(3) = 1]$$
$W_1$ is the time that the first event occurs, and $X(3) = 1$ signifies that one event occured before time 3. The rate of this question is lambda.
Here is what I have done so far:
I know that $$P(W_1 \le s \mid X(3) = 1) = P(X(s) \ge 1 \mid X(3) = 1) = 1 - ... |
I did a bit of math at school and it seems like an easy one - what am I missing?
$$n\times m = \underbrace{n+n+\cdots +n}_{m\text{ times}}$$
$$\quad n\times 0 = \underbrace{0 + 0 + \cdots+ 0}_{n\text{ times}} = 0$$
(i.e add $0$ to $0$ as many times as you like, result is $0$)
So I thought an infinite number of $0$'s ca... |
Is there a set with cardinality greater than the natural numbers but less than the real numbers?
Is there a simple proof which shows this, if the answer is no?
|
I had this strange notion some time ago, and I recently wrote a blog post about it, as a mere curiosity. I don't really consider it a "serious" mathematical question; but out of interest, I wondered if someone on this site could shed some light on what principle might be underlying the idea.
Basically, I envisioned a "... |
I am breaking off a discussion with Mariano from here
I have a map $\mathbb{Z} \stackrel{\left(\begin{array}{c}2\\2\end{array}\right)}{\to} \mathbb{Z} \oplus \mathbb{Z} $
This is the map $(a) \mapsto (2a,2a)$. I thought that the image of this map was just $2 \mathbb{Z} \oplus 2\mathbb{Z}$. But to quote Mariano:
"the im... |
I need to crack a stream cipher with a repeating key.
The length of the key is definitely 16. Each key can be any of the characters numbered 32-126 in ASCII.
The algorithm goes like this:
Let's say you have a plain text:
"Welcome to Q&A for people studying math at any level and professionals in related fields."
Let's s... |
This question is from Dummit and Foote's Abstract Algebra, page 638, question 20. It gives a nice paragraph of hints that basically guides one through the problem, but I'm very stuck at a crucial junction. Any useful hint is much appreciated. I have detailed what I know and what I do not know, but if you just want the ... |
I understand that when we compute a DFT, there are $N$ data points and the indices $n$ and $m$ go from zero to $N-1$ where $y_m$ are the data points in the time domain, and $Y_n$ are the amplitudes in the frequency domain.
My first question is more straightforward. Why do the indices count from zero rather than from on... |
Let's say I have a piecewise function that's continuous in an interval [1,7]:
$f(x) = \left\{
\begin{array}{lr}
-5x + 6 & : x \in [1,2)\\
-4x + 14 & : x \in [2,3)\\
-0.25x + 2.75 & : x \in [3,7]
\end{array}
\right.$
How would I get a discretization of that function that consists of 1... |
$T = \{t_1,t_2,\dots,t_n\} $. while $t_1,\dots,t_n \in \mathbb N$ with $t_i < t_j$ for $i < j$.
For each $t_1,\dots,t_n$, there is another value - Price. for example, for $t_1$, the price is 200.
Let $M$ be a natural number.
I have to find an Iterative algorithm which fullfil: $t_{j+1}-t_j\leq M$ for each j, and the su... |
Greetings All
I have a signal labeled 1) and I have another triangle signal labeled 2) that I would like to have it molded to (I don't want to filter the signal just mold it to fit within the triangle shape). Does anyone know the best way to do this? Do I just multiply / add the signals together?
image of signal link ... |
I am beginning math student and encountered following task which I do not know how to solve:
There is chessboard, ie 8x8 tiles. In the top left corner there is pawn. He cannot go diagonally and he can only move down and right.
1)How many steps will he need to reach the right bottom corner shortest way?
2)How many of th... |
In what ratio is the line joining
$(4,5)$ and $(1,2)$ is divided by the
y-axis?
The solution given in my module assumed the ratio to be $K:1$,this might be very trivial but I can't convinced myself why the consequent is assumed to be $1$?
|
Can you give me an example of a sequence of subspaces of $\ [0,2{\pi}] $ that the legth of them tends to $\ 0 $ but for every $\ x \in [0,2{\pi}]$ there are infinitely many of them such as x lives in them but also infinitely many of them such that x doesn't live in them?
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A little change in that problem:
Logic question: Ant walking a cube
There is a cube and an ant is performing a random walk on the edges where it can select any of the 3 adjoining vertices with equal probability. What is the expected number of steps it needs till it reaches the diagonally opposite vertex?
Taking the cub... |
The difference between transient and steady state probabilities is only that, transient probabilities are time dependent and steady state probabilities are not?
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I was given a Excel spreadsheet with this table:
The user wants to find the lowest price mix amongst the various suppliers. The user wants to constrain the number of products that each supplier gets using this table:
Is there a tool (Excel addin) or technique (algorithm) that would help me in trying to solve this pro... |
Let $V=M^{C}_{n \times n}$ with the standard inner product.
Suppose $T_{P}$ is a linear transformation from $V$ to $V$ such as: $\forall X \in V,\ T_{P}X=P^{-1}XP$ for some invertible matrix $P$.
Show that the following holds: $(T_{P})^{*}=T_{P^{*}}$ (that is, the conjugate transpose of T equals to T with P conjugate ... |
(I have seen this question but it is too complicated for my needs, and my math skills are not good enough to convert the answer.)
I am writing a game and I need a way to increase the armor of the character in a meaningful way: I want the increase in armor to mean a decrease in damage taken (meaning an increase in damag... |
Is this true that for all positive integer $n$?
There is no primitive $2^n$ centralizer group.
We know that, there exist $n$-centralizer groups for $n\neq 2, 3$, and there exists a primitive $n$-centralizer group for all odd $n\neq 3$.
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I am trying to find Minimal Polynomial of $i + \sqrt{2}$ in $\mathbb{Q}$. I was able to determine the minimal polynomial is fourth degree with roots at $i-\sqrt{2}$, $i+\sqrt{2}$,$-i-\sqrt{2}$,$-i+\sqrt{2}$. However I got this answer by guessing at what the roots should be. Is there a general technique for this ... |
Let $a\geq2$, $b\geq2$ be two prime numbers and k be a natural number with $k\leq min(a,b)$.
How can one show that $z := \binom{a+b}{k} - \binom{a}{k} - \binom{b}{k}$ is divisible by the product $ab$?
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I'm learning about the math invovled in PCA. For my purposes here, I'm just trying to understand a 90° rotation matrix. I get the concept of a rotation matrix, but when I look on wikipedia, the Wolfram Mathworld site, etc. I keep seeing the following defined as a 90° counter-clockwise rotation matrix:
|0 -1|
|1 0|
... |
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