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0answers
204 views

How do I solve this bearing/direction problem?

At 2:00 PM, a ship leaves port and travels N15degreesE at a rate of 20 mph. At 2:30 PM, another ship leaves the same port and travels S75degreesW at 30 mph. How far apart are the two ships at 4:30 PM? ...
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votes
0answers
22 views

Functions on $K(X)$ and DVR.

In our definition a variety is an integral and separated scheme $X$ and we denote with $K(X)$ the fild of rational functions on $X$. Let $X$ be a normal variety. Let $D$ be an integral codimension-one ...
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votes
0answers
15 views

Sum of transformations - consequences

Well, in matrix-vector transformation, I know that if we take the composition of a transformation, like: $T(x) = A\cdot x$ and $T$ maps from $R^n$ to $R^m$ $S(x) = B\cdot x$ and $S$ maps from $R^m$ ...
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0answers
58 views

Confused about biased coin probability

A biased coin with a probability of 0.4 showing head is tossed 4 times. a) What is the probability that the number of heads is odd? I believe the answer to a) is ...
0
votes
0answers
24 views

How to minimize the peak value of this matrix multiplication?

What range or value of $\theta$ will minimize the peak value of $Y $? $$ Y = \begin{bmatrix} 1+j & 2+j & 3+j & 4+j \\ -4-j & -3-j & ...
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votes
0answers
46 views

Need help with biased coin probability

A biased coin with a probability of 0.4 showing head is tossed 4 times. a) What is the probability that the number of heads is odd? I believe the answer to a) is ...
0
votes
0answers
32 views

Help with Optimization Problem

Can someone please help me with this optimization problem? I am clueless! :(
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votes
0answers
28 views

cardinality of finite subset

I have the following question: Prove that a set A has the same cardinality of a subset of a Set B, if and only if exists an injective function A to B. I find it hard to prove it because I can easily ...
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votes
0answers
60 views

Estimates for linear finite element nodal basis functions

Let $\Omega\subset\mathbb R^2$ be a domain with $\operatorname{diam} \Omega=H$ and $\mathcal T^h$ be shape-regular triangulation of $\Omega$ with triangular $\mathcal P^1$-elements. (That means we are ...
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votes
0answers
42 views

Cauchy problem in pde

I think that this question is related to chauchy problem in PDE. please explain the solution explicitly? And please which books I should study for such type questions? Especially, the book ...
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votes
0answers
29 views

Homogeneous differential equation of order n

Consider the following homogeneous differential equation of order n: $y^{n)}+a_1(t)y^{n-1)}+...+a_n(t)y=0$ I have to compare the differential equation that satisfies the Wronskian of n solutions of ...
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votes
0answers
42 views

$\mathcal{F}$ is sigma-field in $X$. Is $\mathcal{F}_B = \left\{ A \cap B : A \in \mathcal{F} \right\} $ sigma-field in $X$ and $B$?

Let $\mathcal{F}$ be sigma-field in $X$. Let take $B \in \mathcal{F}$ and let $\mathcal{F}_B = \left\{ A \cap B : A \in \mathcal{F} \right\} $. Questions: Is $\mathcal{F}_B$ sigma-field in $B$? Is ...
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votes
0answers
24 views

Classification of endomorphisms in infinite dimension

I'm interested in the following question : let $E$ be an infinite dimensional vector space and $u$ some endomorphism of $E$. We consider endomorphisms equivalent to $u$, that is, of the form $\alpha ...
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votes
0answers
28 views

Hirzebruch surface

Suppose we have a Hirzebruch surface $S$. Can the blow up of $S$ in a closed smooth point $x$ be obtained as a projective bundle $\mathbb{P}(\mathcal{E})$ for some locally free sheaf $\mathcal{E}$ on ...
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votes
0answers
47 views

Is there any groups $G$ with the property $(*_d)$?

Let $G$ be a finite group of even order has only one non-principal irreducible character $\chi$ of degree $d$, $d\in \mathbb{N}$, with the following property (we name it $(*_d)$): $(*_d)$: There ...
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votes
0answers
9 views

Traveling Salesmen Variation Crossing N points

Can anyone give me an elegant heuristic solution to a variation of the traveling salesman problem with a non-NP running time? For a set P of pairs of locations (X,Y), what is the shortest path that ...
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votes
0answers
50 views

Is this method correct for solving equation?

I have the following equation $z=1.093x^{0.002939}- 0.1887(x^{0.7637} )(y^{0.2306} )- 0.04425y^{0.9143}$ I want to find expression $x$ Is my method correct? I can add powers of same variables? $z+ ...
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votes
0answers
53 views

problem integrating a dirac comb

Let: $$h(t)=\frac{\sin(\pi t(2N+1))}{\sin(\pi t)}$$ $$I=\int_\frac{-1}{2}^\frac{1}{2} h(t) dt$$ when $N\rightarrow\infty$ , obviously (with a change of variable $v=\pi t(2N+1)$ ): ...
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votes
0answers
40 views

I have two Shell Method questions

and I cannot for the life of me get the answers I'm trying to find the volume and here is how I'm setting it up: the first one: $y = 7x - x^2$, y = 10, about x = 2 I'm using $10-(7x-x^2)$ as the ...
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votes
0answers
31 views

Correct usage of probability

I'm trying to understand how to compose statements involving probabilities in a correct way. Assume that lifetime (measured in hours) of a bulb is exponential random variable. Suppose that I ...
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votes
0answers
35 views

DFT Zero-padding : what prepending with zeros does?

I am studying Fourier transform and want to understand better some point regarding zero-padding in DFT. All known sources say that padding is done by appending the data with zeros. However, if I add ...
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votes
0answers
28 views

Discrete fourier transform of a polynomial whose degree is not a power of 2

I need to evaluate a polynomial of degree $n$ at the $n$ cube roots of unity. Simple evaluation would take $O(n^2)$ time. I know that polynomial evaluation can be done in $O(n\log n)$ time using FFT. ...
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votes
0answers
20 views

Goodness of fit test for a normal ditribution

In the example from the web site I was trying out this problem. in page 107 about Goodness of fit test for a normal distribution.Question is about analysis of fat content of hambergers. I ...
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votes
0answers
37 views

Question about $t$-distribution

The random variable $T$ has a $t$-distribution with $20$ degrees of freedom. Find the value of $t$ such that (a) $P(|T|>t)=0.98$ (b) $P(|T|>t)=0.05$ For part (b) am able to find ...
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votes
0answers
82 views

Relationship between cdf of binomial and beta distribution

I'm trying to show that $\int_p^1 \frac{n!}{(k-1)!(n-k)!}z^{k-1}(1-z)^{n-k}dz=\sum_{x=0}^{k-1} {n \choose x}p^x (1-p)^{n-x}$, for all k=1,2,3,...,n I recognize that the LHS is 1-F(p), where F is the ...
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votes
0answers
31 views

Markov inequality conditions

I'd like to show that $Z-E(Z|Z \leq z)\geq 0$ in order to apply Markov's inequality to $P[Z-E(Z|Z\leq z)>z-E(Z|Z\leq z)]$. Can this be shown given $Z\geq 0$ and $0<P(Z \leq z)< 1$?
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votes
0answers
42 views

Finding the splitting field of a function that is not trivial

I have a splitting field question, but I will try my best at attempting the problem to the best of my ability. Consider the function $f(x) = x^{10} + 1$. I want to find a primitive element of the ...
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votes
0answers
40 views

LCM of these polynomials

I'm having a hard time wrapping my head around how to get the lcm of these polynomials $$h(x+h+1), x+h+1, h(x+1)$$
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votes
0answers
28 views

Convergence in probability of excheangeable random variables

I would like to prove the following result: Let $X_1,X_2,\ldots$ be a sequence of i.i.d. random variables (non necessarily Gaussian) and let $Y_{n,k}=\log|X_k-\bar{X}_n|$ if $X_k\ne\bar{X}_n$ and 0 ...
0
votes
0answers
50 views

Show that we have an algebra homomrohpsim

I need to show that we have an algebra homomorphism $\phi: M_n(K)\otimes_KA \simeq M_n(A)$ Where A is a K-algebra and K is some field. I suspect it's really easy but I don't know what to do. Is ...
0
votes
0answers
28 views

Likelihood for Censored, Correlated Data

I am trying to come up with the likelihood for the following data-generating process: $$x_t=\begin{cases} y_t-\theta & \text{if }y_t>\bar{y}(\lambda_1,Y_t), \\ 0 & \text{if }y\le\bar ...
0
votes
0answers
35 views

When is a variety a graph?

How can I determine if a given variety is the graph of a map? For example, I know that the following variety is a 9-dimensional variety embedded in 12-dimensional a/b/c space, along with a rational ...
0
votes
0answers
50 views

GA (Genetic Algorithm) and stochastic simulation to solve optimization in R

My problem is to solve the following optimisation problem using GA (Genetic Algorithm)and stochastic simulation. The goal is to solve the maximisation problem : \begin{equation*} \begin{aligned} ...
0
votes
0answers
25 views

Confidence Interval, t distribution

Exam Question 40 measurements of the Boiling point of the newly developed Alloy gives 95% confidence interval $[923^\circ\mathrm C,933^\circ\mathrm C]$. you can assume that measurement error are ...
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votes
0answers
20 views

Properties of convergence in distribution?

If you have a random variable, W which converges in distribution to N, and another random variable X which converges in distribution to B: i) Will W multiplied by X converge in distribution to N ...
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votes
0answers
16 views

If $E_q=\{x\in[0,1]:\lvert x-pq^{-1}\rvert<q^{-3}\}$, why is then $m(E_q)\le q^{-2}$ ?, ($m$ is measure)

If $E_q=\{x\in[0,1]:\lvert x-pq^{-1}\rvert<q^{-3},\textit{for some $0\le p\le q$}\}$, why is then $m(E_q)\le q^{-2}$ ?, ($m$ is measure) Must it not be $m(E_q)\le 2q^{-2}$ ? Just YES or NO.
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votes
0answers
22 views

how to check slater condition for a constrained optimization problem?

Given any optimization problem that you suppose to solve with Lagrange by thrusting strong duality, you need to be sure the Slater Conditions. And I guess there is no algorithmic way to solve for all ...
0
votes
0answers
70 views

Infinitely many fractions $p/q$, s.t. $\lvert x-\frac{p}{q}\rvert\le\frac{1}{q^2}$.

If $x$ is irrational, there exist infinitely many fractions $p/q$ with relatively prime $p,q$ such that $\lvert x-\frac{p}{q}\rvert\le\frac{1}{q^2}$. $\textbf{!!!I know the proof!!!!}$. ...
0
votes
0answers
38 views

Taylor polynomial of $\sin(x)$

It is asked to construct the Taylor Polynomial $p_n$ (polynomial of order n) of the function $\sin (x)$, defined in $(-1,1)$ around 0. Also, I need to decide if $p_n$ uniformly converges to sine in ...
0
votes
0answers
26 views

Definition of Discontinuities and example

So definition of discontinuity of some function at some point goes like this: A function $f$ is not continious at point $a$, where $a$ is an element of $D(f)$, if there exists $x$, which is an element ...
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votes
0answers
36 views

Concentration Inequalities For Matrices? (Around Mean)

I need a result which talks about concentration of a 'random matrix' around its expected value. I need the following: $Pr(||X-E[X]|| \le \epsilon) \ge \hspace{2pt} ? \hspace{8pt}, X \in \mathbb{R}^{n ...
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votes
0answers
52 views

Basic question about simplifying a square root

I just wanted to know how to get from $\sqrt{12}$ to $2\sqrt{3}$ Because my buddy was teaching me math the other day and gave me a list with some basic exercises to do, one of which is to solve ...
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votes
0answers
32 views

Formula for residence time/turnover rate with unsteady state

I'm not sure this is the correct place to ask my question... but maybe someone could still help me. I'm looking for a way to calculate the residence time/turnover rate. I have the production and ...
0
votes
0answers
12 views

minimal fibrations and diagonals

In the Quillen model structure on simplicial sets, if $f:X\to Y$ is a minimal fibration, is the diagonal $\delta:X\to X\times_Y X$ a fibration? Is a fibration $f$ minimal if the diagonal $\delta$ a ...
0
votes
0answers
25 views

How find this $\beta$,such$(\beta,a_{1})=1,(\beta,a_{2})=2,(\beta,a_{3})=4$

Question: let $a_{1},a_{2},a_{3}$ is three dimensional European space $V$ is a set of standard orthogonal basis,and let $\beta\in V$,and such $$(\beta,a_{1})=1,(\beta,a_{2})=2,(\beta,a_{3})=4$$ Find ...
0
votes
0answers
250 views

How to linearize the product of two continuous variables in linear programming

I have a question when I deal with a linear programming model. The situation is that: I have some constraints in the model. All the constraints are linear, except some terms, which is the product of ...
0
votes
0answers
24 views

sorted list with components in ascending order

Sorry for poor translations, I'm German. I've got a homework to express following in first-order logic: "s is a list, which components are natural numbers in ascending order" Is the following ...
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votes
0answers
30 views

Determining the Kelvin transform

Find the Kelvin transform (relating to $S_1(0)$) of the harmonic function $u(x,y)=\exp(x)\cos(y)$. Here is how we defined the Kelvin transformation resp. the Kelvin transform: Consider ...
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votes
0answers
70 views

A matrix of size $n\times n$ with several properties like Markov matrices

Could you find a square matrix $A=[a_{ij}]$ of size $n$ such that satisfies to following properties 1) For all $1\le i\le n$, $\sum_{j=1}^n a_{ij}=0$ 2) For all $i$, $a_{ii}<0$ and for $1\le i\ne ...
0
votes
0answers
24 views

Undetermined Coefficients and Interpolatory Quadratures

For my homework I'm suppose to use the method of undetermined coefficients to derive an interpolatory quadrature formula of the form $$\int_0^{3h}f(x)dx \cong A_0f(0) + A_1f(h)+A_2f(3h)$$ To solve ...

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