0
votes
0answers
3 views

Please give me an example $d:C[\mathbb{R}]\times‎ C[\mathbb{R}]\longrightarrow\mathbb{R}$ Such that:

I need an example $d$ such that: $$d:C[\mathbb{R}]\times‎ C[\mathbb{R}]\longrightarrow\mathbb{R}$$ $$C[\mathbb{R}]=\lbrace f:\mathbb{R}\longrightarrow\mathbb{R}\ | \ f ‎‎\textit{Is differentiable on ...
0
votes
0answers
15 views

Geometry: Math behind “vanishing points”?

There is a problem in my geometry book which tells me to follow certain steps to find the dimensions of the back of a house. I know how to follow the steps but I can't comprehend HOW the two ...
0
votes
1answer
10 views

Summation Theorem how to get formula for exponent greater than 3

im studying in the summer for calculus 2 in the fall and im reading about summation it gives these following formulas for Summation $$ \sum_{i=1}^n 1 = n$$ $$\sum_{i=1}^n i = \frac{n(n+1)}{2}$$ ...
0
votes
1answer
13 views

Choosing randomly integers from $1$ to $10$

From Question 5 the practice book of the GRE math subject test: Sofia and Tess will each randomly choose one of the $10$ integers from $1$ to $10$. What is the probability that neither integer ...
0
votes
1answer
11 views

How can one calculate the limit of $\frac{1}{x^2-9}$ as x approaches -3 and 3 by hand?

Reviewing math for college after a gap year and so I know this is probably a pretty elementary question, but let me know if it has any interesting implications or alternative solutions or if it ...
0
votes
0answers
12 views

Set theory formula

I picked up a copy of Jech's Set Theory at my school library and I'm reading through it and taking notes. Right at the beginning, though, he mentions something called a 'formula'. Here's the quote: ...
0
votes
1answer
6 views

Is there a general relationship between number of variables and of constraints?

This comes up most notably in linear algebra and differential equations - usually unique solutions come about when the number of constraints matches the number of variables, or in the case of ...
0
votes
0answers
11 views

How do we deal with units when using the modulo operation?

I'm wondering how I should deal with units when I do a modulo operation. What is considered legal and what is not. When I have two numbers that have units such as 13cm and 3cm, I can multiply them: ...
0
votes
1answer
13 views

Finding the first three terms of a geometric sequence, without the first term or common ratio.

Given a geometric sequence where the 5th term = 162 and the 8th term = -4374, determine the first three terms of the sequence. I am unclear how to do this without being given the first term or the ...
0
votes
0answers
7 views

How to solve complicated systems of equations with exponentials?

I'm trying to solve the system of equations at the bottom of this image, http://i.stack.imgur.com/UAITx.png I need to solve for Rohm, Rdf, Rct, Cdl, Cdf, and Voc in terms of the theta parameters so ...
0
votes
1answer
20 views

Why does the method of undetermined coefficients fails for exponential functions for in homogenous ODEs?

(By the "by the above method" it means the method of letting $y=ke^{rx}$ where $f(x)=e^{rx}$ in differential equations of the form: ) Now, I tried to confirm that the method fails when $r$ equals ...
0
votes
0answers
5 views

optimizing over a set of symmetric matrices

I need to minimize an objective function, $f\left(\Lambda\right)$ over a set of symmetric matrices, $S_{p}$ of dimension p, such that all the eigenvalues of $\Lambda \in \left[0,1\right]$. I can set ...
1
vote
2answers
52 views

$f\cdot g=0 \implies f=0 $ or $g=0$.

I know this is kind of an obvious thing to say: Let $f,g \in \Bbb K[x]$, then $$f\cdot g=0 \implies f=0 \text{ or } g=0$$ But to my surprise I couldn't prove it. What's a simple way to do this?
0
votes
0answers
12 views

Within what angle does she need to throw her stone at to hit her opponents?

In curling, it is often necessary to hit and displace an opponent’s stone to win the end. Olivia would like to hit her opponent’s stone with her own stone. If she releases her stone at the hog line, ...
3
votes
1answer
12 views

Question on complete spaces, longer, more specific question.

Let $S \subset C^2[0,1]$ (set of two times differentiable functions $f(x)$ on $[0,1]$) which satisfy the following: $$\int_0^1 f(x)\,dx\leq3$$ Question is $(S,d)$ is a complete metric space, ...
0
votes
0answers
13 views

Singularities of an integral

We have the integral : $$I(t)=-i\int_0^\infty \frac{\log\left[\frac{\sin(t\log\sqrt{1+ix})}{\log(1+ix)} \right ]-\log\left[\frac{\sin(t\log\sqrt{1-ix})}{\log(1-ix)} \right ]}{e^{2\pi x}-1} \, dx$$ I ...
1
vote
0answers
5 views

What is the difference between Lower bound and upper bound in an Interval Graph $G(I)$

As I know that the maximal size of an independent set $IS$ of an interval Graph $G$ is a lower bound. Now what is exactly the upper bound, and when they might be equivalent to each other. are there ...
0
votes
0answers
2 views

How to interpret Realized Volatility and TSRV using R

I am looking at some high frequency data and I would like to know how to interpret and compare Realized volatility (RV) and Two Scale Realized Volatility (TSRV). References below. Given X is the log ...
-2
votes
1answer
14 views

How to get the equation for a one-to-one function given the coordinates.

The one-to-one function is defined as: f(x)={(-8,4)(-6,1)(3,-6)(8,-2)}
0
votes
0answers
14 views

Tricky word problem

Two crews were assigned the job of setting a total of $960$ conduit hangers. By the time the job was completed, one crew had set on $7/8$ as many conduit hangers as the other crew. How many conduit ...
0
votes
1answer
15 views

Directional derivative for differentiable function

In the directional derivative formula $$\frac{\partial f}{\partial v} = \nabla f \cdot v$$ why must $v$ be a unit vector?
0
votes
1answer
14 views

Closed form of a set

Let $V$ be a vector space with $W_1, W_2$ subspaces of $V$. Also, we have the set $\{e_1, e_2, e_3\}$ of linearly independent vectors such that: $$W_1 = \langle e_1, e_2, e_3 \rangle$$ and $$W_2 = ...
0
votes
2answers
22 views

Permutation of Indistinguishable Objects

How many number of two digit numbers can be formed using $\{4,5,6,6\}$ without repetition? I know that $\{45,46,54,56,65,64,66\}$ are the possible answers, but I am wondering if there is any formula ...
0
votes
1answer
13 views

How to find the eigenvalues of this matrix?

Regarding this quadric: $x_1^2+5x_2^2+9x_3^2+4x_1x_2+2x_1x_3+10x_2x_3-2x_3-2=0$ I am asked to rotate, translate and then classify the geometric object. First, I want to remove the mixed terms of ...
0
votes
2answers
26 views

Multinomial Coefficients Definition in expansion of $(1+x+x^2+\cdots+x^l)^n$

The literature defines multinomial coefficients (or extended bnomial coefficients) as $$ \binom{n}{r_1,r_2,\cdots,r_l} = \frac{n!}{r_1!r_2!\cdots r_l!}$$ where $$ r_1+r_2+\cdots+r_l = n$$ Which is ...
0
votes
0answers
12 views

Proof Matrix L with respect to Basis B and C

Good one guys! I'm doing the conceptual exercises of my Linear Algebra book, and I ran up to the following exercise: I tried to use the following theorem: That came from: But it got messy ...
1
vote
0answers
10 views

Can we view the connected component of the Picard scheme $\text{Pic}_0(X)$ as a “kernel” of the first Chern class?

So on a curve, $\text{Pic}_0(X)$ is just the Jacobian variety, and just correspond to degree $0$ divisors. One way to extend the notion of divisors corresponding to a vector bundle is taking the first ...
1
vote
2answers
24 views

Prove that the normed spaces $(C[0,1], \| \cdot\|_2)$ and $(C[a,b], \|\cdot \|_2)$ where $\| \cdot\|_2$ is the Euclidean norm are isometric.

Essentially I'm looking for a bijection $f: C[0,1]\to C[a,b]$ such that$$\|f(x) \|_2=\| x\|_2$$ I don't know how to go about finding this function, but I do know that it is possible. $$\| x \|_2 = ...
0
votes
0answers
20 views

conditional expectation

I got somewhat confused about this condition expectation here. Can anyone help me please?$$$$ Let $v_1,v_2,v_3$ be 3 continuous random variables from an i.i.d distribution, does the equality below ...
1
vote
1answer
25 views

show that the function $\{x_n\}\mapsto \sum_{n=1}^\infty 2^{-n}x_n$ is continuous

This problem comes from an old Preliminary exam: Consider the space $[0,1]\times [0,1]\times \cdots$ (the countably infinite product of $[0,1]$ with the product topology) An element of $X$ may be ...
0
votes
1answer
14 views

Geometric meaning of directional derivative

Suppose $f(x,y)$ is a differentiable function and $v = (a, b)$ is a vector. If $(x_0,y_0) \in D_f$ and $\frac{\partial f}{\partial v}(x_0,y_0) = 0$. What is the meaning of this? Along the direction ...
1
vote
2answers
16 views

Poisson Distribution Word Problem

The image you are looking is a solution to a problem that has been cropped out. I'm certain the solution is incorrect since it does not include P(X=2). Just to be on the overly safe side, I decided ...
0
votes
0answers
11 views

Implicit function theorem conclusion notation?

I am working through implicit function theorem for the first time, and I have the following understanding. Given a system of $n$ equations, \begin{equation} f_i(x_1,\dots ,x_m,y_1,\dots , y_n)=0,\ \ \ ...
2
votes
1answer
24 views

Frazzle game question

In $7^{th}$ grade, in order to learn divisibility, memory, and focus, my math teacher had my pre-algebra class play a game called Frazzle. To play the game Frazzle, each person went around the room ...
0
votes
1answer
19 views

Tensor Products of bimodules over commutative rings

Suppose that $ R $ and $ S $ are commutative rings with identity, $ R \subset S $, $ 1 _{R} = 1_{S} $, $ M $ is a $ (S,R)$-bimodule, $ N $ is a $ (R, S)$-bimodule, $ T = M ...
-3
votes
3answers
33 views

my problem is about probability [on hold]

8 people have to go to hospital during a particular week.what is probability that on atleast one days,atleast two people will go to hospital?
1
vote
0answers
8 views

Partial derivative of polinomial root

I have a characteristic equation of the form $P(x,y,z) = 0$. $P$ is a polynomial in $x$ with degree of 3 and is a first order polynomial in $z$. I computed the value of $x=F(z)$, such that ...
1
vote
1answer
9 views

Understanding Hyperbolic Householder Transformations

Note 1: This post is a continuation of a previous post on Householder transformations. I'm using this post to document my understanding. Please provide your valuable comments. Note 2: All vectors in ...
0
votes
0answers
37 views

Better approximation for prime numbers

The prime number theorem gives this formula for approximating the number of primes up to $n$: $\frac{n}{\ln(n)}$. By looking at this image from Wikipedia, I noticed that the function giving ratio ...
0
votes
1answer
30 views

Show that a group with 21 elements contains at max 3 subgroups with 7 elements

I don't know if lagrange's theorem apply here anyway. I just know that this group can have a subgroup with 3 elements, but I don't know about any theorem that talks about number of elements of the ...
0
votes
1answer
34 views

Using The Riemann Zeta Functional Equation

Riemann was able to establish the following link between the Riemann zeta function and the weighted prime counting function $J(x)$. $$ln(\zeta(s))=s\int_1^\infty J(x)x^{-s-1}dx$$ Using the Mellin ...
-4
votes
0answers
19 views

Adjoint Proof Question

How do I go about proving $adj(A^n)=(adj(A))^n$
0
votes
1answer
18 views

How do I solve for A in the matrix equation $A - B(A./C) = D$?

I've got $A - B(A./C) = D$, and I want to solve for $A$.* $A$ is an unknown 2x1 vector, $B$ is a 2x2 matrix, $C$ is a 2x1 vector, and $D$ is a 2x1 vector. *The notation $A./C$ means each element of ...
0
votes
0answers
30 views

Is this $\sum_{k=1,\theta \in \mathbb{R}}^{k=n}\frac{cosk\theta}{k} $ alternating series for all values of $\theta$?

I have tried to do other form of alternating series I got this: $$\sum_{k=1,\theta \in \mathbb{R}}^{k=n}\frac{cos k\theta}{k} $$ Can I say that the above series is alternating series for all ...
0
votes
0answers
6 views

Underlying utility function behind a linear two-product demand curve

I am trying to find the underlying utility function behind a linear two-product demand model. For that, I use two methods considering the following utility function: \begin{equation} U(q_1,q_2) = ...
0
votes
0answers
18 views

verifying Green's Theorem between 2 Circles

I get the same answer as my textbook only with a negative sign , so I am wondering who is right ...: Verify Green's theorem in the plane for {line integral of} x^2ydx + (y^3- xy^2)dy , where C is the ...
0
votes
0answers
10 views

Is there a name for this type of online optimization problem?

I have a sequence of items $1\leq i \leq n$ that arrive to me one at a time. Each item has a weight $w_j\geq 0$. If I pick up one item, I will not be allowed to pick up any of the next $k$ items ...
0
votes
2answers
32 views

Learning if the possible roots of an equation are different without resolving it

Is there anyway to know if a given equation will have different roots (all of them different to each other). Say: $x^3 - 17x^2 + 5x - \pi = 0$ Is there any property or theorem to know this for ANY ...
1
vote
1answer
10 views

Positive convergent sequence. Existence of another positive convergent sequence with same limit and larger elements

I have a positive sequence which converges to zero, i.e. $a_k \geq 0 \;, \forall k \in \mathbb{N}$ and $\lim_{k\rightarrow \infty} a_k = 0$. Does there exist another sequence $b_k$ with the property ...
0
votes
0answers
48 views

Set Theory (Real Numbers)

I have seen in a book that a number whose square is nonnegative is called real number. How can we explain what a real number is?

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