0
votes
0answers
8 views

Is that possible that a inscribe angle can be greater than 90 degree

I have found a question like following: Its asked that what could be the angle x if BC is not diameter of the circle. So, my question is if it possible to be greater then 90 for an angle like x?
1
vote
0answers
6 views

doubt regarding power of graph

could you help me in clarifying a doubt regarding how to find square of a graph g from graph g.the doubt occurs on 15th page of the document which I have shown you by the link given.the doubt is that ...
0
votes
0answers
1 views

Solving for derivative of Frobenius norm

I am trying to solve the following objective: $\arg \min_{A,C} \|AB\|^2_F + \lambda\|C\|_1$ $\text{s.t. } D = AB + C$ where: $D,A,C \in \mathbb{R}^{d \times n}$ and $B\in \mathbb{R}^{n \times n}$ ...
1
vote
1answer
7 views

Proving that a propositional theory of any cardinality has an independent set of axioms

This is exercise 1.2.19 from Chang & Keisler's Model Theory, which has been giving me a headache for some time now. Let $\mathscr{S}$ be a given propositional language of any cardinality (i.e. ...
0
votes
0answers
11 views

Proof Verification: Putnam 1996 A4

PROBLEM: Suppose we have a necklace of $n$ beads. Each bead is labelled with an integer and the sum of all these labels is $n-1$. Prove that we can cut the necklace to form a string whose consecutive ...
0
votes
0answers
6 views

Allyson replaced 100

Allyson replaced 100 watts Fixture with 15 watts Fixture she estimated that will Fixture burn 2000 h year and that annual savings will be $20.40 what is the cost of her electrical per kilowatt
-3
votes
0answers
8 views

topology problem read

Not a topology since if we consider ({x_n}_{n=1}^{\infty}) where (x_n = 1- \frac{\sqrt{2}}{2n}). Clearly, (x_n \in \mathbb{R}^+ \backslash \mathbb{Q}), (\forall n \in \mathbb{N}). Let (A_n = ...
0
votes
0answers
10 views

find the side of an equilateral triangle given only the distance of an arbitrary point to its vertices

anybody can help me about this? your help will be highly appreciated triangle ABC is an equilateral triangle and theres a point inside of it ( an arbitrary point perhaps). let P, be that point....... ...
0
votes
1answer
13 views

How many boys, girls, men and women are there?

In a village, there are exactly $10$% more boys than girls; $15$% more women than men; $20$% more children than adults. The population is less than $6000$. Solution: $b = g + 0.1g$--------(i), ...
0
votes
0answers
5 views

Ellipse representation when Directrix and focus given

Ellipse has a focus (0;1), a directrix x+y=0 and an eccentricity of 1/2. Find its equation and also draw it.
1
vote
0answers
20 views

How to find intelligently counterexamples for (dis)proofs about matrices?

Let's say I'm asked to give a counterexample for a claim about matrices, such as The elementwise product of two positive semi-definite matrices is positive semi-definite. It's easy enough to do ...
0
votes
0answers
4 views

Polynomial Multiplication through Toom-Cook into Karatsubas

I'm trying to solve a polynomial multiplication problem recursively through using Toom-Cook (Toom-3) once and Karatsuba (Toom-2) five times, although I'm stuck after the first round of Karatsubas. ...
1
vote
1answer
16 views

How find the minimum $\frac{(5y+2)(2z+5)(x+3y)(3x+z)}{xyz}$,if $x,y,z>0$

let $x,y,z>0$, find the minimum of the value $$\dfrac{(5y+2)(2z+5)(x+3y)(3x+z)}{xyz}$$ I think we can use AM-GM inequality to find it. $$5y+2=y+y+y+y+y+1+1\ge 7\sqrt[7]{y^5}$$ ...
-5
votes
2answers
19 views

Linear Transformation $T-T^2=I$

Let T be a linear transformation from a vector space V over reals into V such that $T-T^2=I$. Show that T is invertible Solution: I started by multiplying T on both sides and getting $-T^3=I$
1
vote
1answer
13 views

Longitude and latitude problem

I find this question challenging. I am trying to solve this question for my younger brother. So here it goes: An airplane leaves an airport $X$, 20.6$^0E$ and 36.8$^0N$, and flies due south along the ...
0
votes
1answer
17 views

Question about proof of Cauchy-Schwarz inequality.

I was trying to prove the Cauchy-Schwarz inequality, and came up with the following: $$ |u||v|\cos{\theta} \leq \frac{1}{2}|u|^2 + \frac{1}{2}|v|^2 $$ I got stuck here, did some googling and found a ...
0
votes
0answers
10 views

Maximal $R$-sequences in ideals

If $\alpha_1,...\alpha_s$ is a maximal $R$-sequence in an ideal $I$ ($R$ is commutative with unity), is this always true that $I⊆P$, where $P\in Ass (\alpha_1,...\alpha_s)$? In case $R$ is ...
0
votes
0answers
24 views

convergence of a sequence of cauchy

I would like to ask something about the convergence of a Cauchy sequence in a space $X$ metric. There will be a metric space $X$ such that If $(x_n)$ cauchy sequence in $X$ then $(x_n)$ is not ...
0
votes
0answers
7 views

Characterization of $H^{-1}(U)$

I am trying to understand the proof of characterization of $H^{-1}(U)$ as in Evan's Partial Differential equations. My questions is different to that of this link. In the theorem regarding the same, ...
1
vote
0answers
15 views

Jensen's Formula and the measure of $\{\theta \in [0, 2\pi]: f(e^{i\theta}) = 0\}$

Let $\mathbb{D} = \{z \in \mathbb{C}: |z| < 1\}$. Suppose $f$ is continuous on $\overline{\mathbb{D}}$ and analytic on $\mathbb{D}$ with $f(0) \neq 0$. Then if $r$ is such that $0 < r < 1$ ...
2
votes
1answer
37 views

Quadratic Prime

We had received some questions on Quadratic equations, But I wasnt able to do one. Here it goes: Let $a,b$ be natural numbers $a>1$. Also, $p$ is a prime number. If $ax^2+bx+c=p$ for 2 distinct ...
-1
votes
0answers
11 views

interpolation of the function

Suppose u is any function that interpolates f at x_{0},x_{1},\ldots,x_{n-1} and v is a function that interpolates f at x_{1},x_{2},\ldots,x_{n}. Consider the function ...
0
votes
0answers
7 views

Line bundle on projective bundle

Suppose $X$ is a locally Noetherian scheme, $\pi: X\times \mathbb{P}^n\rightarrow X$ is the projection, and $\mathscr{L}$ is a line bundle on $X\times \mathbb{P}^{n}$ such that $\mathscr{L}$ ...
2
votes
1answer
45 views

Question about left and right derivative.

Let $f(x):\mathbb{R}\rightarrow\mathbb{R}$ be a function such that $\forall x\in\mathbb{R}$ there exist: $$f'_+(x)=\lim_{\delta\rightarrow 0^+}\frac{f(x+\delta)-f(x)}{\delta}$$ ...
1
vote
5answers
30 views

How to show if $a$$\leq$$b_1$, for every $b_1>b$, then $a$$\leq$$b$ where a,b$\epsilon$R?

Not positive on the proper approach to this problem. My first thought: $a $ $\leq$ $b_1$ means either $a=b_1$ or $a<b_1$. Should it broken up into cases? Second attempt: Assume, to the ...
0
votes
2answers
11 views

Simplifying algebric terms

I would like to clarify - when the equation was simplified by dividing both side by 61. why wasnt this equation instead a = 10/61 * b/61 + 230/61 61a = 10b + 230 a = 10/61b + 230
0
votes
0answers
9 views

A basic doubt on ergodic markov chain

Given an ergodic markov chain $\{X_n\}$ is there any easy way to calculate the following in terms of $i$ and transition probabilities ? $$ \inf(\lambda \in \Bbb R_+ : \sum_{n=0}^{\infty} \lambda^{-n} ...
1
vote
1answer
30 views

Find the CDF for this function

Let $R$ be a continous random variable where the sample space is $-1\leq r\leq 1$ with the following probability density $$f(r) = \begin{cases} \frac{1}{4}& \mbox{for} \quad -1 \leq r \leq 0 \\ ...
-1
votes
0answers
11 views

Sharing and Distributing Surplus and Shortage Problem

Allison, Beverly, and Christine have some pieces of chessmen. Half of Allison's chessmen and shared by Beverly and Chris equally, the half of Beverly's are shared by Allison and Chris equally. Lastly, ...
1
vote
0answers
15 views

Decomposing the Complete Graph into Forests

Which spanning forests can we partition the complete graph $K_n$ into? I am primarily interested in partitions into one fixed isomorphism class of forest. I'm also assuming whatever divisibility ...
0
votes
0answers
11 views

Generalized Schur complement theorem

Let $M$ be an $(n+m)\times(n+m)$ real non-symmetric positive semidefinite (PSD) matrix partitioned as \begin{eqnarray*} M=\left(% \begin{array}{cc} A~~B\\ C~~D\\ \end{array}% \right), ...
1
vote
0answers
12 views

Blow up of reduced scheme is reduced

Why is the blow up of a reduced scheme reduced? This is in Vakil's notes (22.2.C) right after he gives the universal property of the blow up involving Cartier divisors, but before the explicit ...
0
votes
0answers
30 views

necessary condition on the sequence $\{a_n\}$ and $\{b_n\}$ such that $\sum a_n b_n$ converges

Is there any necessary condition on the sequence $\{a_n\}$ and $\{b_n\}$ such that $\sum a_n b_n$ converges ?
1
vote
0answers
11 views

Fubini's theorem for complete $\sigma$-algebras vs. non-complete $\sigma$-algebras

Suppose $(X, \Sigma, \mu)$ and $(Y, \tau, \nu)$ are both complete measure spaces. Consider the following two measure spaces: $(X \times Y, \overline{\Sigma \times \tau}, \mu \times \nu)$ and $(X ...
1
vote
1answer
10 views

Distributing Giving out Quarters Suplus and Shortage Problem

Amy, Betty, and Chloe have some quarters. Amy gives some of her quarters to Betty and Chloe, making their quarters doubled. Then Betty dos the same thing, making Amy and Chloe's quarters doubled. And ...
1
vote
0answers
8 views

Regular Value Theorem Using Implicit Function Theorem in Calculus.

I want to prove the follwoing: THEOREM. (Regular Value Theorem.) Let $f:\mathbf R^n\to\mathbf R^m$ be a smooth function and $\mathbf a\in\mathbf R^n$ be a regular point of $f$. Let ...
0
votes
0answers
27 views

Curves through points

An astronomer wants to determine the orbit of an asteroid about the sun. He sets up a Cartesian coordinate system in the plane of the orbit with the sun at the origin. By Kepler's law the orbit must ...
1
vote
1answer
11 views

Issue differentiating the Lambert W function

I want to differentiate the Lambert W function (the inverse of $y = xe^x$), I didn't think it would be that difficult a problem but it's causing me some problems. I tried this method: (1.) Implicitly ...
0
votes
1answer
25 views

Uniqueness of a real number sequence

Let ($x_n$) be a real number sequence. I'm interested in sequence(s) ($y_n$) that we can construct based on ($x_n$) with the property that every term in it is smaller than only a finite number of ...
-5
votes
1answer
30 views

Can someone explain to me in detail why the answer to number's 51 is 1/6 and 53 is 6. [on hold]

51.)limit as x approaches 4 f(x)=(sqrt(x+5)-3)/(x-4), 53.) limit as x approaches 9= f(x)=(x-9)/((sqrt x)-3)
1
vote
2answers
27 views

How to make an expression manifestly symmetric

Believe it or not, the following expression is symmetric under the exchange of the indices $j$ and $k$, i.e. $R_{kj}=R_{jk}$: $$ R_{jk}=j s_js_k-\sum_{n=1}^{\min(N-k,j)}(k-j+2n)s_{j-n}s_{k+n} $$ Where ...
0
votes
0answers
11 views

question for recommending a good textbook in representation of quivers

I am taking representation of quivers, and the lecture notes seems not enough. So could you recommend a good textbook for this course. There is a new book "Quiver Representations, by Ralf Schiffler" ...
11
votes
2answers
65 views

Finding all solutions to the equation $|||||x|-1|-1|-1|-1|=0$

I was presented this question by a student I was tutoring: Suppose $x \in \mathbb{R}$. Find all solutions of the equation $$|||||x|-1|-1|-1|-1|=0.$$ What I explained to the student: Given ...
0
votes
0answers
8 views

Asymmetric Gaussian with compact support

For a genetic program, I need to generate a set of random numbers, summing to 1.0. Please visit http://www.iic.ecei.tohoku.ac.jp/~kato/papers/t.kato_spr2002a.pdf. This paper describes how an ...
2
votes
0answers
52 views

Dummit and Foote as a First Text in Abstract Algebra

I'm wondering how Dummit and Foote (3rd ed.) would fair as a first text in Abstract Algebra. I've researched this question on this site, and found a few opinions, which conflicted. Some people said ...
0
votes
1answer
16 views

The nullity of a square matrix with linearly dependent rows is at least one. TRUE OR FALSE

Here is the answer my textbook gives. http://imgur.com/ycCRoWK I wonder: Why does the author ask this question specifically for square matrices? Is it different for other matrices.
2
votes
1answer
16 views

In uniform circular motion in R^2, is acceleration in the normal bundle?

In physics we learn that accleration is a vector quantity parallel to the radius and orthogonal to the velocity. With the embedding $\mathbb{S}^1 \hookrightarrow \mathbb{R}^2$ and the induced ...
-3
votes
1answer
28 views

CONFUSE about this asgmnt [on hold]

How many nonzero entries does the matrix representing the relation R on $A=\{1,2,3,\ldots,20\}$ consisting of the first $20$ positive integers have if $R=\{(a,b) \mid a >b\}$?
1
vote
1answer
21 views

Determine whether this polynomial form a vector space

I'm doing a question asking "A set of all polynomials with degree exactly 5. Does it form a vector space?" I'm a bit confusing showing multiplication part. If say the polynomial is ax^5+b, when the ...
1
vote
0answers
11 views

Diffeomorphism and hyperbolic points

Suppose $f$ is a diffeomorphism.Prove that all hyperbolic periodic points are isolated. I tried using the mean value theorem using two diferents periodic points (assuming the periodic points arent ...

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