0
votes
1answer
9 views

Does a compact set with non-empty interior have a limit point?

My Question: Let $U\subseteq \mathbb{C}$ open and $K\subset U$ be a compact set with nonempty interior $K^{o}$, then $K$ must have a limit point in $U$. Remark: I think that the statement is true. I ...
0
votes
0answers
3 views

Find the homothetic transformation

In $\mathbb{R^3}$: Find the homothety $\Phi$, such that the following transformations are possible: $$\Phi(P)=\Phi(1,0,-1)= (2,5,0)$$ and $$\Phi(Q)=\Phi(0,1,2)= (0,5,2)$$
0
votes
0answers
8 views

Relating $11111111…1$, $11$ ,and $1010101..1$.

How can we prove the pattern we see in the following observations: $$ \frac{11}{11}=1$$ $$ \frac{1111}{11}=101$$ $$ \frac{111111}{11}=10101$$ .... It seems that if you have $2n+2$ numbers of ...
1
vote
1answer
17 views

Question about non trivial zeros of Riemann zeta function

Riemann zeta function is $$\zeta(s)=\sum\frac{1}{n^s}$$ I read at wiki that the first nontrivial zero is located at $14.134725...$ As long that I could understand it means ...
1
vote
0answers
5 views

Matrix rank and number of linearly independent rows

I wanted to check if I understand this correctly, or maybe it can be explained in a simpler way: why is matrix rank equal to the number of linearly independent rows? The simplest proof I can come up ...
2
votes
0answers
13 views

Is is possible that three countries have three points in common?

On the world map, there are several instances of three countries that have two points in common. For example, China, Russia and Mongolia. Is there any arrangement of three (fictional) countries such ...
0
votes
0answers
4 views

Trapezoid rule for finding coefficient

If we know that $\int_{a}^b t(x)=h \sum_{k=1}^2 dk * t(a+kh)+O(h^m)$ where $h=\frac{b-a}{3}$, how do we find the coefficient d1, d2 and m in the equation? Answer says that d1=3/2, d2=3/2, m=3 I ...
0
votes
0answers
9 views

Showing the vectors $v_1$, $v_2$, $v_3$ are orthonormal.

I have a differential equation $$\frac{dv_i}{ds}=\sum^3_{j=1} a_{ij} v_j$$ for $i=1,2,3$ and where $a_{ij}$ is skew symmetric matrix. For some point $s_0$, $v_1 (s_0)$, $v_2(s_0)$ and $v_3(s_0)$ are ...
-1
votes
1answer
17 views

Determine logarithm versus known values of $ a,b$

We know $\log_{30}(3)=a, \log_{30}(5)=b.$ How to determine $\log_{30}(16)$?
-5
votes
0answers
17 views

I guess I have found a possible explanation of “Collatz conjecture”. So, how can I publish it?

Please anyone help me in this. This is going to be my first one. So, can anyone good me in this.
0
votes
0answers
6 views

Finding equation of tangent at given point

I am trying to find the equation of the tangent line for the given point, given $f(x) = log x$ and point $P(2, log2)$. I know the derivative of $log x$ is $\frac{1}{x ln10}$, and as a result the ...
0
votes
0answers
9 views

Set theory and well-ordering

Let $X \ne \emptyset, X \subseteq \omega$. Show that there is $n \in X, n \cap X = \emptyset$ I am trying to solve this, but I'm a bit confused. It's stated in relation to the wellordering ...
0
votes
2answers
23 views

Find $\det(A)$ of Matrix and condition on a and b

Let $$ A=\begin{matrix} a & b & 1 \\ b & 1 & b \\ 1 & a & a \\ \end{matrix} $$ Find $\det(A)$ in terms of $a$ and $b$, and write down ...
0
votes
0answers
6 views

Finding the maximal product of numbers of permutations

Let $n\geq 1$ be a total number of objects that must be taken from $m\geq 1$ sets of objects. For all $i \in \{1,\cdots,m\}, \ M_i \in \mathbb{N}^*$ denotes the number of objects present in the set ...
-1
votes
0answers
14 views

Find the inverse Laplace transform of $L(s)= \frac{s}{s^2 + 25} e^{-\pi s}$

$$L(s)= \frac{s}{s^2 + 25} e^{-\pi s}$$ I never seen such function. Can exponential function appear in Laplace transform? Help required
-5
votes
0answers
22 views

Find the volume of the following room [1]

I was working on a project which required me to calculate the volume of the room. The picture of the room is given below: I tried splitting the shape across the diagonals but each time end up ...
0
votes
0answers
9 views

Second order total derivative

Suppose we have a function $g: \mathbb R^2 \to \mathbb R$ and $$\nabla g(u,v)=(5v^4-2u\exp(v-u^2), \exp(v-u^2)+20uv^3), (u,v)\in\mathbb R^2$$ Can the function $g$ be twice differentiable, i.e. does ...
5
votes
1answer
40 views

Chinese New Year Equation 2016

In the spirit of Chinese New Year, here's a problem to commemorate the year. $\color{black}{\text{Solve the following equation for positive integers $a$ and $b$:}}$ ...
0
votes
1answer
30 views

A problem of decimals..

The exact problem: For any natural number n>1, write the infinite decimal expansion of $\frac{1}{n}$ (for example, we write 1/2 = $0.4\overline9$ as it's infinite decimal expansion, not 0.5). ...
2
votes
1answer
13 views

Logical equivalence implication between Kleene and Classical logic

For any propositional assertions, $\phi$ and $\psi$, expressed using only the standard propositional logical connectives $\{\lnot,\land,\lor,\rightarrow,\iff\}$, if $\phi$ and $\psi$ are logically ...
-6
votes
1answer
28 views

A question on polunomial

Let $m\in (0,1)$ and ${a_n}{x^n} + .... + {a_1}{x^1} - f(m) = 0$ and $x\in \mathbb{C}$ $f(m) $ is continuous decreasing function of $m$. $a_i\ge0$ for all $i$. $k(m)$ is positive zero of first ...
-1
votes
2answers
17 views

Finding temperature after time.

A thermometer is taken from a room where the temperature is $20^\circ\,\mbox{C}$ to the outdoors, where the temperature is $-7^\circ\,\mbox{C}$. After one minute the thermometer reads ...
0
votes
0answers
9 views

Is the following statement equivalent?

Is the following statement equivalent: $((A \vee \neg C) \wedge ((\neg B) \leftarrow C)) \vee \neg (A \wedge B) \equiv (\neg A \vee \neg B \vee \neg C) $ Our prof gave us an exercise with this ...
0
votes
1answer
9 views

CG-homorphism proof. Stuck at the end!

I am trying to work on some questions back from my uni days, and one has gotten the better of me at the moment! Let $G$ be a finite group and $V, W$ finite-dimensional $\mathbb{C}G$-modules. Let ...
3
votes
0answers
23 views

Check the proof of $\Bbb R$ as set of subsequential limits

I want to prove that there is a sequence in $\Bbb R$ that has all of $\Bbb R$ as its set of subsequential limits. Could someone help me check my proof? If it's not correct, could someone give a proof? ...
0
votes
0answers
4 views

Plane integral for continuous curves

I'm trying to understand complex path integral $\int_C f(z)dz$ for continuous closed curve $C$. Is it necessary that $C$ is rectifiable and not just generally continuous? Do we get all the ...
0
votes
0answers
9 views

another follow up question: modeling with exponential distributions

This a follow up question to the previous two: modeling with exponential distributions a follow up question about modeling with exponential distributions I'm trying to do (c). Denote the ...
0
votes
1answer
13 views

L2 Norm of Inverse of Non-square Matrix Multiplication

Consider a matrix $A\in\mathbb R^{n\times m}$ with $n<m$. Given that $\|A\|_2 = \gamma_0$ and $AA^T$ is invertible, can we find any equality/inequality for $\|(AA^T)^{-1}\|_2$ in terms of ...
3
votes
0answers
17 views

Prime factorization and hcf

For any given integer $n$, we prime factorize it as follows $$n = p_1^{k_1} \cdot p_2^{k_2} \cdots p_r^{k_r}. $$ Let $g = \gcd(k_1, k_2, \ldots, k_r)$ and $m_i = k_i / g$. The function $F$ is ...
3
votes
2answers
72 views

What is wrong with this infinite sum

We know that: https://www.youtube.com/watch?v=w-I6XTVZXww $$S=1+2+3+4+\cdots = -\frac{1}{12}$$ So multiplying each terms in the left hand side by $2$ gives: $$2S =2+4+6+8+\cdots = -\frac{1}{6}$$ This ...
0
votes
0answers
7 views

Is there K and an infinite amount of different primes $a_i,b_i$ so that min|$a_i^y-b_i^x$| <K on natural x,y for all i?

First of all I know that it was proved recently that prime gaps are less than like 7 million for an infinite amount of primes, but I'm not smart enough to follow the proof. I am looking for a ...
0
votes
0answers
10 views

Differential? equation in car dashboard problem

I stumbled upon this question while I was driving my car. On my dashboard I have fuel gauge and engine temperature gauge next to each other, look at the pic: http://i.stack.imgur.com/aDgKj.png Fuel ...
5
votes
2answers
71 views

Anti-derivative of continuous function $\frac{1}{2+\sin x}$

I use tangent half-angle substitution to calculate this indefinite integral: $$ \int \frac{1}{2+\sin x}\,dx = \frac{2}{\sqrt{3}}\tan^{-1}\frac{2\tan \frac{x}{2}+1}{\sqrt{3}}+\text{constant}. $$ ...
3
votes
2answers
17 views

$A$ has more columns than rows and has full row rank, show there exist infinitely many $B$ s.t. $AB=I$

If A $\in M_{m\times n}(R)$ such that $n>m$. Prove that if $\text{rank} (A) = m$ then there are infinitely many matrices $B \in \ M_{n\times m} (R)$ such that $ AB = I_m$ So the question is ...
0
votes
0answers
4 views

Mathematical theory for equally distributed dipole structures with inner equilibration

I'm looking for a mathematical theory for equally distributed dipole structures with inner equilibration. I know, that there exist two magnetic clusters, where the north and the south poles equally ...
0
votes
0answers
14 views

Let $f$ holomorphic funcion in $U$ such that $\left|f\right|$ constant on the border of $K$. Show that $f$ is constant or $f$ have a zero in $K^{0}$.

Let $U\subseteq\mathbb{C}$ be an open and connected set and $K\subset U$ a compact subset with nonempty interior $K^{o}$. Let $f:U\rightarrow \mathbb{C}$ holomorphic funcion such that $\left|f\right|$ ...
0
votes
0answers
7 views

Why hough Transformation detect Same line twice

After using canny edge detector my image looks like Image After Canny Edge detector Then I use Hough transform to extract line. Sometimes I able to find four line. But sometimes Same line detect as ...
0
votes
0answers
15 views

Is a metric's form determined by its signature?

Suppose that we define a 4-dimensional vector space over the real field with a metric with signature (3, 1). Is the scalar product map determined only with this information? For example: a Minowsky ...
0
votes
0answers
12 views

Difference between joint density and density function of sum of two independent uniform random variables

I am not able to understand the difference between the joint density function and density function for a random variable Z = x1 + x2 where x1, x2 are uniform rvs in [0,1]. I think joint density in ...
2
votes
3answers
19 views

Even-odd multiplicative algebraic structure with two distinct identity elements?

What is the algebraic structure for the multiplication of even elements and odd elements? even times even is even. even times odd is odd. odd times odd is odd. i.e. the matrix is ...
1
vote
3answers
33 views

What is the significance of using prime numbers in proving: $x$ is a multiply of $y$?

I came to a problem where it asks me to prove, for example, $n^4-n^2$ is a multiple of $12$. Now, factorize the multiple: $n\times n\times (n-1)\times (n+1)$. Here we have $3$ consecutive integers. ...
3
votes
1answer
29 views

How many ways we can choose items from different boxes

I searched through the internet but couldn't find my answer, which can either be a very simple or a hard one. Assume there are $3$ boxes, which carry, respectively, $1$, $4$, $2$ items. My question ...
0
votes
0answers
11 views

Pulley and chain

Find the length of an endless chain which will hang over a. Circular pulley of radius a so that it is in contact with two thirdsof the. Circumference of the pulley? I saw this question in a test. I ...
-1
votes
0answers
8 views

Warshall algorithm for transitive closure

has someone seen a way of applying Walshall's algorithm for transitive closure by finding the '1' elements for e.g. Alpha 1,2, Alpha 2,3 and then: 1. adding row 2 to row 1 2. adding row 3 to row 2 and ...
0
votes
2answers
26 views

Integral of a measurable function

I do not know what should i keep as title for this question... Question goes like this.. Let $f:\mathbb{R}\rightarrow [0,\infty)$ be a measurable function. If $\int_{-\infty}^{\infty}f(x)dx=1$ prove ...
0
votes
0answers
21 views

Probability to reach final state

Let $~~m,n>0~~$ be some positive integers. We have some system of states. Each state is pair $~~(i,k)~~$ where $~~0\leq i \leq m~~$ and $~~0\leq k \leq n~~$. Starting state is $~~(m,n)~~$. For ...
2
votes
0answers
28 views

What subfields use computers the most and least? (soft question)

What areas within (research) mathematics use computers the most and least? What programming languages are commonly used?
2
votes
4answers
96 views

Easy way to solve logarithms without a calculator?

I would need to be able to solve logarithms without using a calculator, just on paper. The result should be a fraction so it is the most accurate. For example I have seen this in math class ...
2
votes
0answers
12 views

Discriminant of Elliptic Curves

In the study of elliptic curves, specifically in Weierstrass form, you have the equation $E : y^2 = x^3 +ax +b$. However I have found the discriminant comes in two different forms: $\Delta = ...
0
votes
0answers
47 views

Prove that $A+2I$ is invertible [duplicate]

Given $A$ is a square matrix such that $A^{3} = 2I$ Prove that $A+2I$ is invertible and find its inverse. How do I prove that $A+2I$ is invertible? For proving $A-I$ is invertible, I use ...

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