# All Questions

0answers
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### Finding inverse laplace transform without the complex integral method

We know that $L(f(t))=\frac{1}{s^2+4s+8}$. We are asked to find $f(t)$ with an inverse laplace transform. Here is the problem: I know it's possible to do it using a complex integral and the residue ...
0answers
12 views

### Finding $m$ largest numbers from union of $k$ sorted lists $A_1, A_2, \ldots, A_k$

We are given $k$ sorted lists $A_1, A_2, \ldots A_k$ with corresponding sizes $n_1, n_2, \ldots n_k$. How can one find $m$ largest elements (numbers) from union of lists $A_1, A_2, \ldots, A_k$? We ...
2answers
12 views

### Region given by these inequalities in XY Plane

Given region as $0\leq x \leq y$ , $x+y \leq 1$ . I did this as Is this correct ?
0answers
7 views

### Simulation algorithom to maximize expectiation expression

I am running into a optimization problem. I want to find $Q$ such that: $$\max_Q E_{g,h}\log\frac{1+h^HQh}{1+g^HQg}$$ Where $Q$ is the covariance matrix of vector input. $h^H$ is the Hermitian ...
0answers
14 views

### How do I know if a given polynomial is a quasi polynomial?

How do I know if a given polynomial is a quasi polynomial? For example, if I'm given the polynomial: $e^x\tan(x)$ or the polynomial $e^{(i-t)}t^3$, my gut feeling is that they're both not quasi ...
2answers
13 views

### Finding median of union of two sorted (ordered) lists

We are given two sorted list of numbers $a_1, a_2, \ldots, a_n$ and $b_1, b_2, \ldots, b_n$. Question is, how to find a median for list $a_1, a_2, \ldots, a_n, b_1, b_2, \ldots, b_n$. Algorithm should ...
2answers
25 views

### Topology; Definition of the open ball and open sets confuses me

I just picked up T.W Gamelin’s book on topology started reading and got confused when I came to the definition of an open ball on the second page. It says B(x;r) = All y in the set X such that d(x,y) ...
0answers
19 views

### Is this proof clear, complete and readable?

I am trying to prove this statement: $C^2/U(1)$ can be identified with $R^3$ so that the image of the $U(1)$ fixed point is $(0,0,0)$. And I was wondering if someone could tell me if the following ...
0answers
11 views

### How to this Simplify Boolean Expression

Im very weak in math and logic, and currently try doing K-map, and got this as result: $(C'B')+(CB)$ my question is, can this be more simple? I tried it myself, but I got $0$. $(C'C)+(B'B)$ I just ...
1answer
27 views

### formula for summation notation involving variable powers

I need help finding the formula for this summation notation: $$\sum_{k=1}^n{k^{2k} }$$ or $$1^2 + 2^4 +3^6 +.....+n^{2n}$$ And preferably not involving calculus.
0answers
7 views

### Trying to prove concurrence of altitudes of a triangle.

I know that this question had been asked before, but I am not exactly following what the answers say. Doing my own way here: I am puuzzled how to continue? I named the points A,B,C, and the foot of ...
0answers
23 views

### Irreducible and prime elements

In my commutative algebra lecture notes it says: A non-zero element $p$ of a ring $R$ which is not a unit of $R$ is called a prime element if $p=ab$ implies $a$ is a unit or $b$ is a unit. Is this ...
2answers
26 views

### Permutation of positive real numbers

Consider a set of positive real numbers $\{P_1,P_2,\dots,P_n\}$ and a permutation of this set $\{Q_1,Q_2,\dots,Q_n\}$. Is it possible to find a permutation such that ...
0answers
15 views

1answer
23 views

### Deriving angle from sin or cos

How can I derive the value in degrees of an angle starting from either the cos or sin value? $$\cos(t) = c_{1} \quad \text{or} \quad \sin(t) = c_{2}$$
1answer
32 views

### Proving that if the semigroup (A, *) is a group, then the relation is an equivalence relation.

I'm aware that posting exam questions is probably frowned upon, but this isn't homework, I think I'm genuinely misunderstanding some part of the algebra. The question is this: Throughout this ...
0answers
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0answers
32 views

### About an unpredictable sequence of primes [duplicate]

Let $p_n$ denote the sequence of prime numbers, with $p_0=2$. The obvious fact that the sequence $p_n$ is unpredictable is very known. I am asking if there is a mathematical proof for this. Or, this ...

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