All Questions
8
questions
2
votes
3
answers
270
views
How to prove or disprove an inequality with Mathematica?
I mean there exist $\lambda>0, x\in \mathbb R$ s.t. the inequality $$ \frac{3^{\lambda } e^x+e^{3 x}+1}{2^{\lambda } e^{2 x}}<\frac{1}{10^{100}}$$ is valid.
Here are my unsuccessful attempts.
<...
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0
votes
1
answer
74
views
Formalization of one optimization problem or solution of inequalities - Part №2
Continuing the question: Formalization of one optimization problem or solution of inequalities
Let's consider a more complex problem. We have two polynomial:
$p_1=A_2t^2+A_1t+A_0$
$p_2=B_2t^2+B_1t+B_0$...
- 2,444
2
votes
1
answer
79
views
Formalization of one optimization problem or solution of inequalities
I have polynomial:
$p=A_2t^2+A_1t+A_0$
$A_0=(x^2-y^2)+xz$
$A_1=x^2+y^2+z^2+\sin(x)$
$A_2=x^4+y^3+z^2$
$x,y,z$ - parameters, moreover $z$ - the value of which varies in the range $[0,1]$.
Polynomial $p$...
- 2,444
1
vote
1
answer
73
views
Finding the joint domain for a couple of functions of three variables
I have two functions $f_{1}(x,y,z)$ and $f_{2}(x,y,z)$ defined respectively as
...
3
votes
1
answer
378
views
Need help with a linear programming problem
Consider
$1\rightarrow{}x+2y\leq{500}$,
$2\rightarrow{}2x +y \leq{520}$,
$3\rightarrow{}2x+5y \leq{}1200$,
$4\rightarrow{}x \geq{}0$,
$5\rightarrow{}y \geq{}0$,
The above is the set of inequalities ...
- 73
4
votes
1
answer
239
views
Generate convex-hull of a 15 dimensional space
This question follows my last post.
I have a function $ \vec{f}: S^6 \times S^6 \rightarrow \mathbb{R}^{13} $ defined on two 6-dim hyperspheres. We will denote the function $ \vec{f}(\vec{x},\vec{y}) ...
- 1,658
0
votes
5
answers
663
views
Find all the closest positive integer solutions within a bound for a simple linear equation
Suppose I have a linear equation/inequality like
$$xA+yB \leq C,$$
with $x,y \in \mathbb{Z}^{+}_{\neq 0}$ and $A,B,C \in \{x | x = 0.01\mu, \forall \mu \in \mathbb{Z}^+_{\neq0}\}$. I want to find ...
-1
votes
1
answer
294
views
Find a minimum value which satisfies an equation
I have to find a minimum value of "a" which makes x=-a+b+c, y=-a+b+c^2 positive where a>1, 0
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- 21