New answers tagged applications
2
votes
Solving ODE system with less equations
Yes, in this case of a linear equation you do not need to solve the original equation as prerequisite to solve the sensitivity equations.
This is of course different for non-linear equations, as each ...
- 128k
0
votes
The latest examples of civil engineering projects with great mathematical content
A 2024 update: the HS2 project (possibly the largest ever in western Europe) costing over £100 billion. Super-projects like this are massivley intensive on the mathematics with rail viaducts, ...
- 117
0
votes
Minimize travel time of a group of people with a motorbike
Too long for a comment, but this idea may help to prove your statement:
I think it is quite possible to show that everyone has to arrive at the same time in the optimum. Suppose some walking people ...
- 368
0
votes
Factorial of a matrix: what could be the use of it?
CA systems implement all algebraic functions of square matrices, simply as the natural extension of a function $f$ with a zero at $x=0$ to diagonal matrices as arguments that map the functions to the ...
- 3,234
0
votes
Factorial of a matrix: what could be the use of it?
CA systems implement all algebraic functions of square matrices, simply as the natural extension of a function $f$ with a zero at $x=0$ to diagonal matrices as arguments that map
$$x\to f(x) = \sum_1^\...
- 3,234
1
vote
If $\frac{p}{p+q}$ is a negative real number, what can I deduce about complex $p$ and $q$?
Let $p = a + b i$ and $q = c + d i$ for some $a, b, c, d \in \mathbb {R}$. Then
$$\begin{align} \frac {p}{p + q} & = \frac {a + b i}{\left( a + c \right) + \left( b + d \right) i} \\ & = \frac ...
- 1,470
1
vote
Accepted
If $\frac{p}{p+q}$ is a negative real number, what can I deduce about complex $p$ and $q$?
Say $p/(p+q) = -a$ for some real $a>0$. Then $(1+a)p = -aq$. The left-hand side has non-negative real part, while the right-hand side has non-positive real part. This forces the real part of $p$ ...
- 1,586
0
votes
pow and its relative error
You may be able to improve on the error performance by replacing
$$
\operatorname{pow}(x,b)= \exp(b\ln x) \tag 1
$$
with
$$
\operatorname{pow}(x,b)= x^{Int(b)}\exp(Frac(b)\ln x) \tag 1
$$
where $Int(b)...
- 1,249
1
vote
pow and its relative error
The issue is fundamental and if we are limited to working precision then there is nothing that can be done to avoid it.
You are computing a function $f$ of two variables, i.e., $$y = f(b,x) = x^b.$$ ...
- 13.2k
0
votes
Critical Simplices of a Discrete Gradient Vector Field
You're looking to prove that if $q$ violates condition (2) for $[a_1,a_3,\dots,a_j]$ then it also violates (2) for $[a_1,a_2,\dots,a_j]$, which reduces to showing that $d(q,a_2)\leq 2r$.
If $q$ is not ...
- 216
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