Questions tagged [applications]
The [application] tag is meant for questions about applications of mathematical concepts and theorems to a more practical use (e.g. real world usage, less-abstract mathematics, etc.)
1,453
questions
0
votes
0
answers
40
views
How does and has researching mathematical juggling influenced broader branches? [closed]
I've read somewhere that juggling mathematics has influenced maths as a whole at least once with regards to some theorem in, Number Theory, I think.
I'd be curious to know about the connections as ...
-5
votes
0
answers
32
views
x^{2} =εcos(x). Find a two-term asymptotic expansion, for small ε, of the solution. [closed]
a. Sketch the functions in this equation and then use this to explain why there are two solutions and describe where they are located for small values of ε.
b. Find a two-term asymptotic expansion, ...
- 1
0
votes
0
answers
13
views
Help needed Applications Fourier transform on sound wave propagatiom
[This image show an example in a textbook that am having difficulty in understand how they get 2.12.81 and 2.12.82][1]
Kindly help with the value of B
[1]: https://i.stack.imgur.com/k4HaF.jpg
1
vote
1
answer
66
views
The absurdity of $\Gamma(x)$'s minimum, and can it be applied to the factorial?
I know that the Gamma function can be used as a representation of the factorial, but, at the same time, it is an extrapolation of $x!$. The Gamma function is cool and all, but what are its ...
- 641
2
votes
0
answers
21
views
Number of pulsations given an specfic keyboard
I am given a piano that has 88 keys and I am asked to find how many different melodies with 123 pulsations (each pulsation has obviously one key) are there. However, there is a restriction: there has ...
- 315
1
vote
0
answers
53
views
What is the equation and area under curve for Covid load dynamics?
Covid virions on infection, replicate exponentially and once the body's defense system starts attacking it then it also seems to decrease exponentially.
Source
The time period when the PCR test is ...
- 111
7
votes
2
answers
634
views
Negative Numbers in Math & Physics
We say that $-4 < -2$ and that $-3 < 0$ and that $-192 < 24$. I'm aware that there are simple, easily understandable definitions for less than / greater than / equal to e.g. $a < b$ iff ...
- 489
0
votes
0
answers
19
views
Calculating Rate of Change and using differentials to project 3 years from now
Currently, BC is helping $R=5,000$ refugees. The number of refugees that BC must help is rising at a rate of $\frac{dR}{dt}=1,000$ refugees per year. Currently, the number of staff members is $N=100$ ...
- 751
2
votes
0
answers
95
views
Heat from a geothermal well: your take?
Imagine digging a cylinder-shaped (vertical) bore-well of depth $L$ and diameter $r$ ($L\gg r$). The (infinitely thin) cylinder-wall is made watertight and we split the well in half using a kind of ...
- 2,175
0
votes
1
answer
88
views
How taut must a stretchable, horizontally-oriented string be in order for a straight line to approximate the string to within a given margin of error? [closed]
My question deals with a string that can stretch due to its own weight. If the string is allowed to stretch then I'd assume there would always be a bit of a bulge due to gravity.
The only progress I'...
- 411
0
votes
0
answers
51
views
Simulating Particle motion on a surface
I am working on a personal project to model the motion of a particle on a surface.
Using calculus, I parametrized a surface and then found the normal vector to that surface.
Using that normal vector, ...
- 1
3
votes
1
answer
119
views
Why is the transpose so useful?
I am learning linear algebra using the textbook Linear Algebra Done Right, trying to understand the subject through a logical, pure math perspective. I'm, simultaneously, learning applied linear ...
- 360
3
votes
0
answers
104
views
Why all the inequalities?
I have recently seen questions involving bizarre inequalities, usually consisting of cycling over variables; here's one example (see also related links):
$$\sum\limits_{cyc}\frac{1}{\sqrt{2a^2+5ab+2b^...
- 1,736
0
votes
2
answers
54
views
Exercise 1-28 A high school lottery uses two sets of numbered balls...
Exercise 1-28
A high school lottery uses two sets of numbered balls. One set consists of ten white balls numbered 1-10 and the second set contains twenty blue balls numbered
1-20. To play, you select ...
2
votes
1
answer
55
views
Extending baker's percentages to preferment recipes
I'm trying to solve a simple problem I created for myself. I'm no mathematician, so any help is greatly appreciated.
Background
In baking and "baker's math", the amount of each ingredient is ...
- 21
0
votes
0
answers
35
views
Proving a function decays polynomially
Let $f:\mathbb{R}\to\mathbb{R}$ be such that $f(x)=O\left(\left(\frac{1}{\log x}\right)^{\lambda}\right)$ as $x\to\infty$ for some constant $\lambda\in\mathbb{R}$. Can we prove that $f$ decays ...
user1022331
1
vote
0
answers
32
views
Markov Process for fuel consumption
Say I have a gas station where cars arrive to refuel. I know that if the waiting times between arrivals is exponentially distributed with mean $1/\lambda$ time-units, then I can model the number of ...
- 11
2
votes
1
answer
166
views
Is state space representation useful for nonlinear control systems?
I understand that the state space representation is mathematically equivalent to the transfer function representation for linear systems, and that it allows us to solve the corresponding DE by finding ...
0
votes
0
answers
28
views
Information/Applications of a homogeneous Monge-Ampere equation
Does anyone know of any information/applications of the the quasilinear Monge-Ampere equation, $$u_{xx} - u_y u_{xy} + u_x u_{yy} = 0?$$ It appears in Forsyth's Theory of Differential Equations (vol. ...
- 468
1
vote
0
answers
37
views
Efficiency of RREF algorithms
Compute the RREF of the following matrix :$$\begin{bmatrix}1&-1&2&-3&7\\4&0&3&1&9\\2&-5&1&0&-2\\3&-2&-2&10&-12\end{bmatrix}$$
My friend ...
- 4,025
2
votes
1
answer
117
views
Is measure theory only for integrals?
I am trying to self-study probabilistic measure theory after completing my undergrad degree, and I am curious if there are more interesting applications of measure theory aside from Lebesgue ...
- 21
0
votes
0
answers
63
views
Coefficients of a sine series
I am reading a paper on fluid mechanics- https://royalsocietypublishing.org/doi/10.1098/rspa.1954.0197 . Here, the author takes the sum of sines $\overline{WT}=\Sigma_{n=1}^\infty\Sigma_{m=1}^\infty\...
- 1
0
votes
1
answer
42
views
If his overall profit for the year was $\$104.50$, and he invested $300 more in commodities than in REITs, how much was allocated to each investment?
Through monthly deductions from his salary, Noah managed to accumulate 4800 per month last year for his future sabbatical trip. His savings account yielded 4.2% interest, his real estate investment ...
- 751
2
votes
0
answers
68
views
Applications of Gröbner bases for beginners
What are some applications of Gröbner bases that could be interesting to a group of students that more or less only studied Chapter 1 and Chapter 2 of Ideals, Varieties, and Algorithms by David A. Cox ...
- 31
0
votes
0
answers
68
views
Does representing the fresnal integral in terms of the error and imaginary error function have a use?
The Fresnal S integral can be represented with the following:
$$F(a,b)=\int_a^b{\sin(x^2)}\,dx = \frac{-\sqrt{i\pi}}{4}[\operatorname{erfi}(\sqrt{i}\,b)-\operatorname{erf}(\sqrt{i}\,b)]+\frac{\sqrt{i\...
2
votes
0
answers
71
views
Are there any applied mathematics problems which require a set with cardinality greater than the Reals?
I am just asking in general if problems arise in physics, astronomy, or biology which require large cardinalities, i.e. beyond the Reals?
- 29
14
votes
2
answers
195
views
Best way to cut a pineapple ring?
I like to prepare pineapples by first cutting it into rounds and then slicing off the skin with a roast beef slicer. This leaves me with a hexagon "ring" around a circular core:
I then don'...
- 2,538
0
votes
0
answers
44
views
Where to apply binomial expansion?
I would like to know where I could apply the expression as part of other equation
$$\bigg( 1 + \frac{x}{r} \bigg)^r$$
considering $r \in Z$. It means, in what kind of problem I can use this expression....
- 301
1
vote
1
answer
52
views
Help in understanding this exercise (Linear Algebra)
I need some help in understanding the precise request of this exercise.
Let the vectors of the plane be identified with oriented segments exiting from a fixed point, and let's identify $\mathcal{V}^2$...
- 2,418
0
votes
1
answer
77
views
Useful length of Pi?
Not sure where this really fits, so am trying Mathematics first. Feel free to migrate to another StackExchange forum if more appropriate elsewhere. So I was listening to a podcast yesterday that was ...
- 137
0
votes
0
answers
22
views
Interpolating functions into continous functions on topological spaces
In practical modelling, I'd argue that one of the most powerful concepts we have is the ability to interpolate functions between given data points. I want to ask, if any similar idea exists between ...
- 11.1k
0
votes
0
answers
36
views
What else can the principle of induction be used for? [duplicate]
This might be a random question, but I've always wondered, can the principle of induction be used not only for proving sum formulas, but something else? Is there anything else we can use it for?
- 107
0
votes
2
answers
33
views
Perplexity over the proof of linearity for an application
Be $F(x, y) = 3x + 4y$. I have to prove it's a linear appliction.
I am confused about the way to proceed. Is this the right way to proceed?
$$F(x_1 + x_2, y_1 + y_2) = 3(x_1 + x_2) + 4(y_1 + y_2) = ...
- 2,418
2
votes
1
answer
39
views
Is this vector function linear?
I am having problems in understanding the following exercise: $$F: \mathbb{R}\to \mathbb{R}^2; \qquad F(x) = (2x, 3y)$$
I have to say if it's linear.
I am having troubles in understanding where does ...
- 2,418
0
votes
0
answers
28
views
Error while calculating force in 2D flow around a circle
This is statement of the exercise:
In this exercise we consider as example the case of a disk of radius R centered at the origin of coordinates immersed in a fluid of density σ and velocity field $u(x,...
0
votes
0
answers
19
views
Applications of fractional boundary value problems
I would like to ask if we study boundary conditions of fractional boundary value problem involving fractional boundary conditions, they have any real world applications or if boundary conditions do ...
- 51
0
votes
1
answer
98
views
Does removing an open set from topology in $\mathbb{R}$ and associated open sets leads to $\mathbb{R}$ having trivial topology?
Suppose we have $\mathbb{R}$ with the standard topology, and we remove a ball $(a- \epsilon, a+\epsilon)$ from the topology, then what topology do we get, provided we remove only the minimum number of ...
- 11.1k
1
vote
0
answers
22
views
Can the Wiener-Khinchin theorem be correctly applied to a periodic sound signal (such as a sine wave)?
The theorem speaks about a wide-sense stationary random process. Is, for example, a sine wave with a period 1/400 s considered a WSS (or, in general, a periodic sound signal with multiple frequency ...
- 109
0
votes
1
answer
37
views
Linear and almost linear Partial differential equations examples in Sciences
I am interested in learning linear and almost linear PDEs of first order to describe some system or process however I want to learn by real world examples of such a application.Do you know any such ...
- 121
2
votes
0
answers
60
views
Examples of a gradient flow
Suppose we have a gradient flow in $\mathbb{R}^n$ :
$$\frac{d}{dt}x(t)=-\nabla F(x(t)), \qquad x(0)=x_0.$$
where $F : \mathbb{R}^n \to \mathbb{R}$ and $x : \mathbb{R}_+ \to \mathbb{R}^n$. What are ...
- 41
1
vote
1
answer
41
views
How do elements in the algebraic closure of $\mathbb{Q}$ look like?
If one asks give examples of polynomial with coefficients in $\mathbb{Q}$ who don't have zeros in $Q$, simple examples given are: $x^2-3,x^3-3$. All of these have roots of form $(n)^{\frac{1}{m} }$. ...
- 11.1k
3
votes
0
answers
125
views
Classifying divergent sequences in a metric space
To my understanding, in $\mathbb{R}$, we have the following ways in which a sequence can diverge:
The sequence could diverge off into $\infty$ or $-\infty$ (relevant generalization)
Divergence by ...
- 11.1k
2
votes
2
answers
72
views
What is an actual application problem (probability, weather) that uses the binomial series? Does it solve anything?
I'm just trying to figure out what the purpose is of the binomial series? What does it tell us? I did a search and found something talking about probability and weather predicting, but I'd like to see ...
4
votes
1
answer
151
views
Manipulating divergent series for practical applications
I have a series summation of the form
$$
\tag{1}
S(x) = \sum_{i = -\infty}^{\infty} (-1)^{i}\left[\Phi\left(2ix\right) - \Phi\left((2i-2)x\right)\right],
$$
where $\Phi(.)$ is the standard normal ...
- 1,070
3
votes
2
answers
753
views
Real world example of an equation with no solution? [closed]
I have just started reading basic algebra and I have this curiosity that came up when solving basic linear equations. Some equations have no solutions. Are there any real world example of equations ...
- 55
3
votes
0
answers
79
views
Is there any practical use for octonions? [closed]
Quaternions are useful for describing orientation/ rotations in 3- dimensions, however is there much practical use for an 8-dimensional base hyper complex number id est Octonions?
- 31
0
votes
0
answers
13
views
Hypothesis testing on the existence of a hypothesis (satisfying certain criteria)?
My understanding of probability and statistics is as yet not very good, so please correct me if I get anything wrong, terminologically or conceptually.
Suppose I have a set $X$, and a property (binary ...
- 353
5
votes
1
answer
252
views
How does the Pareto distribution represent the 80-20 rule?
According to the current Wikipedia article:
The Pareto principle or "80-20 rule" stating that 80% of outcomes are
due to 20% of causes was named in honour of Pareto, but the concepts
are ...
- 1,681
2
votes
0
answers
37
views
How to think about distence or closeness between various intersecting and non-intersecting sets? [closed]
Edit: I want to add more context. I'm interested in toying around with mathematical modeling of something, where it is helpful to represent the things I'm modeling with sets whose elements are points. ...
- 97
0
votes
2
answers
51
views
What is the formula for cumulative compound interest? [closed]
I would like to start with a principal amount (P) in year 0, then add compound interest (C) to it for year 1, and then add that total value to the starting amount. So for example:
P=1000
C=2.5%
For ...
- 11