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.)
1,488
questions
1
vote
0
answers
57
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
8
votes
2
answers
805
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 ...
- 983
0
votes
0
answers
21
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 $N=100$ ...
- 785
2
votes
0
answers
98
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 ...
- 2,455
0
votes
1
answer
93
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'...
- 887
0
votes
0
answers
80
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
173
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 ...
- 402
3
votes
0
answers
117
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):
$$\sum\limits_{cyc}\frac{1}{\sqrt{2a^2+5ab+2b^...
- 1,835
0
votes
2
answers
95
views
Exercise 1-28 A high school lottery uses two sets of numbered balls...
Exercise 1-28
A high school lottery uses two sets of numbered balls. One set consists of ten white balls numbered 1-10 and the second set contains twenty blue balls numbered
1-20. To play, you select ...
2
votes
1
answer
86
views
Extending baker's percentages to preferment recipes
I'm trying to solve a simple problem I created for myself. I'm no mathematician, so any help is greatly appreciated.
Background
In baking and "baker's math", the amount of each ingredient is ...
- 21
1
vote
0
answers
33
views
Markov Process for fuel consumption
Say I have a gas station where cars arrive to refuel. I know that if the waiting times between arrivals is exponentially distributed with mean $1/\lambda$ time-units, then I can model the number of ...
- 11
2
votes
1
answer
930
views
Is state space representation useful for nonlinear control systems?
I understand that the state space representation is mathematically equivalent to the transfer function representation for linear systems, and that it allows us to solve the corresponding DE by finding ...
1
vote
0
answers
182
views
Efficiency of RREF algorithms
Compute the RREF of the following matrix :$$\begin{bmatrix}1&-1&2&-3&7\\4&0&3&1&9\\2&-5&1&0&-2\\3&-2&-2&10&-12\end{bmatrix}$$
My friend ...
- 4,055
3
votes
1
answer
211
views
Is measure theory only for integrals?
I am trying to self-study probabilistic measure theory after completing my undergrad degree, and I am curious if there are more interesting applications of measure theory aside from Lebesgue ...
- 118
0
votes
1
answer
44
views
If his overall profit for the year was $\$104.50$, and he invested $300 more in commodities than in REITs, how much was allocated to each investment?
Through monthly deductions from his salary, Noah managed to accumulate 4800 per month last year for his future sabbatical trip. His savings account yielded 4.2% interest, his real estate investment ...
- 785
2
votes
0
answers
124
views
Applications of Gröbner bases for beginners
What are some applications of Gröbner bases that could be interesting to a group of students that more or less only studied Chapter 1 and Chapter 2 of Ideals, Varieties, and Algorithms by David A. Cox ...
- 31
2
votes
0
answers
81
views
Are there any applied mathematics problems which require a set with cardinality greater than the Reals?
I am just asking in general if problems arise in physics, astronomy, or biology which require large cardinalities, i.e. beyond the Reals?
- 29
15
votes
2
answers
278
views
Best way to cut a pineapple ring?
I like to prepare pineapples by first cutting it into rounds and then slicing off the skin with a roast beef slicer. This leaves me with a hexagon "ring" around a circular core:
I then don'...
- 2,688
0
votes
0
answers
45
views
Where to apply binomial expansion?
I would like to know where I could apply the expression as part of other equation
$$\bigg( 1 + \frac{x}{r} \bigg)^r$$
considering $r \in Z$. It means, in what kind of problem I can use this expression....
- 459
1
vote
1
answer
57
views
Help in understanding this exercise (Linear Algebra)
I need some help in understanding the precise request of this exercise.
Let the vectors of the plane be identified with oriented segments exiting from a fixed point, and let's identify $\mathcal{V}^2$...
- 3,482
0
votes
1
answer
82
views
Useful length of Pi?
Not sure where this really fits, so am trying Mathematics first. Feel free to migrate to another StackExchange forum if more appropriate elsewhere. So I was listening to a podcast yesterday that was ...
- 137
0
votes
2
answers
38
views
Perplexity over the proof of linearity for an application
Be $F(x, y) = 3x + 4y$. I have to prove it's a linear appliction.
I am confused about the way to proceed. Is this the right way to proceed?
$$F(x_1 + x_2, y_1 + y_2) = 3(x_1 + x_2) + 4(y_1 + y_2) = ...
- 3,482
2
votes
1
answer
45
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 ...
- 3,482
1
vote
0
answers
31
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
1
answer
112
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 ...
1
vote
0
answers
56
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
72
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
127
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
49
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 $(n)^{\frac{1}{m} }$. ...
3
votes
0
answers
178
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 ...
2
votes
2
answers
98
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
173
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 ...
- 1,119
3
votes
2
answers
1k
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 ...
3
votes
0
answers
90
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
5
votes
1
answer
522
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 ...
- 1,751
0
votes
2
answers
104
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
0
votes
0
answers
60
views
Representing Submodular Functions As Maxima of Additive Functions
According to this paper, "every submodular function can be represented as a maximum of additive valuations." It gives an algebraic description as well, but I am having trouble internalizing ...
- 1,922
1
vote
1
answer
121
views
What are the applications of reproducing kernel Hilbert spaces? (outside of statistics/machine learning)
I'd like to learn about some applications of RKHSs outside of machine learning and statistics. For instance, do they feature in physics (maybe quantum mechanics)? It would good to have a brief ...
- 2,134
0
votes
1
answer
270
views
Two questions re. the calculation of total mass in a rod of non-uniform density
I am currently learning about applying integration techniques to the calculation of mass in a rod of varying density. I feel as if I understand the general picture, but I have some specific points of ...
- 418
3
votes
1
answer
38
views
Is there an algorithm for finding the approximate nearest neighbour from an extremely large number of vectors?
Let's say I have some vector $n$ of length 10, and I also have a bag (i.e. multiset) of 1000 numbers, $m$:
$$n = [0.2, 0.3, 0.0, 0.5, 0.8, 0.9, 0.2, 0.6, 1.0, 0.4]$$
$$m = \{0.1, 0.3, 0.7, 0.3, 0.5, 0....
1
vote
0
answers
28
views
Linear application on finite dimensional product space
Consider the set of probability measure $M(X\times Y)$ on $X\times Y$ with $X$ and $Y$ finite dimensional spaces (for example euclidean or discrete space).
Consider the application $f:M(X\times Y)\to \...
- 35
4
votes
3
answers
393
views
Applications of homological algebra in the sciences and engineering
I am looking for elementary applications/examples of the usage of homological algebra in the sciences/engineering. Ideally I am looking for examples that would be accessible to bright undergraduate ...
- 10.9k
0
votes
1
answer
91
views
Understanding and Applying the Half Life Formula
Struggling with this question here:
"One percent of a substance disintegrates in $100$ years. What is its half
life?"
I'm not understanding how to apply the formula $T=\dfrac {\ln 2}k$ to ...
- 1
1
vote
0
answers
58
views
Simplest application of Picard-Lindelöf in the sciences
I am teaching single-variable real analysis and I want to give the students a concrete example of application of the Picard--Lindelöf theorem for a first-order ODE
$$
\frac{dx}{dt}=f(t,x),$$
where $t$ ...
1
vote
1
answer
67
views
Applications of angles in infinite-dimensional inner product spaces
For finite dimentional inner product spaces, the concept of angle between two vectors is widely used in geometry and in physics. Are there any applications of this concept in infinite dimensional ...
- 349
0
votes
0
answers
25
views
Derive a formula for the least squares solution with two column vectors
I am new to this least square solution. If a and b are column vectors in $\Bbb R^N$, then wouldn't the least square solution of a$x$=b be $A^TAx = A^Tb$?
I am really having a hard to visualizing this.
2
votes
0
answers
61
views
Generalized version of Routh's theorem
I am studying the dynamics of vortices in simply connected domains, in other words, in regions that are conformally equivalent to the circle.
Then, through the theory of conformal maps, the ...
- 61
1
vote
1
answer
155
views
I Prove Something is a Category. Now What?
So I am just getting more into category theory, and particularly curious about the applied branches. So this question might come off as terribly naive, since I have not had much exposure to category ...
- 153
4
votes
2
answers
213
views
How can we use Cardano's method to solve a real life problem?
I am making a math project for my school. We can make it on any topic, but should involve some college level math. I have chosen 'Cardano's method' as my topic. I will be showing the method to solve a ...
3
votes
0
answers
93
views
Applications of Pluripotential Theory in real world
I am reading for a math PhD with research in Pluripotential Theory (a subfield in Several Complex Variables). I particularly do study and develop theory related to extremal functions associated with a ...
- 5,815