Mathematics - Science topic

Please look at the text of the section on random walk from page 9 to formula 4.7, where you will find mathematical calculations justifying the probabilistic interpretation of the Riemann zeta function.

I want to understand the mathematics of fluorescence process in terms of excitation and emission wavelengths. I want to develop a general mathematical model with certain specific parameters and without employing a spectrometer, I want to see the emission spectrum mathematically.

Is there a way to model the influence of pH on the electroosmotic EDL potential and velocity field inside the flat microchannel mathematically?

How could one increase data values from weekly to daily observations using mathematical algorithm for interpolation?

The mathematical representation of both equations is same.

Dear scholars,

I am now struggling on a question.

Let's assume that there is a given line or a given arbitrary function defined on a z=0 plane. Now I twist the plane into a non-linear 3D surface that can be represented by any given continuous and differentiable equations. How could I represent this line or function in analytical equations now.

You could think this like "a straight line on a waving flag".

Much appreciated if you have any idea or suggested publications.

Thanks.

Hi

I'm solving nonlinear second order equation by using finite difference method . finally for calculating value at any desired node, knowing three preceding nodes is required however by knowing boundary condition just one of these nodes becomes obvious and still knowing two other values is necessary. it must be noted there are plenty of guesses for values of these nodes which lead to compatible response.

I am preparing for my master thesis in Quantum Image Processing (QImP), i choose to work with [Novel Enhanced Quantum Representation of Digital Images][1] (NEQR).

To convert an image from Classical domain to Quantum domain we need to do a Quantum Image Preparation which in case of NEQR is consists of two steps as shown in the image below:

<a data-flickr-embed="true" href="https://www.flickr.com/photos/144570300@N07/33793456936/in/dateposted-public/" title="NEQR Quantum Image Preparation steps"><img src="https://c1.staticflickr.com/3/2904/33793456936_2d29a8d7e5_z.jpg" width="640" height="373" alt="NEQR Quantum Image Preparation steps"></a><script async src="//embedr.flickr.com/assets/client-code.js" charset="utf-8"></script>

The second step is the one that set the colors. The paper descripe this step as follow

> It is divided into $2^{2n}$ sub-operations to store the gray-scale

> information for every pixel. For pixel $(Y,X)$, the quantum sub-

> operation $ U_{YX}$ is shown as (8) $$ U_{YX} = \Biggl(I \otimes

> \sum_{j=0}^{2^n -1} \sum_{i=0,ji \neq YX}^{2^n - 1} \lvert ji \rangle

> \langle ji \rvert \Biggr) + \Omega_{YX} \otimes \lvert YX \rangle \langle YX \rvert \tag{8}$$

>

> Where $ \Omega_{YX} $ is a quantum operation as shown in (9), which is

> the value setting operation for pixel $ (Y,X)$: $$ \Omega_{YX} =

> {\displaystyle \bigotimes_{i=0}^{q-1} \Omega_{YX}^{i}} \tag{9}$$

Because $ q $ qubits represent the gray-scale value in NEQR, $ \Omega_{YX}$ is consisted of $ q $ *quantum oracles* as shown in (10):

$$ \Omega_{YX}^{i} : \rvert 0 \rangle \rightarrow \Bigl\rvert 0 \oplus C_{YX}^{i} \Bigr\rangle \tag{10}$$

From (10), if $ C_{YX}^{i}=1, \Omega_{YX} $ is a $ 2n - CNOT $ gate. Otherwise, it is a quantum gate which will do nothing on the quantum state.

My question is, how (10) is a $2n - CNOT $ gate if $ C_{YX}^{i}$ is $1$?

From my understanding $ C_{YX}^{i}$ is a computational basis, that is it is either $\rvert 0 \rangle$ or $\rvert 1 \rangle$ and the tensoring of

$ C_{YX}^{i}$ in (9) will produce a column vector.

Also if i interpret $ \Bigl\rvert 0 \oplus C_{YX}^{i} \Bigr\rangle $ as follow: it is the result of $ 0 \oplus C_{YX}^i$ this is just $C_{YX}^i$ because $ 0 \oplus x$ is just $x$. Where $ \oplus $ is XOR. How this will produce a $2n-CNOT$ gate where it is a 3 qubit gate (its matrix is 8 * 8)

[1]: https://www.researchgate.net/publication/257641933_NEQR_A_novel_enhanced_quantum_representation_of_digital_images

please is there any mathematical function that relates the SMD (D32) to the mean diameter (D50)? I actually understand what each of them represent.

thanks

The 2023 ranking is available through the following link:

QS ranking is relatively familiar in scientific circles. It ranks universities based on the following criteria:

1- Academic Reputation

2- Employer Reputation

3- Citations per Faculty

4- Faculty Student Ratio

5- International Students Ratio

6- International Faculty Ratio

7- International Research Network

8- Employment Outcomes

- Are these parameters enough to measure the superiority of a university?

- What other factors should also be taken into account?

Please share your personal experience with these criteria.

Here I attached the journal and the mathematical solution of the Rayleigh number. I need to plot graph exactly in Figure 3 from the journal but I didn't know the command. I have tried using this command,

plot(subs(N1 = 0.5, N3 = 2, N5 = 1.5, a1 = 1, a2 = 3, a3 = 1, Q = 10, R), a = 0 .. 10, 11 .. 22);

but the results show only a single line 2D graph. Hopefully anyone could help me with this. Thank you in advanced.

I know lots of composers have created works around mathematical constructs such as the Fibonacci sequence. I would like to learn if any composers have used mathematical constructs in their music to represent journeys.

How to linearize any of these surface functions (separately) near the origin?

I have attached the statement of the question, both as a screenshot, and as well as a PDF, for your perusal. Thank you.

For writing research articles

I am currently working on the use of metacognitive abilities to improve teacher proficiency of teaching mathematics in Primary schools. I am looking for international collaborators from Japan, Germany, Singapore, Netherlands, USA, Canada and Australia.

Thank you

topics should be where we can mathematics algorithms

I asked people about their knowledge & Interest.

Most had no knowledge but high interest. Now I want to describe this relationship using statistical methods.

I used a likert scale so, the data is ordinal.

Using a Spearman's rank test I get a positive correlation with good significance.

But I don't really understand this result. I expected a negative correlation, since interest and knowledge frequencies have contrary slopes. Does the test look at individual pairs, where those with high knowledge may also have high interest?

PS: How could I form a mathematical equation to describe the relationship (regression)?

I plan to divide my long research article(simulation + mathematical) into two parts, but I am clueless about how to do this. (I can not separate the simulation and mathematical analysis)

I have a few questions regarding the same

1) Do I need to show the common mathematics in both parts?

2) Can the introduction be the same?

3) Can some explanations remain the same in both parts?

Can someone give me the reference of any article divided into two parts?

Complex systems are becoming one of very useful tools in the description of observed natural phenomena across all scientific disciplines. You are welcomed to share with us hot topics from your own area of research.

Nowadays, no one can encompass all scientific disciplines. Hence, it would be useful to all of us to know hot topics from various scientific fields.

Discussion about various methods and approaches applied to describe emergent behavior, self-organization, self-repair, multiscale phenomena, and other phenomena observed in complex systems are highly encouraged.

In my previous question I suggested using the Research Gate platform to launch large-scale spatio temporal comparative researches.

The following is the description of one of the problems of pressing importance for humanitarian and educational sectors.

For the last several decades there has been a gradual loss in quality of education on all its levels . We can observe that our universities are progressively turning into entertaining institutions, where students parties, musical and sport activities are valued higher than studying in a library or working on painstaking calculations.

In 1998 Vladimir Arnold (1937 – 2010), one of the greatest mathematicians of our times, in his article “Mathematical Innumeracy Scarier Than Inquisition Fires” (newspaper “Izvestia”, Moscow) stated that the power players didn’t need all the people to be able to think and analyze, only “cogs in machines,” serving their interests and business processes. He also wrote that American students didn’t know how to sum up simple fractions. Most of them sum up numerator and denominators of one simple fraction with the ones of the other, i.e. as they did it, 1/2+ 1/3 according to their understand is equal to 2/5 . Vladimir Arnold pointed out that with this kind of education, students can’t think, prove and reason – they are easy to turn into a crowd, to be easily manipulated by cunning politicians because they don’t usually understand causes and effects of political acts. I would add, for myself, that this process is quite understandable and expected because computers, internet and consumer society lifestyle (with its continuous rush for more and newer commodities we are induced to regard as a healthy behavior) have wiped off young people’s skills in elementary logic and eagerness to study hard. And this is exactly what the consumer economics and its bosses, the owners of international businesses and local magnates, need.

I recall a funny incident that happened in Kharkov (Ukraine). One Biology student was asked what “two squared” was. He answered that it was the number 2 inscribed into a square.

The level and the scale of education and intellectual decline described can be easily measured with the help of the Research Gate platform. It could be appropriate to test students’ logic abilities, instead of guess-the-answer tests which have taken over all the universities within the framework of Bologna Process which victorious march on the territories of former Soviet states. Many people can remember the fact that Soviet education system was one of the best in the world. I have therefore suggested the following tests:

1. In a Nikolai Bogdanov-Belsky (1868-1945) painting “Oral accounting at Rachinsky's People's school”(1895) one could see boys in a village school at a mental arithmetic lesson. Their teacher, Sergei Rachinsky (1833-1902), the school headmaster and also a professor at the Moscow University in the 1860s, offered the children the following exercise to do a mental calculation (http://commons.wikimedia.org/wiki/File:BogdanovBelsky_UstnySchet.jpg?uselang=ru):

(10 х 10 + 11 х 11 + 12 х 12 + 13 х 13 + 14 х 14) / 365 = ?

(there is no provision here on Research Gate to write square of the numbers,thats why I have writen through multiplication of the numbers )

19th century peasant children with basted shoes (“lapti”) were able to solve such task mentally. This year, in September, this very exercise was given to the senior high school pupils and the first year students of a university with major in Physics and Technology in Kyiv (the capital of Ukraine) and no one could solve it.

2. Exercise of a famous mathematician Johann Carl Friedrich Gauss (1777–1855): to calculate mentally the sum of the first one hundred positive integers:

1+2+3+4+…+100 = ?

3. Albrecht Dürer’s (1471-1528) magic square (http://en.wikipedia.org/wiki/Magic_square)

The German Renaissance painter was amazed by the mathematical properties of the magic square, which were described in Europe firstly in Spanish (the 1280s) and Italian (14th century) manuscripts. He used the image of the square as a detail for in his Melancholia I painting , which was drawn in 1514, and included the numbers 15 and 14 in his magic square:

16 3 2 13

5 10 11 8

9 6 7 12

4 15 14 1

Ask your students to find regularities in this magic square. In case this exercise seems hard, you can offer them Lo Shu (2200 BC) square, a simpler variant of magic square of the third order (minimal non-trivial case):

4 9 2

3 5 7

8 1 6

4. Summing up of simple fractions.

According to Vladimir Arnold’s popular articles, in the era of computers and Internet, this test becomes an absolute obstacle for more and more students all over the world. Any exercises of the following type will be appropriate at this part:

3/7 + 7/3 = ? and 5/6 + 7/15=?

I think these four tests will be enough. All of them are for logical skills, unlike the tests created under Bologna Process.

Dear colleagues, professors and teachers,

You can offer these tasks to the students at your colleges and universities and share the results here, at the Research Gate platform, so that we all can see the landscape of the wretchedness and misery resulted from neoliberal economics and globalization.

Mathematics is a language of all science subjects

There are any papers or studies about the Blended Learning in Mathematics, exactly in (Calculus) ?

Philosophers of science typically recognize two kinds of values in scientific practice: (1) epistemic (or theoretical, or cognitive) virtues, like accuracy, testability, empirical support, etc, and (2) ethical (or social, or regulative) norms, like justice, egalitarianism, openness, etc. Of course, the strict separation of these categories is open to disagreement.

Are there values or norms (of either kind) that are unique to mathematics? Rigour (or provability) is one possibility; computability is another. Can you think of others? Do values play the same kind of role in math as in the natural sciences?

Hi all,

There are instructions on the steps of running ‘align’ in a command-line way as shown in the following explanation found online (https://pymol.org/dokuwiki/doku.php?id=command:align). However, I didn’t found the mathematics or details for PyMOL running ‘align’ through the click-button way in GUI interface. Anyone know the mathematics or details behind it? Thanks a lot!

Yaohui

How can you advise on the methods of mathematical prediction of the causes of salinity?

One of my research questions is about the level of democratic practices in the mathematics high school classroom. When examining the normality of the the demoratic practices, it turned out that they are not normal. In normal samples, we use one-sample t-tests with critical values that fit our assumptions of the level of the democratic practice. For example if we want to take into consideration three levels, we divide (5-1)/3=1.33. This enables us to consider what is below the grade 2.33 weak, what is between 2.33 and 3.66 midium, and what is abover 3.66 high. This serves us in doing the one-sample t-test, where the critical value is 2.33 or 3.66 to verify the level of the variable.

My question is: How can we do that in case of non-normal distribution?

I would like to know the effect of temperature and pressure on the density of Fe2O3 nanoparticles, and if there are some tables or equations that describe the change mathematically.

Combining more than one higher quality has less quality. So how do we express this mathematically? E.g; Let 2x'2 - 4x'2 +6x'2. If it is noticed, one of them has 1 term and the other has 2 terms. So what do we get from here? it looks like 4x'2 =8x 6x'2=12 x sums will be 20x when the derivative is taken. However, if we take their exponent without the differentiation, it will be 4x'2 =16 6x'2 =36. So when more than one higher attribute comes together, it only has less attributes when deriving. THIS IS ANOTHER DEFINITION OF THE DERIVATIVE. THANK YOU. I didn't actually get this out of the way. THERE WAS A LOT OF STARS IN THE PARIS SAINT GERMAIN FOOTBALL TEAM; HOWEVER, WHEN PLAYING TOGETHER, MANY QUALITIES TURNED INTO FEW QUALITIES. THANKS.

I am working with a scale that could be considered to have 11 dichotomous (0-1) and polytomous (0-2, 0-3, and 0-5) items OR 20 sub-items (dichotomous and some polytomous). The sample size is sound (> 700 subjects).

A) If I do an exploratory analysis* with 11 items on half of the (randomized) sample, I get 2 factors. The confirmatory analysis** with the other half confirms the two factors, presenting good adequacy indices values. Some authors also obtained 2 factors, either with similar or different methodology (including item-theory analyses).

B) Moreover, I also tested unidimensionality as some found only 1 factor. Again, all indices are adequate (ECVI slightly higher).

C) However, if I do an exploratory analysis* with the 20 sub-items (similarly to other authors), I get 4 factors. Additionally, just out of curiosity, in the total sample, I get 5 factors!

E) There have also been 3, 4, and 5-factor solutions in the literature, either with 11, 20, or 30 sub-items (all dichotomous).

Basically, I am from a Mathematics background. I found interesting to read ANN but I don't have proper knowledge of ANN, especially in the calculation part. Can anyone help me or suggest me a book considering my situation. Thank you.

Dear talented researchers,

I want to calculate three solar irradiance components (DNI, DHI, & GHI) from these equations which contain logistics, maximum and minimum, Less than, Greater or equal, terms.

How can I use these equations please? I don not know how to use equations 12 & 13 because they have terms such as max, min.

I am not sure, but it seems to be a Logistic map.

1- just for example, how to solve this part from equation 12?

min (1:88 * 10^-8 CO^4, SOLZEN < 77)

2-how to deal with these mathematical operation such as greater than, less than 77, equal or greater than inside these equations?

Thank you very much for your kind response.

Six Nobel Prizes are awarded each year, one in each of the following categories: literature, physics, chemistry, peace, economics, and physiology & medicine. However Mathematics a subject mankind cannot do without is a strange omission and has remained excluded until today. Same with accounting. From 1901 doyens such as Albert Einstein, Marie Curie, Earnest Hemingway were honored with the prestigious Nobel. Do you think it’s time to rethink ?

We are planning to implement matrix based mathematical algorithms on FPGA. Could anyone suggest good book for these topics?

Pls can someone assist me with details on how to calculate effective dose mathematically using exposure parameters such mAs, kV, FFD in x-ray examination

suppose that A and B are two entities. And arrival of B depends on the state of A. The arrival of A is known and can be expressed in mathematical conditions but B can not be as it depends on A. The arrival of entity depends on when A gets processed (Lets say the process is Process 1 with a triangular func of (5,6,7) mins). Whenever A starts to get processed, B is created. I have been able to create the first creation of B logically which relates to A but, I am not sure how to provide the logic for "Time Between Arrival". 

Example

How to find w1, w2,..., wk?

All maximization or minimization

y1=f1(x1,..xn) (maximize)

y2=f2(x1,..,xn) (maximize)

........................

yk=fk(x1,...,xn) (maximize)

F=w1.y1 + w2.y2 + ...+ wk.yk

Mixing of maximization or minimization

y1=f1(x1,..xn) (maximize)

y2=f2(x1,..,xn) (minimize)

........................

yk=fk(x1,...,xn) (maximize)

F=w1.y1 + w2.(1/y2)+ ...+ wk.yk

Is there anyway to relate the Exciton binding energy and Urbach energy of semiconductor of thin film? Can we mathematically relate these two parameters? Any suggestion on this topic would be helpful.

Hello to all

I am an electrical student and I have a question about optimization.

Can you help me?

To optimize (mathematically not meta-heuristic algorithms) the values of the elements and the size of the inductor-capacitor, etc. of an electronic power converter I need a few examples of formulation and simulation. (Preferably in GAMS)

Hello

I'm learning camsol. I studied the mathematical particle tracking method used for modeling in turbomolecular pumps, and I can model a single-stage rotor, but I can not model a single-stage rotor and stator.

Can you guide me, please?

thanks

maryam

I want to draw a bifurcation diagram using either maple,mathematical or Matlab. an example is the attached file.

Stiffness is associated with a small change in the input producing a large change in the output. The phase-field equations such as the non-conserving Allen Cahn and the mass conserving Cahn-Hilliard are stiff differential equations. The solution of these equations represents the dynamic of the interface between two phases. The Allen-Cahn equation is second-order while the Cahn-Hilliard equation is fourth-order nonlinear PDEs whose mathematical form is given in the picture included below with appropriate initial and boundary conditions. The parameter epsilon in the equations represents the thickness of the interface.

Thanks in advance for all of your consideration.

How to analyze the mathematics textbook from the prospective of student‘s use in order to examine how textbooks support students to do mathematics learning？

Is there any theory that could be used for doing such research？or some relevant articles？or give some suggestions？

Thank you very much！

I wish to extend a paper by incorprating the particular feature the authors havent used or considered. However after going through the litreature It isnt clear how much that particular feature plays a role, all I know it does play an very important role for the output that I care about. For experimentation I am assuming a simple linear regression function ax+by where a serves as the contribution to the paper I am extending and x its feature set, my goal is to find the parameter b (mse minimization) by encoding the feature in variable y and thus determine the strength that y plays

However there are some limitation first of that I am assuming the relationship be linear which is very wide of assumption , and I m hoping to consider some kind of non linearity

Question is how do I proceed from here. Is there any mathematical equation I can consider as intial assumption

PS: Note Y is here a continous value not categorical

A very interesting topic, "quantification of randomness" in mathematics it is sometimes reffered to as "complex theory" (although it is more about pseudorandom than randomness) that is based on saying that a complicated series is more random and then there are tests for randomness in Statistics and perhaps the most intriguing test related to information theory -"entropy"(as also being of relevence to and result of second law of thermodynamics), while there are also random numbers generators (pseudorandom numbers generators) and true random numbers generators using quantum computing.

So, what I've been trying to, is making a complete list of all available algorithms or books or even random number generators that will allow me to tell me how much random a series is, allowing me to "quantify randomness".

There are 125 unique infinite series which are pseudorandom that I have discovered and generated based on a rule, now how do I test for randomness and quantify it? Uf the series is random or there is probably a pattern, or something that will allow me to predict the next number in the series given I don't know what the next number is.

Now, do anyone know of any github links based on any of the above? ^ (like anything related to quantifying randomness in general that you think will be helpful).

A book/books on quantifying randomness will be very very helpful too. Actually anything at all...

Is there mathematical relation ship between the twist per turn vs the frequency at which cross talk deep occurring ?

to be published in high reputation journals

Human dynasty in its millennium era. We have identified fire from the friction of stones and now we are interacting with Nano robots. Once it was a dream to fly but today all the Premier league, La liga and Serie A players travel in airplane at least twice in a week due to the unprecedented growth of human science. BUT ONE THING IS STILL ELUDING IN THE GLITTERING PROFILE OF HUMAN DYNASTY.

Although we have the gravitation theory, Maxwell's theory of electromagnetism, Max Planck's Quantum mechanics, Einstein's relativity theory and in most recently the Stephen Hawking's Big bang concepts...… Why can't we still revert back and forth into our life?

I’m currently doing a project and have a categorical independent variable and a continuous dependent variable. I am trying to find which group in the categorical variable produces the highest values for the continuous variable. I have already done ANOVA and post hoc tests. I was wondering does anyone know of any other mathematical or computing methods which could help me with this?

I have a problem with finding references for high-order generating functions. For example in finding explicit formula of this recurrence relation: https://mathoverflow.net/questions/266478/linear-two-dimensional-recurrence-relation

Actually, in my research, there is a three-dimensional recurrence relation. Does anybody have some books about high order generating function in general?

I really appreciate any help you can provide.

I have 2 functions f(x,y) and g(x,y) that depend on two variables (x,y), so I want to find a solution that minimize f(x,y) while maximizing g(x,y), simultaneously??

P.S: These functions are linearly independent.

Metamathematics -- the fundamental logical paradigm of maths -- was never fully defined by Hilbert (nor anyone else), causing severe yet commonly ignored consequences for all branches of maths and maths theory ever since. So, it is difficult to find relevant papers and anybody interested in investigating or discussing the subject.

I want to arrive at a mathematical expression finding the natural frequency of two parallel beams connected by a coupling beam at some location. Is there any helpful theory/literature/approach to get it.

What is the best mathematical approach in each statistical analysis? Does it depend on the analysis level?

Can someone please share the relevant mathematics and explanation for the first order analysis of a BJT current mirror? Any link to an article/book/chapter will be very useful. You can also attach the document if that is convenient.

Thanks.

How to calculate the critical length of fiber in fiber-reinforced polymer composite? Is there any mathematical formula there or we can keep some assumptions?

The problem is described in the enclosed sheet with mathematical expressions.

How to mathematically interpret the formula Kb=Kf (1−Rw)

Hello,

my name is Athanasios Paraskevopoulos, a MSc. student in Mathematics from the Hellenic Open University. I am looking for partners, who work (or used to work) in the field of Didactics of Mathematics.

If you're interested helping me with my study please feel free to contact me via Research Gate or mail: at.paraskevopoulos@protonmail.ch

Thank you and kind regards,

Athanasios

I have a simulation code for a Horizontal Washing Machine.

The code solves the equations of motions of the system by Matlab ode45 and plots the vibration response of the system at the transient state of performance.

In this code, the frequency (omega) is an exponential function of time, as it's stated below (and its diagram is attached to 'the question'):

-------------------------------------------------------------------------------------------------------------------------------------------------------

omega= (1-exp((-0.5)*t))*omega_0+(1-exp((-0.5)*heaviside(t-t1).*(t-t1)))*(omega_1-omega_0);

-------------------------------------------------------------------------------------------------------------------------------------------------------

-----------------------------------------------------------------------------

[T,Y]=ode45(@snowa1,tspan1,initial_vector1);

plot(T,Y(:,1)-mean(Y(:,1)))

-----------------------------------------------------------------------------

It is desired to :

First, increase the frequency to omega_0 by exponential1

Then, increase it to omega_1 by exponential2

But 'the problem' is that:

the displacement response shows an unexpected increase in frequency at the beginning of the second exponential increase (it becomes 20 Hz, which is much larger than the maximum frequency in the simulation- 10 Hz).

Do you know what could be the reason for this response?

Any help would be gratefully appreciated.

How are calculations, the mathematics used to find astronomical objects?

Dear Researchers,

Do researchers/universities value students/researchers having published sequences to the OEIS?

Computing limit of a function at a point is very important task in mathematics. The concept is applicable in science and engineering. Who would compute the limit of the function F at (0,0)? Get an attached file!

Thanks!

I recently came to know about the commercial service https://mathpix.com/ which claims to convert mathematical formulas from (scanned) pdf or even handwritten text to LaTeX.

I have no experience with this. I am interested whether there is an open source solution which solves the same (or a similar) problem.

For thinking - in regard to overtaking "believes, dogmas"

Blind adoption of believes, dogmas by people in populations (Psychology of the Crowd, by Gustave Le Bon) seems to be psychologically coupled and physically from a social scientific point of view explainable:

here, too, synchronization within masses occurs

- and it seems also in accordance to the Kuramoto model.

For this, only a corresponding marketing strategy, seems to be necessary (applied maths / physics).

-------------------------------------------------------------------

Basis:  Yoshiki Kuramoto assumed in 1975 that there is a weak relationship (better coupling) of oscillating systems (oscillators) and that these are almost identical. Kuramoto found that mathematically between each pair of coupled oscillators, their interaction is sinusoidally dependent on the respective phase difference, resulting into the so-called *Kuramoto Model* This even can be illustrated using initially non-synchronous metronomes, which in the course (under certain conditions: moveable surface) synchronize themselves.

This even seems a basic model in nature, biology, chemistry, physics and/or social sciences: – synchronizing of coupled systems:

– collective flasing of fireflies [Buck 1988]

– collective oscillation of pancreatic beta cells [Sherman 1991]

– the heartbeat synchronized with ventilation [Schäfer 1998]

– pedestrian induced oscillations on bridges [Strogatz 2005]

-------------------------------------------------------------------

References

-Kuramoto, Yoshiki (1975) Self-entrainment of a population of coupled non-linear oscillators. In: Araki H (eds.) International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, Volume 39, Springer-Verlag Berlin, Heidelberg. DOI: 10.1007/BFb0013365.

-Buck J (1988) Synchronous rhythmic flashing of fireflies, IIi. Q Rev Biol (63)3), 265–289. DOI: 10.1086/415929.

-Sherman A, Rinzel J (1991) Model for synchronization of pancreatic betacells by gap junction coupling. Biophysical journal 59(3), 547–559. DOI: 10.1016/S0006-3495(91)82271-8.

-Schäfer C, Rosenblum MG, Kurths J, Abel HH (1998) Heartbeat synchronized with ventilation, Nature 392(6673), 239–240. DOI: 10.1038/32567.

-Strogatz SH, Abrams DM, McRobie A, Eckhardt B, Ott E (2005) Theoretical mechanics: Crowd synchrony on the millennium bridge, Nature 438(7064), 43–44. DOI: 10.1038/43843a.

-------------------------------------------------------------------

Credit 'spontaneous synchronization of metronomes' video

https://bit.ly/3IdjYkA

#psychology #synchronization #nature #physics #chemistry #biology

Hello everyone,

Could you please recommend me a tool to draw such a figure for mathematical illustration?

Thanks

Dear friends

One thing I noted in academia is that competition can sometimes be just as fierce as in the world of business.

Sometimes it can be small and petty like who should be first author, often triggered by purely selfish reasons and following justifications.

In other cases competition can be about grands, effectively rendering someone unemployed in some cases. I have seen bullying, discrimination more frequently than in the world of business, the place I come from.

This is truly the dark side of academia, there are also positive things but these are things that make me sick to my stomach.

What is your experience? Do you agree with my rather dark view? If not, why? If yes, how can we fix it?

Best wishes Henrik

Newton's second law, sometimes called the fundamental principle of dynamics, is usually con-

sidered as an irreducible axiom of mechanics. It is actually not a mathematical theorem, but a physical principle based on experiments on our planet. Do you think that this law would be valid in the absolute vacuum, or does it reflect the existence of some omnipresent form of aether which would explain why we need some energy to move an object in the absence of any detectable obstacle or damping of whichever nature? (solid, liquid, gaseous, plasma...)

To help your reflexion, cf.

All remarks are welcome.

If yes, you are welcome here. Please be concise and understandable. Please be ethical when communicating. Experts and amateurs of mathematics are invited. Experts are requested to give explanations if amateurs have insufficient understanding of something.

Please, see also:

https://en.wikipedia.org/wiki/Krasner%27s_lemma#:~:text=In%20number%20theory%2C%20more%20specifically,field%20to%20its%20algebraic%20extensions.

Previous threads can be found here:

https://www.researchgate.net/post/What-is-your-view-on-Fermats-famous-and-notorious-claim-that-he-had-a-truly-marvelous-proof-of-what- came-to-be-known-as-Fermats-Last-Theorem

Please, see also:

Hello experts,

Can some one help me express muti user massive mimo detection techniques like ZF, MMSE, ML, with their mathematical expressions .

Thank you