Mathematics - Science topic

Dear Colleagues, a recent trend in Fractional Calculus is in introducing more and more new fractional derivatives and integrals and considering classical equations and models with these operators. Thus, we have to think about and to answer questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional operators make sense in applications and why?’’, etc. These and similar questions have remained mostly unanswered until now. To provide an independent platform for discussion of these trends in the current development of FC, the SI “Fractional Integrals and Derivatives: “True” versus “False””( https://www.mdpi.com/journal/mathematics/special_issues/Fractional_Integrals_Derivatives2021) has been initiated. In this SI, some important papers have been already published. However, you are welcome to share with the scientific community your viewpoint. Contributions to this SI devoted both to the new fractional integrals and derivatives and their justification and those containing constructive criticism of these concepts are welcome.

Best regards

Yuri Luchko

Hello? Good evening, I would like to ask if there is a questionnaire aligned to the set of indicators on Mathematical Competence given by Sir Turner?

can anyone suggest or interested to have conversation on AI/ML and PLS based mathematical tool. I need to know more information.

Can anyone please confirm whether there exists an explicit mathematical relationship between the gravitational instability growth rate and the corresponding structure (star) formation rate in molecular clouds?

I have formulated the mathematical equation of the vibration problem. The resulting equation is coupled nonlinear differential equation of 2nd order ODE. Please, anyone, suggest to me how to solve it using MATLAB.

I am working on RIS aided communication. Whichever paper I go though, they cook up some complicated mathematics specially optimization problem, which seems to be unsolvable at first. But, then I see they are using some techniques which I have never seen anywhere. Can anyone from wireless comm background tell me, how you people proceed and get those sort of maths?

Hi!

I'm currently working on a Data Science project for optimizing the prices of the products one of the biggest supermarket chains in Mexico.

One of the things that we are working on, is finding the price elasticity of demand of such products. What we usually do, is that, apart from fitting an XGBoost model for predicting sales, we fit a linear regression, and we get the elasticity from the coefficient corresponding to the price (the slope).

However, it is abvious that linear regression is sometimes a poor fit for the data, not to mention that the execution times are way longer since it requires to run separately XGBoost and LR (which is not good considering that there are thousands of products to model).

Because of this, it ocurred to me that we could use numerical differentiation for finding the price elasticity. At last, calculating a numerical derivative is way faster than fitting another model.

However, I'm not sure if this is mathematically correct, since the data does not come from a function.

So the question would be, is this mathematically correct? Does it make sense?

Dear colleagues,

I am researching in a topic related to philosophy and teaching methods. Please, could you point out me if are there any sources on dialectics or contradiction in mathematics education?

Thank you for your answers.

Regards

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.

Does nature understand mathematics?

A connected question is -- How are theory, theorem, and truth related?

I will be glad if researchers and professors answer my question with mathematical formulas or explanations. Thank you so much.

I can't understand why each time we divide by the mass of oxidized NH4-N and multiply by the mass of treated NH4-N.

If we combine and solve the dimensioned constants (G, h, c, e, me, kB) in certain defined ratios, the answers always default to "dimensionless" units MLTVA. The SI units (kg, m, s, A, K) appear to be cancelling each other, suggesting a numerical relationship between them (kg=15, m=-13, s=-30, A=3, K=20).

To test this, 2 sets of units; the SI (G, h, c, e, me, kB) constants and geometrical MLTVA equivalents (M = 1, T = π, ...) are compared (see diagrams below), in every example the numerical solutions are the same. This implies;

1. In defined ratios, the units (kg, m, s, A, K) will cancel each other, i.e.: (3*3) + (-13*3) - (-30) = 0 and so the SI units A^3m^3/s = 1.

2. embedded within G, h, c, e, me, kB are natural units MLTVA, and so G, h, c, e, me, kB are secondary constants. We can use unit-dependent scalars to derive them; c = V * scalar v (v = 11843707.905m/s), Planck time tp = T * scalar t, etc.

The scalars embed the same (kg=15, m=-13, s=-30, A=3) relationship, and so can also be cancelled revealing the underlying natural units;

i.e.: (3*3) + (-13*3) - (-30) = 0 and so scalars (a^3 l^3 /t) = 1

(e/tp)^3lp^3/tp = (A* scalar a)^3(L* scalar l)^3/(T * scalar t) = A^3L^3/T

Results between the 2 sets of units incorporating (G, kB) had a 4-5 digit correlation, (h, c, e, me) 7 digits, and best precision from (c, mu0, R), the scalars had indeed cancelled, and this would seem to support that proposed numerical relationship between the SI units.

The methodology is explained here

1. Is there a logical flaw to the above?

2. Are there other arguments to support/refute this?

3. Is this evidence that ours is a mathematical (simulation) universe?

Some background.

How can we mathematically calculate the critical thickness of polycrystalline(Sputtering) grown thin?

Plz share if yes . I want to know how to get patent in vedic maths.

Is multiverse a differential of possibility, a gradient of cross universe space time planes.

Do multiverses branch or all have separate beginnings.

Are multiverses different mathematical constants or is it different potentials.

How can we progress to a mathematical model of multiverse theory.

First we need a mathematical model of the universe and then we need to generalise it for the multiverse. Is this quantum physical, does this take into account the electromagnetic generation of mass and gravity in a recursive relationship?

Does Arc Length calculus change our notion of frequencies and therefor electromagnetism?

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.

Hello, this is my first post on this site. I'm an undergraduate student doing some Raman spectroscopy of CVD-grown graphene strained on silicon dioxide nanospheres. I notice that D and G' peaks show up in some measurements. The transfer process of the graphene to the silicon dioxide nanosphere-coated silicon chips I would think is far from perfect, as in certainly interferes with the structure of the graphene as there are rips and tears across the sample, as well as impurities and other things. You do however have "pristine" regions that only show G and 2D peaks.

On a loosely related tangent, I'm interested in how the molecular symmetry of graphene plays a role in its Raman spectra, and how that can be expressed mathematically. I wonder if perhaps the mathematical description of graphene in terms of group theory can possibly help explain the redshifts that occur in strained graphene versus unstrained graphene. If anyone has some advice or things to read about that, please let me know!

I have myself tried using the basic method but including incomplete ionization to figure out the depletion width however I failed miserably because of many mathematical roadblocks. I was wondering if this had been done in the literature before and I just missed it.

If anyone can help me in this regard then I would be very grateful. Thanks.

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

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

I am primarily interested in 2-player combinatorial games with perfect information. Useful wiki links are below.

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.

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 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

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.

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 ?

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.