Science topics: Mathematics
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# Mathematics - Science topic

Mathematics, Pure and Applied Math
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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.
Thanks. In the probabilistic interpretation of the Riemann zeta function, the zeros of the function correspond to a uniform distribution of the angular coordinate of the wandering point of the circle.
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How could one increase data values from weekly to daily observations using mathematical algorithm for interpolation?
Hello Nasiru,
What's the reason for wanting these values? That may have more to do with what sort of approach, if any, might make sense.
At first glance, doing this doesn't sound like a good idea to me. Among the reasons:
Any method for taking adjacent weekly values and inserting some estimate for the 6 six "missing" daily values will only bias the estimates of day-to-day variance in scores/values as well as increase the serial correlation across a lag from 1 to 6 days. As well, the presumption of a (perfectly) predictable day to day change is unlikely to be realized in actual measurements.
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The mathematical representation of both equations is same.
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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.
Sorry , this is out my field
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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.
please write the ODE, not only the discretization You used.
however, for multi-step methods you need to create the starting values using a single-step method for all required nodes. Use a discretization of the same accuracy.
Note that the second order ODE could be written as system of two first order ODE.
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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)
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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
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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:
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?
Cenk Tan; There are, of course, several websites that rank the universities worldwide. However, QS is the most famous of which.
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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.
You have only derived one relationship for R. Each of the graphs in Figure 3 show three relationships [1) linear inverted and parabolic; 2) heating from below and cooling from above; and 3) step function] So you need 3 different equations for R. Then there are the three cases [1) N1=0.1, Q=10; 2) N1=0.1, Q=20; and 3) N1=0.5, Q=10]. Maple is doing exactly what you've told it to do: plot one relationship for R. After Maple solves the equation, you could easily paste it into Excel and plot the results.
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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.
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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.
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For writing research articles
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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
Those with creative thinking skills and intelligence
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topics should be where we can mathematics algorithms
you can think of in covid 19, Lung cancer, Brain tumor detection using different deep Learning Techniques and possible to use also ML Algorithms.
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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)?
Hello Lukas,
As the software reports, the estimated Spearman correlation is about .34 (Pearson very close, at about .35). Yes, the correlation is positive. That's because the general trend is that, persons having higher self-rating of knowledge tend to have higher self-rated interest, whereas those with lower self-rated knowledge tend to have lower self-rated interest.
Look within any row of your two-way contingency table, and as knowledge rating increases, you'll see a higher relative proportion of high ratings of interest.
Yes, it's true that the correlation is far from perfect. All that tells you is that you'll find exceptions to the general trend described above as you examine knowledge-interest ratings from the same person over your sample.
Mathematical relationship? (Using 0-5 scales for each variables)
Estimated rating of self-interest = 2.62 + 0.35 * rating of knowledge
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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?
Dear Amit Das,
See my comment precede by >>
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)
>> If the mathematical model is highly original and valuable by itself - you can publish it either separately or along with key simulation results. If the model is quite standard, just briefly refer to it and focus on simulation results. Either way, splitting it on two articles hardly makes sense.
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?
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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.
Jiří Kroc: Greetings Prof. Kroc. In neurology the cutting-edge research is on 1) neurodegeneration, 2) neuroprotection, 3) the unification/entanglement between the nervous system and the immune system and 4) disorders of consciousness. thanks, Mustafa.
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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.
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Mathematics is a language of all science subjects
"The book of nature is written in the language of mathematics."
Galileo Galilei
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There are any papers or studies about the Blended Learning in Mathematics, exactly in (Calculus) ?
The above article is very interesting and it strengthens my conclusions that this problem has been around with up for a long time - at least back to the early 1970''s when I first had experience observing new college students as a TA in grad school. I've taught off and on since the 1960's undergraduate and graduate level courses to both "math majors" and science and engineering majors. My observations were formed originally the early 1970's as the trend of more students taking calculus in high school were less prepared in the mathematical fundamentals and there was a gap in their preparation that showed up at the freshman college level. A teacher in calculus should not have to stop his/her lecture and go over the principle of mathematical induction or the basic analytic geometry of a conic section in freshman calculus. But alas - that was the case. In multidimensional calculus, the students should come in with a firm understanding of linear algebra. However, in my experience that was not always the case. That is the students had holes in their preparations and at some point those holes had to be filled or eventually they would hit a brick wall.
Calculus introduces new and sometimes difficult concepts and the students tend to have little intuition of the concepts of continuity and limits. But without developing a firm understanding and intuition of these and related topological concepts - it is difficult to grasp the calculus. If one does not have the background and facility of understand the fundamental tools of symbolic manipulation (a necessity to do all mathematics), understanding of basic geometry, the basic knowledge of set theory, mathematical induction and logic, it becomes a game of memorization and mechanics. Over time this lack of preparation in the fundamentals has grown more not less prevalent. This lack of preparations is reflected today in that many calculus sequences at the college level include analytic geometry. At one college I have taught specific courses over time, University of South Florida, there is now a required course known as "Bride to Abstract Mathematics." It is a course in logic, construction of proofs, set theory , relations and functions. That is the basic foundations that were once taught in high schools in the US but gave way with the push to present calculus in high school.
I expect we are seeing the same issues arise as subjects like abstract algebra and algebraic geometry become more and more important in applications like computer vision and robotics. It is difficult to apply mathematics to a field when ones understanding of the underlying mathematics has gaps.
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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?
Elegance and parsimony are mathematical virtues. They seem to be aesthetic, rather than ethical or straightforwardly epistemic. However, aesthetics can be an aid to cognition.
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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
"In short, “align” is a automated multi-step superposition algorithm based on dynamic programming and iterative refinement. “align” first performs a per-residue global dynamic-programming sequence alignment for the input atom selections using the BLOSUM62 weightings from BLAST. Then, a per-atom correspondance is established between atoms in the selections. Matching side chains atoms will be included if they were provided in the selection arguments. An initial superposition is then performed followed by up to five cycles of iterative refinement wherein atoms with per-atom deviations over two standard deviations from the mean deviation (if any) are thrown out and the fit is repeated. Finally, the number of atoms remaining at the end of this procedure is printed out along with the resulting RMS value for those atoms."
Pymol offers different alignment methods, which are optimised for different levels of sequence similarity:
Basically, "align" https://pymolwiki.org/index.php/Align does a sequence based structural alignment, first doing a sequence alignment to decide which Calpha atoms to perform a 3D alignment on, then iteratively removing very poorly 3D-fitting atoms from the alignment to reduce the influence of structurally variable loops on the alignment.
In contrast "super" https://pymolwiki.org/index.php/Super aligns two selections by a sequence-independent (unlike align) structure-based dynamic programming alignment followed by a series of refinement cycles intended to improve the fit by eliminating pairing with high relative variability (just like align).super is more robust than align for proteins with low sequence similarity.
"cealign" https://pymolwiki.org/index.php/Cealign aligns two proteins using the CE algorithm. It is very robust for proteins with little to no sequence similarity (twilight zone). For proteins with decent structural similarity, the super command is preferred and with decent sequence similarity, the align command is preferred, because these commands are much faster than cealign.
Each of the commands offers a number of parameters to tweak the method, e.g. setting limits to the maximal gap length and specifying the number of iteration cycles
You can also extend the PyMol capabilities using the "TMalign" module https://pymolwiki.org/index.php/TMalign
To do superpositions between exactly defined atom sets (e.g. in ligands), use "fit" https://pymolwiki.org/index.php/Fit or "pair_fit" https://pymolwiki.org/index.php/Pair_fit
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How can you advise on the methods of mathematical prediction of the causes of salinity?
thank you
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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 really thank all of you for your valuable comments. I attach an article in which to find the significance of the level of democratic practices, we used one sample t-test. My question was about what we do if the data does not follow normal distribution.
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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.
It is very hard to have a unique mathematical expression that will described changes in density x temperature of treatment. It will strongly depends on your synthetical route of the samples, the crystal structure, porosity, and so on.
Normally, increasing the temperature and pressure you will see the densification of the nanoparticles. However, you can see a phase transition that changes the density of the system, so it is not a straightforward analysis. I recommend you to synthesize several NP at a varied range of temperature, then perform porosity/density measurements employing helium pycnometer.
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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.
Maybe you have not captured all of the relevant qualities. Best wishes David Booth
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How can all these discrepancies be explained mathematically?
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).
* Unrotated EFA; maximum likelihood extraction; eigenvalues > 1; based on tetrachoric correlation matrix followed by an oblique rotation (promax).
** CFA with the Diagonally Weighted Least Squares method.
I don't quite understand why the same scale would have 11 or 20 items, but it is not surprising to me that with more items, you could "find" more factors. With more items, there is more room for additional factors (e.g., specific or method factors) to be measured and identified. The more items you use, the more likely it is that some of them will reflect something that is at least slightly different or "unique" relative to the other items. Likewise, with a larger sample size, you have more power to reject models with fewer factors.
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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.
If your background is Mathematics the attached "PNN Primer.pdf" may be useful.
For numerical practice download the NNB DEMO software package (only for Windows), unzip and run. It comes with bundled documentation.
In no time you will be handling neural networks numerically.
This is the link to NNB DEMO, which expires on Thursday May 5, 2022.
Best regards
Daniel Crespin
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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.
Dear Zhwan
I have been thinking in your problem and I b elieve that the logistic part that bothers you could have the following explanation:
Logistics refers to a curve normally known as a sigmoid (very similar to the letter S,) but with right horizontal lines at both extremes, instead fo the curls, and very used in many disciplines, most especially in Artificial Intelligence, and normally varies between -x and x. It is defined as tanh and equal to the ratio between sinh and cosh.
In my opinion, for your geographical position, you should compute the ratio solzen and solalt , and then multiply it by CO^2, which meaning I don’t remember.
Because the sigmoid, and think that we can safetly take a value of 0.5, since it is the average of the linear part of the curve.
Multiplying 0.5 by CO^2 this product MUST be < 77.
Just tu represent that in MCDM is my problem
Therefore, I would appreciate it if you can give me the following values:
CO
CO^4
SOLZEN
SOLALT
1/SOLZEN tan^2
I believe that with this data I could be able to solve the problem using SIMUS.
I agree with your efforts to use algebra and trigonometry, but how are you going to express the < relationships?
Anyway, let me know if you agree with my suggestion, and if you do, give me the values I request.
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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 ?
The Abel prize is a new mathematics prize of the Norwegian Academy of Science and Letters, dedicated to the memory of Niels Henrik Abel (1802-1829) on the occasion of the bicentenary of his birth. It is modeled after the Nobel Prize, and developed from a proposal by the mathematics department at the University of Oslo in fulfillment of a request formulated by the Norwegian mathematician Sophus Lie towards the end of the 19th century.
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AbelPrize.html
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We are planning to implement matrix based mathematical algorithms on FPGA. Could anyone suggest good book for these topics?
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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
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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".
I stuck with this kind of problem. However i want to solve this. I have two types of entities, yet rather than use 2 create modules, these two types of entities are created using 1 create module and then I use assign module to ensure they are different entities. How to ensure that a sum of entities are necessary to be processed and dispose from the system before another sum of entities proceed with different process? Both types of entities will be processed using different processes.What condition can be used in decide module to allow this event?
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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
Yes, I know what you asked about. But my advice was mainly about a transformation of objectives so that they could be "comparable".
As to weights, you should say what you want to calculate, because the "practical backgorund" really matters.
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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.
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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)
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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.
thanks
maryam
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I want to draw a bifurcation diagram using either maple,mathematical or Matlab. an example is the attached file.
Respected sir,
My name is fawad nadeem belong to Pakistan. I am interested in bifurcation matlab code. Kindly provided me the bifurcation code.
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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.
Thank you so much to all of you for your detailed explanation and interest.
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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！
Good morning
Which level?
Best regards
Ph.D. Ingrid del Valle García Carreno
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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
In my view scientific research is about explaining or predicting phenomena. And that is impossible without the use of models, whether they are implicit, or explicit.
And the data are only "visible" by using , whether you are aware of that or not, models. And very often the language of mathematics is used to generate these models. In that sense we all are descendants of Isaac Newton.
Very often I do not see any explicit model, but instead a multitude of procedures in order to process raw data, and basically all is then a question of curve fitting, or one step ahead prediction, where the curve is not known, and the measure of goodness of fit is often not clear at all. And the scientists, that use these models very often do not have a clue about the relation between data and model.
And people from statistics or machine learning barely speak the language of each other. There is hard work to do in University, to redress this, and to partly destroy the Tower of Babel. But as long as we get our papers published , while nearly no one is reading them, the atomization of research will continue.
And that worries me!
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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...
You should check out seminal and fundamental work by Gregory Chaitin starting in 1965 when he was a student in CUNY (City Univ. of New York) and continuing through the 1970's.
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Is there mathematical relation ship between the twist per turn vs the frequency at which cross talk deep occurring ?
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to be published in high reputation journals
Relationship of Laplace Transformations and Beta-Gamma F ( x ).
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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?
Any possibilities in future?
if not..
Why? in terms of mathematics, physics and theology??
Given Albert Einstein's theory of relativity, cosmology regarding the development of the universe, quantum mechanics, future technologies for building interplanetary spacecraft, etc., time travel is theoretically possible. But in practice the building of a time machine by humans is impossible. Even if a man would achieve the required technological development in the next several hundred years, unfortunately he would not have enough time for it. First of all, a person must first solve other global problems, such as the necessary one is urgent, i.e. in the perspective of the next max. 2-3 decades of time, stopping or significantly slowing down the progressing global warming process, achieving zero-emission economy and avoiding a global climate catastrophe, which may occur at the end of the current 21st century. In order for man to be able to create new technologies of the future, to be able to build interplanetary manned spacecraft, etc., he must first save the planet's climate, biosphere and biodiversity from the risk of almost total degradation.
Best regards,
Dariusz
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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?
maybe it will be more clear with an example: (categorical variable = fruit, categories =apple, orange, banana, continuous variable = shelf life in number of Days e.g. 8) I have already used ANOVA to test to see if there are differences between the fruit for shelf life. and have used post hoc tests to find which fruit combinations have different shelf lives (e.g. apples and oranges have different shelf lives)
i am wondering are there any other mathematical/computational methods I can use that will help me determine which fruit has the longest (maximises) shelf life
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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?
Peter Breuer Thank you for your kindly reply, Sir. Yes, that's the generating function that I mean. Do you have any references (papers or books) about this thing? Especially for a higher dimensional.
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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.
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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.
What kind of statements are metamathematics: logical, mathematical, logical-mathematical, philosophical? In the case of Hilbert's claims, they were aimed at finding a secure foundation for mathematical theories, and he thought that this could be achieved if the consistency of arithmetic was established, but that is only an assumption as to "foundation" which, furthermore, results from assuming that logic (because consistency is a formal property studied by theories such as logic) is a kind of guarantee for human knowledge, but logical theories and have their own problems (such as the inapplicability of the principle from the excluded middle to quantum mechanics) and I believe that if the 20th century has taught us a lesson in terms of analytical philosophy and the "foundation of mathematics" it is that it is not even possible to find a deductive language -or an axiomatic system- that is perfect or basic, nor can logic be an unquestionable starting point.
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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.
Please check out the following paper:
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What is the best mathematical approach in each statistical analysis? Does it depend on the analysis level?
You have some question you want to answer. You choose a method that is capable of answering it . Then collect data and use the method. Answer the question and then write it up., Just like in science class. David Booth
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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.
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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?
Dear Vishal Gavande,
Apart from that,
In the Coulomb friction law, the critical shear stress is defined as τ = μp, where μ is the coefficient of friction and p is the contact pressure between the surfaces.
What is critical shear stress?
(solid-state physics) The shear stress needed to cause slip in a given direction along a given crystallographic plane of a single crystal.
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The problem is described in the enclosed sheet with mathematical expressions.
I want analysis in the differential equation.
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How to mathematically interpret the formula Kb=Kf (1−Rw)
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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
okey
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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);
-------------------------------------------------------------------------------------------------------------------------------------------------------
ode command:
-----------------------------------------------------------------------------
[T,Y]=ode45(@snowa1,tspan1,initial_vector1);
plot(T,Y(:,1)-mean(Y(:,1)))
-----------------------------------------------------------------------------
The resulting displacement response is attached to the question.
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.
I understand that the 4DOF system for the washer can be quite lengthy. However, I'm unsure if your question is a control problem. If it is, and the 4DOF mathematical model can be expressed in such form:
x' = f(x) + g(xFc(ω)
where
1. f(x) = [f1(x), f2(x), f3(x), f4(x)]T and g(x) are the nonlinear terms in column vector forms that you derived from the Lagrangian method,
2. Fc(ω) is the control force that represents a function of ω in vector form, and
3. ω (omega) is the control input,
then I think it is possible to design the spin speed profile for the control input, ω, so that the desired responses of x can be achieved. If you want to design the profile, you need to at least understand the mathematical equation for Fc(ω). Do you want to regulate the spin speed at 300 rpm, 600 rpm, or 1200 rpm? Because I see only the signal oscillates within the dimensionless amplitudes ± 4×10–3.
I have plotted the signal according to your suggestion, and compared it with Mahdi's original signal. Note that if t1 > 5/τ, then exp(–τ·θ(t – t1)·t) ≈ 0 after t1, because exp(–0.5·t) has decayed to almost zero.
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How are calculations, the mathematics used to find astronomical objects?
Hi, I agree with Preston concerning the different methods used for planets detection. Now, concerning L1, L2 and L3, if you are talking about the Lagrange points of the Restricted Three-Body Problem. Their positions can be approximated by some simple computations. You can refer to existing literature, for e.g.:
Victor G. Szebehely and F. T. Geyling, "Theory of Orbits: The Restricted Problem of Three Bodies", 1967.
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Dear Researchers,
Do researchers/universities value students/researchers having published sequences to the OEIS?
Dear Marco Ripà ,
I have done both. I cited my work in the sequences and the sequences in my work.
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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!
function f(x) works to do the prediction of accuracy to predict and built the next function of calculus.
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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.
@Knoll, I did it for my research paper. It was about mathematical formulas and equations on panel data econometric model. To open a pdf with MS word, you need to, at first, create a blank word file, then go to the option button on the left corner of the screen, there you will see the option "Open" along with options such as "Save". " Save as". Then click on "Open", then, select the specific pdf file, click on it, and it will be opened on MS word.
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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]
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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.
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Credit 'spontaneous synchronization of metronomes' video
#psychology #synchronization #nature #physics #chemistry #biology
Yes, Björn, these phenomena of spontaneous synchronization of motions include the so-called nano-resonance or Egorov resonance, which explains, for example, the nature of the well-known narrow and intense optical J-band, where, under certain (resonant) conditions, the electronic motion and the motion of the nuclear reorganization of the environment are synchronized. There are good reasons to believe that nano-resonance plays an important role in the life of living organisms.
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Hello everyone,
Could you please recommend me a tool to draw such a figure for mathematical illustration?
Thanks
Actually Adobe Illustrator or even keynote
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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
A first offhand very general remark: Market rules and habits infiltrated into sciences tend to deform scientific explorations and divert individual efforts to some sort of racing competitions...
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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...)
All remarks are welcome.
You may be too affirmative, since nobody ever checked that point (existence of aether) and a large part if the community thinks that it exists in some form or another, as explained in my text. My idea is that in absolute vacuum, matter transfer can be done at no expense (because the "effective mass" of nucleons is 0). The coefficient "1" in the RHS of Newton's law is artificial and corresponds to a choice of units for mass and force, related with our measures and experiments on earth. Maybe, in some distant regions of cosmos, it will be different (the "effective mass" becoming different for the same number of nucleons). This can also help to understand Zwicky's paradox (hidden mass problem).
Checking the existence of aether (or anything similar) would require very sophisticated experiments, maybe the most accessible way would be through the drag which should be perceivable by its action on moving matter, but if it exists it will be extremely weak, which makes the experimental protocol very delicate, cf. my other post https://www.researchgate.net/post/Any_idea_for_proving_or_disproving_the_existence_of_aether
Best wishes
Alain H.
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@Jim Moore
Dear Jim,
Of course no...You are welcome! This misunderstanding arose because you contacted me directly. This gave me the impression of criticism. I've been under all sorts of criticism for almost 2 years now. Accordingly, you could understand my response. In doing so, I have been asking you to "address your messages to EVERYONE". This happened when I began to understand that your messages are not directed entirely to criticism of my materials. [Although, I ask you to agree that it was also on your part...:)]
I ask you to forget this misunderstanding and move forward. I would be very interested in this!
I will reply to second comment later.
Sincerely,
Sergey
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Hello experts,
Can some one help me express muti user massive mimo detection techniques like ZF, MMSE, ML, with their mathematical expressions .
Thank you
For classical MIMO detection, I recommend the paper "MIMO Detection Methods: How They Work" (https://www.diva-portal.org/smash/get/diva2:242286/FULLTEXT01.pdf)
For Massive MIMO, I recommend Chapter 4 in my book that you can download here: http://massivemimobook.com
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Hello,
I am currently working on sensitivity analysis in the context of AHP. I use the online tool BPMSG from Goepel, maybe someone here knows it. However, I have a problem with the traceability of the results. Let's assume that there are exactly 3 criteria in the AHP (C1,C2,C3). Then I would like to know how the final value for an alternative (a1) results if one of the criteria changes in weighting, right?
I'll just say C1 decreases by x. However, the value x that is taken away from C1 must be distributed to C2 and C3. I just wonder which method is used to do this. Is x simply distributed equally to C2 and C3 or does this happen according to the share of C2 or C3 in the sum of C2 and C3?
When I do that, I get the following for the remaining two criteria:
(C1-x) = New C1
(C2 + (C2 / (C2 + C3)) * x) = New C2
(C3 + (C3 / (C2 + C3)) * x) = New C3
Unfortunately, however, I do not know if this is correct. If I multiply the criteria with the corresponding values of alternative a1 and combine the whole thing to a final value, I can calculate the same again with the other alternatives. When I compare the graphs to see how big x has to be to change the final prioritization of the alternatives, I always get the wrong values compared to the online tool. Therefore I would like to know if the redistribution of the weights is correct.
I hope someone can help me despite the long question. Thanks a lot!