Science topics: Mathematics
Science topic

# Mathematics - Science topic

Mathematics, Pure and Applied Math
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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.
Yes!
Refer to my book
Transport of information carriers in semiconductors and nano devices.
Chapter 7. Photon transport.
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Dear Researchers: Please enlist all possible methods available for measuring trend in the historic time series.
The ways for measuring the trend are as follows. I Graphic Method or Freehand. (ii) Semi-Average Method. (iii) Moving Averages Method.
The Trend may be identified by looking at the months that have the same position in each set of three-period patterns. Month 1 is, for example, the first month in the pattern, as is month 4. Sales in month four are greater than in month one.
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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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In The Big Picture (2016), Sean Carroll remarks (page 131): “While math is lumped together with science in many school curricula — and while they certainly enjoy a close and mutually beneficial relationship — at heart they are completely different endeavors.”
Do you agree?
Two examples might help illustrate the issue. Carnot in his 1824 Reflections on the Motive-Power of Fire idealized a steam engine to exclude all losses of heat and all friction. John James Waterston in his 1845 On the Physics of Media that are Composed of Free and Perfectly Elastic Molecules in a State of Motion treated molecules as point particles interacting without friction. In both these examples, the physicists discard extraneous physical features to analyze a physical system. Mathematics in many instances discards all physical elements extraneous to number and geometry. If that is a valid characterization, then one may argue that mathematics merely is an extreme version of idealization used in theoretical physics.
Or not?
Incidentally, Quora raises a similar question in: https://www.quora.com/Are-math-logic-and-science-logic-the-same-thing, with some answers opposing each other.
Math and logic are the foundations of sciences more than anything else. Moreover, they're also a basic culture of sciences. Only in that sense they are different from the rest of sciences. A foundation of a building isn't exactly the apartment you're living at, but without that foundation you don't have a place to live at all.
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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！
Sikai
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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.
Zhwan
My an swers in red
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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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We are planning to implement matrix based mathematical algorithms on FPGA. Could anyone suggest good book for these topics?
I recommended the following books
1- FPGA Implementations of Neural Networks
Springer
Amos R. Omondi, Jagath C. Rajapakse
Year:
2006
Language:
English
2-Guide to FPGA Implementation of Arithmetic Functions
Springer Netherlands
Jean-Pierre Deschamps, Gustavo D. Sutter, Enrique Cantó (auth.)
Year:
2012
Language:
English
3-State Machines Using VHDL: FPGA Implementation of Serial Communication and Display Protocols
Springer International Publishing
Orhan Gazi, A.Çağrı Arlı
Year:
2020
Language:
English
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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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topics should be where we can mathematics algorithms
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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'):
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omega= (1-exp((-0.5)*t))*omega_0+(1-exp((-0.5)*heaviside(t-t1).*(t-t1)))*(omega_1-omega_0);
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ode command:
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[T,Y]=ode45(@snowa1,tspan1,initial_vector1);
plot(T,Y(:,1)-mean(Y(:,1)))
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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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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)
Dear Yahia
Without it is impossible to help you since there are many problems in optimization
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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).
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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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Fermat's last theorem was finally solved by Wiles using mathematical tools that were wholly unavailable to Fermat.
Do you believe
A) That we have actually not solved Fermat's theorem the way it was supposed to be solved, and that we must still look for Fermat's original solution, still undiscovered,
or
B) That Fermat actually made a mistake, and that his 'wonderful' proof -which he did not have the necessary space to fully set forth - was in fact mistaken or flawed, and that we were obsessed for centuries with his last "theorem" when in fact he himself had not really proved it at all?
After retracting my erroneous paper published in Turkish Journal of Computer and Mathematics Education, I have found a new proof and the preprint of my paper has been uploaded in ResearchGate, for public view and comments. The same is attached herewith
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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!
Kindly viait..
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I am aware of the facts that every totally bounded metric space is separable and a metric space is compact iff it is totally bounded and complete but I wanted to know, is every totally bounded metric space is locally compact or not. If not, then give an example of a metric space that is totally bounded but not locally compact.
Euh...The closed L^2 unit ball is not totally bounded since it is closed but not compact. The open unit ball is not totally bounded either, since its closure is not compact.
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Which programming language is best for Mathematical simulation- Matlab or Fortran?
I think Matlab is good
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How long does it take to a journal indexed in the "Emerging Sources Citation Index" get an Impact Factor? What is the future of journals indexed in Emerging Sources Citation Index?
According to Web of Science, ESCI Journal can be included in Science Citation Index (SCI), Social Science Citation Index (SSCI), or Arts and Humanities Citation Index (AHCI), if they meet "Impact Criteria".
Accordingly, journals are included in Web of Science Core Collection (SCI, SSCI, AHCI, and ESCI) if they meet 2 criteria, namely; 1) Quality 2) Impact. The "Quality criteria" comprises 24 sub-criterion, while the "Impact criterion" consist of 4 sub-criteria.
Hence, any journal captured in ESCI have already meet the quality criteria , therefore the quality criteria is the only requirement for journal to be considered in ESCI. Similarly, any journal on ESCI must wait to meet the "Impact Criteria", which can take time, and may be impossible to be predicted. This is because the Impact Criteria is evaluated according to the number of citations the journal is receiving, the performance of authors who published in the journal before, and the number of cross-references between journals in web of science, etc. Waheed Ur Rehman .
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I know that "The Mathematical Intelligencer", "South African Journal of Mathematics" and "The Journal of Humanistic Mathematics" publish book reviews in mathematics.
What other journals publish book reviews in mathematics?
American journal of mathematical and management sciences.
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Assume a mathematical optimization problem with two positive continuous variables:
0 <= x <= 1
0 <= y <= 1000
I am seeking of an efficient way to express in form of linear constraints (possibly with the use of binary/integer variables and big M) the following nonlinear relationship, so the problem can be solved with milp solvers:
• when 0 <= y < 200 then x = 0
• when y = 200 then 0 <= x <= 1
• when 200 < y <= 1000 then x = 1
The numbers 200 and 1000 are indicatively big.
Are there any direct suggestions or papers/books addressing similar problems?
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Jerk is defined as the rate of change in acceleration. But I would like to know some practical applications of Jerk inorder to have better understanding. I kindly request to suggest me some examples.
The application of jerk in physics have many instances and one of the example I can shot is simple that the jerk is nothing but it is all about the rate at which any objects acceleration changes with the time or with respect to time.
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Re: ARTICLE: "Should Type Theory replace Set Theory as the Foundation of Mathematics?" BY
Thorsten Altenkirch
Type Theory is indicated (by the author) to be a sometimes better alternative and a sometimes-replacement for regular set theory AND thus a sometimes better replacement for the logical foundations for math (and Science). It seems to allow turning what is qualitative and not amenable to regular set theory into things that can be the clear particular objects of logical reasoning. Is this the case? (<-- REALLY, I am asking you.)
It is very rarely, if ever, I have addressed anything that I did not have a good understanding of; BUT, here is the exception (and a BIG one). (I HAVE VERY, VERY little understanding of this Article -- even from the most crude qualitative standpoint. You would say I should have researched this more, but it in not my bailiwick , only more confusion, on my part would likely occur, "shedding no light". My sincere apologies. ANYHOW:
:
If indeed things are as the author, Thorsten Altenkirch, says: it seems different things (other than those related to standard propositions in regular set theory) could widen the use of set theory itself yet retaining (including) all of regular set theory (with all of its virtues, as needed). BUT, in addition it is indicated it could be applied to areas (PERHAPS, like biological and behavior science) where present set theory (and the math founded on it) cannot now be applied.
"[ The ] type theoretic axiom of choice hardly corresponds to the axiom of choice as it is used in set theory. Indeed, it is not an axiom but just a derivable fact."
More Quoting of the author: "Mathematicians would normally avoid non-structural properties, because they entail that results are may not be transferable between different representations of the same concept. However, frequently non-structural properties are exploited to prove structural properties and then it is not clear whether the result is transferable." .... "And because we cannot talk about elements in isolation it is not possible to even state non-structural properties of the natural numbers. Indeed, we cannot distinguish different representations, for example using binary numbers instead." ... "we can actually play the same trick as in set theory and define our number classes as subsets of the largest number class we want to consider and we have indeed the subset relations we may expect. ... Hence Type Theory allows us to do basically the same things as set theory" ... as far as numbers are concerned (modulo the question of constructivity) but in a more disciplined fashion limiting the statements we can express and prove to purely structural ones."
"we cannot talk about elements in isolation. This means that we cannot observe intensional properties of our constructions. This already applies to Intensional Type Theory, so for example we cannot observe any difference between two functions which are pointwise equal." ...
"...Hence in ITT (regular set theory) while we cannot distinguish extensionally equal functions we do not identify them either. This seems to be a rather inconvenient incomplete- ness of ITT, [ (common set theory)] which is overcome by Type Theory (HoTT)"
"[It] reflects mathematical practice to view isomorphic structures as equal. However, this is certainly not supported by set theory which can distinguish isomorphic structures. Yes, indeed all structural properties are preserved but what exactly are those. In HoTT all properties are structural, hence the problem disappears. ..."
"While not all developments can be done constructively it is worthwhile to know the difference and the difference shouldn’t be relegated to prose but should be a mathematical statement." [AND}: ...
"Mathematicians think and they often implicitly assume that isomorphic representations are interchangeable, which at closer inspection isn’t correct when working in set theory. Modern Type Theory goes one step further by stating that isomorphic representations are actually equal, indeed because they are always interchangeable."...
..."The two main features that distinguish set theory and type theory: con- structive reasoning and univalence are not independent of each other. Indeed by being more explicit about choices we have made we can frequently avoid using the axiom of choice which is used to resurrect choices hidden in a proposition. Replacing propositions by types shows that that the axiom of choice in many cases is only needed because conventional logic limits us to think about propositions when we should have used more general types."
Oh, here's the link to THE ARTICLE:
The answer is simply no. Additionally, considering "realist (platonic)" and "non-realist (non-platonic)" doesn't actually help with the answer I am going to provide, and the article also begs the question. It's like asking why you like music, is it because it sounds good, or is it because it makes you feel good? Well, that depends on what you mean! Equally, asking a working mathematician about the independence of math, or the construction of math will get you very confused looks. They way one treats math, is ever which is the most convenient, or the most sensible to the person. As such, the article in question does not particularly respect nor delineate the historical and functional differences between these two foundations of mathematics very well. Mathematics is a very broad, messy, overlapping subject. In fact, most of the math I regularly use does not really involve calculations, or functions per se. But, as the article is a pre-print, I assume it simply represents a scribbling of his thoughts.
In order to elucidate my answer better, some background in the cartography of mathematics is needed. There are many different universes (formal distinct foundations of mathematics as unique fields) of mathematics that have their own level of reasoning, and focuses. To name a few, category theory, abstract group theory, analysis, proof theory, many-valued logic, and the list just keeps going. All of which are employed at different levels to ascertain certain properties of math, or even to articulate certain questions. For instance, if one wants to study the different universes of mathematics, category theory is generally involved, and the object considered is called a topos. Or if one wishes to study how numbers work, one can employ number theory to study them as unique things, or you can employ analysis and study them as functions, or you can study them with group theory and consider them as action as well. In this view, no field of mathematics has a primacy over other mathematics, only advantages to the inquiries at hand.
Here is a simple question that I think illustrates the point I am making: is two an element of four, or not? That is to ask, in the construction of numbers, are they considered logically unique (aka type theory), or as informal primitives so that numbers are just simply numbers (set theory)? It is in fact this very question that helps separate type theory and set theory. This question, is akin to asking is meaning found in words or what the words represent? However both are true to a certain degree, and from different perspectives. If we are partial to the former, we are essentially asking, does the construction of words form the meaning they express? Yes, but only if we consider meaning as inherent to language alone (intensional). That is language makes meaning, not the world outside of our minds. If we are partial to the latter however, then words denote things, they are analogs to events, and point to common descriptions that we see (extensional). In the same manner, type theory considers numbers as things in themselves, to say "there are two dogs" is to say two dogs. Because the number two is different then dogs. Equally, computer scientists often employ type theory because it logically constructs things, whereas, mathematicians like set theory because its very good at describing things, and there relationships. It would be very burdensome for a mathematician if we had to logically construct everything from the bottom up. Instead of saying, let us consider a sequence of integers. The computer scientist would have to define every part of that sentence.
I hope this helps clarify the question.
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For writing research articles
read this research paper it will be useful
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One of the central themes in the philosophy of formal sciences (or mathematics) is the debate between realism (sometimes misnamed Platonism) and nominalism (also called "anti-realism"), which has different versions.
In my opinion, what is decisive in this regard is the position adopted on the question of whether objects postulated by the theories of the formal sciences (such as the arithmetic of natural numbers) have some mode of existence independently of the language that we humans use to refer to them; that is, independently of linguistic representations and theories. The affirmative answer assumes that things like numbers or the golden ratio are genuine discoveries, while the negative one understands that numbers are not discoveries but human inventions, they are not entities but mere referents of a language whose postulation has been useful for various purposes.
However, it does not occur to me how an anti-realist or nominalist position can respond to these two realist arguments in philosophy of mathematics: first, if numbers have no existence independently of language, how can one explain the metaphysical difference, which we call numerical, at a time before the existence of humans in which at t0 there was in a certain space-time region what we call two dinosaurs and then at t1 what we call three dinosaurs? That seems to be a real metaphysical difference in the sense in which we use the word "numerical", and it does not even require human language, which suggests that number, quantities, etc., seem to be included in the very idea of ​​an individual entity.
Secondly, if the so-called golden ratio (also represented as the golden number and related to the Fibonacci sequence) is a human invention, how can it be explained that this relationship exists in various manifestations of nature such as the shell of certain mollusks, the florets of sunflowers, waves, the structure of galaxies, the spiral of DNA, etc.? That seems to be a discovery and not an invention, a genuine mathematical discovery. And if it is, it seems something like a universal of which those examples are particular cases, perhaps in a Platonic-like sense, which seems to suggest that mathematical entities express characteristics of the spatio-temporal world. However, this form of mathematical realism does not seem compatible with the version that maintains that the entities that mathematical theories talk about exist outside of spacetime. That is to say, if mathematical objects bear to physical and natural objects the relationship that the golden ratio bears to those mentioned, then it seems that there must be a true geometry and that, ultimately, mathematical entities are not as far out of space-time as has been suggested. After all, not everything that exists in spacetime has to be material, as the social sciences well know, that refer to norms, values or attitudes that are not. (I apologize for using a translator. Thank you.)
Indeed, that is a possibility. Perhaps what we call numbers are labels in a language, as a kind of names that do not really name anything that is literally beyond human language and representations, or that are a way of referring to systems, scales , etc. of which they are a part, mere nodes of a conceptual structure. Some authors have argued that numbers are only signs, signs that are part of representational and notational systems that have proven to be effective, useful instruments to be applied to parts of reality, which are improved and refined over time. However, I believe that it is necessary to take into account the fact that not every system, model or scale works, and this perhaps reveals that there are structural characteristics of the reality to which they are applied that are imposed as limits, that constrain what can be work and what doesn't, and this perhaps means that, although they do not literally describe abstract entities (numbers or geometric figures, for example) as we imagine them, mathematical systems and theories somehow express that which is beyond the representations themselves. You can't use just any geometry to build a house or to explain why Mercury "wobbles" when it's at perihelion, and that suggests that mathematical systems, mathematized theories and models are human creations but they could not be totally arbitrary, so that, even in a metaphorical or indirect way, it should not be ruled out that they represent structural characteristics of the world to which they are applied that is beyond human constructs. We must not forget that we humans perceive in three dimensions, we listen less than dogs, we believe that colors are in things and, to an important extent, we elaborate our theories and build our image of the world accordingly ("the human is the measure of all things" said Protagoras), but there seems to be more and more evidence that, at least the macroscopic physical world is not three-dimensional, so we may never really know what lies beyond us and our representations and to that mystery we must add that of why some models and mathematical theories work and others do not. Greetings.
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I need a clear step wise explanation of the inner workings of the YOLO deep learning segmentation model with all the mathematical nuances.
YOLO is a clever convolutional neural network (CNN) for doing object detection in real-time. With YOLO, a single CNN simultaneously predicts multiple bounding boxes and class probabilities for those boxes. YOLO trains on full images and directly optimizes detection performance. YOLO algorithm is an algorithm based on regression, instead of selecting the interesting part of an Image, it predicts classes and bounding boxes for the whole image in one run of the Algorithm. Ultimately, we aim to predict a class of an object and the bounding box specifying object location. Image segmentation is the task of clustering parts of an image together that belong to the same object class. This process is also called pixel-level classification. In other words, it involves partitioning images (or video frames) into multiple segments or objects.
Also, kindly check these papers:
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Why is it necessary to study the History of Mathematics?
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Hello everyone,
Could you recommend courses, papers, books or websites about modeling language and formalization?
Thank you for your attention and valuable support.
Regards,
Cecilia-Irene Loeza-Mejía
Kindly check also the following very good RG link:
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Is there any mathematical way/method to calculate GRF from kinematic data?
Firstly you should calculate the equation at the centre of mass. And you can using reduction techniques in determinate system to reduce unknowns. exp: neglecting some parameters or some muscles.
Then using Newton laws to calculate forces and moment.
Consider summation of forces in the horizontal an vertical direction separately including GRF and external forces equal to m x a.
Finally consider summation of moments in centre of mass equal to mass moment of inertia x angular acceleration.
By solving these 3 equations by putting knowns, the unknown parameters are calculated.
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Have you ever wondered about using dimensional analysis in mathematics, as we do in physics.
For example, the Pythagoras formula is:
a^2+b^2=c^2
which relates the surface areas of squares resting on different sides of a right-angled triangle.
Therefore, based on a simple dimensional analysis, we may conclude:
a^2+b^2, could NOT be equal to c^3, due to conflict of dimensions.
This is a simple example. How about using dimensional analysis in other mathematics problems.
جميل جدا
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A comprehensive way to find the concentration of random solutions would enhance benefits related with health, industry, technology and commercial aspects. Although beer lambert law is a solution, there are some cases where Epsilon is unknown (Example: A Coca-Cola drink or a cup of coffee). In this cases, proper alternative ways of determining concentration should be suggested.
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I am thinking of the vector as a point in multidimensional space. The Mean would be the location of a vector point with the minimum squared distances from all of the other vector points in the sample. Similarly, the Median would be the location of the vector point with the minimum absolute distance from all the other vector points.
Conventional thinking would have me calculate the Mean vector as the vector formed from the arithmetic mean of all the vector elements. However, there is a problem with this method. If we are working with a set of unit vectors the result of this method would not be a unit vector. So conventional thinking would have me normalize the result into a unit vector. But how would that method apply to other, non-unit, vectors? Should we divide by the arithmetic mean of the vector magnitudes? When calculating the Median, should we divide by the median of the vector magnitudes?
Do these methods produce a result that is mathematically correct? If not, what is the correct method?
The components of random vector in your case are not independent, because they are connected with normalization condition. It means that you can calculate conditional expectations only. Say, M(X|Y) and M(Y|X) in 2D case. And the ME vector in this case consists of conditional components. You should verify, would it be unit vector or not. Concerning median I'm not sure. It is neccessary to think more. In any case it should be calculated using conditional probabilities.
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Hi.
I have a data in which the relationship between two parameters seems to fit to a model that has two oblique asymptotes. Does any one have any idea about what type of function I should use? Please find attached a screenshot of the data. I appreciate any help.
Thanks.
Oblique assymptote rule for rational function - https://www.storyofmathematics.com/oblique-asymptote
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Why the Chi-square cannot be less than or equal to 1 ?
Adrianna Kalinowska There is no special meaning of the value 1 for the khi-square... As a probability function, continuous, the probability of a random variable following a khi-square law to be exactly 1 is 0. As a distance between two contingency tables, it's not clear why 1 should be given a special consideration.
So, I don't really understand the context of your question. Please could you detail?
(By the way, I don"t understand either the origin of the original question and this debate around the value « 1 » in the khi-square…).
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While working in both the software, after loading the training and validation data for the prediction of a single output using several input variables (say 10), it skips some of the inputs and delivered an explicit mathematical equation for future prediction of the specific parameter but it skips some of the input variables (say 2 or 3 or maybe greater). What criteria are these software uses in the back for picking the most influential parameters while providing a mathematical predictive model?
First of all, was the fitness (error) zero (0) at the end of the evolution?
If yes, it means that the skipped variables are not important for the data being analyzed.
If not, it can either mean that some variables are not important or that the evolution is stuck in a local optimum.
Note, that for real-world data, it is unlikely to obtain fitness 0 because of noise or other imperfections (in data collection or measurement).
regards,
Mihai
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Hello everyone,
Could you recommend papers, books or websites about mathematical foundations of artificial intelligence?
Thank you for your attention and valuable support.
Regards,
Cecilia-Irene Loeza-Mejía
Mathematics helps AI scientists to solve challenging deep abstract problems using traditional methods and techniques known for hundreds of years. Math is needed for AI because computers see the world differently from humans. Where humans see an image, a computer will see a 2D- or 3D-matrix. With the help of mathematics, we can input these dimensions into a computer, and linear algebra is about processing new data sets.
Here you can find good sources for this:
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Currently the only proof of Fermat's Last Theorem is very complex and certainly not the proof that Fermat had in mind.
I wonder if it is possible to use a method that drastically
simplifies Wiles' theory, a theory that has received much honors from the entire mathematical community.
My intervention is limited to what Umberto Eco [who I met at the University of Urbino] thinks about Fermat's Theorem. Thank you Dear Dr. Mohamed Azzedine
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can you please tell how to solve the governing equation to obtain the frequencies to compare with the ansys result
Hi
(I haven’t looked at your xml as I doing this from my iPad).
i guess the answer is Yes and No.
Yes, we can use analytical and numerical models, or tests, to find, as best possible natural frequencies. To what effect may be worth pondering.
There are some problem with pipelines.
1) they tend to be very long. Infinite, may be a reasonable approx. Unbounded systems don’t not have modes, they have wave propagation. They can be approximated using modes but you need a lot of them and the modal summation doesn’t always converge as one would want it to.
2) every frequency is a natural frequency for an infinite system, ie you get lots of closely spaced modes, which in turn provides a high modal overlap situation (search RG, it has been discussed before).
3) I imagine that numerical solvers may have a problem with closely spaced modal systems.
4) pipelines tend to lie on something, ie the couple to terrain, again a large system.
So, chasing this problem using modes may not be your best bet.
Wave propagation for analytical models and direct numeric solution for FE probably is the better way to go.
Hope this helps
claes
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Practical applications of special functions of mathematics in the oil and gas industry and related fields, thank you
Special functions approximations (Bessel Functions, Hypergeometric Functions, Confluent Hypergeometric Functions) can be applied to many practical applications of computer science, Physics and many industrial applications. See e.g., https://spie.org/Publications/Book/270709?SSO=1 and the attachment.
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If possible discuss the space, basis, dimension in the context of discreate mathematics and machine learning.
see
A SURVEY OF THE DIFFERENT TYPES OF VECTOR SPACE PARTITIONS
HEDEN, OLOF
Journal:
Discrete Mathematics Algorithms and Applications
Year:
2012
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I want to learn fractal mathematics from scratch. What are the prerequisites and recommended resources for it?
Thanks and regards.
Nishanth
Before talking of fractional order models, it will be better to work on integer orders. After that you can work on fractional order problems easily. There are many references. You can check some of my papers in both fractional and integer forms!
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I am looking for papers that provide explanation analytically as well as mathematically
I hope the following paper are interested to you
1-Computer Vision-Based, Noncontacting Deformation Measurements in Mechanics: A Generational Transformation
Sutton, Michael A.
Journal:
Applied Mechanics Reviews
Year:
2013
2-Vision-based detection of loosened bolts using the Hough transform and support vector machines
Cha, Young-Jin, You, Kisung, Choi, Wooram
Journal:
Automation in Construction
Year:
2016
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Knowing orthometric height, latitude, longitude of a point and reduced level, latitude, longitude of a second point, what's the mathematical expression to compute for the orthometric correction to be applied to the reduced level of the 2nd point to get its corresponding orthometric Height?
Hi Solihu,
The orthometric height is hard to realize perfectly in practice because we need to know the exact path of the plumb line within the topography and the knowledge of gravity variations or mass-density distribution inside the topography at all points along the plumb line. So, the approximation (hypotheses) given by the Helmert (1890) orthometric heights is most used ( Heiskanen & Moritz, 1967, Chapter 4). Also, several refinements have been proposed to the Helmert method to improve models for the value of integral-mean gravity along the plumb line (Tenzer et al., 2005).
---------
Heiskanen, W.A. and Moritz, H. (1967) Physical Geodesy, WH Freeman & Co, San Francisco, USA, 364 pp.
Tenzer, R., Vaníček, P., Santos, M., Featherstone, W.E. and Kuhn, M. (2005) Rigorous determination of the orthometric height, Journal of Geodesy, vol. 79, nos 1-3, doi:10.1007/s00190-005-0445-2
Regards
Abdelrahim Ruby
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I want to know the calculation for following paper. I am attaching the paper. Please help me
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I mean something strictly mathematical and not an algorithmic routine.
For example
The function f(n) produces
1,2,0,0,0,5,0,1,3,8,9,0,0, ...
I need the function f(n) remove the zeros and produces:
1, 2, 5, 1, 3, 8, 9, ...
Unfortunately I missed your post. Possible implementation in Wolfram Mathematica is shown in the attached picture. Of course, Mathematica's native procedure Select looks much more elegant.
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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.
It seems the linearization is accomplished by replacing x1, for x1^2. And separately by replacing x2, for x2^2 & x2^4.
In this way, the surface function is linearized about the origin (0,0), it means we can find f1(x1,x2)=a*x1+b*x2, whilst a and b are calculable in terms of the algebraic parameters, k and c.
But my question transforms to another level. How, we can find a compact algebraic expression for f1(x1,x2), and f2(x1,x2), close enough to the origin. This algebraic expression, need NOT be necessarily linear (it could be a nonlinear function).
Question synopsis:
1--How to find another compact analytical expression equivalent to f1(x1,x2), f2(x1,x2)? (with fair accuracy)
2-- Is it possible to find an approximation near the origin (0,0), for f1(x1,x2), f2(x1,x2), as a function of only one of the two variables (either x1, or x2)?
Regarding the second synopsis, I am to cite another ResearchGate question linked below:
However, the gist of the idea in this link is not clear to me.
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