Science topics: Mathematics
Science topic

# Mathematics - Science topic

Mathematics, Pure and Applied Math
Questions related to Mathematics
Question
Mathematical about the work-related with graphene or any other type of films/coatings.
Lubrication equations in solid films.
The thesis "Aspects of Flow and Viscoelasticity in a Model Elastohydrodynamically Lubricated Contact"
by Ellen van Emden at UT Twente, might give you some ideas!
Question
using BTE how do we get mobilities and conductivity ,more calculation(mathematics) oriented answers would be helpful.
Found this useful,
Refer to chapter 1(Low field electron transport) of Rode's book 'semiconductor and semimetals' . It has a thorough explanation for mobility and conductivity calculations.
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I mean the mathematical component of said process.
What exactly is not clear?
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I am interested in TPACK and mathematics education, can you share recent research articles on both topics here?
For instance:
Of course Yes, give me a little time
Question
Physical reality can be observed. At least part of the structure and behavior of physical reality is perceivable. Humans can communicate about these experiences. Curious humans want to comprehend these perceptions. Humans have designed linguistic tools to be able to communicate about the perceived structure and behavior of physical reality and with these tools, they have constructed structures and models of mechanisms that might explain the perceived structures and mechanisms that physical reality exposes. Some of these structures and models of mechanisms seem to be successful. People discuss the success of these approaches and call this activity exact science. Other humans discuss this activity and call themselves philosophers. Humans are interested in the structure and mechanisms of physical reality because this knowledge helps them survive as individuals and as communities. Part of the exact sciences is formed by mathematics. Mathematics contains structures and models of mechanisms that are not directly derived from perceptions of physical reality. These concepts are derived from abstract foundations. Examples are empty space and point-like objects. Scientists use these concepts to construct vector spaces, number systems, and coordinate systems. The scientists apply these higher-level concepts to construct a model of their living space. The philosophers will immediately indicate that it is impossible to prove that these models are correct. However, these models feature structure and behavior. If the structure and behavior of the models agree more with the perceived models and behavior, then there is a larger chance that the model fits reality. Since reality appears to be very complicated, little chance exists that good correspondence will ever end the dispute.
One of the aspects of the dispute concerns what the best inroad will be for comprehending most of the structure and the mechanisms of physical reality. That is the background of the posed question.
The paper "Sticky Space Coverage" relies on the results of David Hilbert, John von Neumann, and Cantor. I consider them better and deeper-looking mathematicians than the EPR team. They all worked on set theory, vector spaces, and Hilbert spaces. Hilbert cooperated with Einstein on gravitation theory. The paper "The Standard Model of Elementary Fermions and the Hilbert Repository" ; https://vixra.org/abs/2106.0135 offers an explanation for the phenomenon of entanglement.
Question
Dear colleagues, I would like to know if there is a mathematical equation or model to calculate the Soxhlet number of cycles by varying the following parameters:
- the type of solvent
- the volume of the extractor
- the temperature of the solvent heating
if yes how can we apply it? and how much uncertainty it has?
thank you so much
best regards
Suggested reference: D.A. Ellis, "Prediction of multistage solvent extraction operation from limited data", Industrial and Engineering Chemistry, 52(3) March 1960, 251-252.
Question
I need mathematical formula to measure public service quality and organizational impact
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such as Fourier , Hilbert or Laplace transforms in order to analysis and studies in the field of music acoustics.
You my see
1-Transform methods in applied mathematics: An introduction
Wiley-Interscience
Peter Lancaster, Kestutis Šalkauskas
Year:
1996
Language:
english
2-Integral transforms in applied mathematics
Cambridge University Press
John Miles
Year:
1971
Language:
english
Question
Please look at the mathematical construction of theta and zeta functions in the representation of a winding sphere. In this paper, based on the representation of the winding of a sphere, we construct a proof of the Riemann hypothesis of nontrivial zeros. Could you check this proof?
Dear Bayak,
Your idea is certainly interesting, but unfortunately, I am not an expert on topolog,y. I strongly suggest you first meet a professor and talk to him on how you have tackled the problem. Then give him the paper to study. This procedure will make a good beginning. Also, you can start by giving seminars/ lectures on the proof. You will get suggestions for improvements ( if any) And then you get a few people to recommend your paper to a Journal.
Best of Luck and God Bless!
Regards
Dr Kumar Eswaran.
Question
Hi researchers,
I need to find a method of proving a mathematical equation that exist in attached file.
This mathematical equation is about Bessel function.
I will be thankful to hear your helps and advises.
This link might be useful, have a look:
Kind Regards
Qamar Ul Islam
Question
Dear Community,
I want to center (subtract the mean) my data in order to lower my intercept (as close as possible to zero). However, as I have categorical data as well, which I don't know how I can possibly center, I can't seem to lower my intercept.
And the thing is that my dummy variable drive up the intercept... So I don't know to fix the issue.
When I enter only continuous variables that are centered, the intercept is close to zero.
I thank you in advance?
Not sure why you want the intercept being zero, but one way you could easily achieve this is by first finding the (non-zero) intercept and the subtract this value from the response variable.
Question
Dear Colleagues!
I hope you are all doing well. I have a question to all of you. I love to teach and so far I have been teaching everything from international business, marketing, management to organisational psychology. I feel ambivalent towards this however.I love to teach and Im curious in my nature and what better way to learn new things than to teach? However I also feel that if I continue being a generalist It might also be bad since I risk loosing touch with my main specialisation.
My speciality is this :
Best wishes Henrik and professor Hugo 3 months old who keeps me company when Im trying to work :-)
Ps stay safe.
Teaching one subject is more scientific and it will give you more academic background.
Question
I have seen that some equation sets have an explicit way of defining the substrate consumption whereas others have an implicit way. I would like to know how to convert the former into the latter.
For instance, in the attached file, it can be seen that there are two ways to describe the growth of bacteria.
In the first (explicit), the presence of a half-saturation constant suggests that the model is a Michaelis-Menten case. The second is straight a logistic model.
I was wondering if I can convert the first into the second, that is explicit to implicit.
Considering that the Monod term says that
μ = μᵢ[S/(S + K)]
then I can write
Ṅ = μN * logistic term
My question is: Would this modification be mathematically and biologically sound?
If yes, how can I estimate the carrying capacity? For instance, if I know the amount of limiting substance, can I estimate the number of cells that a system can sustain?
Thank you
You will be best judge I think . There are so many model papers of logistic regression on Michales Menten equation - https://www.youtube.com/watch?v=fv6OAVe2vQc
Question
I'm working on constructing a field based on finite undirected and unlabeled graphs. I've selected graph join and graph Cartesian product. But I'm trying to figure out if the latter distributes over the former (or simple graph union).
See
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I want to know how we can relate magnetostriction with Applied magnetic field mathematically? Or if there is any way to derive it using mechanical equations?
There are some classic thermodynamic models to discuss the influence of an external magnetic field on magnetostriction. And we can discuss the influence of external magnetic field on magnetostriction in ferromagnetic materials with different initial stress states.
【1】Shi Pengpeng. One-dimensional magneto-mechanical model for anhysteretic magnetization and magnetostriction in ferromagnetic materials. Journal of Magnetism and Magnetic Materials 2021, 168212. https://doi.org/10.1016/j.jmmm.2021.168212
Question
Hi All,
Can anyone please tell me which mathematical equation can be used to normalize the single ion monitoring quantitation in GC-MS? Thanks in advance!
Nice question
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The field equations originally starting as Maxwell distributions graphs configure a velocity variable. Understanding that in connection to wave theory requires a mathematical transformation of velocity variable into wave function parameter. This may help mathematically to define particle wave quantum relativity quantitatively. Legendre transform theoretically will have a way to provide link among functionality of parameter-variable systems.
Dear
One paper for you
Question
There is a contradiction between the natural width of the energy transition, which is determined by the lifetime at the corresponding energy level and the spectral line width of the radiation line, which is determined by the duration of the wave train.
For example: For the Mössbauer transition, whose lifetime is of the order of 2 years, while the interaction time at the receiving end is about 10^(-10) sec.
Mathematically, this interaction is expressed by the Feynman diagram of the electron - electron interaction, which integrates over the internal photon line, which, together with the delta functions of the vertex parts, limits the photon spectrum.
By the way, the same paradox applies to any other type of collision.
So, is exist (really) the electromagnetic field?
Dear Pratik,
dissatisfaction with quantum theory, among physicists, lies in the fact that it, like any statistical theory, does not allow describing the dynamic processes of individual physical objects. The only physical substantiation of quantum theory is that the exchange of energy between objects occurs (according to Max Planck) in portions of the integer Planck action per oscillatory cycle.
Thus, the phase space of coordinates / impulses (time / energy) is divided into cells, inside which any processes can occur without violating the Planck prohibition (the classical model of the hydrogen atom), and at the border between the cells, the Fourier transform degenerates to the zero component. The space of classical c-numbers is partitioned into symmetric and antisymmetric components. It is possible that this corresponds to splitting the wave functions into even and odd parts (fermions and bosons).
Thus, the task is to construct an internally consistent building of classical mechanics that is compatible with the quantum theory, taking into account the properties of symmetry and interaction parameters.
Question
When we derive the formula for length contraction, we use the direct Lorentz transformation. But for solving the formula for time dilation, we use the inverse transformation. Why is that so?
Question
A question from far away worlds...Life Sciences (cricket) and an hyperbolic function from history of mathematics are trivially juxtaposed to encourage whatever reply.
[The antennas of the cricket roughly complete the less frequently represented branches of the hyperbola in the photographed virtual third and fourth quadrant of the Cartesian coordinate system].
Great correlation ! in picture . please go through one of the special aspects of compuational epidemology -https://www.researchgate.net/post/How_best_fit_regression_method_can_be_applied_to_model_SARS-COV-2_epidemology
Question
They say the best educators are able to make a complex subject easily understood by a child. Perhaps this is a challenge to us all.
Quarternion mathematics can be quite complex to wrap your head around. For educators out there how are you explaining this to your students from high school.
Is a pictorial method the most appropriate under these circumstances.
Hey Joseph,
In my opinion sticking with unit quaternions would be the way to go. At a high school level it may be a good idea to skip the complex math definitions and instead focus on the intuitive "definition" of a unit axis and a rotation about that axis. Depending on the context you could run through an animation/example in 2D or 3D to show how multiplication works, then give the multiplication rules as formulas -- the same way one might do for dot and cross products at the high school level.
I would guess another important question to answer is why a roboticist would use quaternions instead of other representation. Having a short discussion on gimbal lock could be a great motivator, especially if there audience is interested in aerospace applications or robotic arms.
Thanks,
Logan
Question
Mathematics is the basis of exact sciences. The development of mathematics consists in the fact that, among others, new phenomena of the surrounding world, which until recently were only described in the humanistic perspective, are also interpreted in mathematical terms.
However, is it possible to write down the essence of artistic creativity in mathematical models and create a pattern model for creating works of art, creative solutions and innovative inventions? If that was possible, then artificial intelligence could be programmed to create works of art, creative solutions and innovative inventions. Will it be possible in the future?
Do you agree with my opinion on this matter?
In view of the above, I am asking you the following question:
Will mathematics help to improve artificial intelligence so that it will achieve human qualities of artistic creativity and innovation?
I invite you to the discussion
Best wishes
Dear Stan Sykora, Boris Pérez-Cañedo, Baidaa Mohammed Ahmed,
Thank you for answering the above question and participating in this discussion.
Regards,
Dariusz Prokopowicz
Question
what are other possible ways to convert a CW laser to a pulsed laser. Please give all the theoretical and mathematical details.
Output optical power can be achived by optical phase shift in one arm of Mach Zehnder interferometer. π/2 phase shift will lead to destructive interference and lower values of output intencity.
If we consider integrated structure of silicon Mach Zehnder modulator, the phase shift is induced by changing electron and hole concentration along with the effective refractive index.
The attached picture represents output power equation of MZM with a phase shifter in one arm. Indices 1 and 2 corresponds to MZM arms with and without the phase shifter. Index 3 denotes the phase shifter itself. L - length, betta - propagation constant, alfa - absorption coefficient.
Question
More specifically I am looking to analyze and plot non-michaelian kinetics based on functional parameters from BRENDA or similar sites. I do not know how to find the mathematical function describing such kinetics and have not yet been able to find it in the literature.
I would greatly appreciate any help from the community!
You might be able to find some useful equations for the situations that interest you in I. Segel's monumental book "Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems"
Question
Hello Experts,
I want to know that how to find theta maximum when i am using GPS and sphere and surface type distribution. and using cosine distribution.
then i want to know that is there any mathematical calculation to find theta maximum for biasing.
like in the Geant4/examples/advanced/radio-protection theta maximum is 0.003 deg. how they got this using the surface area of source or object. like how can i get for my object ?
any type of help will be appreciated.
Thanks in advance !
Best Regards
Priyanshu
Question
How to transfer the logical description of safe constraints to mathematical description？Any feasible idea？
The following work maybe useful
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• An understanding of theories about how people learn, and the ability to apply these theories in teaching mathematics; It is one of the primary requirements for effective teaching of mathematics, and a large number of scientists have studied mental development and the nature of learning in different ways, and this resulted in various theories of learning.
I totally agree with Darren John Stevens, I consider that it is a precise and detailed reflection, as well as current and fundamental for the time that we are having to live! Many thanks.
Question
Question about the loss of hyperbolicity in nonlinear PDE: when complex eigenvalues appear, what is the effect on flow? I understand that we do not have general results on existence in this case, but is it only the mathematical tools that are lacking where can we show physical phenomena of instability?
Blow -up -analysis -
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Different longitudinal studies, such as the Perry Preschool Project or the Abecedarian Project, have shown that early and effective exposure to different content in ECE students, as science or maths, cause positive effects in children later development not only in academical sphere, but also in personal, social and economic ambits.
There is little interest in teaching children about science due to the many difficulties in this field. Among them
1- Indicators of learning difficulties related to language
The child's speech is delayed compared to his peers.
Limited vocabulary.
Problems with forming sentences, finding words, and using and using language appropriately.
2- Indicators of learning difficulties related to cognitive skills
Poor to follow directions or follow a daily routine.
Slowness in saving and retrieving information - when needed - such as memorizing colors and days of the week.
Forgetting thoughts while talking and not remembering the topic the child is talking about if someone interrupts it.
Problems with motor coordination (eg, jumping, undressing, buttoning, tying shoelaces).
Difficulty finding similarities and differences between different stimuli.
Problems with visual-motor coordination, represented by the child's inability to achieve coordination between hand and eye movement, and he cannot arrange beads, cut correctly, or follow a line while writing.
3- Indicators of learning difficulties related to attention
Moving from one activity to another without the child finishing his previous activity.
Having difficulty following the child to what he hears or sees.
Short attention span of the child, and distraction.
There is a problem with the child following the sequence of information or ideas.
Question
Hi all,
I attached an image file of excel data in which the problem is to predict the value of u by using any mathematical method.so, please share me the procedure or method to be followed to solve the problem.thank you in advance.
You search data imputation in internet there are many tools to predict the missing values.
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Hi all, I am looking for a patterning assessment to use as a pre- and post-test alongside a patterning intervention in mathematics for 7 to 9 year old children.
I know of PASA by JT Mulligan, are there any others?
I hope the following is useful !!
Assessment of Young Children from Culturally Diverse Backgrounds: A Journey in Progress
Notari-Syverson, A., Losardo, A., Young Sook Lim,
Journal:
Assessment for Effective Intervention
Year:
2003
Question
Although there is a reasonable dose of physical and geometrical interpretation of the mathematical formulas and equations, more work is needed to bridge the gap between the theory of mathematics and its applications. For example, let us look to the coplanarity of three vectors, which are typically expressed as a dot and cross products between the three vectors. Based on practical feed back, when the explanation of the coplanarity is broken down into cross product first to generate a perpendicular vector and then then do the do product with the third vector, which is now expressed an orthogonality relationship between two vectors a deeper understanding can be achieved by the students. Indeed more class work is required to take the students through this journey using a step wise approach. I do believe that the teaching of mathematics to engineering students should go to a deeper physical interpretation to facilitate its comprehension and understanding. Your comments are highly appreciated.
I would recommend you to use practical examples from real life. Because your students will stop to ask you then why we need to learn this. When you explain vectors, I would recommend you for example these videos for inspiration how to explain it the way each student will understand it. But I´m sure you are able to find more examples. https://www.youtube.com/watch?v=dpv06SFHtRg https://www.youtube.com/watch?v=ml4NSzCQobk https://www.youtube.com/watch?v=uxlCDQNisU0 When they will have a basic idea what vector is and why it is useful, you can of course solve even more difficult questions and real life problems :) Vectors are all around us. https://www.youtube.com/watch?v=XzsCLlfCgjI
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The gyroscope is quoted as a mathematical gyroscope, that is, the intersecting lines of the equator and one meridian. The permissible movements of our mathematical gyroscope are the proper rotations of the equator and meridian circles and the rotation of the entire structure around the axis passing through the intersection points of the two circles. Since the proper rotations of the circles are specified by the group of diagonal matrices with complex units, and the rotation of the entire structure is specified by the group of special orthogonal matrices, it is expected that the group of motions of the mathematical gyroscope generated by these groups is equal to the unitary group U(2).
It is clear that this construction has a generalization in the form of a mathematical gyroscope of the n-dimensional sphere, which generates the group U(n). Does this construction find application in phenomenological theories of gauge symmetries?
It should be added to the above that the unit hypersphere of an 8-dimensional space with a neutral metric is homeomorphic to the product ℝ4×S3. Therefore, if the unit hypersphere is orthogonal to the vacuum vector field of accelerations of matter in 8-dimensional space with a neutral metric, then the geometry of the unit hypersphere corresponds to the geometry of the vacuum. In turn, the geometry of gauge symmetries S3×S2×S1 is specified by the geometry of an isotropic surface in a 7-dimensional section (obtained by fixing time) of a compactified space with a neutral metric.
Question
I am looking at glacier change in the Andes. I am using SPSS for my statistics. I have been provided with discharge data also, for which I would need to look for a relationship between glacier area, temperature, and river flow over a specific time period of 7 years. Temperature is given in daily minimum/maximums, river flow is monthly, and area change is yearly. Thanks :)
Yes, Daniel Wright, at least partly. But I was also trying to understand whether there are explanatory and outcome variables versus simply looking at associations among the 3 variables.
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Dear colleagues, what do you think of a possible mathematical analogy between a one-sided surface and a Bose-Einstein condensate?
Yes, dear Narasim Ramesh, but not only this. For example, one can consider the behavior of a superfluid liquid on the surface of a Mobius strip or a Klein bottle.
Question
Why CPW square slot antenna gives a wide impedance bandwidth?
Is any mathematical derivation/equation is available for it?
Thank you
Question
Hi everyone! Greetings from Munich!
It appears in my mediation analysis, that X is negatively related to M, and M is positively related to Y. Also, i find a significant negative effect of X on Y through M. But since M is determined as a perceived benefit, i am currently struggling with the interpretation of this indirect effect.
Mathematically, of course, this indirect effect result makes sense since "- x + = -", but can i interpret this by saying the benefit is overridden or is it rather that the benefit "backfires" on Y and thus a negative indirect is found?
Many thanks in advance!
Check out my paper in Journal of Marketing Research where we talk and show empirically how these mediating effects occur in the context of benefits based choice.
Question
Nonlinear mixed-effects models (may) consider data below the limit of quantification (BLQ) in parameter estimation. However, an evaluation of the goodness-of-fit plots (observations vs predictions in particular, using spline interpolation), displays a strong trend (of spline interpolation, but not of the data) in the region of censored data, as if the model disregarded BLQ data and the data were the lower limit of quantification itself, as structured in the database. I believe that the database is structured correctly and that the model considered the censored interval. Apparently this plot is the only one to exhibit this behavior.
Is spline interpolation adequately representing the competence/capability of the final model in this case? How to handle this situation?
Interpolation can be thought of in two ways:
1) Interpolation methods approximate some underlying model
2) Interpolation simply approximates a set of numbers continuously
In case 1), interpolating will capture the essence of the underlying function, if and only if, the data is representative of the fundamental model. Noise will definitely throw your results off.
In case 2), you are simply generating an approximation from a set of known numbers, e.g. Lagrange interpolation; forward, centered and backward Newtonian interpolation, &c. The numbers in hand may or may not represent anything in particular, or, they may not be accurate enough to enable one to gleam the underlying processes. Purely interpolated results can and do grow wild as the power of interpolation is increased.
What I suggest is a low power interpolation of the database, then look at the curve and compare to any model you have in mind. If the interpolated results resemble strongly enough some model, then you may further pursue investigating along that vein.
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I'm looking for referents / references about how/if learning mathematic language prior to grammar impacts comprehension ad interpretation abilities.
Another route but similar purpose, is to understand if enhancing adults' skills on mathematical language understanding can have any impact on the development of their speaking and writing skills.
Does anyone know of any studies, papers around this?
Thank you!
Impacts of a Prekindergarten Program on Children's Mathematics, Language, Literacy, Executive Function, and Emotional Skills
Weiland, Christina, Yoshikawa, Hirokazu
Journal:
Child Development
DOI:
10.1111/cdev.12099
Date:
November, 2013
Question
Is there any mathematical equation to determine the appropriate number of hidden layers for a sequential model?
Hi Hasintha, It's a practical problem and you should make decision about number of hidden layers by checking accuracy of the fitted model.
Question
In literature two formulae are generally used for evaluating Gravimmetric power density (Pd)
1. Pd (W/Kg) = Energy density (Whr/kg) x 3600/ discharge time (s) and
2. Pd (W/Kg) = [106 x V2]/[4 x ESR (Ohm) x mass (mg)]
But it has been found that each equation gives different result for any known value of current density. What may be the reason for it? Which equation is to be used for determining the power density of two electrode supercapacitor?
Dear M. K. Dey
In my personal opinion, there is no point to coincide with the Power density values from GCD or EIS.
The power density value from the first equation depends on the energy density calculated from GCD. (It seems more reliable)
Whereas, power density calculated from the second formula depends upon the characteristic values from the EIS.
For further details of the calculations, you can see this article
Question
is there a deeper fundamental property of neutrino oscillations? How does it work at the field level? is there any advanced mathematical connection or is only a physical fact?
I have a more simple view on the neutrino:
IMO the neutrino is a simple particle with a very weak interaction with matter. This weak interaction gives rise to only a few possible interactions in specific circumstances giving rise to neutrinos with different mass, i.e. there is only one type of neutrino but with different masses according to the interaction which created it.
As far as I know, the neutrino doesn't travel at light speed and, it doesn't follow the mass law "m=m_o gamma".
JES
Question
I designed and made a rotary atomizer with the help of 3D printing. Now, in order to evaluate its performance, I want to measure the diameter of the produced droplets. According to mathematical calculations and theory, the diameter of the droplets is about 100 microns and I want to measure the diameter experimentally.
Please help me in this way how to experimentally measure the diameter of a drop that is produced continuously.
Best regards,
I think the most straightforward (and intuitive) way is what Amit suggests. A good imaging setup (bright light source, and good contrast) will resolve the problem. Regarding the distribution, the image processing of the captured images (depending on your image quality, it may be super easy or super difficult) provides you with the distribution of the droplets. I use a similar procedure for measuring the diameter and distribution of bubbles departing from a boiling surface.
Thanks,
Shayan
Question
Hi everybody,
Maybe a stupid question, but I forgot how to calculate such things. Let's say I have a group of 200 elements (genes). I want to divide this group into n subgroups, each containing 10 elements. However, each element should be present in more than one subgroup. Is there a cool formula to calculate n depending on the number of times each element should be present in independet subgroups?
Thanks,
Johannes
I think you meant set not group! cuz groups are sets with binary operation with 4 axioms (asscoiativity, identity, inverse, and closed operation)
Now, If you have 200 elements and you wanna compute how many subsets with 10 elements you can make, follow this formula
n=200×199×198×....×191÷(10×9×8×...×2)
Question
I got confused when I plotted the graph of -(x^2 - x)^(2/3). the graph shows the function achieves its maxima at x =0 and x =1 but when we follow the procedure of derivatives then we get x = 0.5. Please help me in this.
Let me make a short summary on the example by Vishal kumar Pandey:
We may focus our attention on the interval (-epsilon, 1+epsilon) for some epsilon >0, as a domain of f(x), or even [0,1] (the natural domain of f is R). As Joachim Domsta rightly noticed, if f(x) is differentiable in the vicinity of x0, change of sign of f'(x) at x0 is sufficient for f(x) to have a local maximum or minimum there. Subsequently, by the celebrated argument of Fermat, f'(x0)=0. We do not have this situation in the example discussed here. At x0=0 or x0=1, we do not have differentiability of f at all. Left and right derivatives are +infty and -infty at 0, and similarly at 1. But in these two bad points we have a (global) maximum. No contradiction with what I wrote above.
There is something deeper under the skin: A derivative function f'(x) defined in (a,b) has the intermediate value property (called also the Darboux property), i.e., image of a sub-interval in (a,b) is an interval. This is why f'(x0)=0, when f'(x) changes sign at x0. It is interesting to observe how close is the Darboux property to the Fermat's argument.
Even though the example by Vishal kumar Pandey is within the scope of elementary calculus, it has a significant didactic value. Using it, we can discuss "anomalies" of functions with our introductory math analysis students.
Question
I'm solving differential equation.
u'(x) = a11(x)*u(x) + a12(x)*v(x)
v'(x) = a21(x)*u(x) + a22(x)*v(x)
or simply, U'=AU.
Given A(or, a11/a12/a21/a22) as a function of x, i want general solution for u & v.
Solution for constant A is already known, using matrix-exponential.
But this case, this is for given matrix A as a function!!!, and I found out that the same approach is not valid by my hand.
Hope any keyword or references to go further....please.
Your system is a nonautonomous dynamic system.
You can find the general solution directly. Using the exponential of A(x)
the method works even the matrix includes a variable x.
See the attached article; I hope you will find it useful.
Best regards
Question
Hi everyone. recently I designed a customized semantic segmentation network with 31 layers and SGDM optimation to segment plant leaf regions from complicated backgrounds. can anyone help me how to explain this with mathematical expressions using image processing. thank you
I think the best way is to use the results of the semantic segmentation and samples of leaves from fieldwork to create your mathematical expression using any curve fitting mathematical tool.
Question
I have the x,y data of two curves (solid red and blue in the attached image) and I want to find out the envelope function of the two (dashed magenta curve in the attached image). Is there a way to do it in Origin or Igor? Or in any other mathematical software for instance?
Arani Biswas Deconvolution of a composite peak into its individual peaks plays an important role in the interpretation of many types of graphs including XRD, XPS, FTIR, and PL etc. In this video, I have discussed how to deconvolute simple combined peaks, composite peaks and how to correct missing data in a given peak with the help of deconvolution. In the case you want to further ask about it, please do comment on the specific video, I'll respond to it shortly. I have provided the practice files (OriginLab) here. Thanks
Question
I want to integrate two carbon fiber materials together and want to model it mathematically considering the processes of joining the materials and the possible stress around the joints due to external loads.
I will appreciate if someone can recommend and the numerical methods which one is better suited for this purpose.
Thank you all in advance
Assuming you have a strong join (no delamination issues etc.) then you have continuity of the displacement and the stresses across the join. However, strains will *not* be continuous across the join. The weak form of the elasticity equations will still hold, and energy minimization (for static problems) also holds. Using FEM, make the element boundaries conform with the join to avoid the problems of trying to approximate discontinuous functions (e.g., strains) with the discontinuity inside an element.
Question
In the recent paper which has been exhibited in the 51th Annual Iranian Mathematics Conference entitled "Notes on maximal subrings of rings of continuous functions" we give some
properties of maximal subrings of some classes of subrings of C(X). However, we could not answer the following two important questions in this context.
1. Is every maximal subring of C(X) unit-free (i.e., whenever R is a maximal subring of C(X) and
f is an element of R with empty zero-set, then f is a unit of R)?
2. Is every maximal subring of C(X) uniformly closed (i.e., closed under uniform topology on C(X))?
I would be very delighted if you could let me your opinion about any ideas towards approaching the answers of these questions.
It is not hard to see that for each real number t which is not algebraic over integers, C(X) has a maximal subring R_t which contains t but not t^-1, which immediately implies that the first question is not correct
Question
Can you just assume a situation with no figures or data to back it ? Is it reasonable?
#Logic #mathematics #data
Kwadwo Boakye RE: "Can you just assume a situation with no figures or data to back it ? Is it reasonable?"
Yes to both questions. If you are giving a reductio ad absurdum argument, your assumption is formulated solely for the purpose showing that it is untenable because it entails a logical contradiction or absurdity.
A reductio ad absurdum argument that the square root of two is not rational has been attributed to Aristotle.
Question
As it is well known, Linked Opend Data (LOD) and computational ontologies have great success in the fields of Life Sciences (Biology, Medicine, etc). See e.g. the big LS-cluster at <https://lod-cloud.net/>.
However, I wonder why mathematics are – in comparison – covered only sparsely by ontologies or LOD.
Indicators (to the best of my current knowledge):
Probably there is some (machine-processable) formalization of mathematical knowledge but it seems almost disconnected from the "semantic web" and LOD-bubble.
Questions:
1. Why is this?
2. Should this be changed?
3. If 2., how?
Dear Carsten Knoll. I developed ThingFO two y. ago, so I'm not aware so far that other researchers used it for abstract mathematical concepts like polynomial or complex number as you are looking for. My interest in ontologies started in early 2000. At that moment, we developed a process ontology, and an ontology for metrics and indicators. In the last years we have harmonized semantically those ontologies with ThingFO in the context of the four-layered ontological architecture. Obviously that for indirect metrics and elementary and derived indicators, we use mathematical constructs (formulas, aggregation models), but that is all. These ontologies are specified at the low-domain level.
For MetricsLDO
For IndicatorsLDO
Question
I shared the picture of three parameters 1.Change in Temperature, 2. Change in Relative Humidity, 3. Change in Pressure and respective error value for that.
From the attached data(picture and excel file attached), I need to find the Error value for different input parameter.
If
1.Change in Temperature = 1°C
2. Change in Relative Humidity = 1%
3. Change in Pressure = 1mbar
What is the error value?
If
1.Change in Temperature = 2°C
2. Change in Relative Humidity = 2%
3. Change in Pressure = 2mbar
What is the error value?
If
1.Change in Temperature = 4°C
2. Change in Relative Humidity = 3%
3. Change in Pressure = 2mbar
What is the error value?
Is it possible to find the error value by mathematics. Please tell the way to calculate using calculator or python programming.
if you don’t have the original model that this error term come from then you can’t get the exact answer you’re after. Though you could approximate it by fitting a regression model. E.g. fit a least-squares model to find the best set of parameters a,b,c,d to the equation error = a*temp + b*humid + c*pressure +d.
Question
Teaching Mathematics at school to all students is commonly justified by the opinion that it improves their problem-solving skills and "makes them smarter" (whichever measure is implied by this). I wonder a few things about this:
1) If there is a clear empirical support for this opinion. Does that evidence answer the question of the causality direction between learning maths and cognitive ability? Recommendations on good literature about this would be appreciated too.
2) Do the abilities students develop improve performance for solving problems that are non explicitly mathematical. For example - learning volumes of 3D shapes could improve spatial navigation.
3) And importantly, are these improvements particularly due to teaching maths? E.g. for the previous example - wouldn't learning world maps in a geography class or spatial maze tasks develop spatial navigation more efficiently than learning calculation of volumes?
Thank you!
Mathematics is a subject of data analysis and logical and reasoning apart from application skills to solve problems in New situations
All this procedure and process needs conceptual understanding concrete and abstract thinking abilities Mostly modern ALGEBRA Geometry and Higher mathematics
So Mathematical investigations need cognitive thinking levels
Definetelf Mathematical knowledge and skills help in improving cognitive abilities productive
Question
I need to write a MATLAB code that has the ability to process a GIS image in order to extract the coordinates of the grid points within the red region (R) and that are at least distance "d" from its boundary. Each point in the R is given a weight w1 (attached figure). The same procedure is to be made for the green region (G) but w2 is the weight of any point in G. The gathered data are saved in a matrix formed of three rows: row 1 contains the abscissa, row 2 contains the ordinate, and row 3 the weight.
I am looking forward to getting your suggestions...thanks in advance.
%imshow(im);
BW = im2single(im);
numclust=5;
[L,Centers] = imsegkmeans(BW,numclust); % matlab inbuilt
might help:)
Question
Suppose we have a matrix relation as
A=Bn
where A and B are square matrices and n is a positive integer.
If A is know, how to calculate B? The can be easily calculated by MATLAB. We can get it as B=A(1/n). How to calculate it mathematically?
To Muhammad Ali: Ravindra Munje asked How to calculate it mathematically?
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Does anybody know about an mathematical optimization model which combines vendor managed inventory with fixed lot-sizes for production? That is, a model that performs a simultaneous production and delivery (transportation) planning with respect to production and transportation lot sizes.
So the keyfigures should be fixed lot-sizes for production, transportation assets, capacities and costs from vendor to VMI-stock, known demand on customer (retailer) side and inventory restrictions for the VMI-stock.
It will be also helpful if you just know about any paper or similiar which has recognized this problem.
Dear Hartwig Baumgaertel,
I suggest you to see links and attached files on topic.
Best regards
Question
In daily life single period and multi period inventory system is very necessary things. When the selling period is fixed that is we cant sell things outside that fixed time then it is called may be single period. Lets talk about it what is the actual definition.
Single period inventory models are used typically for determining the optimal order quantity for a perishable product. The most famous example is the Newsboy (Newsvendor) problem, in which the demand for newspapers for a given day is random, there is a cost of overstocking (unsold papers) and understocking (lost profits). The objective is to minimize the expected daily cost and the decision variable is the number of papers to buy (for reselling). this model is useful for any other item that cannot be stocked to be sold in another period, you have to sell it during the period or it is wasted. Many products fit this category: Christmas trees, Halloween costumes, or any other item that is special day or event themed. Fresh produce and meat can be though of in this category as well.
On the other hand, multi-period models are used for items that can be stocked for long periods of time, and demand in subsequent periods can be satisfied from the inventory. The basic EOQ model is the simplest of these models.
Question
We know many largest numbers as googol number(=10^100), googolplex number(=10^googol), and other unimaginable large numbers.
What is the largest known number that is the result of solving a problem in physics or mathematics?
Are they really practical or just based on conjecture?
The largest such numbers I know of come from combinatorial problems, e.g., Ramsey Theory
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I am currently doing a research project on this topic. Any suggestions on academic articles and research papers are welcome.
I would suggest that you skim through conference proceedings papers from ICME (International Congress on Mathematical Education) topic study group number 39 and CERME (Congress of European Research in Mathematics Education) thematic working group number 9 and then search for more journal articles with authors from these two groups. Also, I highly recommend the book "Speaking mathematically: communication in mathematics classrooms" by David Pimm and the series of papers published in "for the learning of mathematics" by Dave Hewitt called "Arbitrary and Necessary" Part 1, 2 and 3 (accessible online)
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Most plagiarism checkers don’t work because they cannot check equations and theorems which are the fundamental core of a mathematics article.
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Dear Colleagues and Authors,
plenty of problems in mathematics, economics, physics, biology, chemistry, and engineering, e.g., optics, radar, acoustics, communication theory, signal processing, medical imaging, computer vision, geophysics, oceanography, astronomy, remote sensing, natural language processing, machine learning, non-destructive testing, and other disciplines, can be reduced to solving an inverse problem in an abstract space, e.g., in Hilbert and Banach spaces. Inverse problems are called that because they start with the results and then calculate the causes. Solving inverse problems is a non-trivial task that involves many areas of Mathematics and Techniques. In cases where the problem is ill-posed, small errors in the data are greatly amplified in the solution, and therefore, regularization techniques using parameter choice rules with optimal convergence rates are necessary.
Currently, I am editing a special issue on "Numerical Analysis: Inverse Problems – Theory and Applications 2021" with a Switzerland-based "Mathematics" MDPI Journal.
I would like to draw your attention to this possibility of submitting research articles:
Please let me know if you need any help.
Thank you for your kind consideration,
Christine Böckmann
Dear Prof. Christine Böckmann, that's great. Feel free to invite me as a Reviewer.
Animasaun Isaac. L. (PhD)
Department of Mathematical Sciences,
Fluid Dynamics and Survey Research Group, Center for Research and Development,
The Federal University of Technology, Akure, PMB 704, Nigeria, West Africa.
Tel.: +2348034117546
Question
It is known in a input / output feedback linearization control that in a closed loop the physical state of the system is transformed into a linear mathematical state, which we have to stabilize by a linear auxiliary control, this linear mathematical state must be obtained, either by successive derivations of its outputs which is not recommended in case of implementation, or by a Luenberger observer.
In this question we want to know how demonstrate that this stabilizing linear control of the closed loop system can be developed via the physical state estimated by a nonlinear Thau observer.
Dear Abderrahmane Senoussaoui,
I suggest you to see links and attached files on topic.
Best regards
Question
Hi,
Is there a mathematical equation or formula to find the extinction coefficient or absorption coefficient of a thin layer based on transmittance or from the refractive index of the material?
please read this paper, you will find what you want:
Optical and electronic properties for As-60 at.% S uniform thickness of thin films: Influence of Se content
also see attached file
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While calculating channel capacity, I wish to know how path loss directly or indirectly affects the Bandwidth. Is there any mathematical relationship in this regard?
See the attached paper which is useful
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Conversely, what attributes of the physical universe do attributes of the natural logarithm model?
For example, the exponential function based on the natural logarithm has itself as its derivative. That seems to model aspects of the physical universe.
What are other math-physics correspondences for the natural logarithm?
Additionally mathematical physics radioactive decay process has exponential or half-life as logarithmic dependence, example, carbon-14 to know age of a tree.
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If anyone could help me. It is my dissertation work. Thank you. I am looking for the matlab code to solve PDE using RBF.
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I am interested in broadening my understanding of the physical assumptions needed to simplify its mathematical description. From these assumptions i will to choose a suitable turbulence model to run the simulation in Ansys.
The problem is fairly basic;
Inlet flow conditions: Velocity in= 44.2 m/s, Mach number inlet = 0.128, atmospheric total pressure and temperature. Turbulent boundary layer thickness @ 4H upstream of the step is 1.9 cm.
Outlet flow conditions: Fully developed flow.
Any advice would be much appreciated
Kind regards
Anton
If you want to use the RANS formulation you should assume your flow field is totally developed. That means you can set the inflow profile according to a statistically mean velocity in a channel
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