Science topics: Mathematics
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Mathematics - Science topic

Mathematics, Pure and Applied Math
Questions related to Mathematics
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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.
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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?
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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.
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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 :)
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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?
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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.
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Why CPW square slot antenna gives a wide impedance bandwidth?
Is any mathematical derivation/equation is available for it?
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Kapil Saraswat please share your paper
Thank you
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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!
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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.
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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?
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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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Is there any mathematical equation to determine the appropriate number of hidden layers for a sequential model?
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Hi Hasintha, It's a practical problem and you should make decision about number of hidden layers by checking accuracy of the fitted model.
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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?
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How about start definition of capacitance (Farad)= (charge/volt); geometric capacitance; gravimetric capacitance (F/mass); energy density (Watt/volume)
If one measure C-f spectra for parametric bias voltage this would be better approach for a capacitive performance of a capacitor.
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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?
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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
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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,
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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
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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
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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)
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I have a derived block formulae and I want to use it to solve second order system of equations using maple. So, I need a sample of maple code which will serve as guide for me
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I need an assistance with a sample coding imple@mentation on block differential forma for first order differential equation
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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.
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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.
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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.
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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
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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
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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.
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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?
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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
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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
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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.
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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.
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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
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Can you just assume a situation with no figures or data to back it ? Is it reasonable?
#Logic #mathematics #data
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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.
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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?
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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.
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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.
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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.
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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!
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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
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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.
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im=imread('GIS.jpg');
%imshow(im);
BW = im2single(im);
numclust=5;
[L,Centers] = imsegkmeans(BW,numclust); % matlab inbuilt
temp_mask = L==1;
figure,imshow(temp_mask);
might help:)
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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?
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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.
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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.
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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.
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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?
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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.
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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
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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
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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.
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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?
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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?
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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?
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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
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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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As a beginner, how can one start research on Machine Learning in Mathematics. Please suggest some research papers.
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see the following papers
An Empirical Study of Machine Learning Algorithms for Stock Daily Trading Strategy
Lv, Dongdong, Yuan, Shuhan, Li, Meizi, Xiang, YangJournal:Mathematical Problems in EngineeringYear:2019
A Proposal on Machine Learning via Dynamical Systems
E, WeinanJournal:Communications in Mathematics and StatisticsYear:2017
A machine learning approach to ornamentation modeling and synthesis in jazz guitar
Giraldo, Sergio, Ramírez, RafaelJournal:Journal of Mathematics and MusicYear:2016
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I need this software to be interactive: allowing to enter a signal on real time of simulation. Maybe SimuLinks can do this, I could not say. I would appreciate all the information you can apport.
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I am developer of Uyamak. Please look at Uyamak. You can use it to simulate a mathematical model in real time. However, communication with a data acquisition card is not yet available.
No need to install and it is free to use.
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I have a query that
How the flatten layer in deep learning model transform pooled feature matrix into a vector??
What is the mathematical equation for flattened layer?
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simply 1xQ; where Q is product of dimensions of tensor at the input. Further help can be taken at https://deeplizard.com/learn/video/fCVuiW9AFzY
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Creep is a time dependent process whereas MD simulation is restrictive in terms of the time scale. Hence to get appreciable strain in fs/ps time range we have to use a stress of GPa magnitude. Can we correlate this data with real-life service condition where only 10-200 MPa stress is observed. Is there any mathematical way of proving that?
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Perhaps only near the peak of stress-concentration tips and Grain boundary/precipitates or near-dislocation regions. If one tries to correlate Creep relaxation and strain, one might fit the data (usually viscoelastic time-dependent+instantaneous deformation) with standard viscoelastic models (Kelvin, Voigt, Maxwell) and/or creep models (Nabarro-Herring, Coble, Harper-Dorn) to find out the parameters, and do some dimensional analysis to represent the data in reduced-dimensional form (Common in Fluid Mechanics, Heat and Mass transfer, CIvil Engg.) using standard method (like Rayleigh, Buckingham-Pi), then even significantly different data may be compared.
To see the strength of scaling laws, see it!
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How does blood perfusion change during hyperthermia and hypothermia? What mathematical expressions exist for these phenomena? I would like indications of research about the subject. Thank you!
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Thank you very much! congratulations on the explanation.
Yes. The Hagen-Poiseuuille Classical Equation relates several parameters for laminar flow through a horizontal pipe (analogous to blood vessels).
So, in your opinion, knowing the relationship between blood viscosity and tissue temperature, and using the Hagen-Pouseuuile equation to determine the flow rate, can I later determine the perfusion?
And how to determine the variation in blood vessel diameter during vasoconstriction or vasodilation?
Thank you very much for participating in this discussion!
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Recently I face some problems with the mathematical ( calculation) on the reference governor and command governor, so I need some help from you all to get which platform or journal can let me understanding the calculation. Thx
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انا لا أعلم اي مجلة من التي تبحث عنها
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  • How was the importance of the zeta function discovered ?
  • why do zeta function contain so much information ?
  • What other areas of mathematics does it relate to ?
  • Are there any books on the RH ?
  • I've heard something about a connection with quantum physics – what's that about?
  • Isn't there a connection with cryptography? Would a proof compromise the security of Internet communications and financial transactions?
  • What are the Extended Riemann Hypothesis, Generalised RH?
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The Zeta function is a very important function in mathematics. Because he was able to prove an important relationship between its zeros and the distribution of the prime numbers. hi.zeta(s=a+ib)=0
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I have a symmetric airfoil with known equation. Now a sine function passes along the airfoil equation like following figure. I want to find the sine function in (x,y) coordinate system.
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PS. The LaTeX file from my previous post after processing
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Dear colleagues,
I invite you to send your articles to the special issue that I edit, together with Dr. Martín Cervantes:
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Terry Tao blogged about this unfortunate event. Kindly share among Mathematical community and increase awareness.
Thanks.
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Oke ... Thank
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I have written two articles about a generalization of Multiple zeta values and Multiple zeta star values. I also presented applications for this generalization including partition identities, polynomial identities, a generalization of the Faulhaber formula, as well as MZV identities. If you are intrested check them out on my profile and give me your opinion.
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The Riemann Z function finds applications in physics Dear Roudy El Haddad, I just cannot remember all of them, but the theory of phase transitions, Planck radiation, statistical sums, we use the identities without too much thinking for several partition functions.
Also, some applications are related to the most general class of Z functions with multiple Z values.
The Riemann Hypothesis is somehow connected to some real eigenvalues of a hermitian “Riemann Operator” so that these zeroes are spectral, according to some authors (Lyon, 2008).
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My dissertation thesis is Perceptions of mathematical ceonceptions depending on MBTI personalities. It can includes methods of solving, understanding, imaginations of math issues, etc. I would like to know if there is any research connects MBTI with solving university mathematics for example methods of solving depending on MBTI, because I was struggling to find something similar.
EDIT: instead of MBTI I should use BIG FIVE TYPOLOGY!
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Maybe the following paper in the same direction
Relationships of Myers-Briggs Type Indicator Personality Characteristics and Self-Reported Academic Problems and Skill Ratings with Scholastic Aptitude Test Scores
Schurr, K. T., Ruble, V. E., Henriksen, L. W.Journal: Educational and Psychological Measurement
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Our knowledge of the world begins not with matter, but with perception. There are no physical quantities independent of the observer. All physical quantities used to describe Nature refer to the observer. Moreover, different observers can take into account the same sequence of events in different ways. Consequently, each observer assumes a “stay” in his physical world, which is determined by the context of his own observations.
If mathematics and physics, which describe the surrounding reality, are effective human creations, then we must consider the relationship between human consciousness and reality. Undoubtedly, the existing unprecedented scientific and technological progress will continue. However, if there is a limit to this progress, the rate of discovery will slow down. This remark is especially important for artificial intelligence, which seeks to create a truly super intelligent machine.
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Dear Boris Menin ,
Golden ratio is a geometric mean or average . it could be apply to every aspect of life even in which amount we have to inhale and exhale to getting the perfectness that also explain by the meditation. The perfectness can achieve by the meditation that reflects in many Indian temples architecture those follow the Fibonacci series pattern in the temple architecture without knowledge of the series but due the devotion towards the god temple construction they constructed temple with meditation. There are also the statue of Gautam Buddha in which we found the golden ratio without knowledge of golden ration . So some where you can see the golden ration and meditation and devotion are the synonyms .
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I am interested in the practical uses of mathematical minimal surfaces in engineering design (such as gyroids, Schwarz surfaces, etc.). Can anyone provide good examples, particularly in art and design (or nature-based design)? I am particularly interested in examples that have been physically created and used for some practical purpose or as art. However, I am having a hard time finding published work on this topic that is not purely computational.
If anyone has published work in this area, please consider sharing it in this thread so we can get a good discussion going.
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On the construction of minimal surfaces from geodesics
By: panelJ.Sánchez-Reyes
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I wish to develop a peer mentoring model based on the content knowledge and pedagogical content knowledge knowledge in Mathematics and technological skills. Unfortunately I cant find a standardized test/ assessment tool to determine their competence level on each domain. Hopefully some of you can help me find a link or way to find an assessment tool ? Thank you in advance
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Hello Ana-Lyn,
You could try:
1. Using released items from NAEP for the high school level (https://nces.ed.gov/NationsReportCard/nqt/help/NQT_Help/!SSL!/WebHelp_Pro/NQT_Help.htm);
2. Using previous versions of PISA items (https://www.oecd.org/pisa/pisaproducts/pisa-test-questions.htm)
3. Using previous versions of TIMMS items (https://nces.ed.gov/timss/released-questions.asp), though these are generally only for as high as grade 8.
Some combination of these sources would likely serve to give you a good starting point for assessing teachers' command of a specific discipline, at least at a level commensurate with that of high school training. Of course, if the teachers you assess are very strong in the discipline (and good at test-taking!), then you may end up with a lot of very high scores (so-called "ceiling effect").
Short of that, you could obviously assemble a group of subject-matter experts, a test-development expert, and attempt to: (a) define the relevant domain of skills that you believe a teacher should possess; and (b) develop and try out items designed to measure whether a given examinee sufficiently possesses each given skill.
Good luck with your work.
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HI Everyone!
I am asking to know by you, expert in cybersecurity and mathematics, if Computer virology (the one of Cohen and Andler) is still an active field of research. That research made in France at Inria at 2000-2010 . I do not see any prosecutor and I do not understand if this is a dead branch or not. I am interested in it in order to understand malware and detect behavior.
Thank you very much for your precious help!
Bye
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Math relates numbers to other numbers. But this is insufficient for physics. Physics models which include a cause-and-effect are more useful and result in bettter human understanding. For example, current models are time reversable. If cause-and-effect is part of the calculation, the model would not be time reversable without another equation showing how energy (entropy) is expended. Further, any proposed model that was only mathematical manupliation would not be considered physics.
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You are correct. Causality and the arrow of time are being consistently ignored as both Quantum probabilities and General relativity seem to develop math models at the expense of little regard for causality. Then there are the many complex papers on how to determine causality after the models have made liberal use of probability and shifting parameters from one side to the other of equations with only the number relations of math as a justification. This is the reason for the question.
The FQXi site seems to be devoting more to causality, sometimes called correlation.
Thanks for your insight. Perhaps, the comment should extend to fundamental principles.
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The parameters are:
1. Stator phase resistance (Rs).
2. Inductances (Ld & Lq).
3. Flux linkage established by magnets (V.s)
4. Inertia (j)
5. Viscous damping coefficient (F).
6. No. of pole pairs
7. Generator speed (wm)
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@ Subir Datta Sir did you got the answers, if yes then please share the designing with me I knew many equations regarding this but I am confused how to calculate these parameters.
Thanking you sir.
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In this link shifted functions are defined as r*(x-o)/100 (where r is the original range)to keep the range between 100. But for optimizing the functions should I generate the values of X between [-100,100] or between [o-100,o+100]? If the function is shifted by o vector then the respective ranges should also change. Because if for 0<-100 or o>100, the global optimum won't fall in the range. And even if I generate the o values between [-100,100] then the function would be shifted in the range rather than being in the range where it is well defined.
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Yes, you must shift all the conditions. All the problem has to be changed: The bounds, the conditions. Finally, you must come back the first problem: the first condition and the first bounds. To interpret the results, you need to return.
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Dear Colleagues,
I would like to invite you to submit both original research and review articles to the Special Issue on "Modern Applications of Numerical Linear Algebra" organised by Mathematics (IF=1.747) ISSN 2227-7390. For more details see https://mdpi.com/si/74727.
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I hope the review process would be fast and how many weeks will it take to index accepted paper in web of science?
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This is my very first encounter with functional equation of this kind, and methods of series solution and differential equations are of not much help. The solution to this problem, or at least the mathematical prerequisites to understand solution to this problem is asked.
This function is asymptotically zero at both +_ infinity, positive otherwise, and has a peak near zero.
If I am correct, then this is the frequency distribution of numbers fed to the sequence xn+1=a ln (xn2) as long as the sequence generated is chaotic and sufficiently large in number (value of a is usually limited to 0.2 to 1.3, Positive and negative signs of a are essentially immaterial except for the sequence is negated after first term) .The sequence is initiated or seeded with number roughly as the same order of magnitude of 1 in both positive and negative side, except for the values that eventually lead to zero or infinity in the sequence. The sequence is allowed to proceed, and frequency distribution of numbers in the sequence are noted, from which a continuous probability distribution may be numerically guessed but not analytically found. The expression to find out formula of the continuous probability distribution comes to me from the following reasoning
  • Suppose, the probability distribution is given by y=f(x). Now, if I consider a "dx" (infinitesimally) thin strip around x, then I come up with f(x) dx fraction of all points required to construct the probability distribution. When this fraction of all points are passed through yet another sequence of transformation through the recurrence xn+1 =a ln (xn)2 , the fraction of points involved must be unchanged. That is, when x is substituted with a ln x2 , the infinitesimal strip area, which changes to f( a ln x^2) d (a ln x^2), must be numerically equal to f(x) dx, thus the functional equation is postulated
  • I am not entirely sure about this reasoning, and experts are welcome to point out my fault of reasoning and show the correct equation , if I am mistaken.
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The operator f{*} is defined as follows
f{g(x)}=1/g(x)\ (the reciprocal of the derivative)
f{x}=1/1
f{x2}=1/2x
f{sinx}=1/cosx
etc,..
We find that this operator works as a solution for the given equation.
You can see
f(a ln x2)/f(x)= (1/2a(1/x))/(1)= x/2a.
You can also replace x with any other function, and the relationship works.
Here f is considered as an operator.
Best wishes
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For a function, usually sign of second derivative (and if it is zero, even/odd index of higher order derivative whose numerical value is zero) is enough to detect whether the extreme point is maximum/minimum/saddle point, if first derivative is zero. For a functional (NOT A FUNCTION), Euler-Lagrange equation plays the role of first "derivative" of Functional. However, it the RHS of Euler-Lagrange equation is set to zero and the resultant differential equation is solved, then how to find whether this function (as solution to differential equation) corresponds to minimum, maximum or saddle "point" of functional?
Unfortunately, the nature of extremum of a functional is usually declared to be "beyond the scope" of most preliminary/introductory functional analysis resources (I have not checked all). How difficult is that mathematics and what are the prerequisites to understand the mathematics involved in finding the nature of functional extremum?
Please note my knowledge on variational calculus, integral equations and transformations as well as group theory and advanced differential geometry is rudimentary.
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Actually, the idea in the case of a functional is the same as in the ordinary calculus: you have to resort to the second variation of the functional, and then to study several conditions depending on the weak or strong character of the critical point (Jacobi condition for weak extrema, Weierstrass condition for strong ones). You can find a readable treatment in the classic book "Calculus of Variations", by Gelfand and Fomin (Dover's edition is very affordable), chapters 5 and 6.
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In the definition of a group, several authors include the Closure Axiom but several others drop it. What is the real picture? Does the Closure Axiom still have importance once it is given that 'o' is a binary operation on the set G?
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I think no need to include closure property, if it is given that 'o' is a binary operation on the set G.
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How to predict remaining useful life (RUL) on used aeroengine and its components level?
(or)
Any standard mathematical relations for RUL?
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THENNAVARAJAN SUBRAMANIAN you may want to employ LSTM. Attached is the paper with the concept of Hochreiter and Schmidhuber (1977).
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I am on a quest to solve how a cell repairs itself through encoding-decoding of proteins. Is there any link to genetic algorithms to solve age old questions such as aging and how we heal?
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Hi,
I suggest you to see this link i hope it's in the topic.
Best regards
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I have calculated EVI2 using landsat 7 surface reflectance images and I am getting values above 1.25 (mathematical maximum for EVI2 based on the formula) in my study area (heavily vegetated). I get a range between 0.2 and 1.8. Many publications stipulate -1 to 1, especially based on MODIS data. I also did a check with Landsat 7 TOA images, and I get ranges from -1 to 1, as the publications say. Does this mean something is wrong with the Landsat 7 surface reflectance images, or should values above 1.25 still be okay?
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It is absolutely fine and fair to get values above 1.25 as you are using a surface reflectance imagery and sine you mentioned that the area is heavily vegetated, the values reflect the colour composite and type of strata so the number and the work is acceptable.
Best wishes and good luck !
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I want to ask if I can get good resources that can explain the mathematical approach behind the Adaptive Model Predictive Control AMPC MATLAB toolbox?
am not be able to find the mathematical analysis behind this toolbox even on the MathWorks webpage.
thank you
Mohamed
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Mathematical programming is the best optimization tool with many years of strong theoretical background. Also, it is demonstrated that it can solve complex optimization problems on the scale of one million design variables, efficiently. Also, the methods are so reliable! Besides, there is mathematical proof for the existence of the solution and the globality of the optimum.
However, in some cases in which there are discontinuities in the objective function, there would be some problems due to non-differentiable problem. Some methods such as sub-gradients are proposed to solve such problems. However, I cannot find many papers in the state-of-the-art of engineering optimization of discontinuous optimization using mathematical programming. Engineers mostly use metaheuristics for such cases.
Can all problems with discontinuities be solved with mathematical programming? Is it easy to implement sub-gradients for large scale industrial problems? Do they work in non-convex problems?
A simple simple example of such a function is attached here.
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It may be useful to make a distinction between 'global' optimisation (where one is given an explicit, non-convex objective function) and 'black-box' optimisation (where the function is not given explicitly). The methods for them are very different.
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Problem: 5 minutes of play are worth more than an hour of study
Knowing that: G = Game S = Gtudy 1 hour = 60 min
The mathematical formula that defines the statement is: 5 x G> 60 x S The quantitative ratio of the minutes expressed in the mathematical formula can be simplified: 60: 5 = 12, therefore the simplified mathematical formula is: G> 12 x S
So, 1 minute of play is worth more than 12 minutes of study Or it can be said that: game G is worth more than 12 times than study S.
Therefore, the quantitative value of physical objects (or of spatial and / or temporal quantities) must be calculated differently from the qualitative value of human life experiences.
Explain why it is possible___________________________________________________________________
___________________________________________________________________________
(Exercise based on Fausto Presutti's Model of PsychoMathematics).
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Agreed with dear David Eugene Booth
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In several discussions, I have often come across a question on the 'mathematical meaning of the various signal processing techniques' such as Fourier transform, short-term fourier transform, stockwell transform, wavelet transform, etc. - as to what is the real reason for choosing one technique over the other for certain applications.
Apparently, the ability of these techniques to overcome the shortcomings of each other in terms of time-frequency resolution, noise immunity, etc. is not the perfect answer.
I would like to know the opinion of experts in this field.
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Utkarsh Singh There is an esthetic reason in why a mathematical method is of interest in signal processing:
-a beautiful algorithm is well articulated, says what it does in few instructions, and does it in a stable and reliable manner
-this hints to the underlying algebra
With powerful and minimal computation, we go deep into algebra structures: group, rings, fields (see references on Evariste Galois as the inventor of "group" as we know it)
-Fourier transform is an interesting invention: it allows to decompose a signal into resonating modes (as for piano music: you produce a sound at frequency F, but also its harmonic NxF...). Naturally there is the aliasing question and the Nyquist theorem for reconstruction
There are many more time-frequency representations: Fourier, Laplace, discrete or continuous, cosine transform, wavelet transform, etc.
The interesting feature of discrete algorithms for those transforms is that you can implement a butterfly structure.
The key idea is to replace a very large number of multiplications (in brute force "non-esthetic" programming) by a smaller number of additions.
This idea worked for me for developing a codec system using underlying GF(n) properties.
See this patent:
The regularity in the processing and the efficiency of the representation go hand in hand.
Let me go back to a very basic mathematical method: the Gram-Schmidt decomposition: take a sequence of n vectors v(1),..., v(n), and the matrix of cross-products m(i,j)=<v((i),v(j)>. The Gram-Schmidt method diagonalises this matrix. It extracts eigenvalues, and eigen vectors. In frequency terms, it extracts modes (resonating modes present in the signal).
This algorithm highlights the efficiency side of the representation: it's projecting the signal onto something found "in itself", call it principal components if you want.
There are only two reasons for choosing a technique in engineering:
-(i) it addresses the problem completely
-(ii)it's economically implementable.
Both criteria are equally important and a good way to find these is to look for elegant, esthetic solutions (minimal and complete at the same time).
Does it help?
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In recent years, many new heuristic algorithms are proposed in the community. However, it seems that they are already following a similar concept and they have similar benefits and drawbacks. Also, for large scale problems, with higher computational cost (real-world problems), it would be inefficient to use an evolutionary algorithm. These algorithms present different designs in single runs. So they look to be unreliable. Besides, heuristics have no mathematical background.
I think that the hybridization of mathematical algorithms and heuristics will help to handle real-world problems. They may be effective in cases in which the analytical gradient is unavailable and the finite difference is the only way to take the gradients (the gradient information may contain noise due to simulation error). So we can benefit from gradient information, while having a global search in the design domain.
There are some hybrid papers in the state-of-the-art. However, some people think that hybridization is the loss of the benefits of both methods. What do you think? Can it be beneficial? Should we improve heuristics with mathematics?
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I am surprised that a known scholar with a long experience in the transportation domain maintains such a hard stance on heuristic search. Obviously, we live in a world where extreme opinions are those which are the most echoed. Truth is, assuming that all practical optimization problems can be solved to optimality (or with approximation guarantees) is essentially wishful thinking. Given this state of art, better integration of exact and heuristic algorithms can largely benefit the research community. At the risk of repeating myself, here are some important remarks to consider:
• CPLEX and Gurobi (the current state of the art solvers for mixed integer programming optimization) rely on an army of internal heuristics for cut selection, branching, diving, polishing, etc... Without these heuristic components, optimal solutions could not be found for many problems of interest. CPLEX has even recently made a new release permitting a stronger heuristic emphasis (https://community.ibm.com/community/user/datascience/blogs/xavier-nodet1/2020/11/23/better-solutions-earlier-with-cplex-201). MIP solvers also heavily depend on the availability of good (heuristic) initial solutions to perform well. For many problems, cut separation is also done with heuristics. In the vehicle routing domain, we have a saying: heuristics are the methods that find the solutions, exact methods are those that finally permit to confirm that the heuristics were right (sometimes many decades later, and only for relatively small problems with a few hundred nodes despite over 60 years of research on mathematical models)...
• The machine learning domain is quickly taking over many applications that were previously done with optimization. Among the most popular methods, deep learning applies a form of stochastic gradient descent and does not guarantee convergence to optimal parameters. Neural networks currently face the same scrutiny and issues as the heuristic community, but progress in this area has still brought many notable breakthroughs. Decision-tree construction and random forests are also largely based on greedy algorithms, same for K-means (local improvement method) and many other popular learning algorithms.
• Even parameter tuning by the way is heuristic... I'm sorry to say that, but most design choices, even in the scientific domain, are heuristic and only qualify as good options through experimentation.
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Hi
I would really appreciate if someone helps me out with this MATLAB problem. I have uploaded both MATLAB file (which is not working properly) and the question.
Thank you very much in advance
#MATLAB
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Hi, you can directly use the following MATLAB function : fminsearch that uses the Nelder-Mead simplex (direct search) method instead of trying to implement your own version. Best
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In the lands with ancient plain sediments, the courses of rivers change dramatically over time for easy movement and the arrival of rivers to an advanced geomorphic stage.
Are there mathematical arrays that achieve digital processing such as spectral or spatial improvements or special filters to detect buried historical rivers?
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Ruqayah Al-ani The digital elevation model (DEM) is a good component in the field of remote sensing and GIS. The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model (GDEM). The ASTER GDEM needs further error-mitigating improvements to meet the expected accuracy specification. The RMSE values can be used to represent the DEM errors, in addition to mean error and standard deviation (stddev).
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