Science topics: Mathematics
Science topic

# Mathematics - Science topic

Mathematics, Pure and Applied Math
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Hi frds,
Need a good weather probability calculator. Would like to calculate the probability of e.g. 10 degrees Celsius on a day above the average. Has anybody got good research/formulas?
Which distribution is assumed in the probability calculation? Normal one?
One possible approach is presented in the attached word document
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I am thinking of the vector as a point in multidimensional space. The Mean would be the location of a vector point with the minimum squared distances from all of the other vector points in the sample. Similarly, the Median would be the location of the vector point with the minimum absolute distance from all the other vector points.
Conventional thinking would have me calculate the Mean vector as the vector formed from the arithmetic mean of all the vector elements. However, there is a problem with this method. If we are working with a set of unit vectors the result of this method would not be a unit vector. So conventional thinking would have me normalize the result into a unit vector. But how would that method apply to other, non-unit, vectors? Should we divide by the arithmetic mean of the vector magnitudes? When calculating the Median, should we divide by the median of the vector magnitudes?
Do these methods produce a result that is mathematically correct? If not, what is the correct method?
For vectors X1=[x1,1;x2,1;..,xn,1]; X2=[x1,2;x2,2;..,xn,2];,.., Xn=[x1,n;x2,n;..,xn,n]
M=[m1,m2,..mn] - vector median,
where
m1=med(x1,1; x2,1;..,xn,1)
m2=med(x1,2; x2,2;..,xn,2)
- - - - - - - - - - - - -
mn=med(x1,n; x2,n;..,xn,n)
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I have no mathematical experience and no statistician to help me.
Thank you, Anton Vrdoljak.
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Is it possible to decompose a conditional probability with three or more elements (i.e. events) into conditional probability of only two elements or the marginal probability of one element? Knowing this decomposition, it would help to solve higher order Markov Chain mathematically. I also know that this decomposition can be solved if we add assumption of conditional independent.
To make it concrete here is a negative example:
P(c│a,b)=(P(a,b│c)∙P(c))/(P(a│b)∙P(b) ).
Notice that the RHS still contains a conditional probability with three elements P(a,b│c).
Assuming conditional independent on c, we have P(a,b│c)=P(a│c)∙P(b│c). Thus, the conditional probability decomposition becomes
P(c│a,b)≅(P(a│c)∙P(b│c)∙P(c))/(P(a│b)∙P(b) )
My question is whether this type of conditional probability decomposition into one or two element is possible without making assumption. If it is really unsolvable problem, then at least we know that the assumption of conditional independent is a must.
For my opinion we can use any product formulas only under condition of independence. For example the formula that you used P(a,b│c)=P(a│c)∙P(b│c) is valid if a and b are independent each from other. Both may be dependent from c. But it can be the case of so called "false dependence". For example a is the usage of energy, b is sale of warm clothes, c is decreasing of tempetature.
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During the lecture, the lecturer mentioned the properties of Frequentist. As following
Unbiasedness is only one of the frequentist properties — arguably, the most compelling from a frequentist perspective and possibly one of the easiest to verify empirically (and, often, analytically).
There are however many others, including:
1. Bias-variance trade-off: we would consider as optimal an estimator with little (or no) bias; but we would also value ones with small variance (i.e. more precision in the estimate), So when choosing between two estimators, we may prefer one with very little bias and small variance to one that is unbiased but with large variance;
2. Consistency: we would like an estimator to become more and more precise and less and less biased as we collect more data (technically, when n → ∞).
3. Efficiency: as the sample size incrases indefinitely (n → ∞), we expect an estimator to become increasingly precise (i.e. its variance to reduce to 0, in the limit).
Why Frequentist has these kinds of properties and can we prove it? I think these properties can be applied to many other statistical approach.
Sorry, Jianhing. But I think you have misunderstood something in the lecture. Frequentist statistics, which is an interpretation of probability to be assigned on the basis of many random experiments.
In this setting, on designs functions of the data (also called statistics) which estimate certain quantities from data. For example, the probability p of a coin to land heads is given from n independent trials with the same coin and just counting the fraction of heads. This is then an estimator for the parameter p.
Each estimator should have desirable properties, as unbiasedness, consistency, efficiency and low variance and so on. Not every estimator has these properties. But, in principle one can proof, whether a given estimator has these properties.
So, it is not a characteristics of frequentist statistics, but a property of an individual estimator based on frequentist statistics.
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Provide me the detail mathematical calculation for the measurement of uranium, thorium and potassium with their daughter progenies.
The solution is not a mathematical formula!
The question can be approached by two ways:
a) experimental: prepare homogenous standards having the same density and geometry as your samples, #1 material with low K,Th,U content, #2 same as #1 with known amount of K added, #3 same as #1 with known amount of Th added ,and #4 same as #1 with known amount of U added.
From the differences between measurements #N-#1 you may deduce the contribution of each of the three elements to the spectrum and, more specifically, the contribution of each of them to three regions of interest corresponding to strong peaks of each element, usually 1.46 MeV for 40K, 2.61 MeV for Tl208 (progeny of Th) and 609 keV for Bi214 (progeny of U), assuming secular equilibrium in Th and U families, or at least the same disequilibrium conditions in sample and standards.
It is then possible to calculate a matrix relating the measurements in the 3 ROIs to the three activities.
b) Monte Carlo simulation. The NaI detector is usually quite simple and can be simulated with a good accuracy. Experimental measurements are still necessary to evaluate the gaussian broadening of the peaks at the different energies, and an experimental validation of the MC model is always desirable.
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Hello,
For correlation analysis between body composition variables and blood hormone levels,
I have data from two different blood analysis methods but the same units; ECLIA & CLIA.
I wonder if there is any statistical and mathematical error when I run correlation analysis using the data together.
If it cannot,
Is there any suggestion for using these data together for statistical analysis?
Thank you very much.
If the methods are different, it is likely that there is no correlation ...
However, it would help a lot to know the datasets and the processing you say you have done.
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Mathematics is a subject most pupils love to hate; how did your journey into the world of mathematics proper begin?
My predisposition to mull with numbers and mathematical equations consistently, even though I do not specialize in the math field as a professional, is due to having FUN filled mentors early in life. They were so creative to attach images and anecdotes to math problems that my sense of wonder and fun was constantly tickled as I trundle along mathematical mines and problems. Missing the correct answer was not occasion for embarrassment but for more opportunities to discover funny and creative ways to approach math problems with new, innovative, and fun-filled attempts. My mentors showed me the short-cut methods, the winding methods, and the funny but sure fire methods. I do not believe I ever hated math. Math is FUN!
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Famous mathematicians are failing each day to prove the Riemann's Hypothesis even if Clay Mathematics Institute proposes a prize of One Million Dollars for the proof.
The proof of Riemann's Hypothesis would allow us to understand better the distribution of prime numbers between all numbers and would also allow its official application in Quantics. However, many famous scientists still refuse the use of Riemann's Hypothesis in Quantics as I read in an article of Quanta Magazine.
Why is this Hypothesis so difficult to prove? And is the Zeta extension really useful for Physics and especially for Quantics ? Are Quantics scientists using the wrong mathematical tools when applying Riemann's Hypothesis ? Is Riemann's Hypothesis announcing "the schism" between abstract mathematics and Physics ? Can anyone propose a disproof of Riemann's Hypothesis based on Physics facts?
Here is the link to the article of Natalie Wolchover:
The zeros of the Riemann zeta function can also be caused by the use of rearrangements when trying to find an image by the extension since the Lévy–Steinitz theorem can happen when fixing a and b.
Suppositions or axioms should be made before trying to use the extension depending on the scientific field where it is demanded, and we should be sure if all the possible methods (rearrangements of series terms) can give the same image for a known s=a+ib.
You should also know that the Lévy–Steinitz theorem was formulated in 1905 and 1913, whereas, the Riemann's Hypothesis was formulated in 1859. This means that Riemann who died in 1866 and even the famous Euler never knew the Lévy–Steinitz theorem.
I thought it would be better to type my work. Here is a link to the acceptable version of the article : https://www.researchgate.net/publication/364357359_A_contradiction_in_the_formula_of_Poisson_which_destroys_Riemann's_Hypothesis
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Everybody is eager to see the New winner of the Millenium Prize. Please share all your incomplete works about the Millenium Prize problems of Clay Mathematics Institute in order to collaborate for the solutions.
I am actually using the different nabla operator which I demonstrated mathematically in my published work: " A thesis about Newtonian mechanics rotations and about differential operators ".
This demonstrated differential tool enables to deal differently with the millenium problem about Navier-Stokes equation if the coordinates are not in the Cartesian. Furthermore, I proved that the field of velocities is not equiprojective.
I also suggest many ideas about complexity of P problems with my article that ends with a contradiction..
I will be waiting for your collaborations.
I thought it would be better to type my work. Here is a link to the acceptable version of the article : https://www.researchgate.net/publication/364357359_A_contradiction_in_the_formula_of_Poisson_which_destroys_Riemann's_Hypothesis
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Say I have a satellite image of known dimensions. I also know the size of each pixel. The coordinates of some pixels are given to me, but not all. How can I calculate the coordinates for each pixel, using the known coordinates?
Thank you.
Therefore, you have 20x20 = 400 control points. If you do georeferencing in Qgis, you can use all control points or some of them, like every 5 Km (16-points). During resampling, all pixels have coordinates in the ground system.
If you do not do georeferencing (no resampling), then you could calculate the coordinates of unknown pixels by interpolation. Suppose a pixel size a [m], then in one km, you have p = 1000/a pixels, and therefore known coordinates have the first(x1,y1) and the last(x2,y2) pixel. The slope angle between the first and last pixel is:
s = arc-tan[(x2-x1)/(y2-y1)]. Therefore, a pixel of a distance d from the first pixel has coordinates x = x1 + d.sin(s) and y = y1 +d.cos(s). You can do either row of column interpolation or both and take the average.
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Any idea why the solution of the attached equation is always zero at r=0? It seems simple at first look, however, when you start solving, you will see a black hole-like sink which makes the solution zero at r=0 (should not be). I used the variable separation method, I will be happy if you suggest another method or discuss the reasons.
I also attached the graph of the solution, showing the black hole-like sink.
Thanks
Dear, a very good discussion. CONGRATULATIONS
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Hello Friends and Colleagues,
Can anyone suggest a mathematical book that helps me to build my own mathematical equations and functions? I want to convert real-life problems(natural sciences) into mathematical formulations.
Note that I have basic knowledge of mathematics.
For me the following book is very useful
Functional Equations and How to Solve Them (Problem Books in Mathematics)
Springer
Christopher G. Small
Year:
2006
Language:
English
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Plz share if yes . I want to know how to get patent in vedic maths.
WO 2017/037729 A1: Concurrent architecture of Vedic multiplier-an accelerator scheme for high speed computing
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didactics of mathematics
Students should be shown the application of mathematics from a practical point of view. On the other hand, it is necessary to respect the theoretical side of mathematics, which is not easy for everyone to learn.@Peter Kepp Rickardo Gomes
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Hello everyone,
I would like to know how to locate mathematically a damage on a blade.
Usually a frequency analysis of the blade and a comparison with a similar healthy one helps to determine a default or damage on a blade. However, how could someone locate that damage?
Hi fellow researcher,
I think the answer depends on what kind of equipment you have on your disposition and what is your purpose. The simpler way is to have a model blade and compare it to the blade you want to determine the integrity using the physical properties of the blade.
For example, if you have an accurate sound sensor and a device that produces an specific sound profile in the model blade you can use this device to produce a similar sound in the test blade. Comparing the Fourier decomposition of frequencies of the sound produced by the test blade will give you information of cracks and non-uniformity in density produced by the forging process or even if the material the blade was made is of quality or not.
You can do a similar approach with thermodynamics. you can heat Specific spots on the test blade. As cracked regions do not conduct heat as well as non-cracked regions you will observe anomalies in the heat map of the blade.
Notice you don't really have to calculate something, but just know what to expect with a model blade data.
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for different approach
Dear, to understand the NATURE
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I'm struggling to understand the method followed in the following analysis. Can someone please explain how the author got the values of Δ_1 and K_1 that justify its analysis?
I have tried to isolate "Δ" and "K" by setting Equation (B8) equal to zero. but I have failed to get similar conditions.
P.S: I'm new to mathematical modelling, so I really need to understand what's going on here. Thanks
The RHS is a fraction, whose numerator and denominator are quadratic expressions in Δ. Therefore the fraction takes positive values when numerator and denominator are of the same sign...
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why to quantize a Hamilton-Jacobi theory with fractional derivatives?, what are the physical or mathematical advantages?
Also, Hamilton-Jacobi theory can be applied with not only fractional derivatives but also, definition of fractional derivatives and integrals on time scale Yazen Alawaideh
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How to people propose a new optimization algorithm. I mean what is the baseline? Is there any intuition or mathematical foundation behind it?
The question is too general. To generate the basic idea of the algorithm, you need to know the detailed statement of the problem. Typically, the process of developing an algorithm starts with the identification of your problem complexity class. If there is no evidence or clear feeling that the problem is NP-hard, then it is reasonable to try to develop a polynomial algorithm for solving it. Such algorithms are usually based on the use of specific properties of the problem. Sometimes it is possible to construct a polynomial algorithm based on the general scheme of dynamic programming, taking into account the specific properties of the problem.
If the problem is known to be NP-hard, then branch-and-bound methods, dynamic programming, and their modifications often work well for a relatively small problem dimension. Sometimes it is possible to build a successful formulation of the problem in the form of an integer programming model, followed by the use of appropriate methods or ready-made software. For high-dimensional problems, you can either use well-known metaheuristics, or develop your own approximate algorithm. In the latter case, success is usually based on the use of the problem properties. As you can see, in any case, it is useful to start by studying the specific properties of your particular problem.
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When solving mathematical equations or system of equations there are things that are considerable; such as the Universe or domains...
Because, some equations may have no solutions or impossible to solve., at all. If a solution or some solutions exist for an equation or systems of equations, there are regions or intervals containing the solution(s). Such considerations may be important when applying numerical methods.
What are basins of attractions?
Dear, Tekle Gemechu basins of attraction comes from the dynamical system and chaos theory. It is related with systems behavior. There are several example of basins of attraction. Therefore, definition and examples of basins of attraction are given in scholarpedia. Below scholarpedia's link:
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The dimensioned physical constants (G, h, c, e, me, kB ...), can be considered fundamental only if the units they are measured in (kg, m, s ...) are independent. The 2019 redefinition of SI base units resulted in 4 physical constants assigned exact values, and this confirmed the independence of their associated SI units. However there are anomalies which occur in certain combinations of these constants which suggest a mathematical (unit number) relationship (kg -> 15, m -> -13, s -> -30, A -> 3, K -> 20) and as these are embedded in the constants, they are easy to test, the results are consistent with CODATA precision. Statistically therefore, can these anomalies be dismissed as coincidence?
We begin by assigning geometrical objects instead of numerical values to the Planck units, these objects can then be combined Lego-style to form more complex objects, from electrons to planets, while still retaining the underlying attritbutes (of mass, length, time...). Solving the constants using this approach provides evidence for a unit relationship.
For convenience, the article has been transcribed to this wiki site.
...
Some general background to the physical constants.
Hi Hieram, youre welcome! Imho fun should be induced by fruitful scientific research supported by open commenting one other’s ideas (opposed to endless fruitless repeating discussions what presumingly not cannot ever workuntil it does) like iSpace („integer-Space„ or „complex-Space“ when treating the i as the one for a complex number) able to derive and decipher inter-relationships, dependencies and calculate exact arbitrary precision numerical values for most but all constants of nature.
Also recently a new true quantum geometric iSpace-IQ unit system has been developed, able to directly represent native quantum relations of contants while keeping strictly compatible to MKSA/SI system showing a single *time* based conversion factor, effective predicting quantization of time itself.
So - no - being a true long time Apple expert consultant i’d say we do not need to fear to be sued for (at least not in the foreseeable future ;-) ). And please all take the time to read thru the very short yet imho rreally convincing math of both of my newest papers to be found on my RG home.
Here is a link to RG summary of my iSpace project:
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I am aware of the facts that every totally bounded metric space is separable and a metric space is compact iff it is totally bounded and complete but I wanted to know, is every totally bounded metric space is locally compact or not. If not, then give an example of a metric space that is totally bounded but not locally compact.
Metric space A is said to be a totally bounded if every Cauchy sequence in A has convergent sub sequence
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What are the areas where mathematics are been applied medically.
Fertility rate, mortality rate, menstrual period, gestation of the fetus week per week compare to the physiological and patological symptoms, body weight and body height to determine the healthyness, the length of conjugata vera, conjugata diagonale, etc to assest the passage for labour the baby need sectio caesarea or not. Count the weeks of gestation to know the maturity of embrio or fetus organ systems, mengukur tinggi fundus uteri dengan meteran untuk menaksir masa kehamilan, ukur jarak dari symphisis pubis dan proccesus xyphoideus sebagai patokan, ukur lingkar lengan atas dengan meteran, menentukan masa subur untuk fertilisasi dengan perhitungan penanggalan, dll.
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Does nature understand mathematics?
A connected question is -- How are theory, theorem, and truth related?
Theories and Theories of Truth | SpringerLink
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I am trying to model a business scenario mathematically for my research paper but I do not have the required skillset. What is a legitimate way to find and get help. Are there any online sources or paid services. Do I need to add the expert a co-author? What type of solutions exists.
I have many times served as an applied mathematician on a multi-disciplinary team, including, for instance, biologists, meteorologists, geologists, hydrologists, etc. The other team members possessed essential knowledge to the success of the project but not the math skills. This is good for you to recognize in the study of business because nobody knows everything. A diverse team can solve problems that a single individual cannot. I would have the biologists explain over and over again that part they understood (like fish behavior or metabolic needs) and I would create a model. Then we would run the model and ask, "Is it responding the way you expect it to?" One of these interesting projects considered production of peanut butter crackers and cheese crackers sold in vending machines manufactured on the same assembly line at a factory on the road from my house to the school. Walk over to the Mathematics Department and find a graduate student studying applied mathematics who is looking for a project. You can help each other.
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Why use metaheuristic algorithms when there are so many mathematical optimization tools available, like GAMS?
According to Dr. Ben Cardoen and Dr. Ghulam Mohy-ud-din answering this question is hard, but it's easy to understand if you can understand the objective function.
The objective function is a means to maximize (or minimize) something. This something is a numeric value. In the real world, it could be the cost of a project, a production quantity, profit value, or even materials saved from a streamlined process etc.
There are lots of optimization problems in fields of researches which have varying Objective Functions. The main mathematical optimization tools (As you mentioned) are Gradient-based, which requires the objective function to be Derived and some of them are based on stochastic search (searching around the search space randomly), but as you know:
-Some objective functions cannot be Mathematically modeled or they are too hard to be modeled Mathematically so researchers are unable to use Gradient-Based methods.
-Some objective functions can be modeled mathematically but they are overly complex, like NP-Hard problems and etc. So using mathematical methods is not logical.
-Some objective functions are Non-Monotonic, so the stochastic methods might not find the right answer for the optimization problem (because they cannot escape local optima).
-Some objective functions are Discontinuous, Non-Differentiable etc. so again Gradient-Based methods are unusable.
So here is where the Heuristic or Meta-Heuristic Optimization Algorithms help researchers.
These algorithms are designed to find the global optima and escape from local Optimas. These designs are named by "Exploration" and "Exploitation" in which Exploration refers to searching the unexplored area of the feasible region while exploitation refers to the search of the neighborhood of a promising region. One of the challenges of optimization algorithms is to find the appropriate balance between Exploration and Exploitation.
Sincerely yours,
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Dear Colleagues, a recent trend in Fractional Calculus is in introducing more and more new fractional derivatives and integrals and considering classical equations and models with these operators. Thus, we have to think about and to answer questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional operators make sense in applications and why?’’, etc. These and similar questions have remained mostly unanswered until now. To provide an independent platform for discussion of these trends in the current development of FC, the SI “Fractional Integrals and Derivatives: “True” versus “False””( https://www.mdpi.com/journal/mathematics/special_issues/Fractional_Integrals_Derivatives2021) has been initiated. In this SI, some important papers have been already published. However, you are welcome to share with the scientific community your viewpoint. Contributions to this SI devoted both to the new fractional integrals and derivatives and their justification and those containing constructive criticism of these concepts are welcome.
Best regards
Yuri Luchko
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1) What's the difference between SCILAB and MATLAB?
2) Which one would you recommend?
3) Which one is the most friendly user?
Hi Sunday Emmanuel Fadugba I have no experience with SCILAB (and very little with MATLAB). What I can recommend is using Mathematica (if you can afford it; or maybe you can use the free version on Raspberry Pi) or Julia (free). Hope it helps.
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How can we analyze the propagation constant in slab waveguides? Is there a mathematical formula for this parameter?
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If interested you can send different articles from Piaget theory in the learning of mathematics through play.
I agree that it starts in Piaget's sensory-motor stage of play. Mary Reilly's Systems Explanation of play: Learning through play and the Third form of Information Processing theories mirror and expand on Piaget's Theory of play and learning.
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my article is about the relationship between playing and increasing intelligence via mathematics. this a longitudinal research which has done since 4 years ago until to year. it is a pre-test- post-test research with control group. results are wonderful. assessment tool in this research was Stanford-Binet test. I am following to a journal in grade Q1. I would be grateful if someone could help me.
Just based on the metrics I would suggest that you might have a look at:
Educational Studies in Mathematics https://www.springer.com/journal/10649 CiteScore 3.6 (SJR Q1 journal), Impact factor 2.853 (JCR Q2 journal)
ZDM – Mathematics Education https://www.springer.com/journal/11858 CiteScore 4.1 (SJR Q1 journal), Impact factor 2.481 (JCR Q2 journal)
Journal of mathematics teacher education https://www.springer.com/journal/10857 CiteScore 3.6 (SJR Q1 journal), Impact factor 1.786 (JCR Q2 journal)
Research in Mathematics Education https://www.tandfonline.com/journals/rrme20 CiteScore 3.4 (SJR Q1 journal), ESCI indexed (so no impact factor and Q ranking (yet))
Best regards.
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Chaos Theory, Chaotic dynamics
Dear Shireen,
There are data-driven and parametric that you can utilize to detect chaos. If the system is well-defined, a good starting point can be Lyapunov Exponent and Poincare map. If you have only output of the system then you need data-driven methods like 1/0 test or entropy-based methods.
Regards
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If any mathematical equations for coupling of pmsm and pmsg in matlab?
coupling equations available in ODEs and also built-on ode45, ode15, ect code in matlab.
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A study by Po-Shen Loh shows that quadratic equations can be solved using a clever trick that reduces guessing and cramming formula. Kindly follow this link to see examples of quadratic equations solve by Po-Shen Loh https://www.youtube.com/results?search_query=po+shen+loh+quadratic .
Could this idea be applied in class? if so, could it be generalized for other topics in mathematics?
By practical applications
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Can anyone please confirm whether there exists an explicit mathematical relationship between the gravitational instability growth rate and the corresponding structure (star) formation rate in molecular clouds?
Thanks a lot, dear Javad Fardaei, for the article
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I have formulated the mathematical equation of the vibration problem. The resulting equation is coupled nonlinear differential equation of 2nd order ODE. Please, anyone, suggest to me how to solve it using MATLAB.
Dear Sandip,
to answer your question, I agree with Abdelghani: you have 1) to transform the 2nd order equations into 1st order ones and then 2) to use a MATLAB ode solver to numerically solve the resulting 1st order system.
To do step 1), you have to introduce new variables that correspond to first derivatives. For instance, let us say that you have a system of two 2nd order ODEs in x=x(t) and y=y(t), e.g. x''=f(t,x,y,x',y') and y''=g(t,x,y,x',y'). Then you can introduce two dummy variables X=x' and Y=y' (for example) and get a system of four 1st order ODEs: x'=X, X'=x''=f(...), y'=Y, Y'=y''=g(...).
Then, in order to apply step 2), you have to define a variable vector, say v=[x,X,y,Y], and a function, say myFun, that defines the system. In this case:
function vder = myFun(t,v)
vder(1)=v(2); % this equation corresponds to x'=X
vder(2)=f( t, v(1), v(3), v(2), v(4) ); % you should actually write your original equation for x''=X'=...
...etc...
end
Then, choose an ODE solver (for example ode45) and solve the system by using the basic command [t,v] = ode45(@myFun,tspan,v0); where tspan is an interval for the independent variable (e.g. tspan=[0,10]) and v0 is a vector containing the initial values for x, X=x', y, and Y=y'. So please notice that you must provide initial values for the first derivatives!
You can find more details about all this stuff here: https://www.mathworks.com/help/matlab/math/choose-an-ode-solver.html
Hope this helps! :-)
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I am working on RIS aided communication. Whichever paper I go though, they cook up some complicated mathematics specially optimization problem, which seems to be unsolvable at first. But, then I see they are using some techniques which I have never seen anywhere. Can anyone from wireless comm background tell me, how you people proceed and get those sort of maths?
Optimization is a broad field of mathematics and not some mysterious quackery. I am not surprised that someone from another field entirely (wireless communications) might not be familiar with these topics. This is why I stress the importance of multi-discipline teams. Nobody knows everything. If you get smart people from different fields together in the same room to discuss a problem, you may find some clever solutions that any one person alone would never come up with.
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Hi!
I'm currently working on a Data Science project for optimizing the prices of the products one of the biggest supermarket chains in Mexico.
One of the things that we are working on, is finding the price elasticity of demand of such products. What we usually do, is that, apart from fitting an XGBoost model for predicting sales, we fit a linear regression, and we get the elasticity from the coefficient corresponding to the price (the slope).
However, it is abvious that linear regression is sometimes a poor fit for the data, not to mention that the execution times are way longer since it requires to run separately XGBoost and LR (which is not good considering that there are thousands of products to model).
Because of this, it ocurred to me that we could use numerical differentiation for finding the price elasticity. At last, calculating a numerical derivative is way faster than fitting another model.
However, I'm not sure if this is mathematically correct, since the data does not come from a function.
So the question would be, is this mathematically correct? Does it make sense?
From my experience, I would not use a linear predictor for elasticity. I know your question is asking about mathematically correct solutions but I don't think that's your issue. I would probably use logistic regression as a first choice.
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Dear colleagues,
I am researching in a topic related to philosophy and teaching methods. Please, could you point out me if are there any sources on dialectics or contradiction in mathematics education?
Regards
An activity theory perspective on contradictions in flipped mathematics classrooms at the university level, Helge Fredriksen and Said Hadjerrouit, 520-541, 2019
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Please look at the text of the section on random walk from page 9 to formula 4.7, where you will find mathematical calculations justifying the probabilistic interpretation of the Riemann zeta function.
If the distribution of the zeros of the Riemann zeta function is implicit in your question, then you may find the following paper exciting:
Regards,
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I will be glad if researchers and professors answer my question with mathematical formulas or explanations. Thank you so much.
Hi, it should be taken into account that it is actually 'stress' doing the deformation for us. So when you use a roll with a smaller radius, the contact area between the roll and the sheet/foil is also smaller, increasing the stress.
Stress = Force / Area
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I can't understand why each time we divide by the mass of oxidized NH4-N and multiply by the mass of treated NH4-N.
Look at the attached screenshot search and I think your question is answered if I understand you. Best wishes David Booth
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How can we mathematically calculate the critical thickness of polycrystalline(Sputtering) grown thin?
Thank you, Dr. Len
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Hello? Good evening, I would like to ask if there is a questionnaire aligned to the set of indicators on Mathematical Competence given by Sir Turner?
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I want to understand the mathematics of fluorescence process in terms of excitation and emission wavelengths. I want to develop a general mathematical model with certain specific parameters and without employing a spectrometer, I want to see the emission spectrum mathematically.
One can construct simple model (Shifted Harmonic Oscillator model) and derive tractable equations to obtain absorption and emission spectra.
1. Absorption and Emission Lite: Assume ground and excited states are shifted classical Harmonic Oscillator. Ground state |g> energy: Eg(R) = 1/2 ω2R2 & Excited state |e> energy: Ee(R) = 1/2 ω2(R - R0)2 + ΔE. Treating R classically one gets absorption (Ia) and emmision (Ie) spectra as:
Ia(e) = exp[(e-ΔE)2/2σ2] Ie(e) = exp[(E-ΔE + ω2R02)2/2σ2] (Arbitrary Units)
absorption and emission is peaked at different energies and the difference is ω2R02 --- stokes shift, see: https://en.wikipedia.org/wiki/Stokes_shift
σ is the linewidth caused by molecules coupling to environment (Homogeneous Broadening) caused because individual molecules see slightly different environment, e.g. ΔE (Inhomogeneous Broadening) is different for different molecule.
2. Absorption and Emission Pro: Same as 1, but treat R quantum mechanically,
this gives |g>|v0> , |g>|v1> ... |g>|vn> states and |g>|v0'> , |g>|v1'> ... |g>|vn'> where |vn> is nth vibrational state centered around 0 and |vn'> nth vibrational state centered around R0.
• Energy of |g>|vn> --> <vn|<g| H |g>|vn> = (n + 1/2)ℏω and
• Energy of |g>|vn> --> <vn'|<e| H |e>|vn'> = (n + 1/2)ℏω + ΔE
With this we write the absorption at T = 0K ( or ℏω >> kT)
Ia(e) = ∑n |<vn'|v0>|2 exp[(e-ΔE - nℏω)2/2σ2]
= ∑n (1/n!) * (ωR02/2)n exp[-(ωR02/2)2] exp[(e-ΔE - nℏω)2/2σ2]
Ie(e) = ∑n |<v0'|vn>|2 exp[(e-ΔE + nℏω)2/2σ2]
= ∑n (1/n!) * (ωR02/2)n exp[-(ωR02/2)2] exp[(e-ΔE + nℏω)2/2σ2]
|<v0'|vn>|2 are Franck-Condon factor,
|<v0'|vn>|2 = |<vn'|v0>|2 = (1/n!) * (ωR02/2)n exp[-(ωR02/2)2].
3. Absorption and Emission Pro Max: Same as 2 but at finite temperature T. Assuming instant thermalization --> states are population according to Bolzmann distribution,
Ia(e) = ∑mn |<vn'|vm>|2 exp[(e-ΔE - nℏω)2/2σ2] * Pm
= mn |<vn'|vm>|2 exp[(e-ΔE - nℏω)2/2σ2] * (exp[-βmℏω] /∑kexp[-βkℏω])
= ∑mn (1/n!) * (ωR02/2)n exp[-(ωR02/2)2] exp[(e-ΔE - nℏω)2/2σ2] * (exp[-βmℏω] /∑kexp[-βkℏω])
Ie(e) = ∑mn (1/n!) * (ωR02/2)n exp[-(ωR02/2)2] exp[(e-ΔE + nℏω)2/2σ2] * (exp[-βmℏω] /∑kexp[-βkℏω])
Pm = (exp[-βmℏω] /∑kexp[-βkℏω])
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Hello, this is my first post on this site. I'm an undergraduate student doing some Raman spectroscopy of CVD-grown graphene strained on silicon dioxide nanospheres. I notice that D and G' peaks show up in some measurements. The transfer process of the graphene to the silicon dioxide nanosphere-coated silicon chips I would think is far from perfect, as in certainly interferes with the structure of the graphene as there are rips and tears across the sample, as well as impurities and other things. You do however have "pristine" regions that only show G and 2D peaks.
On a loosely related tangent, I'm interested in how the molecular symmetry of graphene plays a role in its Raman spectra, and how that can be expressed mathematically. I wonder if perhaps the mathematical description of graphene in terms of group theory can possibly help explain the redshifts that occur in strained graphene versus unstrained graphene. If anyone has some advice or things to read about that, please let me know!
In perfect graphene, the D-peaks are by symmetry not Raman active. ideal graphene should only show the single G-peak. However, when there is anything disturbing the symmetry and structure, the condition is relaxed and the D-peaks become visible. Hence, their name D for "defect" peaks. Based on the relation of peak intensity or the integrated intensity below the modes, the quality of graphene layers can be quantified.
There are numerous reviews on Raman spectroscopy in graphene, explaining which information can be extracted and how they can be extracted from analyzing the spectra.
You should be able to quickly find numerous more articles.
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I have myself tried using the basic method but including incomplete ionization to figure out the depletion width however I failed miserably because of many mathematical roadblocks. I was wondering if this had been done in the literature before and I just missed it.
If anyone can help me in this regard then I would be very grateful. Thanks.
If you can send me a sample data file, I can have a look at it...
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please is there any mathematical function that relates the SMD (D32) to the mean diameter (D50)? I actually understand what each of them represent.
thanks
Thanks for this
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I am primarily interested in 2-player combinatorial games with perfect information. Useful wiki links are below.
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In statistics, Cramér's V is a measure of association between two nominal variables, giving a value between 0 and 1 (inclusive). It was first proposed by Harald Cramér (1946).
It is actually considered in many papers I came accross that a threshold value of 0.15 (sometimes even 0.1) can be considered as meaningful, hence giving hints of a low association between the variables being tested. Do you have any reference, mathematical foundation or explanation on why this threshold is relevant ?
Regards,
Roland.
I made a mistake in my answer. I gave you the information for the COntingency coefficient. For the Cramer V, there is a table of effect size which depend on the degree of freedom of the Cramer V. See: https://www.real-statistics.com/chi-square-and-f-distributions/effect-size-chi-square/
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Is there a way to model the influence of pH on the electroosmotic EDL potential and velocity field inside the flat microchannel mathematically?
Thank you Masuduzzaman.
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How could one increase data values from weekly to daily observations using mathematical algorithm for interpolation?
Hello Nasiru,
What's the reason for wanting these values? That may have more to do with what sort of approach, if any, might make sense.
At first glance, doing this doesn't sound like a good idea to me. Among the reasons:
Any method for taking adjacent weekly values and inserting some estimate for the 6 six "missing" daily values will only bias the estimates of day-to-day variance in scores/values as well as increase the serial correlation across a lag from 1 to 6 days. As well, the presumption of a (perfectly) predictable day to day change is unlikely to be realized in actual measurements.
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The mathematical representation of both equations is same.
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Hi
I'm solving nonlinear second order equation by using finite difference method . finally for calculating value at any desired node, knowing three preceding nodes is required however by knowing boundary condition just one of these nodes becomes obvious and still knowing two other values is necessary. it must be noted there are plenty of guesses for values of these nodes which lead to compatible response.
please write the ODE, not only the discretization You used.
however, for multi-step methods you need to create the starting values using a single-step method for all required nodes. Use a discretization of the same accuracy.
Note that the second order ODE could be written as system of two first order ODE.
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The 2023 ranking is available through the following link:
QS ranking is relatively familiar in scientific circles. It ranks universities based on the following criteria:
2- Employer Reputation
3- Citations per Faculty
4- Faculty Student Ratio
5- International Students Ratio
6- International Faculty Ratio
7- International Research Network
8- Employment Outcomes
- Are these parameters enough to measure the superiority of a university?
- What other factors should also be taken into account?
Cenk Tan; There are, of course, several websites that rank the universities worldwide. However, QS is the most famous of which.
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Here I attached the journal and the mathematical solution of the Rayleigh number. I need to plot graph exactly in Figure 3 from the journal but I didn't know the command. I have tried using this command,
plot(subs(N1 = 0.5, N3 = 2, N5 = 1.5, a1 = 1, a2 = 3, a3 = 1, Q = 10, R), a = 0 .. 10, 11 .. 22);
but the results show only a single line 2D graph. Hopefully anyone could help me with this. Thank you in advanced.
You have only derived one relationship for R. Each of the graphs in Figure 3 show three relationships [1) linear inverted and parabolic; 2) heating from below and cooling from above; and 3) step function] So you need 3 different equations for R. Then there are the three cases [1) N1=0.1, Q=10; 2) N1=0.1, Q=20; and 3) N1=0.5, Q=10]. Maple is doing exactly what you've told it to do: plot one relationship for R. After Maple solves the equation, you could easily paste it into Excel and plot the results.
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I am currently working on the use of metacognitive abilities to improve teacher proficiency of teaching mathematics in Primary schools. I am looking for international collaborators from Japan, Germany, Singapore, Netherlands, USA, Canada and Australia.
Thank you
Those with creative thinking skills and intelligence
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topics should be where we can mathematics algorithms
you can think of in covid 19, Lung cancer, Brain tumor detection using different deep Learning Techniques and possible to use also ML Algorithms.
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I plan to divide my long research article(simulation + mathematical) into two parts, but I am clueless about how to do this. (I can not separate the simulation and mathematical analysis)
I have a few questions regarding the same
1) Do I need to show the common mathematics in both parts?
2) Can the introduction be the same?
3) Can some explanations remain the same in both parts?
Can someone give me the reference of any article divided into two parts?
Thanks for the suggestion. I will try to do the same if it can be done in my work.
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Most had no knowledge but high interest. Now I want to describe this relationship using statistical methods.
I used a likert scale so, the data is ordinal.
Using a Spearman's rank test I get a positive correlation with good significance.
But I don't really understand this result. I expected a negative correlation, since interest and knowledge frequencies have contrary slopes. Does the test look at individual pairs, where those with high knowledge may also have high interest?
PS: How could I form a mathematical equation to describe the relationship (regression)?
Hello Lukas,
As the software reports, the estimated Spearman correlation is about .34 (Pearson very close, at about .35). Yes, the correlation is positive. That's because the general trend is that, persons having higher self-rating of knowledge tend to have higher self-rated interest, whereas those with lower self-rated knowledge tend to have lower self-rated interest.
Look within any row of your two-way contingency table, and as knowledge rating increases, you'll see a higher relative proportion of high ratings of interest.
Yes, it's true that the correlation is far from perfect. All that tells you is that you'll find exceptions to the general trend described above as you examine knowledge-interest ratings from the same person over your sample.
Mathematical relationship? (Using 0-5 scales for each variables)
Estimated rating of self-interest = 2.62 + 0.35 * rating of knowledge
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In my previous question I suggested using the Research Gate platform to launch large-scale spatio temporal comparative researches.
The following is the description of one of the problems of pressing importance for humanitarian and educational sectors.
For the last several decades there has been a gradual loss in quality of education on all its levels . We can observe that our universities are progressively turning into entertaining institutions, where students parties, musical and sport activities are valued higher than studying in a library or working on painstaking calculations.
In 1998 Vladimir Arnold (1937 – 2010), one of the greatest mathematicians of our times, in his article “Mathematical Innumeracy Scarier Than Inquisition Fires” (newspaper “Izvestia”, Moscow) stated that the power players didn’t need all the people to be able to think and analyze, only “cogs in machines,” serving their interests and business processes. He also wrote that American students didn’t know how to sum up simple fractions. Most of them sum up numerator and denominators of one simple fraction with the ones of the other, i.e. as they did it, 1/2+ 1/3 according to their understand is equal to 2/5 . Vladimir Arnold pointed out that with this kind of education, students can’t think, prove and reason – they are easy to turn into a crowd, to be easily manipulated by cunning politicians because they don’t usually understand causes and effects of political acts. I would add, for myself, that this process is quite understandable and expected because computers, internet and consumer society lifestyle (with its continuous rush for more and newer commodities we are induced to regard as a healthy behavior) have wiped off young people’s skills in elementary logic and eagerness to study hard. And this is exactly what the consumer economics and its bosses, the owners of international businesses and local magnates, need.
I recall a funny incident that happened in Kharkov (Ukraine). One Biology student was asked what “two squared” was. He answered that it was the number 2 inscribed into a square.
The level and the scale of education and intellectual decline described can be easily measured with the help of the Research Gate platform. It could be appropriate to test students’ logic abilities, instead of guess-the-answer tests which have taken over all the universities within the framework of Bologna Process which victorious march on the territories of former Soviet states. Many people can remember the fact that Soviet education system was one of the best in the world. I have therefore suggested the following tests:
1. In a Nikolai Bogdanov-Belsky (1868-1945) painting “Oral accounting at Rachinsky's People's school”(1895) one could see boys in a village school at a mental arithmetic lesson. Their teacher, Sergei Rachinsky (1833-1902), the school headmaster and also a professor at the Moscow University in the 1860s, offered the children the following exercise to do a mental calculation (http://commons.wikimedia.org/wiki/File:BogdanovBelsky_UstnySchet.jpg?uselang=ru):
(10 х 10 + 11 х 11 + 12 х 12 + 13 х 13 + 14 х 14) / 365 = ?
(there is no provision here on Research Gate to write square of the numbers,thats why I have writen through multiplication of the numbers )
19th century peasant children with basted shoes (“lapti”) were able to solve such task mentally. This year, in September, this very exercise was given to the senior high school pupils and the first year students of a university with major in Physics and Technology in Kyiv (the capital of Ukraine) and no one could solve it.
2. Exercise of a famous mathematician Johann Carl Friedrich Gauss (1777–1855): to calculate mentally the sum of the first one hundred positive integers:
1+2+3+4+…+100 = ?
3. Albrecht Dürer’s (1471-1528) magic square (http://en.wikipedia.org/wiki/Magic_square)
The German Renaissance painter was amazed by the mathematical properties of the magic square, which were described in Europe firstly in Spanish (the 1280s) and Italian (14th century) manuscripts. He used the image of the square as a detail for in his Melancholia I painting , which was drawn in 1514, and included the numbers 15 and 14 in his magic square:
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
Ask your students to find regularities in this magic square. In case this exercise seems hard, you can offer them Lo Shu (2200 BC) square, a simpler variant of magic square of the third order (minimal non-trivial case):
4 9 2
3 5 7
8 1 6
4. Summing up of simple fractions.
According to Vladimir Arnold’s popular articles, in the era of computers and Internet, this test becomes an absolute obstacle for more and more students all over the world. Any exercises of the following type will be appropriate at this part:
3/7 + 7/3 = ? and 5/6 + 7/15=?
I think these four tests will be enough. All of them are for logical skills, unlike the tests created under Bologna Process.
Dear colleagues, professors and teachers,
You can offer these tasks to the students at your colleges and universities and share the results here, at the Research Gate platform, so that we all can see the landscape of the wretchedness and misery resulted from neoliberal economics and globalization.
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Mathematics is a language of all science subjects
"The book of nature is written in the language of mathematics."
Galileo Galilei
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Complex systems are becoming one of very useful tools in the description of observed natural phenomena across all scientific disciplines. You are welcomed to share with us hot topics from your own area of research.
Nowadays, no one can encompass all scientific disciplines. Hence, it would be useful to all of us to know hot topics from various scientific fields.
Discussion about various methods and approaches applied to describe emergent behavior, self-organization, self-repair, multiscale phenomena, and other phenomena observed in complex systems are highly encouraged.
Formation of Zoonoses: Climate Change and Anthropogenic Factors Expanding the Area of Zoonosis
Hemorrhagic fever with renal syndrome is a non- transmissible viral zoonosis widespread in Russia. It is considered one of the most important natural focal diseases. We examined leptospirosis and tularemia as climate-dependent diseases of bacterial etiology. Leptospirosis is transmitted only non-transmissively, while tularemia, in addition to a number of non-transmissible pathways, is characterized by a facultative- transmissible pathway, and arthropods, primarily blood- sucking dipterans, act as mechanical carriers.
Among the transmissible natural focal diseases of various etiologies, we examined tick-borne encephalitis, ixodid mites-borne borreliosis (Lyme disease), mites- borne typhus (mites-borne rickettsiosis), and Crimean hemorrhagic fever.
West Nile fever is one of the most important natural focal diseases transmitted by mosquitoes. The most unfavorable situation was observed in Astrakhan, Volgograd, and Rostov regions. They account for the vast majority of cases of the disease.
A classic example of anthroponosis is malaria. The epidemiological situation at the present time can be considered favorable given that the number of imported cases is small (about a hundred per year) and local cases are rare. However, malaria is also a classic example of a disease that can quickly regain its position when control is loosened.
Model analysis of changes in the distribution of Ixodidae
mites and malaria mosquitoes showed that their habitats were influenced by the observed climate change which is significantly expanding in the northern and eastern regions, and the reduction is negligible.
The prerequisites for an increase in the incidence of these infections and their wider spread persist.
Climate-related risk factors include expansion of the areas of arthropod vectors and an increase in their numbers, as well as a similar increase in the number and expansion of the areas of vertebrates, mainly murine rodents, which are reservoirs of natural focal infections and carriers of vectors in nature. A new risk factor is the importation of exotic vectors into the territory of Russia, as well as their rooting, the importance of which increases with the expected warming.
Countermeasures (adaptation measures) against climate-dependent infections include prevention (vaccination), strengthening monitoring of the species composition and number of vectors and reservoirs of infections, and increasing the scale and effectiveness of combating them. These measures also include personal protective equipment against them. The enhancement of the effectiveness of these measures should be based not only on the actual improvement of these funds but also on the improvement of the sanitary and epidemiological
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There are any papers or studies about the Blended Learning in Mathematics, exactly in (Calculus) ?
The above article is very interesting and it strengthens my conclusions that this problem has been around with up for a long time - at least back to the early 1970''s when I first had experience observing new college students as a TA in grad school. I've taught off and on since the 1960's undergraduate and graduate level courses to both "math majors" and science and engineering majors. My observations were formed originally the early 1970's as the trend of more students taking calculus in high school were less prepared in the mathematical fundamentals and there was a gap in their preparation that showed up at the freshman college level. A teacher in calculus should not have to stop his/her lecture and go over the principle of mathematical induction or the basic analytic geometry of a conic section in freshman calculus. But alas - that was the case. In multidimensional calculus, the students should come in with a firm understanding of linear algebra. However, in my experience that was not always the case. That is the students had holes in their preparations and at some point those holes had to be filled or eventually they would hit a brick wall.
Calculus introduces new and sometimes difficult concepts and the students tend to have little intuition of the concepts of continuity and limits. But without developing a firm understanding and intuition of these and related topological concepts - it is difficult to grasp the calculus. If one does not have the background and facility of understand the fundamental tools of symbolic manipulation (a necessity to do all mathematics), understanding of basic geometry, the basic knowledge of set theory, mathematical induction and logic, it becomes a game of memorization and mechanics. Over time this lack of preparation in the fundamentals has grown more not less prevalent. This lack of preparations is reflected today in that many calculus sequences at the college level include analytic geometry. At one college I have taught specific courses over time, University of South Florida, there is now a required course known as "Bride to Abstract Mathematics." It is a course in logic, construction of proofs, set theory , relations and functions. That is the basic foundations that were once taught in high schools in the US but gave way with the push to present calculus in high school.
I expect we are seeing the same issues arise as subjects like abstract algebra and algebraic geometry become more and more important in applications like computer vision and robotics. It is difficult to apply mathematics to a field when ones understanding of the underlying mathematics has gaps.
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Philosophers of science typically recognize two kinds of values in scientific practice: (1) epistemic (or theoretical, or cognitive) virtues, like accuracy, testability, empirical support, etc, and (2) ethical (or social, or regulative) norms, like justice, egalitarianism, openness, etc. Of course, the strict separation of these categories is open to disagreement.
Are there values or norms (of either kind) that are unique to mathematics? Rigour (or provability) is one possibility; computability is another. Can you think of others? Do values play the same kind of role in math as in the natural sciences?
Elegance and parsimony are mathematical virtues. They seem to be aesthetic, rather than ethical or straightforwardly epistemic. However, aesthetics can be an aid to cognition.
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Hi all,
There are instructions on the steps of running ‘align’ in a command-line way as shown in the following explanation found online (https://pymol.org/dokuwiki/doku.php?id=command:align). However, I didn’t found the mathematics or details for PyMOL running ‘align’ through the click-button way in GUI interface. Anyone know the mathematics or details behind it? Thanks a lot!
Yaohui
"In short, “align” is a automated multi-step superposition algorithm based on dynamic programming and iterative refinement. “align” first performs a per-residue global dynamic-programming sequence alignment for the input atom selections using the BLOSUM62 weightings from BLAST. Then, a per-atom correspondance is established between atoms in the selections. Matching side chains atoms will be included if they were provided in the selection arguments. An initial superposition is then performed followed by up to five cycles of iterative refinement wherein atoms with per-atom deviations over two standard deviations from the mean deviation (if any) are thrown out and the fit is repeated. Finally, the number of atoms remaining at the end of this procedure is printed out along with the resulting RMS value for those atoms."
Pymol offers different alignment methods, which are optimised for different levels of sequence similarity:
Basically, "align" https://pymolwiki.org/index.php/Align does a sequence based structural alignment, first doing a sequence alignment to decide which Calpha atoms to perform a 3D alignment on, then iteratively removing very poorly 3D-fitting atoms from the alignment to reduce the influence of structurally variable loops on the alignment.
In contrast "super" https://pymolwiki.org/index.php/Super aligns two selections by a sequence-independent (unlike align) structure-based dynamic programming alignment followed by a series of refinement cycles intended to improve the fit by eliminating pairing with high relative variability (just like align).super is more robust than align for proteins with low sequence similarity.
"cealign" https://pymolwiki.org/index.php/Cealign aligns two proteins using the CE algorithm. It is very robust for proteins with little to no sequence similarity (twilight zone). For proteins with decent structural similarity, the super command is preferred and with decent sequence similarity, the align command is preferred, because these commands are much faster than cealign.
Each of the commands offers a number of parameters to tweak the method, e.g. setting limits to the maximal gap length and specifying the number of iteration cycles
You can also extend the PyMol capabilities using the "TMalign" module https://pymolwiki.org/index.php/TMalign
To do superpositions between exactly defined atom sets (e.g. in ligands), use "fit" https://pymolwiki.org/index.php/Fit or "pair_fit" https://pymolwiki.org/index.php/Pair_fit
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How can you advise on the methods of mathematical prediction of the causes of salinity?
thank you
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One of my research questions is about the level of democratic practices in the mathematics high school classroom. When examining the normality of the the demoratic practices, it turned out that they are not normal. In normal samples, we use one-sample t-tests with critical values that fit our assumptions of the level of the democratic practice. For example if we want to take into consideration three levels, we divide (5-1)/3=1.33. This enables us to consider what is below the grade 2.33 weak, what is between 2.33 and 3.66 midium, and what is abover 3.66 high. This serves us in doing the one-sample t-test, where the critical value is 2.33 or 3.66 to verify the level of the variable.
My question is: How can we do that in case of non-normal distribution?
I really thank all of you for your valuable comments. I attach an article in which to find the significance of the level of democratic practices, we used one sample t-test. My question was about what we do if the data does not follow normal distribution.
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I would like to know the effect of temperature and pressure on the density of Fe2O3 nanoparticles, and if there are some tables or equations that describe the change mathematically.
It is very hard to have a unique mathematical expression that will described changes in density x temperature of treatment. It will strongly depends on your synthetical route of the samples, the crystal structure, porosity, and so on.
Normally, increasing the temperature and pressure you will see the densification of the nanoparticles. However, you can see a phase transition that changes the density of the system, so it is not a straightforward analysis. I recommend you to synthesize several NP at a varied range of temperature, then perform porosity/density measurements employing helium pycnometer.
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