Science topics: Mathematics
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Mathematics - Science topic

Mathematics, Pure and Applied Math
Questions related to Mathematics
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Some modular functions, such as the Riemann zeta one, display a fractal behaviour.
Does also the curve of the j-function display power law properties, or a scale free structure?
It it feasible to calculate the j-function's power law slope, or its Lyapunov exponent? Is the j-function somehow correlated with the Feigenbaum constant of logistic plots?
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@ Fabio,
It seems very nice example. Did you mean the discriminant of the (Klein's J-function) ? In general, some of modular forms are Fractals.
But not all of them.
Best regards
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There are lots of Optimization method /Evolutionary algorithms (EAs) in literature. Some of them is more effective (for solving linear/nonlinear problem) compared to other. But we don’t know which will fit our model. As a result we checked for everything as we can do. But cant get the desire result. Some of those methods are 1. Genetic algorithms (GA) ; Haupt and Haupt (2004) 2. Pattern search (Mathlab) 3. Particle swarm optimization (PSO), Binary Particle Swarm Optimization (BPSO); Eberhart and Kennedy (1995) 4. Bee optimization; Karaboga and Bosturk (2007) Pham et al (2006) 5. Cuckoo algorithm; Yang and Deb (2009, 2010) 6. Differential evolution (DE) ; Storn and Price (1995, 1997) 7. Firefly optimization; Yang (2010) 8. Bacterial foraging optimization; Kim, Abraham and Cho (2007) 9. Ant colony optimization (ACO) ; I Dorigo and Stutzle (2004) 10. Fish optimization; Huang and Zhou (2008) 11.Raindrop optimization ; Shah-Hosseini (2009) 12.Simulated annealing ; Kirkpatrick, Gelatt and Vecchi (1983) 13.Biogeography-based optimization (BBO), 14. Chemical reaction optimization (CRO) 15. A group search optimizer (GSO), 16. Imperialist algorithm 17. Swine flow Optimization Algorithm. 18. Teaching Learning Based Optimization (TLBO) 19. Bayesian Optimization Algorithms (BOA) 20. Population-based incremental learning (PBIL) 21. Evolution strategy with covariance matrix adaptation (CMA-ES) 22. Charged system search Optimization Algorithm 23. Continuous scatter search (CSS) Optimization Algorithm 24. Tabu search Continuous Optimization 25. Evolutionary programming 26. League championship algorithm 27. Harmony search Optimization algorithm 28. Gravitational search algorithm Optimization 29. Evolution strategies Optimization 30. Firework algorithm, Ying Tan, 2010 31. Big-bang big-crunch Optimization algorithm, OK Erol, 2006 32. Artificial bee colony optimization (ABC), Karaboga,2005 33. Backtracking Search Optimization algorithm (BSA) 34. Differential Search Algorithm (DSA) (A modernized particle swarm optimization algorithm) 35. Hybrid Particle Swarm Optimization and Gravitational Search Algorithm (PSOGSA) 36. Multi-objective bat algorithm(MOBA) Binary Bat Algorithm (BBA) 37. Flower Pollination Algorithm 38. The Wind Driven Optimization (WDO) algorithm 39. Grey Wolf Optimizer (GWO) 40. Generative Algorithms 41. Hybrid Differential Evolution Algorithm With Adaptive Crossover Mechanism 42.Lloyd's Algorithm 43.One Rank Cuckoo Search (ORCS) algorithm: An improved cuckoo search optimization algorithm 44. Huffman Algorithm 45. Active-Set Algorithm (ASA) 46. Random Search Algorithm 47. Alternating Conditional Expectation algorithm (ACE) 48. Normalized Normal Constraint (NNC) algorithm 49. Artificial immune system optimization; Cutello and Nicosia (2002) 50. fmincon .
Besides this there are many other optimization algorithm recently invented which are generally called Hybrid optimization Technique because it’s a combination of two method. If we share our experiences then it will be helpful for all of us who are in the field of optimization. I may be missing some methods, researcher are requested to add those algorithms and the way of use like many model needs initial value, weight, velocity, different type of writing objective function etc. I am facing some problems that’s why I make this format which will definitely help me as well as all other researchers in this field. Expecting resourceful and cordial cooperation.
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Abu, you are not very clear. If you want to discuss effectiveness, then you need to define what that is, and run experiments on a huge set of carefully randomized test problems in order to make any claims about one method being better than another. I have mentioned on more than one occasion that if you have a deep knowledge of your problem and its properties, chances are very slim that a metaheuristic will be the winner against your own devise.
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Can you give me information about journals that have monthly publications and do not prolong the period in the evaluation of research and acceptance of publication?
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I am searching for mathematical expression
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There are many ways of ascribing theoretical and statistical mathematical expressions to experimental data but it would good to know where the data came from first, what the model is, if any, how much data there is, etc.
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Trying to understand the Kalman filtering with all these example of the EKF and is it properly done ?
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I advise you to read the book "KALMAN FILTERING. Theory and Practice Using MATLAB. Fourth Edition" by M.S. GREWAL and A.P. ANDREWS
A very useful book for those interested in the Kalman filter.
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Mathematics are limited to the measurement of limited things but whenever we talk about infinite universe or invisible things there are no solution in form of mathematical equation. The quantum mechanics or quantum computing could also not express or explained in terms of mathematics.
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Dear Debopam ,
I am agree with you that for recognition ,pattern matching , neural network , visual processor and permanent memory are required . But all the process complete so fast without taking time . But their are sorting required for pattern matching and signals those generated by retina are processed by the visual processor and again addressing and searching required from the permanent memory .
Quantum computing solve many problem but not every one.
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The great mathematician David Hilbert set out twenty-three important problems in mathematics in 1900. One of the famous outstanding ones is the Riemann zeta hypothesis. One might argue that once a good problem is found someone somewhere will eventually find the answer. Even if the 'sometime' can be a long while, as in the case of Fermat's last theorem, still, I am inclined to the view that finding a good problem is sometimes more important than finding the answer to a good problem. On the other hand, perhaps good problems are becoming more abundant? Problems concerning the internet for example only came into existence with the internet. What is your view? Which is harder, finding a good problem or finding its answer?
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It is difficult to find problems which are deep, beautiful and perspective in the sence of impact for developing Mathematics in the future. Much more easier to pose hard problems as well as boring ones. That is why journals are full of such kind papers even there are whole journals of such kind. Solution of a problem may occur easy or hard that is difficult to be recognized before solution. The bright example is the 3rd problem of Hilbert that was solved very quickly. Generally speaking abilities of finding difficult but attractable problems and solving them don't coincide. Who possess both qualities are classic mathematicians as Euler, Poincare, Kolmogorov and oth. Those who able to pose enough difficult and attractible or useful problems and is able to solve them belong to the cathegory of happy mathematicians. That I wish to my fellows.
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I have consistently been able to formulate many matrix algorithms, used throughout mathematics as hyper spaces. Somehow it seems natural to me. If I can see these toplolofoes I may be able to help formulate how to transform, restructure them to what you seek.
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Dear Lenore Mullin,
I assumed the operators have a group structure, i.e., operations over the elements under consideration.
This helps to create a suitable norm ( based on the given operations)
and consequently, a normed space which is equivalent to a topological space.
Best regards
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Is it possible to manage with supply chain in a more effective way?
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Dear Abu Hashan Md Mashud ,
Kindly clarify your question.
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What other types of spatial descriptors, such as matrix and graph, exist?!!!
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Dear Behrouz,
The spatial descriptors symbols based on the nature of the given data.
There are curves to describe the solution set of relations y=f(x), G(x,y)=0 as st. lines parabolas, circles, etc.
Also, surfaces describe the solution set of relations G(x,y,z)=0 as st. planes, ellipsoid, elliptic cones, general manifolds.
Where (x,y,z) represent the coordinates of a point in the real space.
Also, intervals, areas, and volumes describe regions.
Sequences are described as dots or points in the coordinates system.
Graphs to describe edges and vertices as trees and cycles Triangulations of surfaces. Matrices to arrange a given data in rows and columns as the coefficients of some equations. Also, we have tensors to describe higher dimensional data as M_ijk for a three-dimensional matrix that has rows columns and heights.
Block matrices where the entries of a matrix are matrices. Vein diagrams to describe sets, their unions, and intersections.
AB for vectors( with arrow cap), <AB,AC> angles between vectors.
Also, notations play an important role in describing mathematical objects such as ∫ Integrals and d/dx differentials notations to describe physical quantities as areas and slope of tangents. ∑ Summations to express infinite series. |A| for matrix determinant, || X||_l to describe norms.
o , *, n! as composition, group multiplication, factorial, in addition to the universal quantifiers. Also, nth √ radicals to describe some algebraic numbers. Continued fractions [a:b,c,d,......] to express real numbers
as transcendental and algebraic numbers. Mathematics is rich with universal notations that describe data.
Best regards
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I am working on the beam steerers based on the phase gradient metasurfaces. Mathematically, I have calculated that beam will steer at an angle of 32 degree. However, in the intensity plot which is attached herewith, it can seen that wave is propagating at a certain angle but how can I ensure that whether it is propagating at the angle of 32 degree or not.
Thanks in anticipation.
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I don't know about CST, but in HFSS, or OpenEMS, I would extract E&H vectors, and calculate S vector.
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Dear everyone,
What is the mathematical relation between coherence length and coherence time in an FSO channel. The transmitting laser has centre wavelength of 1550 nm.
Suppose the atmospheric channel has a coherence time of 0.5461333 × 10^-6 s. what will be the coherence length. Please let me know if further information is required.
With regards,
Dhiman Kakati
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here is a few information about the channel:
FSO transmitter aperture diameter: 5 cm FSO receiver aperture diameter: 20 cm Beam divergence: 2 mrad Index refraction structure (Cn^2): 5e-015 m^(-2/3) Coherence time: 0.5461333333333334e-006 s
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Is there any document giving a mathematical representation of the working of AttributeSelectedClassifer in WEKA?
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The Attribute-Selected-Classifier is a combination of 2 steps: (1) dimensionality reduction through attribute selection, and (2) classification. The user gets to choose and customize from a variety of DR methods and classifiers in WEKA.
You can check the 2 steps separately:
- First, the DR step, by looking into the different attribute selection methods in WEKA. For some of the them, you can find reference and more information in the description of the method (see examples in the screenshots attached).
- Second, the classification step, by looking also for the information provided in WEKA. A good idea would be to check other published research, comparable to your needs, and see what classification methods are used.
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In mathematics, we prove many theorem by contradiction method.. I want to know this method is applicable in nature or not ....
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Proof by contradiction is valid only under certain conditions. The main conditions are:
- The problem can be described as a set of (usually two) mutually exclusive propositions;
- These cases are demonstrably exhaustive, in the sense that no other possible proposition exists.
Under these circumstances, if all but one of the cases are proven to be false, the remaining case must be true.
It is useful when the proposition of interest is hard to prove, but the contradictory proposition(s) is/are easy to disprove. These conditions do, of course, apply well to many mathematical problems.
For example the simplest proof that the square root of two is irrational is a proof by contradiction. We can state the problem as two mutually exclusive cases; A: sqrt(2) is irrational; or B: sqrt(2) is rational. And this is an exhuastive set; there is no other possibility. It is quite hard to show that A is true directly; but it is quite easy to show that assuming B generates a contradiction and must therefore be false. (See https://en.wikipedia.org/wiki/Proof_by_contradiction#Irrationality_of_the_square_root_of_2).
In the 'natural' world, this still works when these basic conditions hold. Finding one black swan (or a blue one) is essentially a proof-by-contradiction that "All swans are not white". (observation of a single black swan conclusively contradicts the only possible alternative proposition, that "all swans _are_ white").
But the natural world is often messier than this. First, we are often much more interested in partial generalisations (eg "_most_ swans are white") and that is impossible to prove or disprove conclusively without exhaustive counting (though statistical inference allows the statement to be rejected as improbable after suitable sampling exercises). Further, there are often many alternatives of interest, we cannot always disprove all but one, and even if we can, we cannot rule out the possibility of another, unknown case. Proving something is not a cat does not prove that it is a dog. It may be a mouse. And if we also prove it is not a mouse, there are plenty more furry animals to work through, and even after we have gone through all the known furry animals, we may be still looking at a new, previously unknown, species.
So the principle always works if the basic conditions above hold; but it is not valid if they don't. And in the natural world, if those conditions _do_ hold, we're either very lucky, or we have made some improbably sweeping generalisation that is trivially refutable.
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I am doing M.Tech in Mathematics and Computing from IIT Patna and I want to go for Ph.D. after M.tech. I am from Mathematics background (M.Sc.). I want to know the research opportunities in the fields of network science and artificial intelligence.
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Hey there,
You can find interesting topics, related to artificial intelligence, in "https://www.quora.com/What-are-the-hot-topics-in-artificial-intelligence-for-research". In general, neural networks (in particular, convolutional neural networks) have received many efforts of the research community, therefore, this is an important/relevant topic.
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Hello everyone!!
im just wondering, is it possible to find the hourly Tidal levels?
if we have understood the different factors contributing the Tidal levels, i guess it is possible to determine the Tidal wave levels.
i'm from the different background i don't know whether the techniques have developed for the estimation/deterimining the Tidal levels.
so please suggest if there is some method as such?
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Hi Praveen,
There are two options:
1. generate tidal model by using global model of ocean tides. There are plenty models available freely, for example Tide Model Driver (TMD). You can run it in Fortran or Matlab. Here is the link http://volkov.oce.orst.edu/tides/global.html
2. instantly get observational dataset from University of Hawaii Sea Level Center (UHSLC). They provide hourly and daily sea level data globally. At least, here, you can find the nearest station to your area of interest. Here is the link https://uhslc.soest.hawaii.edu/data/?fd
Good luck
Jaya
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Does light scattering occur more in less viscous solution than the highly viscous polymeric solution? Is there any such relationship or mathematical expression like this?
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This conversation is getting very confused now - or is it just me?
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Can you help me find a conference with a close date and can I send a summary and complete research in these months? Note that the required conference in the discipline of mathematics
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Can somebody help me find the right formula to calculate customer's savings at retirement from this function: retirement_savings(PMT, i, start_age, end_age).
Python mathematics.
Function 2: Retirement Savings Calculator
Build a function retirement_savings(PMT, i, start_age, end_age) that calculates your customer's savings at retirement, if they:
  • invest an amount, PMT at the end of every year (with the first payment made in exactly one year's time from now),
  • at an interest rate of i% per year, compounded annually.
  • They just turned start_age years old, and
  • they want to retire at the age of end_age
IMPORTANT: Your function may not call any of the other functions you've defined in this project (i.e. you may not call savings_calculator(PMT, n, i) inside this function)
You can assume that start_age < end_age, and both are positive integers.
In [0]:
### START FUNCTION 2 def retirement_savings(PMT, i, start_age, end_age): # YOUR CODE HERE # Remember to round your answer to 2 decimal places: FV = round(FV, 2) return FV ### END FUNCTION 2
IMPORTANT: Your function needs to return an float value rounded to 2 decimal places.
If your answer is not rounded correctly to 2 decimal places, you will receive 0 for the question.
Make sure that the following tests all give a True result:
In [0]:
retirement_savings(20000, 0.1, 20, 35) == 635449.63
In [0]:
retirement_savings(10000, 0.1, 40, 60) == 572749.99
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finally find it Anubhav Das, check this one:
FV=PMT*(((1+i)**(end_age-start_age)-1)/i)
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Can Eigen value and Eigen vector be explained in terms of its use in Data Science. How it can be described in layman's terms to normal amateur in this field?
Any help in terms of applications, use, concepts, real world examples in the field of Data Science and Machine Learning would be appreciated.
Please share your experience of real world research in this area, explain and discuss over here instead providing links to papers and articles. Really appreciate it.
Thanks in advance!
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Eigenvalues describe the proportion of variance contributed by each of the eigenvectors derived from transformations (rotations) of the original set of variables to orthogonal variables (uncorrelated). This generally results in a reduction of the number of variables (eigenvectors) needed to explain the majority of the total variance among the origanal variables. The contribution of each original variable to the direction of the eigenvalues means that the most important of all the variables can be summarized in just a few vectors.
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For the sake of interest I was out looking for a discussion of functions in computer science as generalized functions. I started my search by something such as "computer functions as mathematical functions". NO paper discusses functions in computer science in terms of set theory, and they compare (not equate) mathematical functions and functions in programming. Where did I miss the buss? Mathematics need not be done with numbers, although the largest application of mathematics is to numbers.
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Short answer. The use of the term "function" as a designator in commonly-used programming languages is actually a mistaken use of the mathematical notion having the same name. It seems that, in the early days of computer software and programming language development, the choice of nomenclature was in some sense a corruption of the mathematical usage. It wasn't malicious, but an over-reaching that was perhaps not well-understood at the time.
In programming languages, "function" is used to designate a specific computational procedure. For appropriately-written procedures, there is establishment of a specific algorithm for some similarly-named mathematical function. It is not the function, it is an algorithmic procedure. When accurate, the correspondence between represented operands and the represented result satisfies the relationship established for the mathematical functions domain and range members.
There are many procedures for the same function, in this sense (and there can be many mathematical characterizations of the same function).
The clouding of nomenclature becomes an issue when one needs to deal with the fact that mathematical use of functions need not have any direct connection with computation.
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Dear Scholar
Yes
This method does NOT follow any known principles of Mathematics including , Euclid's ELEMENTS. Hence the method adopted here is ORIGINAL and the result is EXTRAORDINARY. The world of Mathematics now see the REAL / TRUE/ EXACT / Algebraic Pi Value
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Dear Sarva Jagannadha Reddy,
in writing "Latest Finding is pi lies between 3.13.........to 3.147....." you referred to the book "Calculus and Analytic Geometry" (Edwards and Penney, 1985) of which you have presented here a single column (img027-1.jpg). Yes, these numbers are there (big arrow), but they are NOT the full truth! To understand this, just read again carefully what is written at the beginning of this book page (#295):
"... the value of the integral can---in principle---be approximated with any desired degree of accuracy be choosing n sufficiently large."
This means that the result marked by the big arrow is meaningless: It is not the final result because it was obtained using a value for n that was NOT sufficiently large to get the required accuracy.
So, what do you get when you do the calculation again, not using n = 10 as in the book but n = 25 or n = 100? Remember: The larger n, the higher the accuracy!
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I have some difficulties in finding the correlation between some variables at TIMSS result, for instance correlation between mathematics achievement and bulyying at school. I hope someone there can show me in doing that.
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For more information, please refer to:
. Landau, S. and Everitt, B. S.(2004). A Handbook of Statistical analyses using SPSS.
.Howitt, D. and Cramer, D.(2008). Introduction to SPSS.
A simple guide on SPSS is attached.
Regards,
Zuhair
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I'm measuring fluorescence intensity in 24-well plates using a plate reader.
example.
Configuration 1: Excitation 396nm, Emission 509nm, Gain 100
Sample 1 value: 100
Configuration 2: Excitation 488nm, Emission 510nm, Gain 50
Sample 1 value: 5000
This 50-fold difference in fluorescence intensity values happens for almost all samples (including blanks). What is due to?
What is the mathematical formula that explains this relationship between Excitation-, emission wavelengths and "gain"?
Thanks!
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There is no mathematical formula. What you are observing is the result of the fact that each fluorophore has characteristic excitation and emission spectra (which can depend on the solvent). For organic fluorophores, these spectra have a sort of bell-shaped curve appearance, with fluorescence intensity increasing as the optimal wavelength is approached from either direction. If you are using excitation and emission wavelengths that are near the optimal excitation and emission wavelengths of the fluorophore, you will see higher fluorescence intensity than if you use wavelengths that are farther from the optima. If you are using fluorescein, for example, you would use the 488 and 510 nm settings, which are close to the optima for fluorescein. If you use different wavelengths, you will get a lower fluorescence intensity (at the same gain). The proportionality will be the same for every sample containing the same fluorophore.
Here is an example of excitation and emission spectra:
The gain setting allows you to change the sensitivity of detecting the fluorophore by changing the voltage on the detector. The higher the gain, the higher the signal, but also the higher the background signal. Sometimes, the instrument is set up to choose the gain setting automatically based on the intensity detected in a sample. If the sample is very fluorescent, it will choose a lower gain than if the sample is less fluorescent, in order to avoid saturating the detector with too much light.
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I am trying to make mulitple choice mathematics [fourier series, PDE and etc] questions and upload questions in blackboard.
I dont have a format of this process. can any one give the format and tell the procedure for it.
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what about the use of latex?
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I want to know the mathematical relation in calculating the % of an isolated compound from plant material of a know mass. eg. I started with 250 g of plant material and isolated a flavanoid of mass 0.5 mg.
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Dear Alhassan Mahama,
Apply the formula % of yield of an isolated compound from plat material
= {(amount of the isolated compound extracted from the material plant) /
(amount of the compound contained in the plant material)} x 100
Note that the unit of the numerator and of the denominator must be same.
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What is the meaning of noise in conventional optical fiber and photonic crystal fiber? What should be its mathematical expression?
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Thanks sir,
I am deriving a new formula pertaining to PCF. I SHALL INFORM ABOUT THE SANE
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how to solve delay parabolic pde using MATLAB?
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I'm very glad that Vitalii Pertservil could you help.
Good luck and
All the best
Mirjana
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I want to know how the trace of matrix A(given A is positive semi definite) and polynomial function associated with A i.e. x^T*A*x are related ? (here x is any vector except x=0)
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@Wulf Rehder and @D. Barrios Rolania thanks for your answers
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I'm looking for a free fea software,but my background is in industrial chemistry, so I 'don't have the mathematical basis.
Is possible to make some calculations with an user friendly interface?
Thank you for your help
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Thank you for your reply,
I would like to study the stresses in the ceramic refractory material field, honestly I'm a chemist and my background is not so important in terms of math.
That's why I was asking for a simple platform, obviously if it exists....
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What are surface wave modes? How can we calculate them for a particular substrate to design the microstrip antennas? Kindly provide the mathematical expressions.
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following
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Is anyone working on Polynomial Splines for modelling noisy time series? I need the related research works with mathematical construct. I'll requiring help to model a highly noisy time series with a clear mathematical construct.
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If your data is highly volatile and contains some underlying frequency assumptions, I'll advice you try to identify and separate the high and low frequency component using e.g., wavelet decomposition of the time series. Then you can model the low frequency component using splines, and identify a statistical distribution of the high component, which you may add on as noise. Alternatively, if you have a priori information about the nature of the data (e.g., monotonicity), then you may solve the problem using splines, where the coefficients are determined by constrained optimization. You may want to read my paper
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Good morning,
I'm currently trying to compute laplacians on a deformed lattice and i'm trying to use the equation 2.3 of this paper in my work: https://arxiv.org/pdf/hep-lat/9810051.pdf
The thing is, i'm working with a U(1) gauge field that makes avoid me to simply use this formula.
In fact, is there something like the mean value theorem for gauged derivatives? My function would not be harmonic but something like "gauged harmonic":
"D^2 f = 0" where $D = \partial + i A$
Let me just add that i'm more into physics than mathematics, and thus i don't understand fully mathematical publications. In fact, i'm working in 2d and cartesian space. Hoping i was clear enough.
Thank you in advance for you help.
Best
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It is an interesting subject
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From the physical significance point of view it can be described that that (tao)q/(tao)T>0, then hyperbolic behaviour will be observed; if that ratio = 0 then parabolic behaviour will be observed and if that ratio<0 then diffusive thermal behaviour will be observed.
But from the point of classification of partial differential equation, how this can be analyzed?
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I never worked on such PDE, try to reduce to a system of first order PDE and then work using the eigenvalue problem. You should get a 3x3 matrix and express the conditions for which the eigenvalues are real or not.
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For some time now, we have been listening to the changes implied by the advent of the Technological Singularity, as a point of no return.
The discussions are as versatile as they are disturbing.
In that moment of increasing autonomy and perhaps independence from Artificial Intelligence, it seems to be evident that technological changes will exceed the human capacity to assimilate them.
Authors such as: (Theys, 2012), (Kurzweil, 2012); (Ruiz, 2013) (Cordeiro, 2016), among others
They have offered a very abundant discussion to the rspect
How do you imagine philosophy in that new horizon?
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I think that philosophy is always at the level of the respective state of science and technology, especially since a whole series of philosophers have also embarked on a full study of physics, biology or chemistry, also in the context of mathematics and technology, just as scientists and engineers have embarked on philosophy.
The more the possibility of human self-destruction begins to become reality and how today the quality of life of later generations is in danger of being diminished by the exploitation of limited resources, by war or by omission of measures, the more the question of the limits of technology, growth and political oppression becomes an issue in philosophy. Man is not only a learning being, he is also a being that produces conflicts and dilemmas. It is precisely where progress seems to be at its greatest that we become aware of this.
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Our civilization continue to evolve at an amazing pace. Methematics plays a crucial role in this evolution. What are the some of the most important mathematical discoveries made during the modern era?
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the greatest mathematical discovery of the modern era is asymptoric methods of nonlinear mechanics ( N. M. Krylov, N. N. Bogoliubov and Yu. A. Mitropolsky).
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Euler and Newton are considered as the best mathematicians. Gauss, Weierstrass and Riemann are considered as the best theorist. Archimedes is often considered as the greatest mathematical genius who ever lived. I am not interested in google searches and links. What do you think?
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Hi,
The best 10 mathematicians are:
1-Leonhard Euler
Leonhard Euler was a Swissmathematician, physicist, astronomer, logician and engineer who made important and influential discoveries in many branches of mathematics like infinitesimal calculus and graph theory while also making pioneering contributions to several branches such as topology and analytic ...
He is not only a prolific writer in Mathematics but also there is a beauty in the theorems, concepts made by him. Very interesting mathematician.
2-Srinivasa Ramanujan
Srinivasa Ramanujan
He is the greatest self educated mathematician ever. He gave more than 3000 theorems.
He made substantial discoveries without any formal training in mathematics and he made around 3900 theorems compiling them in two books without having anyone to teach him. He mastered trigonometry at age 12.ne
3-Carl Friedrich Gauss
Carl Friedrich Gauss
Johann Carl Friedrich Gauss was a German mathematician who contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, mechanics, electrostatics, astronomy, matrix theory, and optics.
Even though I like Leonard Euler very much, due to the beautiful theorems invented by him, I feel Gauss would stand as greatest mathematician of all times, if we consider the rigour of his mathematical analysis and his ability.+7
4-Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist and mathematician who is widely recognised as one of the most influential scientists of all time and a key figure in the scientific revolution.
He should be on the top of the list. He is just the greatest mathematician who ever lived! Afterall he's the founder of the most important branch of mathematics-"calculus". So please! Vote for him.+21
He is the only human being to be argued as the greatest mathematician ever and the greatest physicist ever at the same time.
Gauss is cool be only a mathematician, Einstein is fine and dandy but only a physicist. Newton is in a league of his own.
The greatest scientist ever has invented calculus, the most important branch of mathematics.
5-Euclid
Man euclid is best he must be in top.
6-Archimedes
Archimedes of Syracuse was an Ancient Greek mathematician, physicist, engineer, inventor, and astronomer.
I believe Archimedes should go to the top 3 he invented buoyancy and the principle of the lever. the principle of the lever is the first principle ever to be introduced. He also made the spiral pump, which is still used today. Archimedes tried in finding the value of pie which helped in the building of the great pyramid of Giza in Egypt
Without him and the ancient Greek mathematicians and physicists we will still live in caves and eat bananas like monkeys.
In rating these geniuses one needs to take account of what they had to build on. Gauss and Euler we were original but had 1500 years of other brilliant minds as a starting block- what Newton called “ the shoulders of giants “. Archimedes got there out of almost nothing. I would put him top.
7-Aryabhatta
He is the best mathematician ever... His works were not converted into books that was the reason why he was not famous as Euler. He invented trigonometry which is most essential field in geometry.. He proved theorem of Pythagoras much before but they were not converted into books therefore we say it Pythagoras theorem.
The first inventor of Zero and pi.. And the first astronomer who said that the earth is round not Copernicus... Europeans stole many concepts of Indians and certain other Eastern countries.. He said that there are 7 satellites of Saturn before 8000 years and now NASA scientists does not had find the 8th one..+41
His works suggest that he was a man who possessed superhuman brains. He was more than a millennium ahead of the west. He knew about gravity, different properties of the solar system, size of the earth, trigonometry, value of pi, length of an year accurate to four places after decimal, eclipses, properties and nature of the mystic no zero, etc. He also used another different approach to integral calculus in order to calculate different areas.+2
Aryabhatta first invetor zero and find decimal system he is great.
8-Gottfried W. Leibniz
9-Bernhard Riemann
Paved the way for general relativity+6
His Hypothesis is still motivating research today!+3
Certainly one of the best there has been.. an outstanding student of Gauss giving us spectacular theorems with a lot to think about like the Riemann Zeta Function+2
I think he's the second to greatest(with Pythagoras being #1) - Squidward48new
10-René Decartes
This guy is huge in Physics Mechanics Engineering with Statics and Dynamics. Either at rest calculations to encase with tons of examples or just constantly in motion yet again confines the action beautifully struggling to understand what is going on. Future is these might be done in real time however some background might be needed. With Rene Descartes all this became possible which is good Christianity Christmas. Awesome contributions and dared to where naught been having without and again might have been delays. Those just get the job done and the name attribution to...well it is Rene Descartes. - iliescu.
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Hi I need help for my thesis.
My thesis is about teaching fraction concepts for primary pupils and I struggling to identify the appropriate constructivism learning approach.
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Hi Nanteni,
There may be many different approaches to bring-out with the students' existing concepts on fractions. For example, the teacher may ask about students' experience of having pizza at home. It is usually delivered into pieces. Teachers may ask the students about how many pieces were there when they ate some. Other relevant questions may be about how many pieces one student had, how many other persons were there and so on. The teacher then may summarize with the concept of fraction and, finally, introduce the fraction characteristics and operational laws to the students and something new to learn.
All the best to your thesis.
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Dear Researchers,
I am wondering if there is any other mathematical writing of the factorial. If it is, i need some papers.
Thank you and best wishes.
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Dear Nassim,
One defines x! := Gamma(x+1) for any x > 0, etc (see any book on mathematical analysis). Recall that the Euler Gamma function can be extended.
Sincerely,
Octav
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Intuitively, staleness of information or data is directly proportional to elapsed time. Is there any mathematical function to model staleness w.r.t time, in communication domain ?
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I would be very grateful if I could be assisted with a copy of the above article. I am developing a paper of which the Fennema-Sherman Mathematics Attitude Scales will be of help.
Thanks
Best regards
Osman
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Dear Kasimu,
Please see the attached document. Thanks.
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When we proforming a CV in acid aqueous solution from 0 to -1.5 V, the polarization curve can be observed for hydrogen evolution. The Faradaic current continueously to decrease and show no peaks. I understand that people say large infinitely sufficient amount of H+ in 0.5 M H2SO4 is the reason, but can some one explain to me mathematically why the current is infinitely large, since the concentration of H+ in 0.5 M H2SO4 is only 1M after all.
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A eminently efficient removal of gas bubbles during water electrolysis is, still, a challenge[1]. The bubbles, during electrolysis, "crop" the chaotic current oscillatory[2] AC-peaks, due to the (3D, apparently 2D) poison resistance[2] of the WE, "enclosed" by bubbles. So, it is not[1] easy to recognize an integral current peak, as a common, credible, (quasi-)DC current peak.
1. Increasing Gas Bubble Escape Rate for Water Splitting with Nonwoven Stainless Steel Fabrics https://www.ncbi.nlm.nih.gov/pubmed/29098849
2. An oscilloscope[3] will help to watch these chaotic (AC) current oscillatory. Adjust the Time per Division setting to (about) 1ms (mSec).
3. Use an "i to V" (i of cell) converter, and a differential V-probe.
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I want to include a condition for the transfer function G(s) which is equivalent to the statement mentioned above inside inverted commas but I am not able to describe it mathematically. I was wondering if I could use the L2 norm in this case .
Please advise.
Thanks
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1. If one wants to write in symbols the fact that "|f(x)|<1", then there is no possibility to use just a norm.
2. If one wants to write in symbols the fact that "|f(x)| \le 1", then it is possible to write this equivalently with the use of the sup-norm:
" || f ||\infty \le 1"
3. (if needed) Consult, please the TeX convention:
"\le = less then or equal to"
"\infty = the symbol of infinity (the rotated the eight 8 by 90o ) ".
4. Explanation. Writing "|| f ||\infty < 1" means a stronger condition, that there exist a number 0 \le q <1, that all values |f(x)| are less than q. In order to see the difference more precisely, consider |tanh(x)|<1, for all x. Despite this, we have || tanh ||\infty = 1.
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I am trying to come up for an analytical solution for resistance and current flow in an electrochemical half cell. (see attatched cell diagram). I can probably do it by expanding the matrix to a high order but would like if some maths whizz could show me and analytical solution to it.
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Peter, a pdf file please?
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I need to make a relatively quick calculation of confluent Heun function (It is HeunC in Maplesoft Maple notation) values with different parameters in different points. I understand that it is possible to solve a Heun equation numerically, but that way seems not to be effective.
Of course, it is possible to use, e.g. Maple, for numerical procedure realization I need this in my study, but applying some series expansion or hypergeometric functions is more preferable.
So, I would appreciate simple (because I'm not a pure mathematician) information about series expansions of the Heun confluent function, its expression by hypergeometrics or any other known functions which are available to realize the numerical calculation.
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If you have a series expansion valid for |z| <1, you can try to sum it via extrapolation methods for |z| >1, e.g. Levin-type algorithms, Borel, ...
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I'm trying to get a distance matrix between my different datapoints in a bidimensional space (one variable in X axis, another in Y, simple). To get the distance forming the matrix, i will use euclidean distances, and, due to X and Y variable being in different scale/units, I want to standardize them (for example, using a rank between 0 and 1, or using the mean as 1, doesn't matter).
Until here, everything is okey. But when I'm about to request this normalization in SPSS, the programme asks me if I want to perform this standardization "by variable" or "by case". I don't understand the difference between this two procedures and the help in the programme doesn't look very helpful.
Kindest regards,
Quique
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I do agree what Prof Roy and Morse have answered. You have to go for standardization by variable. The only intention is to compare the different variables contribution on a single scale. No matter in which units the different variables are taken; standardized value is for comparison between them. So that like can be compared with like.
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If we have the Mean and Median of a data set is there a mathematical formula to find the Mode using this two factors (Mean, Median)?
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No. Think of these two situations:
a) we have the numbers 0, 2, 3, 5, 5. The mean and the median are both 3
b) we have the numbers 0, 0, 3, 5, 7. The mean and the median are both 3
In both cases the mean and the median are 3, but the mode differs. The mean and the median do not uniquely determine the mode.
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I am writing code for multi-carrier data transmission over time varying multi-path channel in MATLAB. Mathematically , received signal can be represented as,
y=x(t)*h(t,delay)+n(t)
Impulse response of channel with 5 multiple paths has been designed in this work. complex gain and delay of multiple paths have also been calculated. Since channel is time varying the size of transmitted signal and impulse response of time varying channel are different. Please anybody tell me how to transmit the signal through time varying channel having multi-paths in MATLAB
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Hello,
Maybe you can look for Rappaport wireless communications book, he show how it works, and the code is esay when you understand it!
look for this book chapter
Regards
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I am studying integral transforms (Fourier, Laplace, etc), to apply them in physics problems. However, it is difficult to get books that have enough exercises and their answers. I have found that in particular the Russian authors have excellent books where there are a lot of exercises and their solutions.
Greetings,
Ender
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I liked "Transforms in Signals and Systems" by Peter Kraniauskas a lot. A few years back I went through a lot of these books, but this is the one that helped me the most.
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The closed mathematical form of bivariate g-h distribution is not available in the literature so please help me any approach is available. Also, suggest me how to generate data from bivariate g-h distribution in R.
Thank you.
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Thank you Sir
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I have written all mathematical questions that I need in Matlab, but the figures are not come out because some of the results is 0 and NaN. I have tried many times to check and change the codes but it still does not work. Here, I upload my Matlab code, maybe you can help me to check where my mistakes are. Thank you in advance.
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Thank you very much for your answer Mr. Morton O'Kelly,
That's true, I think I should minimize the number of time steps.
I still could not fine where exactly the error is. But after I analyzed one by one, the errors are in the loop and plot. The dx and dt there, is not the derivative.
Actually in this task I should calculate the temporal variation of elevation and flow rate at the locations i=2, 10, 15 and 20, inside the lagoon for t=43200-57600 s and the spatial distribution of maximum elevations and flow rates in the lagoon with 20 cells discretization. The boundary condition at the left open sea boundary is tidal with T=14400 s and amplitude equal to ζο=1.00 m, while at the right open boundary I should apply several equations.
Once again thank you.
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As we know that the Curl of linear velocity is equal to twice the rotational velocity (Mathematically). In practical life if it is possible to construct a Curl operator which transform the linear velocity into rotational velocity, then it will be very helpful for our society. Please share your opinion/s....
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It is quite simple to construct a 3x3 matrix for the curl operator, for example in the Cartesian system as
i j k
d/dx d/dy d/dz
u(x) v(x) w(x)
You can also use the Maple software for symbolic calculus
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I am looking for references to work similar to that of Takeshi Miyakawa (2016) comparing the case of proof in the Japanese and the French curricula, or Christine Knipping (2002) comparing proof teaching in German and French classes. These studies are illuminating about the impact of language, communication and culture on the actual meaning of "proof" in the school context. They also open questions -- and address them -- about the interaction between proof and the mathematical content at stake. I would like to make a survey on this issue. For that I need more references to bilateral or multilateral comparative studies.
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Thanks for the links.
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I need to find a equation which can be used to describe a graph. I have attached file which contains more details. Is there any curve fitting software that I can use.
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Dear PushKar
I completely agree with Marek Gutowsky about the two meanings that the operation of fit of a series of data can take. Just to complete Marek's answer:
If we have a theory (the model, a known functional relationship) that connects the observable data space to the model parameter space we we are solving an inverse problem. In this first case the objective is to obtain the unknown parameters in our theory (ie the unknown coefficients of a known functional relationship).
In the case in which there is not a theory that connects the data space to the model space we will talk about the simple regression operation whose objective is to carry out an interpolation and / or extrapolation of the same data consistent with the trend of available data and not of a theory.
However, in both cases it should be advisable to have the error on data. The fit will depend on a misfit function (depending on the differences between observed and predicted/regressed data). The availability of the data errors, in fact, allows, on the one hand, to identify which are the data that can be considered outliers, and on the other, to fix a fit threshold: that is the "precision threshold" of our fit.
The "model precision" (functional with minimum mistfit), conceptually, not is the same of "model exactness" (truthfulness of your functional choice)
In the second case (regression of a curve), in the absence of a priori information, or hypotheses, and when we want to regress an experimental data set with a polynomial curve (your first data set), a good practice would be to choose the polynomial curve with the lowest degree within the limits of the error band.
The same principle in my opinion should also be applied in the case of the use of non-polynomial functions (eg power law or logarithm or other functional forms), as in your second second data set; considering the function (predicting your data in the error band) characterized by the lowest number of parameters (for example, as indicated by Marek, a decreasing exponential function characterized by a background parameter and an exponent parameter).
These good practices are in accordance with a general approach that is established by the Occam's principle (pluralitas non est ponenda sine necessitate: it is useless to complicate the model if there is no need).
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I need some literature anout pronkens encountered in teaching mathematics. It might be in elementary, secondary or college level. Thanks.
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Cockburn & Littler (2008) mathematical misconceptions
China (2004) the trouble with maths
Dehaene (1997) the number sense
Mason & Johnston-Wilder (2004) Fundamental Constructs in mathematics education
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If we have two-nodes and one relay, where two-nodes can communicate with each other using the help of Decode-and-Forward relay node. How to implement it in two-phase transmission instead of three-phase??
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There are two methods. One is using two-way relay. In the first phase, Source and destination transmit to the relay. In the second phase, relay transmits in the either direction after decode and re-encoding.
Decoding and re-encoding is generally not considered as a phase
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I have complete numerical data and would like to take derivative of the response. Also, the x variable is constant numerical value while y variable is changing. So which formulae to use for calculating 1st derivative.
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Thanks!
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Are the Euler–Mascheroni constant, π + e, π − e, πe, π/e, πe, π√2, ππ, eπ2, ln π, 2e, ee, Catalan's constant, or Khinchin's constant rational, algebraic irrational, or transcendental?
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The irrationality measure (or irrationality exponent or approximation exponent or Liouville–Roth constant) of a real number x is a measure of how "closely" it can be approximated by rationals. Generalizing the definition of Liouville numbers, instead of allowing any n in the power of q, we find the least upper bound of the set of real numbers μ such that
{\displaystyle 0<\left|x-{\frac {p}{q}}\right|<{\frac {1}{q^{\mu }}}}📷
is satisfied by an infinite number of integer pairs (p, q) with q > 0. This least upper bound is defined to be the irrationality measure of x.[3]:246 For any value μ less than this upper bound, the infinite set of all rationals p/q satisfying the above inequality yield an approximation of x. Conversely, if μ is greater than the upper bound, then there are at most finitely many (p, q) with q > 0 that satisfy the inequality; thus, the opposite inequality holds for all larger values of q. In other words, given the irrationality measure μ of a real number x, whenever a rational approximation x ≅ p/q, p,q ∈ N yields n + 1 exact decimal digits, we have
{\displaystyle {\frac {1}{10^{n}}}\geq \left|x-{\frac {p}{q}}\right|\geq {\frac {1}{q^{\mu +\epsilon }}}}📷
for any ε>0, except for at most a finite number of "lucky" pairs (p, q).
For a rational number α the irrationality measure is μ(α) = 1.[3]:246 The Thue–Siegel–Roth theorem states that if α is an algebraic number, real but not rational, then μ(α) = 2.[3]:248
Almost all numbers have an irrationality measure equal to 2.[3]:246
Transcendental numbers have irrationality measure 2 or greater. For example, the transcendental number e has μ(e) = 2.[3]:185 The irrationality measure of π is at most 7.60630853: μ(log 2)<3.57455391 and μ(log 3)<5.125.
The Liouville numbers are precisely those numbers having infinite irrationality measure.
  1. Zudilin, Wadim (2004). "An essay on the irrationality measure of π and other logarithms". Chebyshevskii Sbornik (in Russian). 5 (2(10)): 49–65. arXiv:math/0404523 📷. MR 2140069. Zbl 1140.11036.
  2. Jump up^ Sondow, Jonathan. (2004). Irrationality Measures, Irrationality Bases, and a Theorem of Jarnik.
  3. Jump up^ The irrationality measure of π does not exceed 7.6304, according to Weisstein, Eric W. "Irrationality Measure". MathWorld.
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I'm looking for some working definitions and operationalisation of mathematical problem solving and mathematical word problems to support this section of my literature review. Do word problems sit within problem solving or are they interrelated?
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My book, "The Language of Mathematics: Utilizing Math in Practice", deals with this subject, in particular, "translating" a natural language description into a mathematical model. See http://www.language-of-mathematics.eu and the link there to the publisher's (Wiley's) web page for the book.
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We are searching for a mathematical correlation for the droplets size distribution of liquid when atomized by air blast.
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There are a bunch of models that are used. For example: normal, log-normal, Rosin-Rammler-Sperling-Bennett (RRSB), Nukiyama-Tanasawa distributions. The last 2 are often quoted and you'll see them in the literature from the 1930's to 1950's or 60's. In particular, I am personally skeptical of using RRSB as this involves a log-log approach which constricts the middle part of the distribution. Taking logarithms 5 times (the RRRSB approach where the first R is 'Rawle') will compress the data even further and almost anything can be fitted to such a model. All the above are empirical models, the emphasis being on the word 'model'. However, the data are the data and may not be constrained by a theoretical model.
However, nothing is better than actually measuring the droplet size distribution and using a model-independent approach. This is the modern route and most light scattering measurements are processed in this manner.
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Why or why not?
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I think that rational thoughts are independent from language. Sometimes I have new ideas while sleeping and then have a problem to translate them into normal language and writing down after waking up.
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With known mass and area i.e. width and length values of a known geometry.
How to calculate mathematically film thickness of water film/layer which will be developed from that specific mass of liquid ??
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It is possible to measure thickness t by the so-called weight difference method via the following formula
t = m/Ad,
where m is the mass, A the area and d the density of the film material as Dmitry Zaitsev suggests. Be careful, this formula is not accurate as d changes.
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Hi ,
I have the question regarding difference between scattering parameters of an active RF component and a passive Rf component. Do we need to follow same mathematical relation to calculate S-parameters and reflection coefficient, which is used for passive component or there is different mathematical relation.
Regards
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Very informative inputs have been made by all the contributors regarding the intrinsic nature of [S]. I will just make a small addition regarding measurement. [S] of active devices especially transistors are tabulated for specific set of bias conditions and will change if bias conditions are changed. I found this to be a common oversight by students when I teach courses related to microwave engineering.
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I want to solve a mathematical algebraic equation.
For example, T^2+exp(-T)+T^3+...=0. where T is a variable to be found. Moreover, I know T through another approach is near 5, T ≈ 5 (from engineering art and intuition). Meanwhile, I want to know, whether I am authorized to use an approximation (expansion) for exp(-T), which is valid for T roundabout 5, and then place the approximation (expanded expression) into the preceding equation; T^2+exp(-T)+T^3+...=0, and solve the simplified equation to get the exact T. This is like a math trick or cheating. So I am clearly looking, if I am authorized and allowed to use an approximation for exp(-T) for T near 5 and plug it into the investigated equation to get T, or I should find a thoroughly other valid approximation through a wide range, for example valid for -inf<T<inf, and then replace it into the equation and find T.
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The 'menu' in the Answer states (quote): Identify yourself as an expert by providing high-quality answers. My (this) answer to 'A philosophy to validate analytical approximation to solve a mathematical algebraic equation?' is certainly not Mathematical. However, I would like to point out that all the 'posts'/answers to the question are very informative, instructive and well thought out (even the single line/sentence answers and/or responses). This is one of the best discussion topics that I have seen for a long time and MOST CERTAINLY keeps the (or a) mathematical mind interested. Even those who enjoy so called 'recreational mathematics'.  
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Kinematic viscosity and thermal conductivity relation using mathematical equation
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Hi,
There is no relationsship between these two thermodynamic properties. High viscosity oils can have the same thermal conductivity as low viscosity oils if the substance class is the same or nearly the same. The same is true for oils with "high" thermal conductivity (polar ones) and oils with low thermal conductivity for viscosities. The can have the same viscosities from 0.x to xx.xxx at room temperature but other thermal conductivity. This depends only on the substances.
Some dimensionless numbers like Prandtl number combine some thermodynamic properties to forecast or compare observations in real circumstances. The properties in such numbers are mostly not connected by physical meaning like temperature dependence of thermophysical properties.
This comment is only to keep things in mind and driving the discussion in the right direction.
Best Regards
Steffen.
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I am currently working on a study to determine how learners can understand geometrical theorems better using invariant examples. Specifically the cyclic quadrilaterals.
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Dear Melissa, this is a beautiful idea!
An invariant characterizing cyclic quadrilaterals is "the sum of opposite angles is 180°".
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I'm a PhD student in Applied Mathematics seeking for an answer to the above question. I know of Evolutionary branching in Ecology and Evolution. What other fields of Sciences and Engineering are there cases where branching occurs naturally?
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I've been working over a paper that I've found to be very interesting. It . is concerned with Scale Free Random Networks. It develops networks from a geometrical basis of vertices, edges and kth order trees. They use percolation as a mechanism to propagate the network. The authors have used excellent reference materials esp Eros and Reyni . The most helpful part of this work comes a desire to develop overall understanding. They create a perspective for understanding the genesis of trees, and some of their structural evolution, rather than present an encyclopedic presentation that gives the end result
Mean Field Scale free Networks Barabasi,A,L, Albert, A, Heong, J
arXiv-mat/9907068vl
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Hi,
I was trying to assign the pressure and the mass flow rate at inlet for my case in Fluent, but after some research, I've found that u can't do that because it's mathematically over specifying.
but someone suggest that i can use UDF to override this part, can this method work? and where exactly i just use it, in mass flow rate condition or in pressure-inlet condition?
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The AMG solver of ANSYS fluent works better (say does not come to divergence) if you apply the mass flow inlet option rather than pressure.
The creation of UDF code for mass flow rate is a bit hard but it is worth it.
If you should have asked more questions, contact me:
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-Up to now we usually use the classical mathematics the origin of which is at the end of the 19th century and/or at the beginning of the 20th century. Even the contemporary quantum physics, astrophysics, and AI of the 21st century are still using that classical mathematics! In von Neumann's quantum mathematics there is no any anomaly whatsoever in Thomas Kuhn's 'The Structure of Scientific Revolutions': why?
-Thanks for your answers! Marc
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Dear Marc ~
When I think of the mathematics of “classical” physics (hydrodynamics, properties of materials, Maxwell’s electromagnetism, Einstein’s gravitational theory, etc) I see that it is predominantly based on the concept of continuity. Space and time are thought of as continuous variables and physical phenomena are desribed by continuous “fields”. The appropriate mathematical tools are differential equations. “Discreteness” rather than continuity entered physics with Planck’s “quantum” concept, which led to the “non-classical” physics of quantum theory. By analogy, I would identify “classical” mathematics as the mathematics of continuity; "non-classical" mathematics would then be the mathematical study of discrete structures. But those branches of mathematics already exist, so I admit to being rather puzzled by the question "Where is the 'non-classical mathematics'?"
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Does it produce a same physical realization ( apart from mathematical similarity) by applying only Fourier Transform or Hilbert Transform followed by Fourier Transform.
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When you take the spectrum of an analytical signal, its the spectrum of a complex signal and is hence not symmetric. Hilbert transform is effectively convolution with the hilbert kernel 1/(pi*t) in time domain, in frequency domain, this transforms to the signum function which selects one side of the spectrum. Thus the fourier spectrum of the analytical signal of a real valued single channel signal is one sided and hence asymmetric.
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Mathematics has its own beauty and importance. It has different applications in various fields and is used to solve many real world problems in society and industry. How does it correlated with art, poetry, literature, culture, music and so on ?
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As every other discipline, mathematics is also beautiful; let's say, more beautiful than others. Other disciplines create problems; mathematics not only create but also solve problems. Painting and sculptures incorporates the idea of projective geometry. Meter and rhymes are a form of mathematics in poetry. In music and dance, periodic functions find ample applications. Let's enjoy the beauty of mathematics!
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I've created an eLearning resource. My sample group consists of 22 Biology and 7 Environmental Science students. How do I find out if there is a correlation (or difference?) between 1) the scores achieved in the test and the course taken 2) the scores achieved in the test and the students' year of study (first year, second year, final year)
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Dear Nur,
before you can determine the appropriate test, you have to find out the distribution type. Because you have a small sample size, I suggest the Shapiro-Wilk test. After performing the test, we can choose the right test. In this calculation, there are no correlations, but comparisons between 1) two or 2) more than 2 groups. Thus, you have to chosse following test:
For normally distribution:
1) t-test
2) ANOVA
For non-normally distribution:
1) Mann-Whitney-U-Test
2) Kruskal-Wallis-test
Best regards
Tanja
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-The general definition by Bertalanffy (himself): "Ein System ist eine Menge (im mathematischen Sinn) von Elementen, zwischen denen Wechselbeziehungen bestehen". (This is what I heared more times during scientific congresses): ergo: it is (more or less) identical to a set.
-However, Bertalanffy's definition regards only the inner environment: there is (according to him): (a) no question about an empty set (which is a big problem in mathematics, as far as I know); (b) he (Bertalanffy) does not speak of the outer environment (Popper's world 1 and Herbert Simon's inner and outer environment).
-What could be your answer? Thanks, Marc
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In my view, in a set, the elements can have separate existence whereas in a system all the members have simultaneous existence.
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I used different methods for generating the criteria’s weight in MCDM methods. Results demonstrate that the rate of changing in the weight of the criteria in the Shannon entropy method is negligible (changing the weight of the results are very low). does anyone know about the reason for the results?
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Dear Farzin
Interesting question. I have been thinking about it and the answer that comes to me is:
Weights from eigenvalues or by geometric mean belong to the domain if linear algebra.
Weights from Shannon entropy come from using logarithms