Science topics: Mathematics
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Mathematics - Science topic

Mathematics, Pure and Applied Math
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The emergence of new infinite system (new 'infinite' idea, new number system and new limit theory) determines the production of "new mathematical analysis". The mathematical analysis based on the classical infinite system is called "classical mathematical analysis", and the mathematical analysis based on the new infinite system is called "new mathematical analysis (the fourth generation of mathematical analysis)".
There is no infinite related mathematical analysis without the “infinite related number forms”. So, the “quantitative cognizing work on infinite related number forms” is an important and unavoidable task for mathematical analysis. But our studies have proved that in present mathematical analysis, people have been admitting the being of “potential infinite, actual infinite” concepts, unable to deny their qualitative differences and the important roles they play in the foundation of present classical infinite theory system and, unable to deny that the present classical mathematical analysis is basing on present classical infinite theory system. The fact is: on the one hand, present classical mathematical analysis can not avoid the constraining of “potential infinite--actual infinite” concepts and their relating “potential infinite number forms--actual infinite number forms”; on the other hand, no clear definitions for these two concepts of “potential infinite--actual infinite” and their relating “potential infinite number forms--actual infinite number forms” have been constructed since antiquity, thus naturally lead to following two unavoidable fatal defects in present classical mathematical analysis:
(1)it is impossible (unable) to understand theoretically what the important basic concepts of “potential infinite, actual infinite” and their relating “potential infinite number forms--actual infinite number forms” are. So, in many “qualitative cognizing activities on infinite relating mathematical things (infinite relating number forms)” in present classical mathematical analysis, many people actually don’t know or even deny the being of “potential infinite, actual infinite” concepts and their relating “potential infinite number forms--actual infinite number forms”--------the “qualitative cognizing defects on infinite relating mathematical things (infinite relating number forms)”.
(2)it is impossible (unable) to understand operationally what kind of relationship among the important basic concepts of “potential infinite, actual infinite”, their relating “potential infinite number forms--actual infinite number forms” and all the“infinite number forms as well as their quantitative cognizing operations” are. So, in many “quantitative cognizing activities on infinite things (infinite number forms)” in present classical mathematical analysis, many people have been unable to know whether the infinite relating number forms being treated are “potential infinite number forms” or “actual infinite number forms”, no one has been able to avoid the confusing of “potential infinite number forms” and “actual infinite number forms”, no one has been able to know whether or not treating “potential infinite number forms” or “actual infinite number forms” with the same way or different ways. What is more, many people actually don’t know or even deny the being of “potential infinite number forms” and “actual infinite number forms”--------the “quantitative cognizing defects on infinite relating mathematical things (infinite relating number forms)”.
The above two fatal defects have decided since antiquity the absence of “infinite carrier theory” and the confusion of “abstract infinite concept and its concrete infinite mathematical carrier” which have been making us impossible to construct the scientific and systematic theory of “infinite related concrete number form (the mathematical carriers of abstract infinite concept)”, impossible to construct the “potential infinite--actual infinite” relating number forms as well as the “potential infinite--actual infinite” relating number system and its relating treating theory, thus unavoidable forming an insurmountable obstacle in the “quantitative cognizing process on infinite things (infinite number forms)” in present classical mathematical analysis. And, it is impossible to know what those “’both potential infinite number forms and actual infinite number forms’, ‘neither potential infinite number forms nor actual infinite number forms’ mathematical things” are, and can only treat all of them with the “flow line (pipelining)” unified approach (such as the three formal languages in three generations of mathematical analysis: before standard analisis, standard analisis, non-standard analisis). So, many members of different infinite related paradox families in present “potential infinite--actual infinite” based classical mathematical analysis have been produced one by one naturally (the newly discovered “strict mathematical proven” Harmonic Series Paradox is a typical example), forming a thousands-year old suspended huge black cloud of paradoxes over present classical infinite related science and mathematical analysis.
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The paper “REAL” ANALYSIS Is A DEGENERATE CASE of DISCRETE ANALYSIS
by Doron ZEILBERGER (for a copy see http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/real.pdf) seems to be relevant to this discussion:
" Continuous analysis and geometry are just degenerate approximations to the discrete world, made necessary by the very limited resources of the human intellect. While discrete analysis is conceptually simpler (and truer) than continuous analysis, technically it is (usually) much more difficult. Granted, real geometry and analysis were necessary simplifications to enable humans to make progress in science and mathematics, but now that the digital Messiah has arrived, we can start to study discrete math in greater depth, and do real, i.e. discrete, analysis."
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Dear Researchers Fellows,
I am seeking a post doctoral position in mathematics education working on integrating technology in teaching and learning mathematics or educational measurement.
Any suggestion is highly appreciated.
Best regards,
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Eric Hsu's website (which was created in cooperation with the SIGMAA on RUME group) lists multiple resources for positions in mathematics education as well as more general resources:
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Considere a completely randomized design, where every unit is randomly assigned to a treatment group. Let's say we have 30 observations and 3 treatment groups. When we choose one observation at random, it has 1/30 of chance of being selected, then the second one has 1/29, and so on. However, I've been told that there is a mathematical proof showing that, in the end, every single observation has the same chance of being selected to be part of a treatment group.
Is this true?
Thanks & Regards.
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If 3 observations are selected from 30 observations for 3 treatments then we will get a sample containing 3 from a population containing 30.
In this case, the probability of each of the 30 observations to be selected in the Ist draw is 1/30.
The probability of each of the remaining 29 observations to be selected in the 3rd draw is 1/28.
Now, an observation will be selected in the sample if it is selected in any of the 3 draws.
The probability that it is selected in the sample is given by
P(it is selected in 1st draw) + P(it is not selected in 1st draw).P(it is selected in 2nd draw) + P(it is not selected in 1st draw & 2nd draw).P(it is selected in 3rd
draw)
which becomes
1/30 + (29/30).(1/29) + (29/30). (28/29). (1/28)
which is equal to 3/30 =1/10
Therefore, the probability that each of the 30 observations is selected in the sample is 3/30 =1/10.
This is the required result.
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Hi,
How many mL of FeCl3.H2O solution is required to just dissolve 1 g of copper in 1 hour? Please provide the chemical and mathematical equations too!
With Regards,
Suhas D.
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Almost impossible to answer, since the time of reaction is strongly depending on the surface of copper and concentration of the FeCl3 solution . A simplified approach would be :
Cu + 2 Fe3+ --> Cu2+ + 2 Fe2+
-> 1eq Cu requires a minimum of 2 eq FeCl3 x H2O
1g Cu = 15,7366 mmol
so you will need about 31,4733 mmol of Fe(III)
in the case of FeCl3 x6 H2O (most common hydrate) [ 270,29] this amounts to:
about 8,507 g dissolved in a appropriate amount of water.
Or 31,47 ml of a 1M solution.
Now the time strongly depends on the Cu surface area and Fe(III) concentration the diffusion -> temp. and so on.
I hope this helps.
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I know how to plot a 2D real vector. Let's say I have a vector 'a' represented in a row matrix, a = [1 1]. I can plot it in xy plane and I will be getting a line having the equation x=y.
Similarly, I know how to plot a complex number. Let's say I have a complex number z=a+ib. I can plot in real-imag plane and I will be getting a similar line having the equation x=y.
But I don't know how to plot a complex vector 'c' represented in a row matrix, c = [1+i 1+i].
Kindly guide in plotting other alternate complex vectors such as [1+i 1-i], [1 i], [i 1]
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Dear Hakeem,
V = ( a+ib, c+id,e+if)= (a,c,e)+i(b,d,f):
Any complex component corresponds to a point in R^2
A vector of 2 complex components requires a representation
in R^2 X R^2 which is homeomorphic to R^4.
A vector of 3 complex components requires a representation
in R^2 X R^2 XR^2 which is homeomorphic to R^6.
The geometry of R^4 or R^6 is not attainable in general as simple as R^3 ,
but we can imagine their projections.
For physics and to tackle some problems in physics as electromagnetics
when dealing with ( sinusoidal field), the American physicists J.Willard Gibss, (1880), invented the idea of bi-vector, where the complex vector splits into two real vectors as the following: the complex vector
V = ( a+ib, c+id,e+if)= (a,c,e)+i(b,d,f)
where the real part of V=Re(V)=(a,c,e)
and the imaginary part of V = Im(V) = (b,d,f)
( following your question V = ( a+ib, c+id) (a,c)+i(b,d) )
and applying this definition, it is easily proved that :
"all multilinear identities valid for real vectors are also valid for
complex vectors"
The geometry and algebra of such representation are available in the attached paper, hope you find it useful in your research.
Best regards
PS.
The suggested presentation is not unique, we can use the tools of differential geometry to tackle such complex vectors based on the mathematical model under consideration.
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Hi everyone,
Is there some suitable mathematical or empirical law that allow us to get the stress drop of an earthquake and the corner frequency; using the seismic moment?
thank you all
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Thank you very much, it's very helpful,
thank you.
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Mathematics has been always one of the most active field for researchers but the most attentions has gone to one or few subjects in one time for several years or decades. I'd like to know what are the most active research areas in mathematics today?
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Yes, mathematics has been always not only one of the most active field of the researchers, it was for a long time along with philosophy one of the first sciences. But, it’s hard to say what are the most active research areas in mathematics today or what are the most important scientifically explored in mathematics. Less and less support is provided for purely fundamental mathematics is nowadays, and more and more is required to solve specific problems by "someone else" i.e. mathematics turns into a servant of other sciences
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Do you know if there is a mathematical approach (or any publication that came out with something similar) that state the age cut-off between the [(206/238)/(207/206)], and [(206/238)/(207/235)] discordancy degree calculation?
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Several papers have touched on this recently, including:
In my opinion you need to look at your own data to inform this decision.
Nick
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Is there a quantitive measurement of how equilateral a triangle? Such as the following:
Triangle A(2,3,4)
Triangle B(3,3,3)
Triangle C(10,10,1)
Is there a measurement such that 0 is a triangle that doesn't satisfy the triangle inequality theorem and 1 is a perfect equilateral triangle, assuming that a triangle's side length range is not infinity but rather constrained between (0,c].
Therefore I should get:
Triangle A = some value between 0 - 1
Triangle B = 1
Triangle C = value close to 0
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Dear Juan Gerardo Alcazar I think you are right, but you need some measure which is invariant when you apply homothetic transformation on the triangle, otherwise similar triangles would yield different results. If you do this you will see that the proposed answers are really different.
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The Monod equation is a mathematical model for the growth of microorganisms. But the mushrooms do not follow this trend as they have a phase where spawn running is carried out. Also, the biomass increase is differed from other microbes.
The attached images shows the difference.
Please tell me can we still use Monod equation to to express specific growth rate of mushrooms and substrate utilization?
or which model will be more suitable in my case?
Thanks
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Respected Mirosław Grzesik Sir,
Is it possible to derive a new model in my case, as all mushroom species follow the trends as given in the image above?
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I know that an infant's brain can repair itself when damaged but why doesn't the same happen in adults after stroke or brain injuries?
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The infant brain has better plasticity than the adult brains. The regeneration of brain and vessel in the damaged region occurs in both infants and adults, which means the brain can also regrow in adult to some extend. However, the ability of regeneration seems to be higher in infants. Additionally, infant brain has more "clean space" to establish the neuronal circuit for functional restoration.
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Relativistic gamma can only be positive, in the time dilation equation.Hence , modulus of relativistic gamma has to be applied. If this error is taken into prudent account, cosmic speed of particles greater than 1kg and 1s is one-third the speed of light.Hence only meagre, kinetic relativistic effects are possible in nature.
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It is not really a mistake, you add that you only consider the positive branch of the square root so that you avoid things like when v = 0, x = - x' and things like that.
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For shell elements, is the elasticity tensor for linear-elastic & isotropic materials the same in a local curve-linear (convected) system vs. a local Cartesian system?
I wonder because intuitively, for a shell element & linear-elastic isotropic material, the only direction that matters (material-property wise) is the z direction. And in this case, the local z axis is aligned with the curve-linear coordinate system. But how do we mathematically show it?
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Let's wait the author's reply.
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If we have a matrix with both zeros and ones, in Matlab we just 'find' command to find the indexes of those nonzero elements. But how can we find it mathematically . can anyone help me with that.
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Is 1+1=0?
Is it worth to do a computation (especially for large matrices) if Mathlab finds all your 1s quickly?
If your answers are "yes", simply add the n by n matrix full of 1 to the yours. The result b_ij=0 says that a_ij=1 in the original matrix, and vice versa.
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Suppose I find 1000,00(one lakh) 2x2 matrix responding to eogenvalues : e1,e2
Then which one I will accept and which 99999 matrices to reject.
Give yoir views. My findings are mathematically correct.
B.Rath
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@Preter Breuer
In the question e1=/= e2 .
Then suggest your answer.
B.Rath
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I have been struggling to get endorsement for putting preprint in arXiv, but I a unable to get it. What is the best method to get endorsement in arXiv for physics or mathematics?
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The arXiv started the endorsement requirement for some highly demanded areas (like physics-hep) some years ago, due to the insistence of lots of cranks wanting to publish their "papers" there. The endorsement works as follows: you must look for someone who is actively uploading papers in the arXiv and has the "Endorser" flag. When you look for a preprint in the arXiv, you will notice at the bottom of the page a link like that:
Which authors of this paper are endorsers?
By clicking on it you will see who can endorse you. Look for some person who knows you or your work, then ask this person to endorse you. If she agrees, then try to submit your paper. You will receive the "need for endorsement" message, asking you to provide the mail of one possible endorser. Then, after you give the name of your endorser, she will receive an email saying:
"XYZ requests your endorsement to submit an article to the ABC section of arXiv. To tell us that you would (or would not) like to endorse this person, please visit the following URL:
The endorser will click on the link and will be asked for a code which is available in the mail. That's all, you have been endorsed.
The endorser will be reminded that she is NOT asked to judge the quality of the work, just to make a statement about her confidence in your status as a working scientist. But, of course, the first one that should be convinced about the quality of your work is yourself, because someone will have to raise her hand to support you.
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The state [uud] is given. The transposition (12) is a symmetry of this state e.g. (12)[uud]=[uud]
Let us calculate the result under acting of the cycle (132):
(132)[uud]=[duu]
But (132)=(23)(12), so
(132)[uud]=(23)(12)[uud]=
=(23)[uud]=[udu].
Where is the mistake?
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Во-первых, я никакой ни дохтур.Дорогая Ева, вы не ответили
----------
У вас есть сообщество почитателей Яноша Больяи?
-----
Если этого нет, то я буду вторым, после вас.
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First, I am not a doctor. Dear Eve, you did not answer ---------- Do you have a community of admirers of Janos Bolyai? ----- If not, then I will be the second, after you.
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Like AI, space technology etc.
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A very wide field of technologies in a variety of sectors, indeed. For example chemical science and industry. See:
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physical mathematics
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Thanks dr @a. M. Abdallah its very usfull
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As we are investing money in research, only fruitful research is able to generate money And loop completed. but most of us investing money on research but only for publishing paper.no income generation.
Being a researchers I wish to know how to address this issue.
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Fruitful research means that the research has already been completed. What about new research ideas?
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Hi all,
I would like to know how to generate mathematical proofs and theory. Is there any material that I can study? ..What do you think?
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There are a number of publications relevant to this. A classic one is Polya's "How to prove it". There are other suggestions at https://www.quora.com/What-are-some-good-books-on-proofs.
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How to solve the pell's equation for d = 1 x^2 - dy^2 = k?
Also how can I solve the generalized pell's equation x^2 - 5 y^2 = k
for fraction solutions?
One more,how to find number of tuples of (a,b,c) a,b,c belong to integers satisfying a^2 + b^2 = c^2 and p=a+b+c given p.For this I tried p=2*m*(m+n) taking general variable transform a = m^2 - n^2 , b = 2 * m*n ,c = m^2 +n^2 and created inequalities sqrt(p/2)<m<sqrt(p/4) but in this case I missed some solutions since if m is irrational and n is too then then m^2 - n^2 is integer,and if m*n can be integer too if both of then have same irrational parts.Still I ran a loop in python programming on m^2 in (p/4,p/2) and then finding n^2 by the perimeter's equation.I have to loop for p = (2,1500000). I taking more than 4 hrs.Any suggestions how to optimize ?(Also p can only be even can be checked very easily so loop is only over half of 1500000 values)
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In the formula a = m^2 - n^2 , b = 2 * m*n ,c = m^2 +n^2 that generates Pythagorean triples the variables m and n can be always chosen to be integers. For the proof see https://en.wikipedia.org/wiki/Pythagorean_triple#Proof_of_Euclid's_formula
and references in that article.
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In reference to the attached presentation material regarding the sum of the following infinite series 1+2+3+4+... the following comments are due
• The obvious answer is a huge positive whole number beyond our imagination
• But what if a theory wants the answer not to be so?
• Are we allowed to challenge the theory?
• Are we allowed to bend the rule or even cheat to get the desired value?
• Is this bending, of the rule, only applies for exceptional cases or can be exercised freely?
My conclusions are
  • It is a well-known fact that how feeble tricks are used in mathematics to obtain some haphazard values from divergent series to baptize certain theories in physics.
  • Three types of tricks are used to obtain the desired results
  1. Ignoring or hiding divergent quantities
  2. Ignoring or hiding conditions for formulas
  3. Extending the domain of a formula
  • These tricks simply erode confidence in mathematics as a sure scientific tool.
  • It is a legitimate question that if these flagrant deceptions are exercised to fool ourselves, who knows what other tricks are used to obtain desired results from complicated mathematical derivations?
The main question is; why for heaven’s sake, mathematics needs cheating in dealing with new challenges in science. Either it is not competent enough to cope or it is just a subjugated slave in the hand of any popular theory
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Ziaedin Shafiei Dear Ziaedin,
The problem depends on how one defines and accepts a trick. If we understand by a trick a "skillful act" that can be put in simple sequences of logical steps, then it is a mathematical act. If we understand by a trick an act intended to "deceive or mystify" others or oneself, then this clearly cannot be accepted. The problem is accepting illogical ideas put in deceptive bright capsules.
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Is there a mathematical way to determine how much data points are required to map a 3D object?
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Aparna Sathya Murthy : A shape is fixed by three point in 3D. In terms of translations and rotations, you can think of it this way. If point A maps to A', that takes care of three translations, but the shape can freely rotate attached to A'. If a second point B maps to B', the shape can only rotate around line A'B'. A third point C' fixates that last degree of freedom.
Chin Fung Tsang : If there are deformations, we are not talking about linear transformations anymore; the "degrees of freedom" (if that term still makes sense) might be infinite. The number of points needed depends on the accuracy you want. There is no general recipe.
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Many simulation software's are killing the basic knowledge one should have of his field but use of these software's are sometime more helpful and productive then the theoretical knowledge, what you people thinks?
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Your very nice conference paper shows results from MATLAB/Simulink and Mathematica simulation. How can I get a copy of you MATLAB/Simulink and Mathematica programs?
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Thanks for reading, I can add both software as soon as possible.
Best regards
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Though I know the mathematics behind Bicubic Interpolation, but I still unable to get a proper understanding on how is it applied on an image?
I know it works on an 4*4 pixel patch and takes into consideration surrounding 16 pixels to compute the value of the interpolated pixel, but how is it applied to an image as a whole?
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Applying it as an FIR or IIR filter would be the most efficient way. Design the filters to estimate the local polynomial coefficients at every given pixel, or to evaluate the (least-squares) fitted polynomial at the interpolating coordinates of interest. Look into the design of Savitzky-Golay filters for some ideas.
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What are the possible effects of gender variables on student instrumental genesis in mathematics? In CAS (from GeoGebra or from other mediums) environment?
What are possible resources and theoretical foundations for the topic?
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What is "instrumental genesis in mathematics"?
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What is the mathematical justification for the staggering grid (leap-frog) used in the FDTD method? any references?
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Consider a simple PDE model equation like the first order one df/dt+df/dx=0.
If you integrate in time between generic times t1 and t2 you get
f(x,t2)-f(x,t1) = - Int[t1,t2] df/dx dt
This is an exact expression. Now you approximate the integral in the RHS using the second order accurate mean value formula at tm=(t2+t1)/2:
f(x,t2)-f(x,t1) = - df/dx|(x,tm) * dt
Finally, you discretize the spatial derivative around x using a second order central formula
f(x,t2)-f(x,t1) = - [f(x+dx/2,tm)-f(x-dx/2,tm)]/dx * dt
now just set t1=t-dt/2 and t2=t1+dt and you get an explicit scheme that is second order accurate in time and space. Generally, the values f(x+dx/2) and f(x-dx/2) requires further spatial interpolation. In literature, you can find similar discretizations but over 2*dt and 2*h stencil.
Of course this is not a staggering. Be careful that a consistent scheme does not necessarily implies numerical stability.
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Please provide the mathematical details of the phenomenon, specifically for a parabolic path if path property is required
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Another, incomplete, homework problem, whose statement, as might be expected, is meaningless.
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What can be suitable theoretical framework(s) for technology integration in mathematics classrooms implementing flipped classrooms?
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Dear Hussein A. Tarraf,
the answers to this RG question refers to a good range of didactic theories:
This article and the links therein may be related to your research area:
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First a large size matrix requires sufficient memory to inverse the matrix. Secondly, there are several mathematical techniques are available to solve the inverse of a matrix. But in handling a large matrix, still I couldn't find any faster and accurate method which can solve this problem with less memory consumption as well.
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It depends on the matrix and no universally fast method exists!
In particular its eigenvalue characteristics and rank of the matrix or the pattern of non-zero elements. For sparse and patterned matrix which are usually seen in numerical solutions of PDEs (like FEM and FDM) there are well established methods which are developed over years and some of them are very efficient:
In general, if you want to invert a full matrix of size N X N you have to do O(n3) arithmetic operations (without applying any numerical tricks).
But we have methods for inverting sparse matrix of size N X N which are as efficient as O(N log N) like Thomas Algorithm (see below)
If you want more in depth discussion on numerical method s for inverting a matrix, there numerical efficiency and palatalization see these three:
1- Yousef Saad web page:
2- Works by Roland Freund (UC Dvais Department of Math)
3- Book by Gene H. Golub of Stanford:
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Hi
i am doing my study on economic complexity. i need to solve its formula mathematically
can any one have its formulation?
i attach research paper regarding economic complexity
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What do you mean by solving? It is an eigenvector centrality measure, which is a common descriptive metric used in social network analysis. It's calculated from an adjacency matrix of a network. In this case the edge weights are calculated from cross-country trade data on a bipartite graph.
By the way I have some reservation about the practical ability of ECI to measure the knowledge capital in an economy, because countries with only a short slice of the value-chain localized, but with a high diversification, can get overestimated by the index. Using value-added terms could be more useful.
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I have studied systems theory in the more complex mathematical version and have a handout in Dutch describing an organisation as a system with the primary process and two kinds of feedback loops. But that contsins no reference to official literature and none in English. Who can point out a useful source?
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Thanx all, my question has been answered! This is no longer a question. LH
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FEV1 is measured by spirometry and lung impedance are calculated by FOT/IOS methods. Do these methods have any mathematical relation? Can we interpret lung impedance by knowing FEV1?
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@ tarig: Dear Doctor, even if we assume it mathematically as done. would that "relation" be the same for both healthy and damaged lung? we all know, a damaged lung is less compliant, and so high resistances would be scored to get a small mobilized volume. then we are just talking here of "another" way to calculate the pulmonary compliance !!
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In optimization problem often we use local optimum but is it global? Or are there any meta-heuristics algorithm to obtain global solution? If there any then what is the name of that algorithm and if possible how we can get that solution?
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I wish not to let you down, but the basic answer is "very seldom", and another one is "you will not know if you have stumbled upon an optimal solution, because there is no natural termination criterion based on the concept of optimality". (In contrast, a branch-and-bound, or branch-and-cut, methodology is based on local AND global bounds on the optimal value generated throughout the procedure, and in most cases the correct procedures will either fix some variables to their optimal values before termination, and they will be able to discard a very large portion of the search space based on parts of the search space being infeasibie or inferior, in which case we do know for sure that an optimum has been reached.)
If you have a structure of the problem that makes it emanable to be solved by special methods, such as Benders decomposition - when you have a mix of integer variables and continuous variables. you also have a fail-proof method.
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In Mathematics, delay differential equation is one type of differential equation in which the derivative of the unknown function at a certain time and stochastic differential equation is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution. Therefore, share your valuable ideas on "How to distinguish between Delay differential equation and Stochastic differential equation?"
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Thanks for sharing some papers on above mentioned one @ A.M. Abdallah.
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I am looking for a mathematical relationship to approximate the location at which abutments start affecting the flow field or velocity field of the current. Basically the distance where the abutments starts to disrupt the flow.
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1- It depends on the Froude number, if Fr<1 you see wakes in the surface on the headwater before the bridge.
2- It is boundary layer theory, just consider the abutment as a wall and write law of the wall towards the center of the river .
3- If you are caring about the bridge scour and practical aspects see the relations in "Hydraulic Design of Safe Bridges" (FHWA Publication Number: HIF-12-018)
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Suppose there are 5 samples having different means (sample means). Statistical testing of hypothesis may lead to the result that the 5 sample means are equal. It is clear that the 5 sample means are not mathematically. However, they are equal statistically.
Does this fact lead to the necessity of framing of a definition of statistical equality (i.e. equality in statistical sense) ?
Thus the question is
"Is there necessity of framing of a definition of statistical equality (i.e. equality in statistical sense) ? "
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@ Ayman Amin ,
In hypothesis testing, the null hypothesis of the equality of population means is not rejected if the difference among them is found to be insignificant. Thus, the insignificance of difference is regarded as equal here.
However, logically insignificance of difference does not imply " equal " but zero difference implies " equal" .
This may lead to the necessity of statistical definition of equality as I feel.
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Is anyone working, has worked, or knows about research/practice with using narratives or stories to teach mathematics at the undergraduate level (not for little children)?
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Thanks for your answers, all great recommendations. I was wondering if you have used a story that was particularly well received by your students? Could you share details?
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I do not know What is a Mathematical Definition of Big Data?
Can you help me?
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Thank you for your answers, my comments are as follow.
1. Dear Professor James F Peters, your recommended paper is important, but is not related to "Mathematical Definition of Big Data". 20 years I published a book on essentials of Discrete Mathematics. I hope to give a definition of big data like definition of group. I also think the definition of data warehouse, which has mathematical flavor. However, data mining has not Mathematical definition, machine learning has not Mathematical definition.
2. Dear Paulo Laerte Natti
" a set larger than 100,000 data is Big Data" is not a Mathematical definition. I have considered your idea in my
[1]. Sun Z, Wang PP (2017) A Mathematical Foundation of Big Data. Journal of New Mathematics and Natural Computation. 13(2): 83-99. DOI: 10.1142/S1793005717400014
3. Tareq Al-shami
"A collection of data that we cannot (or find difficulties to) deal manually. Numerically" has a little mathematical flavor, but it is not Mathematical definition.
For "A set of big data is not less than one hundred data" please also see Sun Z, Wang PP (2017), mentioned above.
4 Dear Santhosh Kumar Balan,
Thank you for your papers, I will download each of them for reading
5. Dear Emmanuel Gonzalez
Your non-academic industry-grade definition: Big data D(M,C1,C2,T) is an M-dimensional data that is or will be processed by a computer with capacity C1, interpreted by a specialist with competency C2, over a period of time T, such that C1 can be changed to
Big data D(C1,C2,T V) is data that is processed by an entity E1 with capacity C1, interpreted by an Entity 2 with competency C2, over a period of time T, such that data can be changed into big value V. where entity is a set of humans, computing machineries, robots, intelligent agents.
This is a market-oriented definition, or pragmatic definition.
For your definition, M-dimensional data should be replaced as data, have a look at topology, distance is nothing there, therefore, M-dimensional is too specific. "interpreted by a specialist", is replaced by entity, it is better.
a computer is replaced by entity. Similarly, in German, das Sein, is the most general concept in philosophy.
Best regards
Prof. Zhaohao Sun
2018-8-23
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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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I have a set a={x1,x2,x3}, b={y1,y2,y3} and c={z1,z2,z3}. X are financial variables from my dataset, Y and Z are financial variables from other dataset. Each value is in thousand dollar. I want to find which set (set b or set c) is closer to set a. So, I used the euclidean distance. But, the resulted distance is too big because the difference between value is thousand of dollar. Hence, I divided each distance with the mean of set a to make it smaller with range of 0-1:
Distance (b,a) = euclidean(b,a)/mean(a)
Distance (c,a) = euclidean(c,a)/mean(a)
I'm not sure if this is mathematically correct or not. Is there any better way?
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I would consider a normalization based on the max distance... In other words, you have a N dimensional space with some vectors having some modulus values. Compute the max modulus of the vectors and use it to normalize.
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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 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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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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Do you need to find a Scopus conference? On the IEEE website, you can find events by parameters, including conference dates and fields of Interest.
An example of search results can be found at the link:
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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.