Science topics: Mathematics
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Mathematics - Science topic

Mathematics, Pure and Applied Math
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Is there any relation between NPs size and energy band gap, I mean how the energy band gap vary with the nanoparticle size? please provide your answer with a mathematical relation if there is?
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Generally, band gap energy increases with decrease of particle sizes, which is called quantum confinement effect. You can observe this effect through UV-vis spectroscopy, which shows a blue shift in the spectrum by decreasing the particle size. Please search about this title by using “quantum confinement effect”.
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How I can get the inverse Laplace transform of
L-1((1/(s+a)^2)*F(s))
where F(s) is variable function (we can say it is discrete and random)
OR how I solve this first order non-homogeneous differential equation,
y'+y = f
where f is variable function (we can say it is discrete and random)
Thanks in advance
Nasser
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Dear Nasser
There are some questions posed by your affirmation (discrete and random).
1 - In a first approach and looking only at the the expression L-1((1/(s+a)^2)*F(s))
what I would do was a) See which is the Region of convergence of F(s). I assume it is, at least, Re(s) > 0. Fix the integration path at some Re(s) = c.
b) Perform a bilinear transformation s --> z that transforms the straight line Re(s) = c into the circle centred at z=0 and with radius 1. Put z=e^{i(2pi/N)k} with k=0, 1, 2, ... N-1. Its is convenient to use a high N= 2^K, K positive integer. c) use the inverse FFT.
Yo can find these things in any book on Signals and Systems.
2 - You say that the function is discrete. In this case, it would be better to use a discrete-time formulation using a difference equation and the Z transform.
If you want to "talk" directly, send a mail to mdo@fct.unl.pt
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Wondering if there is even mathematical tables to help with word problems?
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Thanks for suggested help everyone!
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Is there any rapid publication journals that are indexed by SCOPUS in the area of Computer Science ,Mathematics, Applied Mathematics & Optimization
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Proceedings of the Japan Academy, Ser. A, Mathematical Sciences
and
Bulletin of the Australian Mathematical Society
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The prescriptive curricula indicate the evaluation standards on the one hand and on the other demand the teacher's evaluation of general and Niss competences for the secondary education stage.
Is not it contradictory? or is it complementary?
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Dear Cardenoso,
Objective evaluation is to look in to the content of a mathematics course whether it meets the objective of the course it intends to achieve in a particular field and at a particular level, indicating level of complexities, relevance and degree of abstractness. Evaluation of competencies on the other hand is geared towards the people involved in the course, either students or professors who intend to teach.
Regards,
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One is euler's method.
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For your particular question: "What are the other methods of differential equation?"
Especially you have mentioned that Euler's method but it is used to solve a differential equation associated with either initial or boundary conditions moreover it is used to get numerical solution only. Solving differential equations typically involves integration. Unfortunately, solving differential equations is usually more complicated than just writing down an integral and evaluating it. The only kind of differential equation that can be solved that way is the simplest kind of first order differential equation that can be written in the form separable equations, homogeneous, linear differential equations , nonlinear equations and etc.
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Solve this homogeneous problem
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Solution:
Given below
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whether there is a definition of the point?
certainly a well-defined?
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In general a point refers to an element of some set called a space. More specifically, in Euclidean geometry, a point is a primitive notion upon which the geometry is built which mean that a point cannot be defined in terms of previously defined objects in modern mathematics.
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Calculus (Latin, calculus, a small stone used for counting) is a branch in mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change[1], in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient.
Historically, calculus was called "the calculus of infinitesimals", or "infinitesimal calculus". More generally, calculus (plural calculi) may refer to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, variational calculus, lambda calculus, pi calculus, and join calculus.
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Mathematics is the branch of science that deals with logic, decision-making, assumptions, deductions, the clarity of thought and ability to solve the problems in a calculative manner. It is the branch of Mathematics that deals with the finding and properties of derivatives and anti-derivatives of functions by methods originally based on the summation of infinitesimal differences. The two main types are differential calculus and integral calculus.
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Dear Scholar
The following are FACTS:
1. Polygon based 3.1415926...has been thrust on circle as its Pi.
2.Pi has been called a transcendental number since 1882.
3. From 1882 we have been told that Squaring a Circle is an UNSOLVED GEOMETRICAL PROBLEM.
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4. Hippocrates' work has been ignored , although squaring of circle was done. It is a Historical Blunder.
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5. In Hippocrates period 500 BC , EXACT Pi Value was unknown.
However, he DID square a circle.
6. His work is PURELY THEORETICAL because of the unknown exact Pi value.
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7. With the discovery of the EXACT Pi VALUE in March 1998, (3.1464466...) Hippocrates" work has turned into a PRACTICAL WORK from then on wards.
8. Hence, HIPPOCRATES OF CHIOS IS THE TOP MOST MATHEMATICIAN IN THE WORLD ( He is already called A FOUNDING FATHER OF MATHEMATICS ) whether the Mathematical World accepts it or not.
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"The following are FACTS:" -- No, they aren't! And here is why:
"1. Polygon based 3.1415926... has been thrust on circle as its Pi." -- There are many ways to obtain the decimal representation of pi, not only the polygon method; therefore, 3.1415926... is not polygon based. Here are two examples for other ways to obtain pi: 1.) Euler's infinite sum of the inverses of the squares of all natural numbers: pi^2 / 6 = 1/1^2 + 1/2^2 + 1/3^2 + 1/4^2 + ... = 1/1 + 1/4 + 1/9 + 1/16 + ... (cf. https://www.youtube.com/watch?v=d-o3eB9sfls); 2.) Leibniz's infinite sum for arctan(1): pi / 4 = 1 - 1/3 + 1/5 - 1/7 - 1/9 + ... (cf. https://proofwiki.org/wiki/Leibniz%27s_Formula_for_Pi).
"2. Pi has been called a transcendental number since 1882." -- In his publication "Ueber die Zahl pi", F. Lindemann has shown why pi is a transcendental number. The essence is that Euler's number e ist transcendental, and that e raised to an algebraic power is also transcendental. However, since e^(i pi) equals -1 (cf. https://www.youtube.com/watch?v=F_0yfvm0UoU and https://www.youtube.com/watch?v=mvmuCPvRoWQ or https://www.youtube.com/watch?v=Yi3bT-82O5s and https://www.youtube.com/watch?v=-dhHrg-KbJ0) and since -1 is not transcendental, pi cannot be algebraic (cf. https://www.youtube.com/watch?v=seUU2bZtfgM).
"3. From 1882 we have been told that Squaring a Circle is an UNSOLVED GEOMETRICAL PROBLEM." -- Since thanks to Lindemann we know why pi is transcendental, we immediately know also that it is impossible to square a circle. Therefore, this geometrical problem isn't an unsolved problem anymore, because it's not a problem anymore: We know the solution -- namely, that there is no solution.
"4. Hippocrates' work has been ignored, although squaring of circle was done. It is a Historical Blunder." -- Since thanks to mathematical logic we know that squaring the circle is impossible, we need not care about anybody's efforts to square the circle. All such claims are illusions; at best, they are more or less close approximations.
This settles the matter from the mathematical point of view. It just remains to test the various mathematical predictions by real-world investigations, determining pi experimentally.
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Suppose we have a set of players, i.e., {p1, p2, ..., pn} and each player has three different strategies, i.e., {s1, s2, s3}. They play m number of games. In each game, each player seeks to maximize its profit by selecting a strategy with highest playoff. The profit associated with each strategy is as follows.
1) Payoff for selecting strategy s1 is zero
2) Payoff for selecting strategy s2 is a real number, which is calculated using some formula f1
3) Payoff for selecting strategy s3 is also a real number, however, it is calculated using another formula f2
I want to prove the existence of Nash equilibrium when all the players select one of the available strategies.
I have searched on web and found several documents, however, I couldn't get a clear idea to prove it mathematically.
Any help is deeply appreciated. Please let me know if I have missed any information. Thank you in advance.
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@Felipe Please find attachment to see the formulas.
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I am currently analysing data on whether there is a difference in the level of understanding between maths and science using a sample of year 1, year 2 and year 3 students. I am also looking at whether the level of understanding improves across the year groups. I am running a mixed ANOVA, however my homogeneity of variances for science were violated. Can I run it anyway?
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You can use weights to account for heterogeneous variances. The weight are typically chosen proportional to the reciprocal of the variance (what will give lower weights to groups with higher variance).
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People usually say that the number greater than any assignable quantity is infinity and probably same in the case of -ve ∞.
We are dealing with infinity ∞ in our mathematical or statistical calculations, sometimes we assume, sometimes we come up with it. But whats the physical significance of infinity.
Or
Anyone with some philosophical comments?
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Mathematicians have a precise definition of infinity that can be used to prove theorems about it. A set S has infinite size if it is possible to create a 1-to-1 correspondence of the elements of S with the elements of a proper subset of S. For example, the positive integers S = {1,2,3,...} is an infinite set because there is a 1-to-1 correspondence between S and the even integers in S: 1 <-> 2, 2 <-> 4, 3 <-> 6, 4 <-> 8, ... Such a 1-to-1 correspondence is impossible for finite sets.
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  • Zero because how come there is value for nothing?
  • Infinity because how come there is a value for everything?
  • Does the fact that we use Infinity and Zero to express ideas mean that our mathematical system is flawed? Not necessarily in a bad way, maybe because there is no other way to express such ideas ,that we know of, other than using zeros and Infinities.
  • Isn't mathematics supposed to be the most determinist thing we know, how come its so uncertain?
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1/0 is singularity, not 0. 0 and infinity are mathematical constructs, not physical. Physics has to measure values, and neither 0 no infinity is measurable.
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Rubik's cube is a fascinating toy which involves transformations or permutations. I'm curious, what is the mathematical group of 3 x 3 x 3 cube.
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Denote by R, L, U, D, B, F, respectively, the quarter turn clockwise when you look at the Right, Left, Up, Down, Back, and Front face. Use small letter combinations to name each edge and each corner; for example, the upper right corner near you is fur, and the bottom edge near you is uf. It does not matter if you call it uf or fu as long as you keep track of it consistently. For example, the set of edges and corners of the front face is {uf, rf, df, lf, urf, rdf, dlf,luf}.
You have a group with group elements R, L, U, D, B, F, the 4th power of any of which is the identity, acting on the set of 20 pieces of 8 corners and 12 edges. For example, the effect of R on that set is the permutation (uf rf df lf)(urf rdf dlf luf). For group action, I use the notation XY to mean apply X first, then Y. The quintessential complication is RU (or any two that share an edge), and using the above notation, one can write down exactly the effect of RU on the 20 pieces: It rotates the corner fur by 1/3 turn and cyclically moves the 5 corners and 7 edges. In permutation notation, the effect on fur is (fur urf rfu), for example.
It is easy to see that (R^2 U^2)^3 will swap two pairs of edges, that (RUR'U')^3 will swap two pairs of corners (prime denotes inverse), and that URUR'U'R'U'R'U will cyclically rotate 3 edges. ("Easy" to see because the effect of, say R^2 U^2, in cyclic permutation notation on the set of corners and edges consists of cycles of length 2 and 3; hence, the 3rd power will leave only those of length 2, namely, the transpositions I informally call "swap".) Call these three sequences A, B, C, respectively. These three are the most one needs to solve the cube, using conjugation X(G)X' where X is any sequence you want and G is any of the A, B, C. For example, to flip a pair of edges (by flip, I mean, for example, the permutation (ur ru)(df fd)), use any sequence X to introduce a flip into one edge of the pair of edges you want to flip (messing everything else up in doing so does not matter because X' will undo), perform A to swap the pair with some other (innocent bystander) pair, perform X' to put everything else back, then perform A to swap the two pairs back (which will restore the "innocent bystander" pair). The net result is the flipping of a pair of edges. Perform an analogous sequence using B to rotate a pair of corners, i.e. Y B Y' B for some Y that introduce a rotation of one corner of the pair of corners you want to rotate.
So, the group of the cube has 6 elements (R, L, U, D, B, F), the 4th power of any of which is the identity, and is generated by (R^2 U^2)^3, (RUR'U')^3, and URUR'U'R'U'R'U. (You can probably eliminate the URUR'U'R'U'R'U from this list since any cyclic permutation can be written as a product of transposition, but be careful that (R^2 U^2)^3 effects a pair of transpositions, not a single transposition.)
This is how I did it in the 4 days between the last day of class and graduation when I was in college.
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What additional information does the phase measurement in a frequency-domain imaging technique provide compared with the continuous wave technique that measures only the amplitude of the diffuse light?
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A phase shift of a frequency modulated light source is almost equivalent to a change in mean flight time of the photons and hence provides information about the mean free path length of the photons through the tissue. This information is distinct to that provided by a change in amplitude, which is the only variable measured in continuous wave (CW), and helps in distinguishing the degree to which attenuation is a result of either scattering or absorption events. In certain cases, such as diffuse optical tomography, it is possible to separate scattering and absorption using CW measurements by solving a regularised inverse problem, however frequency domain measurements will typically improve this separation by reducing the non-uniqueness.
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I find that having deep knowledge in other disciplines throws light on my core intellectual disciplines, history, psychology, etc, making me more aware of limitations of thought. For others, this may not help. For those involved with maths, knowing other disciplines probably has no or little affect on their insight into their core discipline.
What do you think and what is your preference?
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with advanced age and cooperation with other academic people it is normal that experience becomes interdisciplinary. In particular psychology and its results of research cover a wide disciplinary radius, 150 years earlier empirical psychology was to a big amount physiology, but researchers who worked were or became philosophers (or medical educated, or physicists), the discipline, for instance in Germany, was represented by historical figures like Wundt, Fechner, Georg Elias Müler, and also, as by pure philosophers, like W. Dlthey (making a difference between explaining nature, but understanding psychological experience). The discipline went - against Diltey - the way of natural science. But all results of experience can have useful effects of enriching that disciplines which were the original sources in the end of 19th century.
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I look for mathematical theory of Differential equations like
Picard–Lindelöf theorem and Carathéodory's existence theorem that deal with existence/uniqueness of differential equations. I hope some purely theoretical reference can address such theoretical methods not just applied methods.
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Theory of Ordinary Differential equations" by Coddington. If you find the previous one advanced, there is "An Introduction to Ordinary Differential Equations" by Coddington too. The first one is very complete and have a lot of things that I have never seen in other books. The second one is very basic (there is almost no qualitative theory), but proves the validity of some techniques usually used to solve ordinary differential equations. They also gives some explicit formulas for solution in special cases.Carmen Chicone's book "Ordinary Differential Equations with Applications" is good too if you want to study better the qualitative theory.
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How can we establish mathematical relationship between S11 and arbitrary geometry?
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If you don't want to measure the result which is the best solution then there are many commercialy available modelling packages using FDTD, FE, TLM and boundary element algorithms. All will give you answers. Beware, these are sophisticated tools and you really have to know what you are doing when using them. In particular, the way in which you describe the antenna feedpoint is critical for the S11. Never accept a modelled answer at face value. You must always test your model by varying its parameters and looking for convergence. Also, remember that a model is a model and not reality.
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It is said that fixed point theory has lot of applications not only in the field of mathematics but also in various disciplines. Which one is the most important?
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Applications to non linear differential and integro-differential equations - many.
Applications to algeria geometer - Borel Fixed Point theorem.
Applications to Game Theory - Browder Fixed Point Theorem.
Applications to non-zero sum game theory and particularly the Nash equilibrium in economics - Kakutani Fixed Point Theorem.
Applications to geometry and topology of manifolds - Atiyah-Bott Fixed Point Theorem.
These are just a few of the many types of fixed point theorems and applications.
For a more complete list see.
The analysis of nonlinear relationships in systems that arise in the sciences, engineering and even the social sciences (e.g., economics) often end up being expressed in the terms of nonlinear equations and/or mappings and the solution is a fixed point of such a mapping. My paper - available on Research Gate - on asymptotic integration of a large class of non-linear functional differential equations - is a good example of the power of fixed point theorems in a addressing complex not linear problems.
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There are number of well studied mathematical and computational techniques used in the crypto analysis of public-key crypto systems?
Which are the most effective?
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Cryptanalysis is the science of cracking codes and decoding secrets. It is used to violate authentication schemes, to break cryptographic protocols, and, more benignly, to find and correct weaknesses in encryption algorithms.
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I want to predict the Passenger car unit (PCU) values of different vehicle types using ANN and ANFIS. Is it possible to return a series of equations in the output layer of ANN (or) ANFIS model?
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The equations generated are usually based on sigmoid basis functions, and the number of weights and biases will depend upon the the number of hidden neurons.
More on the form of equations:
2. Mishra et al. (2017):
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I am looking for recent subjects in the area of using Markov chains in queueing models or theory for the thesis of a master student in mathematics.
Thanks a lot in advance.
Mohamed I Riffi
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these are real topics that my graduates have done in recent years
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How wind speed is mathematically related wind power???
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For more detailed information see e.g.
JoD
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Dear All,
x/y=d*exp(-p*t)/(d+p)
In the above equation
known values= x/y(ratio 4/2=2), d=18.2 and t=6.25, need to calculate "p". One way is to adjust the "p" until you get the x/y=2, for this way i need to go manually onebyoine. I have 400 for all this I have to go manually and adjust the "p" values.
Is there is a way to rearrange the equation or excel method to back calculate "p" values automatically. I would highly appreciate any help and suggestions.
With many thanks
Vince
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Solution p = (1/t) * W[(dty/x)*exp(dt)] - d
where W is the Lambert W function which you can implement in excel using https://github.com/mdscheuerell/Lambert-W-in-Excel
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By "gentle" I do not mean that I am afraid of formulas - I studied mathematics myself. But I would prefer literature that may serve as a first course in Bayesian statistics.
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There is more:
John R. Kruschke. (2011). Doing Bayesian Analysis. A tutorial with R and BUGS. Amsterdam: Academic Press.
McElreath, R. (2015). Statistical Rethinking: A Bayesian Course with Examples in R and Stan. Chapman & Hall.
And here is the book I am writing, currently:
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  • Is there anything such as true randomness, or is it just a delusion? If yes, why? If not, why?
  • Is there a branch of knowledge dedicated to only the study of randomness?
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This is an interesting question with not so obvious answers. In addition to the helpful observations already made, there is a bit more to add.
A good RG discussion to check concerning this question (and the implementation of a so-called true random number generator) is
See, for example, the observation by @ Mario Stipčević using a photon counter. See, also, Mario Stipčević
Another important RG discussion on randomness is ongoing at
See, also:
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What are some of the most important formulas in mathematics?
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1+1=2
  • Differential equation
  • Gaussian integral (integral from -inf to +inf of exp(-x²) = sqrt(pi))
  • Cauchy–Riemann equations
  • Chapman–Kolmogorov equation
  • Clairaut's equation
  • Fredholm integral equation
  • Hill differential equation
  • Ishimori equation
  • Laplace's equation
  • Maurer–Cartan equation
  • Pell's equation
  • Poisson's equation
  • Riccati equation
  • Sine–Gordon equation
  • Verhulst equation
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  • Does such an equation exist?
  • Can it ever exist, or is it mathematically impossible?
  • Is this equation relevant to Chaos Thoery and Quantum Mechanics? If yes how?
The equation I am seeking for behaves something like this :
f(1) = 2
f(1) = 8
f(1) = 2.4
f(1) = 9005
f(1) = 0
f(1) = 3
Please excuse my ignorance.
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If any element from the domain associate with more than one element in the range, then it is not a valid function as per the definition. Hence there should not be any f(x) which returns multiple values for any x. The reason is the functions are not associate with a status variable and once a function is defined, the definition remains static.
However your question is closely related generating random numbers. We cannot model a "real" random number generator to work even in a digital computer. What we can really model is just a "pseudo" random generator in which the output sequence will be re-occur after a certain point.
The question is not related to chaos theory as well.
I do not have any idea about your last question.
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The present day theory of generalized functions does not allow the existence of powers of the Dirac delta. However, this technical infeasibility might not reflect the mathematical "truth". It would therefore be very interesting to see potential applications of such powers of the Dirac delta. It may point us the way out of this dilemma.
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Dear Professor Jens Fischer,
You can go through the paper and references therein
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We understand from the infinite related mathematics history that in present classical mathematics (such as classical mathematical analysis and classical set theory) basing on classical infinite theory system, there has been an avoidless theoratical and operational defect whenever we conduct the quantitative cognizings to “infinite related mathematical things” with limit theory--------the confusions of “potential infinite, actual infinite” concepts and the absence of the whole “theory of infinite mathematical carriers” have been making us humans unable to study and cognize scientifically the foundation of limit theory (the “limit theory needs its own foundation” even has never been considered about). And, because of this very fundamental defect, it is very difficult for people to really understand scientifically what kind of mathematical tool limit theory is and how to operate with this mathematical tool scientifically in pracdtical quantitative cognitions to “infinite related mathematical things” in infinite sets. So, following four questions have been produced and troubling people long:
(1)Do we use limit theory treat “potential infinite mathematical things” or “actual infinite mathematical things”?Do we need different limit theories for “potential infinite things” and “actual infinite things”?
(2)Is limit theory a “quantitative cognizing tool” or “qualitative cognizing tool”, a “precise cognizing tool” or “approximate cognizing tool”?
(3)When we conduct the quantitative cognitions to different infinite sets, how can we use limit theory to analyze, manifest and treat those number forms of X--->0 elements inside them (such as those number forms of X--->0 elements in [0, 1] real number set)?
(4)What on earth is the foundation of limit theory?
We understand from the infinite related mathematics history that it is the absence of limit theory’s foundation that results in the production and suspending of so many “infinite related paradox families” in present mathematical analysis and set theory.
Our studies have prooved that limit theory is needed whenever there is the concept of “infinite” in our science and whenever we need to conduct the quantitative cognizings to “infinite related mathematical things”. The emergence of the new infinite theory system (especialy with its “theory of infinite related carriers” and nothing to do at all with “potential infinite--actual infinite”) lays a scientific foundation for limit theory and enable us to answer above four questions clearly and scientifically:
(1)Limit theory has nothing to do at all with “potential infinite mathematical things” or “actual infinite mathematical things”. It is a special mathematical quantitative cognizing tool for “infinite related mathematical carries”. Only one limit theory is needed.
(2)Limit theory is a “quantitative cognizing tool”,------an“approximate quantitative cognizing tool” for “infinite related number forms” in our mathematics (an “1<1 paradox” was once created to express the nature of limit theory: 1=3×⅓ = 3×0.333333……<1).
(3)When conducting practical quantitative cognitions with limit theory to mathematical things in infinite sets, what we should do first is “really doing analysis on the infinite related mathematical carriers” being quantitative cognized according to the “theory of mathematical carriers as well as its infinite related number spectrum and set spectrum” in new infinite theory system-------to know what position they are in “new infinite related number spectrum and set spectrum” and what kind of quantitative natures they have, then to decide how to conduct the scientific quantitative cognizing operations with limit theory, but not the indiscriminately “pipeline limit theory operations”.
(4)The new infinite theory system (especially its theory of “infinite related mathematical carriers”) is the foundation of limit theory.
The emergence of the new infinite theory system has decided the emergence of the new limit theory.
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interesting
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I am a graduate student in Mathematics and interested in Algebraic Geometry , In particular questions on Moduli Space . Now to start thinking about some problem for research what kind of question we may ask?
Are there any paper that will be very helpful?
How to start thinking about it.
Looking forward for help and suggestion.
I got problem posted on internet , like compatifying moduli space and motivic structure.
But I am not sure about those problem in initial research.
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Please visit this link you will get enough information
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log(a+bx) is concave since its double derivative is less than zero. (mx+c) is a straight line, so I can consider it as either concave or convex. But how can I prove mathematically that the ratio of the two is quasiconcave?
It is known that, a,b,c,m > 0.
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The answers hitherto given refer to concavity/convexity, whereas the question asked for a proof of quasiconcavity, which is a much weaker notion. A function f: X\to \R is said to quasiconcave iff f^{-1}([a,\infty[) is concave for every a\in \R. Concave functions are quasiconcave , but there are (many) quasiconcave functions that are not concave. A typical (and interesting) example of quasiconcave (and quasiconvex) function is a fractional linear function x\mapsto (ax+b)/(cx+d) on the domain \{x | cx+d>0\}. Furthermore, the composition of a quasiconcave function with a fractional linear function is quasiconcave on \{x|cx+d> 0 and (ax+b)/(cx+d) \in dom(f)\}, hence log((ax+b)/(cx+d)) is quasiconcave. (I suspect that you wanted to ask about this function instead of log(ax+b) / (cx+d), but I may be wrong, of course.)
For twice differentiable functions of one variable a sufficient condition for quasiconcavity is that f''(x)<0 at all points where f'(x)=0. You may try to check this or to check other sufficient or equivalent conditions, s. e.g. chapter 3.4 of Boyd & Vandenberghe: Convex Optimization. On any interval where your functions is increasing (or decreasing) , it is quasiconvex and quasiconcave. It is quasiconcave on any interval, where it is unimodular (i.e. increasing for x<=m and decreasing for x>=m). In your example it should be possible to find corresponding intervals (depending on the parameters.)
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I need a plagiarism software particularly which checks plagiarism for mathematical equations?
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Turnitin and Ithenticate programs are useful for that
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Dear all,
One can expand the expression (x+y)^1/2 ?
Thanks all of you,
Abdelmounaim
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This is not the same; it is an example of the extended binomial formule given for INTEGER n over real exponents (here equal 1/2). it a corollry to the Taulor formula for analytic functions.
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Dear Scholar
Geometry is the study of the Earth. Earth is a planet and is a member of the Solar family. Sun is a Star. So the planets and stars are 13 to 14 billion years old.
Mathematics is invented by man. Man came just 100 thousand years ago. It means Geometry is far far older than Mathematics which came very recently
Therefore Geometry should be first and mathematics next
Further , every concept in it has a support of a construction like other subjects of Natural Science such as Geology, Zoology, Botany, Physics, Chemistry
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Mr. Sarva, Can you interpret geometrically the mathematical solution of five linear equations in five unknowns? By the way, I agree with my friends Colton and K. Karthik. Thanks, Amir
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Please read attached file.
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Hi,
This observation is correct. Many mathematicians in various institutions and countries resent the impact factor as a measure of scientific excellence since it does not reflect accurately the value of papers in their field. Mathematics is an exact science, but its citation dynamics is similar to the social sciences. One bibliometric rule is that every science field has a different citation dynamics, and the comparison should take place within fields and not between them.
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Looking to connect with scholars in Brazil who study mathematics education of secondary/primary students who have learning disabilities/marked at twice exceptional.
Thanks!
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I'm sorry, I don't know anyone.
Regards!
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- Do the high school students perceptive economics too mathematical and difficult which result in non-enrollment in this degree?
- Is this choice related to students' GPA?
- Do the related field of study such as finance, accounting, business make students' choice toward economics more difficult?
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Thank you for your feedback...
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One of the central themes in Dynamical Systems and Ergodic Theory is that of recurrence, which is a circle of results concerning how points in measurable dynamical systems return close to themselves under iteration. There are several types of recurrent behavior (exact recurrence, Poincaré recurrence, coherent recurrence , ...) for some classes of measurability-preserving discrete time dynamical systems. P. Johnson and A. Sklar in [Recurrence and dispersion under iteration of Čebyšev polynomials. J. Math. Anal. Appl. 54 (1976), no. 3, 752-771] regard the third type („ coherent recurrence” for measurability-preserving transformations) as being of at least equal physical significance, and this type of recurrence fails for Čebyšev polynomials. They also found that there is considerable evidence to support a conjecture that no (strongly) mixing transformation can exhibit coherent recurrence. (This conjecture has been proved by R. E. Rice in [On mixing transformations. Aequationes Math. 17 (1978), no. 1, 104-108].)
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For “the definition of coherent recurrence (for measure/ measurability-preserving transformations) ” see, e.g., in: 1) [P. Johnson and A. Sklar, J. Math. Anal. Appl. 54 (1976), no. 3, 752-771], 2) [R. E. Rice, Aequationes Math. 17 (1978), no. 1, 104-108], 3) H. Fatkić, “O vjerovatnosnim metričkim prostorima i ergodičnim transformacijama (with a summary in English)” on ResarchGate; 4) [ B. Schweizer, A. Sklar, Probabilistic metric spaces, North-Holland Ser. Probab. Appl. Math., North-Holland, New York, 1983; second edition, Dover, Mineola, NY, 2005].
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The fundamental defects of “potential infinite and actual infinite” confusions in present classical infinite set theory have been making us humans unable to study and cognize scientifically the foundation of “one-to-one correspondence theory” (the “one-to-one correspondence theory needs its own foundation” even have never been considered about). And, because of the absence of this very foundation, it is very difficult for people to really understand scientifically what kind of mathematical tool “one-to-one correspondence theory” is and how to operate with this mathematical tool in practical quantitative cognitions to elements in infinite sets. So, following five questions have been produced and troubling people long:
(1)Are the elements in infinite sets “potential infinite things” or “actual infinite things”?
(2)Are there different “one-to-one correspondence theories and operations” to “potential infinite elements” or “actual infinite elements” in infinite set theory?
(3)How do we practically carry on “one-to-one correspondence” operations between two sets-------do we have “‘one single element’ to ‘one single element’ correspondence” or “‘one single element’ to ‘many elements’ correspondence” or “‘many elements’ to ‘many elements’ correspondence”?can we arbitrarily alter the elements’ “special nature, special existing condition, special manifestation and special relationship among each other” in infinite sets during the “one-to-one correspondence operations” for quantitative cognitions (such as alter all the elements in Natural Number Set first [1x2, 2x2, 3x2, 4x2, …,nx2, …] = [2,4,6,8, …,e,…] (not the correspondence between N and E but E andE), then prove it has same quantity of elements in Even Number Set)?
(4)What kinds of the elements in two different infinite sets are corresponded-------- do we have “‘one single original element’ to ‘one single original element’ correspondence” or “‘actual infinite elements’ to ‘potential infinite elements’ correspondence” or “mixture correspondence of ‘actual infinite elements’ and ‘potential infinite elements’”?
(5) What on earth is the foundation of “one-to-one correspondence theory”?
The fundamental defects in present classical infinite set theory have made us unable at all to answer clearly and scientifically above five questions. So, when carrying on practical quantitative cognitions to elements in different infinite sets with “one-to-one correspondence theory”, one can do very freely and arbitrarily--------lacking of scientific basis. For example: it is because of acknowledging the differences of elements’ “special nature, special existing condition, special manifestation and special relationship among each other” between Real Number Set (R) and Natural Number Set (N), one can prove that the Real Number Set (R) has more elements than N (the Power Set Theorem is proved in the same way). But, as what has been discussed in above 2.1 .1, we are able to prove with exactly the same way “the mother set has more elements than its sub-set”, “Rational Number Set has more elements than Natural Number Set”, “Natural Number Set has more elements than odd number set” ,...; we can even apply the widely acknowledged method of altering elements’ “special nature, special existing condition, special manifestation and special relationship among each other” to prove “Natural Number Set has more elements than Natural Number Set”, “odd number set has more elements than even number set”, “even number set has more elements than odd number set”, ....
Basing on the new infinite theory system with the “infinite mathematical carriers theory”, the Second Generation of Set Theory provides us with the scientific foundation of “one-to-one correspondence theory” and enable us answer above five questions clearly and scientifically:
(1)the elements in infinite sets are “infinite related mathematical carriers” with explicit quantitative nature and definition, indicating the existing of “abstract infinite law” and nothing to do at all with “potential infinite--actual infinite”. This decides one of the major differences between the first and the second generation of set theories-------the elements in different infinite sets have their own “special nature, special existing condition, special manifestation and special relationship among each other. So, it is really possible that different infinite sets have different quantity of elements and people can take them really as “visible and tangible infinite related mathematical things (such as the new numbers in new number spectrum)” for the quantitative cognitions
(2)the elements in infinite sets have nothing to do at all with “potential infinite elements” and “actual infinite elements”, there is only one identity for them-------“infinite related mathematical carriers” with explicit quantitative nature and definition; So, there is only one “one-to-one correspondence theory and operation” for them.
(3)it is explicitly stipulated that only “‘one single original element’ to ‘one single original element’ correspondence” operation is scientific (allowed) when comparing two sets for the quantitative cognitions and, during this process, any operations of arbitrarily altering the elements’ “special nature, special existing condition, special manifestation and special relationship among each other” are unscientific (not allowed).
(4)in the Second Generation of Set Theory, because of nothing to do at all with “potential infinite--actual infinite”, it is impossible to have any troubles produced by the confusion of “potential infinite --actual infinite”.
(5)the new infinite theory system (especially its theory of “infinite related mathematical carriers”) is the foundation of “one-to-one correspondence theory”.
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Pls see bour book Intermediate Set Theory, F R Drake and D Singh, Chapter 1,etc. John Wiley, 1996.
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A conjecture is a mathematical statement that has not yet been rigorously proved. Conjectures arise when one notices a pattern that holds true for many cases. ... Conjectures must be proved for the mathematical observation to be fully accepted. When a conjecture is rigorously proved, it becomes a theorem. Share your favorite conjecture as a answer for this? let we know some beautiful unsolved statements in the field of science and Maths?
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Dear Jack Son,
Goldbach's Conjecture:
Every even number n > 2 can be written as
n = Prime + prime or n = 1 + prime.
4 = 1 +3 ,
6= 1+5= 3+3
8= 1+7 = 3+5
10 = 7+ 3 = 5 + 5, etc.
It has very nice consequences in mathematics.
Do you know why? Because it is simple, popular,
school students can understand it's meaning.
It is a big challenge for human intelligence.
Not proved yet.
Best Wishes
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The number 1 is neither prime nor composite. why?
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@peter Kepp
You said
[There are no units -i and +i ] and
[The square root of minus one is solved by me. It´s the reform of mathematics.]
What? Are you sure?
Do you know what Integral domains are? Euclidean domains?Unique factorization domains? Modular arithmetic? Elliptic curves? Gaussian Integers? Units? unitary divisors? Generalizations of Euler function?
P-adic integers? Cyclomatic integers?? Unique factorization domains?
Do you hear the proof of last Fermat's theorem? Etc.
Let me tell you something about the Euclidean domain of Gaussian integers:
Z[i]={ a + ib, a,b in Z }
The nunits are 1 , -1 , i , -i .
Primes in Z are not necessary primes in Z[i]
5 is prime in Z but 5 = (1-2i)(1+2i) is not prime in Z[i]
7 is a prime in Z and it is prime in Z[i].
I invite you to new horizons in analytic number theory.
Any introductory textbook in this field can help.
Best wishes
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Hello, I am facing some struggles with maths, gel elecrophoresis and my DNA samples. I need to use 1uL of 6x loading dye and MQ water to equalize DNA samples for GE. The average DNA sample load for GE well is 5 uL + 1 uL of loading dye + 4 uL MQ water, but I want them all to be even, like, for instance, 3,2 will need 1,8 MQ to reach the equality.
I got NanoDrop data (the concentrations are like 16,4 ng/uL, 13,4... and etc.), but I cannot reach my goal described above due to my problems with the logical chain of actions.
My DNA samples were washed with the elution buffer of 50 uL. I am not even sure if I am calculating the total amount correctly as well (it is a basic formula, but I guess that I am confused by the results I keep having, so I hope someone could help me to understand my issues and shed some light on the matter).
Thank you!
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Hi Polina, the simplest solution is, first fix the total DNA amount to be visualized in gel, i.e., 100 ng.
-Then calculate the amount of sample you need for 100 ng, if your concentration is 20 ng/nl, then you need
100ng divided by 20 ng/ul=5ul sample. if you have different concentrations, your sample volume will be different. i.e., 6ul, 7 ul...so on.
-Now 1ul of 6XLoading dye in each sample (depending on your sample volume you can increase Loading dye amount).
-Add distilled water to make 10 ul total volume of sample (if you have 6 ul DNA, add 1 ul loading dye, and 3 ul of distilled water to make 10 ul solution). You may scaled up like this way for all your samples.
-For gel electrophoresis, DNA Equal Concentration of Samples are important not the Equal Volume of samples.
Best wishes.
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I have read informative research paper on SWCNT and its mathematical equation. My work begin with implementing SWCNT FETransistor in comsol and observe the change in resistance by applying different voltage but after reading research paper i came to know that before designing directly in comsol I need to implement CNT equation in Matlab.
Kindly suggest me proper links to simulate those equation in matlab or few links of videos or research paper which help me to simulate SWCNT in matlab and COMSOL.
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Thanks kawsar I will try to have a look on it..
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Space-Filling curves like Peano, Osgood, Hilbert, Lance-Thomas ones.
Reference paper:
Hans Sagan, A geometrization of Lebesgue space-filling curve, Mathematical Intelligencer, Vol. 15, n. 4, 1993
Thanks.
Gianluca
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This is a great question. In addition to helpful answers already given, there is a bit more to add.
The following RG research project on Hilbert space-filling curves may interest the followers of this thread:
More importantly, see also
New Gosper space-filling curves are introduced in
More to the point, for a 2018 paper on space-filling curves, see
and the 2017 paper at
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Please refer to the following article for more details:
'The Fields Medal should return to its roots...' by Michael Barany at link: https://www.nature.com/articles/d41586-018-00513-8
Reference link:
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Grigorij Perelman is an excellent counter-example. A loner - as far as I can see - who happened to solve one of the toughest outstanding problems imaginable. Why is he not worthy? I wouldn't call him mainstream, by any means - none of the winners can be said to be mainstream. The claim made above is based on correlation - not causality - as there is no way it can be proven that the award has been given to someone based mainly on her/his sex, country, or university. It's bogus.
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The emergence of new infinite system determines the production of "new infinite set theory"--------The infinite set theory based on the classical infinite system is called "classical infinite set theory (the First Generation Of Infinite Set Theory) " while the infinite set theory based on the new infinite system is called "new infinite set theory (the Second Generation Of Infinite Set Theory)".
The same mission and same cognizing contents decide the two similarities between the two set theories.
1 The same qualitative-quantitative cognizing motivation and idea
It is a must to carry on the qualitative-quantitative cognizing activities on “infinite related mathematical things (such as elements in infinite sets and the quantity of elements in infinite sets)” by both new and classical set theories; especially in many practical quantitative cognizing operations, most “mathematical contents” in infinite sets are treated as “mathematical things with visibal and tangible quantitative nature and meaning” by both new and classical set theories.
2 the same quantitative cognizing tools
Both new and classical set theories use one-to-one coresponding theory and limit theory to carry on quantitative cognitions to those “infinite related mathematical things” in infinite sets.
It is these two similarities between new and classical set theories that decides many invaluableners intellectual wealth accumulated since antiquity in classical set theory are reserved in new set theory.
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Dear Geng,
I can't quite understand your language. The survival of Mathematical theories does not depend on their ages, but their consistency. This is why I cannot consider the terms "old" and "new" as logical axioms of validity.
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There seem to be a wide variety of shapes in the biological world . In 2d we have various shapes of leaves. In 3d we have anthills , trees , fruits and animals with different shapes. All of them are closed surfaces , mostly convex. The jack fruit has thorns on its surface . Why is this so? What is being optimized?How can we fit a mathematical function to describe these shapes? This is a general exploitative question and all are welcome to suggest views.
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This is a good question. From shapes and sizes of living things in nature, I will add behaviors as well, why they behave differently according to seasons, is survival and continuity in existence. As most of you pointed out, for instance the shape and sizes of trees in desert areas (tiny in an optimal way) are clearly indicative of a purpose driven natural process to optimize resources of water beneath and survive in the desert. For the actual sequential processes, the Fibonacci sequence is one vital process in which branches of brocolis, cabbages and others multiply. These acts and process are purely mathematical and the very reason we say nature is mathematical. Galileo here is a right person to mention, "The universe can not be read until we know its language in which things are written, which is mathematics"
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A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole numbers that can be divided evenly into another number. The first fewprime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.Numbers that have more than two factors are called composite numbers.
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Can any one suggest me any textbook or website for finding the most of the mathematical stuff related to Hyperspectral image Classification ?
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Dear Professor,
This website contains research papers in
Hyperspectral image Classification
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Dear friends:
The graph of the equation
f(x, y) = 0
gives rise to many interesting curves in the plane for different choices of the function.
One such choice of f(x, y) led me to the following graph of the equation f(x, y) = 0.
I have the following questions:
1) Can you name this geometric shape?!
What does it remind you of?
2) Any noticeable symmetry property?!
Thank you for your thoughts.
Best wishes
Sundar
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I thank all for your answers.
Especially, I like to thank Debopam Ghosh - it does look like the blade of an axe. Thanks a lot!
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For a Mathematics Postgraduate, who is interested in doing his PhD in areas related to Algebra and Analysis, what research field would you suggest. Preferably, the domain should be promising and relevant as per the current research interests of the Mathematics community in particular and the society in general, both theoretically and practically?
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This is a good question. In addition to the helpful answer already given by @ Romeo P.G , there is a bit more to add.
Rich sources of algebra in contemporary mathematics can be found in the following areas:
Homology Computation using Pyramids (HCP) leads to the study of generators of homology groups. For an introduction to homology theory, see Section 2, starting on page 4 in a 2006 Vienna University of Technology report:
A very readable introduction to computing generators of homology groups is given in Section 4.2, starting on page 7. Notice that HCP has a number of practical applications such as the computer vision and the study of digital images (sse, e.g., Section 5, starting on page 12 in the HCP paper.
Membrane Topology focuses on the study of f homological quantum field theories. For the details, see
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I have the following result (mathematical proof suppressed):
"In a one-dimensional real space, the number of points between any arbitrary point and its immediate neighbor is indeed infinite. "
I would like to know whether this result already exists in mathematics literature or not. If exists, then please provide me the relevant references. (The above result as it is is not Cantor's continuum hypothesis, but seems to contain it as a subset, which I haven't yet proved and work is in progress)
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It is a well known fact explainable via the notion of linear scale (used already in some answer above), which - being not sufficiently precise - can be (for didactical reasons) replaced by ruler, known from elementary geometry (see e.g.
for getting my understanding of the notion).
If one assumes that between every two different points on the line there is another third point, then the infinity becomes clear (without referring to much deeper axioms of the set theory). However, there are two axioms involved about the (mathemtical) line:
- any point B in the closest neighbourhood of a point say A is not equal A
- between every two different points on the line there is another third point
It is not sufficiently strict definition of the line, only an example of possible formulation of some possible postulates. For strict definition fulfilling standard requirements accepted by the mathematical community is much more complicated; getting into the details - indeed - one needs studying math for couple of years.
Another problem is, whether the mathematical line corresponds to the line or the real world; by some atomistic philosophers - it is not the same, if the atoms need to have some size greater than some minimal, be it 10^{-123} meter. And what is the unit meter? Which (non-visible) points should be taken as the base points. Again we are coming to postulates - this time about the real world.
I think that the main problem of this thread is the definition of infinity, and separation of mathematical from physical models, and many other meta-questions like:
How can be accepted someones (non-professional) ideas if they are not written in commonly accepted terms (by the professional readers)?
How to explain briefly rules of some domain to an outsider who is falsely convinced that he/she understands the domain sufficiently well?
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This is a question for Mathematicians and Mathematics lovers and the others!
This video may help every body to start.. https://www.youtube.com/watch?v=QYyuZ3_PQ4M
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Bourbaki was not an experiment, it was a PROGRAM. Program, on one hand, to unify mathematics and, on the other hand, to put it at the highest level of generality (or abstraction). None of these directions worked precisely as Bourbaki's members intended, as the development of mathematics in the recent 30, or so, years shows. Nevertheless, it was the most serious attempt in those directions since G. Cantor's revolution.
Definitely, "bourbakism" reflected on teaching mathematics in France. I have a book by G. Choquet on plane geometry intended as a high-school textbook. A very good idea, high level of abstraction, but only for good and very good students. On the other hand, as an undergraduate at Warsaw University in Poland, I was taught mathematical analysis based on the Dieudonne's book. Similarly, I was studying Bourbaki's book on real functions. The beauty of Boubaki's presentation is still stunning.
Speaking of logic, one should realize that the concept of mathematical logic, when Bourbaki started its activities before WWII, was is the making.
Except for Alfred Tarski, there was the largest group of other logicians in one place in the world (13 people, including two professors). BTW, it was Boleslaw Sobocinski (after WWII professor at the University of Notre Dame) who introduced the so-called "inverse Polish notation" to the world of computer science. This notation was earlier used by J. Lukasiewicz in his work on logic. Sobocinski was named the "father of computer logic" in the US. It goes away from Bourbaki, but is relevant.
These are my two cents on Bourbaki.
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I'm so eager to learn about micro-mechanics, however, I can't find a source that discuses it in a simple way. Most of the sources I found starts immediately with complicated mathematical equations, without introducing the subject. I would also appreciate it if you can offer me some advice about the knowledge that I need to acquire before exploring micro-mechanics.
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" It serves primarily as a graduate level textbook, intended for first year graduate students ..." For you - Chapter 1: Introduction (1,684 KB):
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I have two independent groups and for calculating differences in variance I want to use VR (variance ratios):
VR = variance of group A / variance of group B
So if it's correct, how I should calculate the standard error of VR? And is there a way for interpreting VR (e.g., it is small, large, or significant)?
Thank you in advance,
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Isn't it urgent to simlify?
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The long history of mathematics generally lacks a distinction between pure and applied maths. Yet in the modern era of mathematics over, say, the last two centuries, there has been an almost exclusive focus on a philosophy of pure mathematics. In particular, emphasis has been given to the so-called foundations of mathematics — what is it that gives mathematical statements truth? Metamathematicians interested in foundations are commonly grouped into four camps.
Formalists, such as David Hilbert, view mathematics as being founded on a combination of set theory and logic (see Searching for the missing truth), and to some extent view the process of doing mathematics as an essentially meaningless shuffling of symbols according to certain prescribed rules.
Logicists see mathematics as being an extension of logic. The arch-logicists Bertrand Russell and Alfred North Whitehead famously took hundreds of pages to prove (logically) that one plus one equals two.
Intuitionists are exemplified by LEJ Brouwer, a man about whom it has been said that "he wouldn't believe that it was raining or not until he looked out of the window" (according to Donald Knuth ). This quote satirises one of the central intuitionist ideas, the rejection of the law of the excluded middle. This commonly accepted law says that a statement (such as "it is raining") is either true or false, even if we don't yet know which one it is. By contrast, intuitionists believe that unless you have either conclusively proved the statement or constructed a counter example, it has no objective truth value. (For an introduction to intuitionism read Constructive mathematics.)
📷
Plato and Aristotle as depicted in Raphael's fresco The school of Athens.
Moreover, intuitionists put a strict limit on the notions of infinity they accept. They believe that mathematics is entirely a product of the human mind, which they postulate to be only capable of grasping infinity as an extension of an algorithmic one-two-three kind of process. As a result, they only admit enumerable operations into their proofs, that is, operations that can be described using the natural numbers.
Finally, Platonists, members of the oldest of the four camps, believe in an external reality or existence of numbers and the other objects of mathematics. For a platonist such as Kurt Gödel, mathematics exists without the human mind, possibly without the physical universe, but there is a mysterious link between the mental world of humans and the platonic realm of mathematics.
It is disputed which of these four alternatives — if any — serves as the foundation of mathematics. It might seem like such rarefied discussions have nothing to do with the question of applicability, but it has been argued that this uncertainty over foundations has influenced the very practice of applying mathematics. In The loss of certainty, Morris Klinewrote in 1980 that "The crises and conflicts over what sound mathematics is have also discouraged the application of mathematical methodology to many areas of our culture such as philosophy, political science, ethics, and aesthetics [...] The Age of Reason is gone." Thankfully, mathematics is now beginning to be applied to these areas, but we have learned an important historical lesson: there is to the choice of applications of mathematics a sociological dimension sensitive to metamathematical problems.
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Dear i want to write a thesis of phd maths in the area of fluid mechanics for that we have to write a synopsis . I am requesting to know a problem in which can i research.
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You will find it hard to be successful if you do not have a thesis advisor with experience in the area. If you do, you need to talk to him or her and trust their intuition and experience in what is a good problem in the thin area between the trivial and the impossible and that fits your background and skills.
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For example, a few decades ago it was unimaginable perform statistical works without having a broad domain of mathematics, but now everybody uses it only following the instructions of a SPSS program.
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Dear Jesus Retto,
I have been specializing in AI for years now.
YOU CANNOT DO AI WITHOUT MATHEMATICS. WE ARE EVEN JUST LOOKING FOR THE MATHEMATIC MODEL AND WE WORK IN THE MATHEMATIC LANGUAGE.
EXCEPT IF YOU JUST WANT TO KNOW WHAT IT IS.
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"It is widely accepted that there are no inherent gender differences in mathematical ability or intelligence" Sunday Times Jan 21 2018 p5.
"Differences in intelligence have long been a topic of debate among researchers and scholars. With the advent of the concept of g or general intelligence, many researchers have argued for no significant sex differences in g factor or general intelligence[1][2] while others have argued for greater intelligence for males.[3][4] The split view between these researchers depended on the methodology[1] and tests they used for their claims.[5]... Some studies have concluded that there is larger variability in male scores compared to female scores, which results in more males than females in the top and bottom of the IQ distribution.[8][9] Additionally, there are differences in the capacity of males and females in performing certain tasks, such as rotation of objects in space, often categorized as spatial ability." Sex differences in intelligence Wikipedia Jan 21 2018
What the ST article probably meant is that it is widely accepted that this topic cannot be rationally discussed in the popular media.
This is a highly contentious issue, but surely society would greatly benefit from knowing the answer. For individual researchers, however, their careers and reputations could be trashed by studying this topic. I heard a very highly cited professor of psychology say that his wife had begged him not to give the lecture that turned out to be a straightforward literature review of cognitive sex differences.
I am posing the question here as RG is one of the very few places that topics like this can be sensibly discussed.
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There is a huge amount of scientific studies that abusing (or misinterpreting) their results, it’s not impossible. These probabilities shouldn't stop scientific researches. Sex differences in neuropsychological abilities is a very important field of study in psychology that can support other psychological researches (e.g., in sampling) or can help us especially in education and our requests from each gender. An interesting point is that when it seems that males are better in some abilities, females sound better in some other.
Regard,
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I have time series data from multi channel EEG. I am looking at various symbol based complexity measures. As a preliminary step I have to convert my time series to symbols based on some logic (as simple as order dynamics or zero crossing)
I am looking for better methods/algorithms to generate symbols from EEG time series.
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Hello,
have you looked at SAX ( Symbolic Aggregate approXimation, invented by Eamonn Keogh and Jessica Lin)?
You may find the info and all references at http://www.cs.ucr.edu/~eamonn/SAX.htm
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I obtained a Power length relationship formula
V=5.5* (0.62*L + 3*P/100)^(1/2) .
L = distance in km
P= Power in kW
V= Voltage in kV
When I applied it to my case study it proves inaccurate.
Please does anyone know of any other formula with similar relationships.
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Sufficiently answered,
A caution, earlier empirical formulae were voltage regulation based / loss based / temperature rise based/criteria applicable for radial lines, single m/c infinite source or long lines with ideal voltage sources. In integrated network with FACTS controllers, voltage and line length relationships have lost significance. For HVDC for example length is no limit and voltage options are based on choice of device and over all economy.
For cables, yes reactive power continues to dictate length and reactive compensation, and mechanical handling etc.
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The major concern is how sensitive the AR model to data non homogeneity.
Kindly, I need some references.
thanks in advance
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Autoregressive (AR) modelling is based on assumption of stationarity which implies homoscedasticity and constant mean. Heteroscedasticity makes AR modelling unreliable for forecasting. To study the sensitivity of AR modelling to heteroscedasticity can best be done by simulation.
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mathematics
log
exponent
infinity
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Hi,
the value of log(0) depends on the base of the logarithm!!! log(0)=−∞ if base>1 (the usual cases of base= e, 10 or 2.). But if base<1, log(0)=+∞ and if base = 1, log(0) is not defined.
Regards,
Fabrizio
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I want to interpolate the amount of product formed (as concentration or % of conversion) vs reaction time in a biocatalysis process. The fitting equation should have as (y) the amount of product and as (x) the reaction time. I thought to use as the fitting equation the integrated form of the M&M but I am not able to find the correct mathematical form. Or should I use another equation?
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Without any knowledge about the experiment parameters i can only guess which equation might suit your problem.
Having the product [P] as (y) results in some pretty ugly equations most of the time. I'm assuming no inhibitory effects.
[P] = [S]° - Km * W { X }
or alternatively (for the amount of conversion)
[P]/[S]° = 1 - Km/[S]° * W { X }
where [P] is the concentration of product P and [S]° is the initial concentration of the substrate S.
W is the Lambert-W function (or prodlog). You can try
X = [S]°/Km * exp[ ([S]°-vmax*t) / Km ]
as an argument for that function. I hope your program can fit this prodlog-function.
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In Taguchi’s optimization, for calculating S/N ratio (Smaller-the-better), we use the formula.
S/N = -10Log10[mean of sum of squares of measured data]
In this formula, why the term ‘-10 Log10’, whether it has any mathematical derivation/clarification for this method? Also what is the meaning/significance of DOF in Taguchi's design.
Please share
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Thank you Fausto Galetto sir
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Do you find your students trying to stay away from complex mathematical solutions? what is the reason?
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Dear
So thanks
Insightful words
regards
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I think asking and formulating questions have a big impact on our lives, so I was wondering what techniques do you use to formulate your questions, and how much time you set for formulating the Question ?
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It is a very interesting question for me. I am taking part in RG question answer section actively from November, 2017. Still today I asked perhaps 75 questions. Some of them are coming in my mind as such. I got idea of some questions during giving answer of question of other RG members.
I am writing popular scientific articles from 2002. It may have some effect, I do not know.
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The fundamental defects in present classical infinite related science system have decided the barber paradox (one of the members of Russell’s Paradox Family) is really an unavoidable and unsolvable problem for present classical set theory.
In present classical infinite related science system, it has been admited that the concept of infinite is composed by both “potential infinite” and “actual infinite”. On the one hand, no one is able to deny the qualitative differences and the important roles “potential infinite--actual infinite” play in the foundation of present classical infinite theory system; on the other hand, no one is able to deny that the present classical set theory is basing on “potential infinite--actual infinite” concepts as well as its related whole present classical infinite theory system. The fact is: any areas in present classical infinite related science system (of couse including present classical mathematical analysis and set theory) can not run away from the constraining of “potential infinite--actual infinite” concepts-------all the contents in present classical mathematical analysis and set theory can only be existing in the forms of “potential infinite mathematical things” and “actual infinite mathematical things”. But, the studies of our infinite related science history have proved that no clear definitions for these two concepts of “potential infinite--actual infinite” and their relating “potential infinite mathematical things--actual infinite mathematical things” have ever been given since antiquity, thus naturally lead to following two unavoidable fatal defects in present classical set theory:
(1)It is impossible to understand theoretically what the important basic concepts of “potential infinite” and “actual infinite” and their relating “potential infinite number forms, potential infinite sets” and “actual infinite number forms, actual infinite sets” are and what kinds of relationship among them are. So, in many “qualitative cognizing activities on infinite relating mathematical things (such as all kinds of infinite sets, elements in infinite sets, numbers of elements in infinite sets)” in present classical set theory, many people even don’t know or actually deny the being of “potential infinite” and “actual infinite” concepts as well as their relating “potential infinite number form, potential infinite sets” and “actual infinite number forms, actual infinite sets”--------it is impossible at all to understand clearly and scientifically the exact relationship among the important basic concepts of “infinite, infinities, infinite many, infinitesimals, infinite sets, elements in infinite sets, numbers of elements in infinite sets”, ... So, it is impossible at all to understand clearly and scientifically all kinds of different infinite sets (such as lacking of the “’set spectrum’ for the overall qualitative cognictions on the existing forms of infinie sets”), elements in an infinite set (such as ”are the infinie related elements potential infinite mathematical things or actual infinite mathematical things, how they exist?”), numbers of elements in an infinite set (such as ”are they actual infinite many or potential infinite many?”), the “one-to-one coresponding theory and operation” in infinie sets (such as ”are the potential infinite elements coresponding to potential infinite elements or actual infinite elements coresponding to actual infinite elements or actual infinite elements coresponding to potential infinite elements?”) ,... --------the unavoidable defects of qualitative cognition on infinite sets and their elements.
(2)First, it is impossible to understand whether the “elements in an infinite set, numbers of elements in an infinite set and all kinds of infinite sets” being cognized in present classical set theory are “potential infinite mathematical things” or “actual infinite mathematical things”, whether there are different theories and operations for “potential infinite mathematical things or actual infinite mathematical things”, and it is impossible at all to understand correctly (scientifically) in present classical set theory the natures of infinite related quantitative cognizing theories and tools (such as limit theory and the “one-to-one coresponding theory”) and their operational scientificities-------- it is impossible at all to master correctly (scientifically) the operational competences and skills of limit theory and the “one-to-one coresponding theory” thus resulting in no scientific gurantee for the operations of limit theory and the “one-to-one coresponding theory”; second, it is impossible at all to judge the scientificities of many infinite related quantitative cognizing activities in present classical set theory, people in many cases can only parrot every bit of what have been done by others or do as one wishes to treat many “not—knowing—what” infinite mathematical things with the unified way of “flow line” (any “infinite sets”, “elements of an infinite set”, “elements’ number of an infinite set” can either be “potential infinite” or “actual infinite”, neither be “potential infinite” nor “actual infinite”, first “potential infinite” then “actual infinite”, first “actual infinite” then “potential infinite”, ,,,), those believed and accepted Russell’s Paradox, Hilbert Hotel Paradox, Cantor’s operations of “cutting an infinite thing into pieces to make different super infinite numbers” and “proving the uncountability of real number set by diagonal method” as well as the famous “applying Russell’s Paradox to prove the Power Set Theorem” are tipical examples of “potential infinite--actual infinite” confusing operations--------the unavoidable defects of quantitative cognition on infinite sets and their elements.
We understand from our science and mathematics history, the fundamental defect in present classical set theory disclosed by the members of Russell’s Paradox Family is: looking for something belongs to an infinite set but is impossible to be found inside this infinite set--------no logic in our science can solve such paradox family as all the members of Russell’s Paradox Family are produced by the confusion of “potential infinite” and “actual infinite”.
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The power set theorem is no paradox. Its demonstration is also valid on finite sets.
Besides, the distinction between countable and uncountable sets is essential to measure theory which is part of analysis.
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Knowledge representation may be constructed as an attempt to formally capture and describe human sensory and perceptual data. But is knowledge representation via ontologies etc., anything more than the application of logic and mathematics?
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This is an excellent question. In addition to the excellent answers already given by @Dejenie A. Lakew and @Peter Samuels, there is a bit more to add.
By way of starting an answer to this question, consider the following threads (that includes this thread):
Logic and a wee bit of mathematics (set theory) dominate knowledge representation in
Mathematics has more importance in knowledge representation in
More to the point, it is apparent that knowledge representation is not merely an application of logic and mathematics. Instead, logic and mathematics provide a concise language as a means of expressing knowledge, which is something quite different from logic and mathematics.
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We may share instrument and compare data with ours.
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This is a worthwhile question with many possible answers. In addition to @Amir W. Al-Khafaji's very interesting answer, there is a bit more to add.
In North America, science, mathematics and technology are mixed together. When that mix becomes dominated by technology, there is a tendency for students to become too dependent on what the technology tells them.
In Europe, the situation varies from country to country. In Italy, for example, classical education in science and mathematics is more important than technology. In that case, the potential for the birth of great scientists and mathematicians is greater than it is in North America.
The prevalence of classical education is also very high in universities in the Middle East. The situation is very mixed as we move towards Asia. For example, students in Mathematics in Pakistan receive very high level training. Perhaps the followers of this thread can comment on the situation in Taiwan, China and India or in Korea and Japan.
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