Science topics: Mathematics
Science topic

Mathematics - Science topic

Mathematics, Pure and Applied Math
Questions related to Mathematics
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I am looking for compact formula for approximation of Mittag Lefller function.
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See the attached file of Prof. J. C. Prajapati.
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I want to calculate properties of metal foam by a mathematical formula without destruction of material and without use of any software is it possible
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May be the following papers help you, hope
(1)Manufacturing routes for metallic foams
John BanhartJournal:JOM Journal of the Minerals, Metals and Materials SocietyYear:2000
(2)Metal foams: a design guide: Butterworth-Heinemann, Oxford, UK, ISBN 0-7506-7219-6, Published 2000, Hardback, 251 pp., $75.00
Michael F Ashby, Anthony Evans, Norman A Fleck, Lorna J Gibson, John W Hutchinson, Hayden N.G WadleyJournal:Materials & DesignYear:2002
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To integrate a mathematical function from -inf to inf in MATLAB, I am using from trapz but i am finding it difficult as the variable like d(X), X has to be like ( -1000,1000,2000), but since i have to integrate it from -inf to +inf, if you have any suggestions to look into please let me know
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Good question...
That should help, there are some good examples
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33, is a number surrounded by a special mystique. For many years, 33 has fascinated the mathematical community by starring in one of the apparently simpler cases of a diophantine equation, but which is nevertheless pending resolution.
Diophantine equations are defined as “polynomial equations that involve only sums, products and powers and in which both the coefficients and the only valid solutions are whole numbers.” In short, nothing less than the ABCs of mathematics.
It might seem easy to express the number 33 as the sum of the cubes of three whole numbers – that is, to find a solution for the equation a3 + b3+ c3= 33 – but no one had yet succeeded since 1955 when mathematicians set out to solve this mathematical mystery.
This challenge has been on the table since the 3rd century AD, when the equations were enunciated by the Greek mathematician Diofante of Alexandria.
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33 is not a Lucky number, as you may check:
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mathematical solution , please find attached file
computer vision , linear algebra , mathematics , grey level co-occurrence matrix
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I hope that the attached article helps you to do your assignment.
Best regards
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The article is in French with the title "essai sur le probleme des trois corps".
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Could you paraphrase your question so that it can become clearer.
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Mathematics is crucial in many fields.
What are the latest trends in Maths?
Which recent topics and advances in Maths? Why are they important?
Please share your valuable knowledge and expertise.
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For me, as well as for majority of other researchers, Mathematics is the language of Science!
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this is axiomatic set theory . these axioms are needed for set theory and not for mathematics. so can we avoid them since the involve use of predicate and property. will experts guide in detail. can the use be restricted by using a mapping rather than property or predicate notion ??
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You mentioned in your question that "these axioms are needed for set theory and not for mathematics", but this is not a simple claim.
Separation and replacement axioms are needed for establishing many important results dear to mathematicians. For instance, it is fundamentally necessary to prove recursion theorem for natural numbers. Replacement, on the other hand, is necessary for establishing transfinite recursion.
(Note: one do not need separation, for it is provable using replacement)
Further, you asked about using mappings instead of properties. This is indeed possible for replacement:
One can use functions directly in replacement axiom.
Replacement: if F is a function and A any set, then {F(x) | x in A} is a set.
However, the stronger version would be provable using the other axioms of ZF and the weak version of replacement.
Strong replacement:
If F(x, y) is a property the behaves like a function, then for any A, {F(x) | x in A} is a set.
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In the chapter Constructible Sets of Set Theory: Third Millenium Edition (Thomas Jech), Jech defines Godel operations for building the contructible universe. This can be seen as a strategy for considering the generation of sets as operations. This may interest you.
About your question: I keep hearing that some subtheory of "hereditarily finite" set theory is OK that way, but I have only a fuzzy idea what it is and am too lazy to look it up ...
Hereditarily finite sets axiomatization is known as the 'set theory equivalent of peano arithmetics'. These theories are very closely connected: they are bi-interpretable. The idea is: you remove the infinity axiom, say that every set is finite and that every member of each set is finite. In this theory, the axiom of separation and replacement become the equivalent of the axiom of induction in arithmetics.
Notably, it is known that ZF can provide a model construction for PA and thus it can provide a model construction for this set theory. Using completeness theory for first order logic, it means that ZF proves consistency of this theory.
But, this is even more general. ZF has a property called reflection. It means that ZF provides truth predicates for any set-size part of itself. In particular, the class of hereditarily finite sets is a set in ZF. Therefore, ZF provides a truth predicate for it, i.e. ZF proves the consistency of hereditarily finite set theory.
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As "the first generation of infinite set theory" is based on present classical infinite theory system, contradictory concepts of "potential infinite” and “actual infinite" make people unable to understand at all what the mathematical things being quantitative cognized in set theory are-------- are they "potential infinite things” or “actual infinite things " or the mixtures of both or none of both? People have been unable to understand at all what kind of relationship between the quantitative cognizing theory and the unavoidable concepts of "potential infinite, actual infinite" in set theory: If the mathematical things being quantitative cognized are "potential infinite”, what kind of "potential infinite” cognizing idea, operations and results should people have; if the mathematical things being quantitative cognized are "actual infinite”, what kind of "actual infinite” cognizing idea, operations and results should people have; if the mathematical things being quantitative cognized are the mixtures of both or none of both "potential infinite” and "actual infinite”, what kind of mixing cognizing idea, operations and results should people have? Is there "one to one correspondence" theories and operations for "potential infinite elements” or “actual infinite elements" or the mixtures of both or none of both? Why?
As it turns out, the quantitative cognizing theories and operations (including the theory and operations of one to one correspondence and limit theory) for those infinite related mathematical things in "the first generation of infinite set theory" are lack of scientific foundations: It is impossible to know at all what the relationship among all the quantitative cognizing behaviors in infinite set theory and the concepts of "potential infinite” and “actual infinite" is and how to carry out scientific and effective operations specifically to different kinds of infinite related mathematical things. Therefore, it is very free and arbitrary for people to conduct quantitative cognitions to any infinite related mathematical things in "the first generation of infinite set theory" : It can either be proved that there are as many elements in Rational Number Set as there are in Natural Number Set or that there are more elements in Rational Number Set than there are in Natural Number Set; the T = {x|x??x}theory can either be used to create the Russell’s Paradox or to create "Power Set Theorem", make up the story of “the Hilbert Hotel forever with available rooms” ------- strictly make all the family members of the Russell's Paradox mathematicization and turn all the family members of Russell's Paradox into all kinds of Russell's Theorem; ... However, because it has nothing to do with applied mathematics, it is impossible to verify the scientificity of many practical quantitative cognitive operations and results in set theory. Therefore, there are far more unscientific contents in the quantitative cognitive process of present classical infinite set theory than in present classical mathematical analysis, because it can be more arbitrary!
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Dear Geng Ouyang,
Read word by word, paragraph by paragraph, chapter by chapter the book "Set Theory and it's Logic" by Willard Van Orman Quine, and you will understand my reaction to your writings. Good luck!
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What is the most accurate way of calculating wind direction (2D NESW), wind speed and vertical wind movement using 3D Ultrasonic Anemometer data in the form of uX-uY-uZ m/s (or U-V-W vector) data? I am looking for calculations, methods and/or sources for these approaches.
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I am planning to do research in text classification but , how can I improve the performance of the chosen machine learning algorithm by enhancing classification through derivation of mathematical equation.
I am not perfect in mathematics , can anybody suggest me, what i have to do to, what study i need to do in order to derive a new mathematical equation which improves the performance of a chosen ML algorithm .
Please help me out!!!!!!!!!!!
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Hi All,
Let us assume that we have two points, A & B; whereas A (X=8, Y=2) and B(X=3, Y=4).
I am trying to figure out if I can get any useful and rational "single value" from point A's X & Y together to compare it with the "single value" from point B's X&Y. For instance, to say 8+2=10, while 3+4=7 , that means point A has more impact than point B.
Please, try to support your answer with proper theory from any discipline.
Is there such a thing in math? If not, can be invented?
Thank you very much for your replies and time.
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Dear
Badeel Al-Mahdawiy
Your question is not complete. You are trying to find the (power ) or (measure) of some ordered pair (a,b) compared with other order pairs (c,d).
So, you need to add more information about your problem.
As an example, if we have a circle C(p,r) with radius r and center p, then we can measure the power of the point A, P(A) = d2 - r2 of any point A(a,b) concerning the circle C where d is the distance from the point A into the center P, and hence
we can compare the powers of distinct points.
P(A) has a geometrical interpretation,
If P(A) < 0, then A is inside the circle.
If P(A) > 0, then A is outside the circle.
If P(A) = 0, then A is on the circle.
I hope this discussion inspires you to find a way to present a suitable mathematical model for your problem.
Best regards
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In statistics, Cramér's V is a measure of association between two nominal variables, giving a value between 0 and 1 (inclusive). It was first proposed by Harald Cramér (1946).
It is actually considered in many papers I came accross that a threshold value of 0.15 (sometimes even 0.1) can be considered as meaningful, hence giving hints of a low association between the variables being tested. Do you have any reference, mathematical foundation or explanation on why this threshold is relevant ?
Regards,
Roland.
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The way I like to think about statistical analysis is in three parts: 1. Statistical significance ( p-value ). 2. Effect size. 3. Practical importance. The results in 1 and 2 inform 3, but there's no magic cutoff in 1 or 2 that can determine 3. Practical importance can take into account financial considerations, moral considerations, feasibility. We try to use p-value cutoffs and standard interpretations of effect size statistics to provide rigor to our conclusions, but the reality is that it all comes down assessing the results in a practical context. That being said, it's fine to say p < 0.05 is "significant", Cramer V of 0.3 is "medium", but then the hard work is assessing the practical importance.
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How to estimate the resonating modes by looking surface current in CST Microwave studeo ? I am attaching a surface current Image. I am not able to determine the higher order modes here at 40 G Hz. The fundamental mode is at 6.8 G Hz i.e. TM10 and matching to mathematical calculations.
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From navigation tree go to
2D/3D results--->Port Modes--->Port
Click on e1, if it is perpendicular to direction of propagation,than it's TE. As well as you will see the mode type (wheather TE/TM/TEM) will appear at the left-bottom corner of the screen.
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Please give a mathematical description
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There are multiple ways of doing so:
* Train the model to generate point forecasts, and then use simulations of multiple predictions to then calculate the prediction intervals. You can use MCMC or Dropout at prediction time to perform the simulation. Uber for example uses Dropout to calculate the uncertainty of their LSTM forecasts.
* You can train the LSTM to predict the parameters of a predefined distribution (Normal, Poisson, etc...) and then calculate both your forecasts and your intervals by sampling from the distribution. Amazon's DeepAR model uses this approach.
* You can also train the model to predict forecast quantiles directly - i.e. instead of the output of the LSTM being the mean or the median, the output can be the 85% quantile or the 95% quantile, etc...Amazon's MQ-RNN forecaster uses this approach.
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Chaos exists not only in the mathematical world, but also in real life. From the quote: "All creativity begins in chaos, progresses in chaos and ends in chaos" ( Ralph Abraham), it follows that creating starts from chaos. Since the connection between imagination and creativity is obvious, can a direct connection be made between chaos and imagination?
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Yes the imagination will be autom,atically converted to chaos thru the term MISUNDERSTANDING .
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I have a signals of force over a contraction period. I hoping to fit my signal to a mathematical function. I have been exploring models of the muscle. Does anyone have pointers, suggestions or advice?
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This really depends on how the force was measured and whether you have any additional information i.e. position, movement, other physiological signals etc.
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Perron's paradox, emphasizes the danger of assuming a solution to a mathematical problem exists, if the solution is actually nonexistent.
For example, if we assume the largest natural number exists and it is N, therefore if N>1, then N^2>N, and this contradicts our hypothesis that N is the largest natural number, hence the largest natural number is N=1, and this is illogical, hence it emphasizes the danger of assuming a solution exists while it is actually nonexistent.
I think there is a glitch under its underpinning. Let's ponder it again:
If you do not know what is the largest natural number, or you do not know the largest natural number does not exist, then you have no basis for your mathematical operations, and you have no insight on anything in the na?ve mathematics. You would not also understand the sign lesser or greater (< or >), hence you cannot conclude N^2>N, is a paradox (contradiction), because you have no insight on foundation of mathematics, it means you do not know natural numbers (alphabet of mathematics) and the sign > or < is meaningless to you and you cannot conclude N^2>N, is a contradiction because you cannot interpret the inequality N^2>N when you do not understand the comparison sign (> or <) and hence you are helpless!
Hence, Perron's paradox will tell you nothing about the largest natural number, it means Perron's paradox cannot lead you to contradiction and to get the result that N=1. It only makes you dizzy about your assumption, and can one by one rebuff all your assumptions and make you assume another assumption. You assume N=2, and again reach contradiction, and hence N=3, and so on, until you fathom the answer reaches infinity, or probably conclude it does not exist. Also using mathematical induction, you can move from N=1 to N=2 and hence forth from N to N+1, and conclude (limit N) goes to infinity hence the largest Natural number in infinity or actually does not exist.
Perron's paradox does not underline the danger of assuming a solution exists to a math problem, while it is actually nonexistent. It actually highlights the danger of not having any information, insight and realistic idea about a math problem. Consider you've assumed the solution to a differential equation is twice continuously differentiable (it means it is C2), whereas actually it is not C2, but it is probably C1. Then there is no danger to hinder your assumption, except you would probably face a contradictory conclusion. But this is no danger, only this contradiction would tell that you should modify your assumption and narrower your hypothesis, it means you should again assume another solution or hypothesis, probably you should revamp your hypothesis to C1 continuity of the solution to the differential equation under investigation. If this again led you to contradiction, you should assume the solution is discrete or else.
Hence, I think Perron's paradox is not resourceful, whilst it is only a sophistry, while too many mathematicians believe the proof for existence of a solution to a math problem is only mathematical detail, nothing helpful, as any problem would have some type of solution: continuous/discrete/smooth/jagged or so on…
Let me know your viewpoints on this discussion.
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Thank you for the comments. Regards.
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Hi!
I'm a math teacher.
I think and I believe that starting with kindergarten math and music must be almost a whole for the student.
In fact, the education without the culture, and the culture without the education are nonsenses.
So, the mathematics without the music and the music without the mathematics (in sense that the last is the music of the knowledge) are nonsenses too.
I believe in a future world which will understand such trues.
In short, I am very curious about this project.
Sincerely yours,
BNN
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Music activities as well as medicine, drama, etc. can have an extremely divergent charge for thinking. Children need to learn to think and more to create. Through music, they can put maths as I asked in a problem recently. Also through play, specially designed didactic music games I designed. If you are interested contact me freely.
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I'm interested in digging deeper about the question : What are the affordances of video to research and practice in education?
Please feel free to suggest a good paper on this theme. If it is connected to mathematics education, it would be even better...
Thank you for your consideration.
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Hello, Mathieu
I really like this chapter by Rogers Hall:
Hall, R. (2000). Videorecording as theory. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 647–664). Mahwah, NJ: Lawrence Erlbaum.
I appreciate his argument and examples that our choices of video recording methods are based in our theories of learning, activity, and mathematical/science practice. If you search in the same time period, you will find several related pieces published by Rogers and Reed Stevens. Much of that research was focused on mathematics and/or science learning.
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A reasonable method of defining an integral that includes the HK integral is to say a Schwartz distribution $f$ is integrable if it is the distributional derivative of a continuous function $F$. Then the integral $(D)\int^b_a f=F(b)-F(a)$. The resulting space of integrable distributions is a Banach space that includes the space of HK integrable functions and is isometrically isomorphic (with Alexiewicz norm) to the continuous functions vanishing at $a$ (with uniform norm).
If $F=C$ is the Cantor(the Devil's staircase) function and $\langle C'\rangle$ (we use notation $\langle C'\rangle$ to avoid confusion and in some situation $C'$) is the distributional derivative of $C$, then
$(D)\int^0_1 \langle C'\rangle=C(1)-C(0)=1-0=1$. Note that $\langle C'\rangle$ is a measure.
If here $C'$ denotes derivative in classical sense then $C'=0$ a.e. and $(HK)\int^0_1 C'=0$.
Suppose $F$ is continuous on $[a,b]$. Also suppose $f(t)=F'(t)$ exists except on a countable set $Q=(c_k)$; define $f$ arbitrarily on $Q$. Then
Then $\int_a^t f(x) dx $ exists and equals $F(t)-F(a)$.
See for example
"An Open Letter to Authors of Calculus Books". Retrieved 27 February 2014.
NEWTON–LEIBNIZ FORMULA AND HENSTOCK–KURZWEIL INTEGRAL ZVONIMIR \v SIKI\'C, ZAGREB
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Dear Miodrag,
Fist here is definition of the Henstock–Kurzweil integral :
The set of KH-integrable functions forms an ordered vector space and the integral is a positive linear form on this space. On a segment, any Riemann-integrable function is KH-integrable (and of the same integral).
For relation between the gauge integral and the Lebesgue and Riemann integrals, i suggest you to see links and attached file on topic.
Best regards
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I need a definition for a search.
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I have searched TIMSS high and low but cannot find out what they base their questions for students' engagement and attitudes in Maths on...is it the Self-Description Questionnaire? If so, is it Marsh's SDQ III (1990)
Many thanks
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Many thanks Jack Son
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What would be the logical mistake if indicial equation roots are actually different by an integer, but still mathematically one solves the equation following the route of non-integer difference, still evaluated at ordinary singular point? Suppose,the ODE is of second order. Would doing so might result in two linearly independent solutions whose one particular linear combination in a terminating series? I am following textbook on Ordinary and Partial differential equations by Dr. M.D. Raisinghania, but logic behind the method is not mentioned in the book.
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The logic is that we need to find two independent solutions. If they differ by an integer, one can be obtained from others by setting few zero coefficients on series. You can find the proof of it from Kreyszig Advanced Engineering Mathematics book (Appendix 4)
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While reading FEM by J .N Reddy I have notice that the shear strain term is taken as sum of (dw/dx) and Ф for mathematical convenience. I didn't understand why we should take slope in negative instead of positive. Cant we solve the problem in other way round?
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As Ф is negative around axis y, see the attached figure
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I was wondering if there is a connection between exponential function and reciprocal function, because if we look at the graph of reciprocal function, horizontal and vertical asymptote looks like exponential function.
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Using the Maclaurin power expansion, for |x| < 1
x/(1-x) = x{1+ x + x2 +..+ x?+..}
= x + x2 + .. + x? + ..
The exponential function has an approximation
ex = 1 + x + (1/2)x2 + (1/6)x3+....
Notice that
|ex - 1 - (x/(1-x))| = O(x2)
therefore, for small values for x
the given rational function is a good approximation of an exponential function.
Best regards
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I am looking for the mathematical formula for calculating the sample size.
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The following equation shows the formula
n=[ 4r (1-r) (f) (1.1)] / [(0.12r )^{2} p(n_{h})]
where: - n: the sample size required for the main indicator expressed by the number of households (see the following sub-sections below) Identify the main indicator). 4: - The factor necessary to achieve a 95% confidence level. - r: the expected or potential spread (coverage rate) of the indicator to be. Estimation 1.1: Factor to increase sample size by 10% for non-response. deff abbreviation: f - - 12r.0: maximum margin of error at a confidence level of 95%, defined as 12% of r (therefore representing 12% of the relative sampling rate, r.) - h: average household size. If the sample size in the survey is calculated using the baseline indicator based on the smallest target group by percentage of the total population, the accuracy of the survey estimates for most other key indicators will be better.
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what is the important factors that affects in student achievement in (TIMMS) in Eighth Grade Science in (Alain - Abu Dhabi )
Which Factors are more influential on student achievement in international study (TIMMS)?
Will these factors for mathematics differ from the factors for science on the one hand and will they differ for the fourth grade from the eighth grade on the other hand ?
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I develop only my MINT and MINT-Wigris program and have no testing except for problem solving in mathematics.
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Some time, I could not find the abbreviated names of some journals.
Is there any website contains all of them.
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No, but in a wide range..
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Nowadays, so many people are concerned with converting CGPA to Percentage on a 4.0 scale. There is a common method in which they multiply the CGPA by 25 since one CGPA is equivalent to 25 in Percentage system but this is clearly not scientific and accurate since the CGPA is calculated in a range base. So, I would be grateful if anyone can come up with a statistical or mathematical equation to convert CGPA to Percentage?
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Hello all,
The "multiply by 25" works so long as: (a) you've created a GPA that is weighted by the number of credit hours (as indicated in my earlier post); and (b) the maximum value of a mark is 4.0, since the conversion of proportion: GPA/max GPA to a percent (e.g., multiplying by 100) may be re-expressed as (100/4)*GPA, which equals 25*GPA. The fact that the full equation is algebraically equal in this case does not make it (the shortcut) incorrect!
I don't see that an alternate method is called for, but perhaps there is some other goal that Rebwar Mala Nabi may have had in mind that wasn't clear in the query.
Cheers,
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Is it possible to patent a mathematical (with algorithm ) model used for variables calculation of a chemical process, knowing that there are different models patented for the same chemical process ?
and what if my model is based on another model but with major equations modifications and improvements, can I still patent it ? (of course, while citing the prevuous work).
Thank you.
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Hey all, in order to open the discussion, you'll need to be aware of a few basic principles: a) patentability conditions, b) freedom-to-operate & doctrine of equivalence and c) exceptions of patentability.
a) a patent can be granted when your 'technical' invention is 1° new, 2° inventive and 3° industrial applicable. This third condition is 'here' important here because when talking about algorithms and mathematical formulae, they should be implemented in a particular application, such as a device, an apparatus, a process, etc. More particularly it is not enough to explain only the theoretical background, then you can choose for a scientific publication.
b) be aware of these already patented models, and you'll have to determine their scope of protection. When they claimed broadly and you use these already claimed features (in valid patents, covering your geographical market), you can be attacked for infringement, when entering these markets! So, you'll have to check your freedom-to-operate (FTO) for vending your product, with or without your own patent. Moreover, you can also be accused based on the doctrine of equivalence, when not exactly the same features of the patented technologies of others, but applying the spirit of invention even with your own slight differences. When you solve the same problem in a small different way, applying the fundamentals of the patented technologies, you'll need their authorisation to commercialize, like a license. A profound patent study is required here.
c) some 'non-technical' issues are not patentable, or at least open for discussion. This is i.a. the case with computer implemented inventions (software). This is mentioned in art.52 EPC (European Patent Convention): https://www.epo.org/law-practice/legal-texts/html/epc/2016/e/ar52.html. More specifically, art. 52 (2) (a) en (c) are important here. In the US: https://www.uspto.gov/web/offices/pac/mpep/consolidated_laws.pdf, art. 35 U.S.C. 101 and 103 are important. However, it could give you the impression that patentability is easier, less exclusions, etc... Case law in US states that abstract ideas and just data can be patented. Here again, the condition of a specific applications is required.
To finish my small intervention , a practical approach in a patent database. One of the patent classes that be used to search for models is: https://worldwide.espacenet.com/classification#!/CPC=G05B17/00. An example of a granted patent in this field is https://worldwide.espacenet.com/publicationDetails/originalDocument?FT=D&date=20190925&DB=EPODOC&locale=en_EP&CC=EP&NR=2556414B1&KC=B1&ND=4#. In order to select the granted patents (or thus those that are patentable by the EPO) you'll have to choose EPB in the field of the publication number and combining this with the CPC field: G05B17/low. Another very important Class is https://worldwide.espacenet.com/classification#!/CPC=G16C
Another example: https://worldwide.espacenet.com/publicationDetails/originalDocument?FT=D&date=19990811&DB=EPODOC&locale=&CC=EP&NR=0494110B1&KC=B1&ND=4#. When looking at the claims: claim 1 describes a process for the estimation of the physical parameters....using a computer. The classifications G06F17/50: https://worldwide.espacenet.com/classification#!/CPC=G06F17/50 (which is broader for multiple applications) and G06F19 can also be very useful to search. https://worldwide.espacenet.com/classification#!/CPC=G16B are related to ICT applications (bioinformatics).
So, to conclude: 1° try to find similar granted patents and have a look at the claims what they exactly claim, 2° detect patents that you can infringe and check their legal status (preferably with professional assistance) in the framework of your FTO. If you don't have FTO, your are blocked for your future steps, if FTO think about step 3, 3° ask for a patent professional to analyze your model in order to evaluate the novelty and inventive step, and the techncial application. When you solve the problem with a feature that is not obvious for a skilled person and you don't use the fundamentals of earlier valid patents, unless you can agree a cross-license or an agreement of use, patentability is on the floor. The best.
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I’m trying to make a 4:1 ratio of two solutions. One solution is a 5mL soln. at 20% (w/v) and the other is a 100mL soln at 10% (w/v), respectively. Normally this is easy when both concentrations are the same, but how do I do the ratio with different concentrations? A mentor is recommending diluting the 20% solution to 10%, but this would defeat the purpose right? I’m sure there is a mathematical formula that would make things easier to understand. Thanks all.
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Ok but you want the concetration of the chemical species in the two different solutions to be the same?
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I am looking for mathematical framework to calculate the co-ordination number of any element in a given compound.
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The coordination number of Al be 4, with whole charge -2.
The coordination number of Na be 1 since this is neutral.
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Every common source avoids the derivation, saying it to be too difficult. Where can i fiend volterra's original derivation? Knowing which mathematics would be necessary?
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In the inhomogeneous viscid Burgers' equation:
u_t+m u_x+λg(u)=νu_xx,
what is the significance of λ(coefficient of source term)?
what is the significance of m(associated to flux function)
Which of the following statements is mathematically correct?
1.When λ=0 the Burgers' equation becomes homogeneous
or
2. When g(u) tends to zero then the Burgers'equation becomes homogeneous
3.Both statement 1. and 2 can be used
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First of all, if you talk about the Burgers equation then m can only be the velocity u(x,t). The Burgers equation indeed is also rewritten with the convective term in the conservative form d/dx(u^2/2).
The source term is generally a forcing term such that the solution is statistically steady (in equilibrium) with the action of the diffusive term (RHS) whne periodic boundary conditions are prescribed. Without such forcing, the final solution would be the rest.
For homogeneity of the non-linear equation, any function u(x,t) satisfying u(λx,λt)=λnu(x,t)" where n is any integer, is a homogeneous function and differential equation which involves homogeneous function is called homogeneous differential equation.
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We know that mathematicians study different mathematical spaces such as Hilbert space, Banach space, Sobolev space, etc...
but as engineers, is it necessary for us to understand the definition of these spaces?
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Yes, we do have to know about the spaces, at least during our university studies, to enables us to expand our mind into abstact level, that will be very usefull for design activities
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In field theory, a primitive element of a finite field GF(q) is a generator of the multiplicative group of the field. In other words, α ∈ GF(q) is called a primitive element if it is a primitive (q ? 1)th root of unity in GF(q); this means that each non-zero element of GF(q) can be written as αi for some integer i.
For example, 2 is a primitive element of the field GF(3) and GF(5), but not of GF(7) since it generates the cyclic subgroup {2, 4, 1} of order 3; however, 3 is a primitive element of GF(7).
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can you using turbo pascal of simple programming..if have a problem can calling me or sending a message to help
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Where can I find validated protocols of teaching mathematics to healthy elderly and to elderly with moderate dementia as an independent variable in a longitudinal research study testing the synergy of cognitive training and physical exercise in preventing dementia or slowing the onset of dementia?
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Math protocols is a good start to snurge the memory , while unless there is a inner interest on individuals depending on format or framework of mathematic game.
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"PSNR of image increase an the entropy of image increase (in watermarking)". How one can prove this statement mathematically.
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Sanjay Kumar In my opinion, obviously PSNR is somehow proportional to the Entropy. But, I think if the PSNR increases (which means the image has lesser noise components) then Entropy should decrease. As noises only add randomness and undecidability to the original signal which in turn increases the Entropy. Therefore, I beg to differ with the statement "PSNR of image increase an the entropy of image increase (in watermarking)".
Please feel free to correct me if I don't get your question.
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Not established at all ! who is the first founder of algebra in mathematical history ? Websites below are very interesting but not satisfactory !
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The scientist is characterized in that they is interested in everything (“how?” Or “who?”). But the next questions are: "why?" and "for what?".
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Brain signals Analysis for fMRI images.
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From the literature I am familiar with, I can say that the most numerous are studies of brain activity in the reading process. This is probably due to the great interest in his disorders and the problems of dyslexia. I have practically never encountered such studies of brain signals when performing various mathematical tasks. At the same time, the claim is that the left hemisphere dominates this type of operation.
In your study, you should consider the different involvement of the brain departments in solving arithmetic (non-verbal) and verbally-assigned (text-based) tasks. I'm sure you'll find a difference in the organization of brain signals in these two types of tasks.
I wish you success and look forward to seeing the results of your experiment!
Neli
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Respected Researchers,
Is it right to submit a mathematical paper on arXiv before it is submitted to any journals? Please help.
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It is right also because, in case of unfair and predatory behaviour on part of the reviewers, or of anybody else who might have got a preview of your work, one can always point out to your arXiv preprint, which has an official submission date on which you can base a priority claim. On the other hand, people who engage in such behaviour would often also be ready to just copy from your arXiv preprint without quoting. Personally, I feel safer putting everything on arXiv. I also have several contributions which, for different reasons, were never published on peer-reviewed journals, but I am happy that they are accessible on arXiv all the same. It also gives immediate visibility to your work, since arXiv preprints pop up almost immediately on e.g. Google Scholar profiles, which saves one a lot of effort in terms of letting people know what one is doing.
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The musical melody is a structure consisting of a series of two types of entities: tones and pauses. Each tone has two properties: pitch and duration; each pause has one property - duration. According to these properties, they can compare to each other. The result of a comparison can be identity or difference.
Hypothesis: some combination of tones and pauses give us a sense of beauty, others don’t. Let us assume that beauty is proportional to the quantity and variety of the identity relations that the melody structure contains.[1]
Question: how can we determine the quantity and variety of identity relations in a given melody structure if we know that there are:
1. identity relations between individual tones and pauses;
2. identity relations between relations. (example: A and B are different in the same (identical) way as B and C; duration of A is half of the duration of B just like (identically) the duration of C is half of the duration of D; etc.)[2]
3. between groups of tones (and pauses)
And a second question: by which method can we create structures that contain maximum quantity and variety of identity relations?
*********
[1] About the reasons behind this hypothesis seePreprint , part 3.
[2] The structure must be observed throw time. If we play the tones and pauses of a beautiful melody in random time order the beauty will be lost. These types of relations allow us that.
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Quite true. There is a danger that rationalization of beauty can lead to its destruction. Explaining a joke just makes it not funny. However, curiosity, desire for knowledge, seems to be stronger.
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Dear Colleagues
Hope you all will be fine
The optical carriers can be written in mathematical form as shown in attached figure.Please let me know how we can write/show linearly polarized LP modes in mathematical form such as shown in attached figure?
I will be very thankful for your kind help.
Regards
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Let (X1, p1) and (X2, P2) be metric spaces and define metrics on X1 x X2 as follows: For x = (x1,22), y := (41,42) E X1 x X2, let (a) di(x,y) := p? (x1, y1) + P2(x2, y2), (b) dz(x, y) := V(21(x1, y?))2 + (P2(x2, y2))2. (i) Prove that di and d2 define identical topologies. (ii) Prove that (X1 x X2, d?) is complete if and only if Xi and X2 are complete. (iii) Prove that (X1 * X2, d?) is compact if and only if X, and X, are compact.
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I am just wondering why bachelor degree programme in Statistics is run in the department of Mathematics in some universities. Mathematics is a major tool in Physics, just like in Statistics, but I have never heard or seen any Mathematics Department running a bachelor degree in Physics. Is this practice doing more harm than good to the training of statisticians?
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Mathematics is a major tool in statistic
Yes, there are subtle differences between mathematics and statistical thinking. This writing distinguishes between the types of thinking during the test and the classification of mathematical and statistical tasks. In statistics, we use mathematics tools to solve problems (such as using algorithms and formula, theoretical probability models, and many forms of graphical representations). However, we rely heavily on data and context in statistical thinking. Statistical questions begin with a context in which individuals must make decisions about how to collect data to investigate problems. In some cases, data are already collected, and statistical questions stem from interest in the data set. In all cases, it is impossible to do a sense of statistical problem without knowing the details of the situation surrounding the data. Context can help shed light on why there are extreme groups or certain groups within the data or whether we should exclude outliers. For example, when studying the typical value of foot length, one can determine the extreme values ??by looking at the data. The age of people whose feet have been measured (in inches) may be noticeable contributing to understanding how data is disseminated and divided. If the data value of 26 inches is present, the context is the foot length of students aged 11 to 13 years may warrant a decision to exclude the value in the analysis and interpretation of the results. The question of measurement is another important distinction between statistics and mathematics. In mathematics, measurement usually refers to an understanding of units and accuracy in problems that deal with most concrete measures such as length, area and size. But, in statistics, measurement can be more abstract. For example, when thinking about how to measure intelligence or the speed of city life, there is no obvious way. Instead, researchers and statisticians should decide how best to measure what is being studied and often do it in different ways.
Variance and uncertainty in conclusions is another major difference between statistics and mathematics. In mathematics, the results are usually reached by deduction, logical evidence, or mathematical induction and usually there is one correct answer. Statistics, however, uses inductive inductive and conclusions are always uncertain. This is largely due to the interpretation of the context and methods surrounding data collection and analysis. It also stems from the nature of heterogeneity of problems. For example, “How old are teachers in my school?” Is a statistical question that predicts age variation. One will need to decide where to get data from (school teachers), to measure (age) and choose appropriate statistics (central tendency or variation measures) and graphical presentations to answer the question. In contrast, given the set of data
Teacher age points and asking students to find the average data set is not a statistical issue since the answer is definitely finding the number one using an algorithm. Another example in bivariate data is the appropriate linear function between height and weight. In mathematics, students are often asked to find a (deterministic) job through a set of points. In contrast, statistical questions focus on the level of certainty one can achieve when using the "most appropriate" function to predict one variable based on the other. In particular, one looks at the extent to which such extrapolation can be made based on the context and the amount of error associated with the prediction. In summary, some of the salient features we bring in statistical questions include the role of context, measurement, volatility, and uncertainty. Mathematics serves as a tool to help statistical inquiry questions, but not the only end of the statistics themselves.
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Is a physical basis that necessarily requires constancy of the speed of light a logical impossibility, or is the constancy of the speed of light the result of ideas not yet found or applied?
Does isotropy require constancy of the speed of light?
Jensen’s inequality for concave and convex functions, implies for a logarithmic function maximal value when the base of the log is the system’s mean. Mathematically, this implies that the speed of light must be uniform in all directions to optimize distribution of energy. This idea has a flaw. Creation of the universe happened considerably before mathematics and before Jensen’s inequality in 1906. Invert the conceptual reference frame and suppose that Jensen’s inequality is mathematically provable in our universe because it is exactly the type of universe that makes Jensen’s inequality mathematically true in it. A mathematical argument based on Jensen’s inequality goes around in a circle. Are there reasons, leaving aside Jensen’s inequality (or even including Jensen’s inequality), that require constancy of the speed of light?
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The discussion is about the light speed in the same medium(in general, the space vacuum). For example, does the light speed affected by the gravity
(Diffraction phenomenon) when passing near black holes? It has no meaning to study the light speed in a medium where light can not penetrate.
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I wanna calculate the value of Magnetic susceptibility and magnetic permeability form my characterization graph in origin. Is there any related video can you suggest??
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You can find out the permeability from the slope of the initial curve.
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If we have: z = f (x,y) and z = f (t), could you please answer to my below questions:
1) Can I say: x = f (t) and y = f (t)?
2) How can I analyze dz/ dt?
Thanks in advance for your help.
Best Regards
Gholamreza Soleiman
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Z is a function of x,y and z is also function of t.this is exists only when x,y are functions of t.
by total derivative we can analyze dz/dt .
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I have found that some mathematicians disagree with meta-heuristic and heuristic algorithms. However, from a pragmatic point of view such algorithms often can find high-quality solutions (better than traditional algorithms) when tackling an optimization problem but the success of such algorithms usually depend on tuning the algorithms' parameters. Why some mathematicians are against these algorithms? is it because they don't posses a convergence theory?
I am looking for different arguments on the situation.
Thank You!
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This question is similar to another one that I have seen. My response to that one was basically this:
1. I don't know any mathematicians who are prejudiced against heuristics per se. Many of them (myself included) use them regularly.
2. I do know a lot of mathematicians who are fed up with people claiming to invent dozens of "new" meta-heuristics every year (like harmony search or the bat algorithm), when really they are just old ideas expressed in fancy new words. Actually, many people in the heuristics community are unhappy with it as well.
3. I also know people working in combinatorial and/or global optimisation who are fed up with people saying "problem X is NP-hard, and therefore one must use a heuristic". This shows a breathtaking ignorance of the (vast) literature on exact methods (and approximation algorithms) for NP-hard problems.
(By the way, I agree with Michael's comment about "matheuristics" being a very interesting research direction.)
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I'm trying to design a wavelet. I extracted signal from transient for my wavelet. How to calculate coefficients of low-pass and high-pass filters for wavelet transform filter bank?
Maybe you can recommend some literature. I have read many literature about wavelet (Mallat, Daubechies and other mathematical books) but it's require deep knowledge in mathematics.
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Dear Valery,
To calculate the coefficients for a wavelet filter you can check:
To use custom wavelets for a filter bank you can check:
If you would like to like to read some additional wavelet literature together with some tutorials and practice assignments to better understand the "deep knowledge in mathematics," I would recommend:
Hope this helps!
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Many are saying that statistics is not a branch of mathematics. They say that statistics is just partly using mathematics while the other parts are on language skills especially in the interpretation of results.
Thanks.
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Preferably conference scheduled for early 2020.
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Also
ENUMATH 2019 — European Numerical Mathematics and Advanced Applications Conference 2019
30 Sep 2019 - 04 Oct 2019 ? Egmond aan Zee, Netherlands
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It would seem that the answer should be negative. However, if you think about it, the answer is not so obvious. Indeed, it is enough to take the vector field of accelerations (velocities) of particles as ether and we will get a mathematical definition of moving matter. Another question is where and how it moves this matter and why we do not see it, but this question may already have an answer1. Matter moves on the surface of the seven-dimensional sphere, and it is invisible because we move with it.
1)
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In simple words, the ether is a flow of particles whose motion obeys the principle of least action. This flow (ether) moves from a less stable position to a more stable position, and its geometry is given by minimal surfaces. In addition, minimal flows form topological singularities that are associated with elementary particles. Closed minimum flows (elementary particles) have different degrees of stability, and the minimum flow as a whole also fluctuates.
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Hello everyone,
I am thinking how the function should look like in order to generate this kind of curve shown below.
I am guessing the variables should be :
  • the radius that increases by "x" after every half-rotation,
  • how many rotations should take place before stopping.
Can anyone shed some light on this?
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t = 20:0.1:40;
x = t.*cos(t);
y = t.*sin(t)
plot(x,y)
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In quasicrystal, a different set of tilling can form the quasicrystal. However, most of the mathematical theory is trying to explain the quasicrystal tilling from one starting point and not from a different setpoint ( 2 or 3 points with some specific distance) to explain the tilling pattern, which these set points can expand at the same time. This will bring a question of what is the best tilling, packing density, the maximum area of QC tilling, ...
My question is how we can explain this by the relation between the degree of packing and tilling pattern?
Regards,
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this book is interesting
Metamaterials - Beyond Crystals, Noncrystals, and Quasicrystals – CRC-Taylor & Francis
Cui T.J., Tang W.X., Yang X.M., Mei Z.L., Jiang W.X., (2016)
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Let us have Minkowski space-time, which must be curved so that its metric does not change, and the coordinates cease to be straight lines. How can I do that? In this matter, a hint can be found in the mathematical apparatus of quantum mechanics. Indeed, if we take the Pauli matrices and the Pauli matrices multiplied by the imaginary unit as the basis of the Lie algebra sl2(C), then the four generators of this algebra can be associated with the coordinates of Minkowski space-time not only algebraically, but also geometrically through the correspondence of the elements of the algebra sl2(C) and linear vector fields of the 4-dimensional space. Then the current lines of the vector fields of space-time become entangled in a ball, which, when untangled, surprisingly turns into Minkowski space-time.
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In fact, in the previous post, the path from Dirac's quantum geometry to Einstein's geometry was indicated, and the mathematical apparatus for successfully passing this path must be found in the mechanism of local algebras of vector fields1.
1)
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Visuals are commonly used to help the low level students understand maths but who's to say it can't benefit everyone.
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We, humans, are essentially a visual animal. So, it is no surprise that everybody benefits from visual representations.
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If we have a fourth order polynomial as follows:
f(X)=a*X^4+b*X^3+c*X^2+d*X+e
how to make this equation on the following form:
f(X)=-(m*X^2+n*X+y)^2. I tried to extract the all terms of the second equation and compare the terms coefficients but it didn't work.
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To get your request you need the following conditions to be satisfied:
(3b2-8ac)/(bd-16ae) = (bc-6ad)/(cd-6be) = (bd-16ae)/(3d2-8ce)
with all coefficients a,b,c,d and e are negative values.
The proof ( Using the resultant techniques)
Example:
f(x) = -(x2+3x+1)2 = -x? - 6x3 -11x2 - 6x -1
a = -1, b = -6, c = -11, d = -6, e = -1
Check the conditions:
(3(-6)2-8(-1)(-11)/(-6)(-6)-16(-1)(-1))= 1
((-6)(-11)-6(-1)(-6))/(-11)(-6)-6(-6)(-1))= 1
((-6)(-6)-16(-1)(-1))/(3(-6)2-8(-11)(-1))= 1
Best regards
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The attached file is such a proof.
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The first file below is an updated published version of the above. If are interested in the impacts of this look at the other attached files.
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As we are aware of the importance of eigen values of matrix and also the mathematical efforts needed to solve for the same. But can we reduce those efforts or can we at-least generalize the method to compute all the eigen values. As we know:
1. power method is mostly used numerical method to compute eigen value , but as the size of matrix increases it's not smart approach to use this method.
2. Using characteristic polynomial , computationally, is even cumbersome approach because one needs numerical method to find the roots of characteristic polynomial.
Can there exist any algorithm which can be used on general matrix to find the eigen value??
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In addition to the helpful answers, I have a little bit to add. Mathematicians failed to find exact roots of polynomials with degree n > 4 ( Galois theory). Numerical approximations are a must. The study of autonomous dynamical systems or similar problems is necessarily based on the eigenvalues. But exact solutions are far-fetched, so they turn to study the qualitative behavior. Bounds of the eigenvalues are enough to predict the solution behavior of the whole system under discussion.
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"How teachers work to verbalize and individualize mathematics in preschool classes?"
this question posed in "mathematics in early childhood: An investigation of mathematics skills in preschool and kindergarten students."
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Thank you to all, so i should study more.
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I want to know the in-depth working of LCA (including mathematics)
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Hi,
LCA can be applied on mixture data. Regarding the resources, there are lots of textbooks about such models. One of the important references is:
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Division, Multiplication, Addition and Subtraction (DMAS) is the elementary rule for the order of operation of the Binary operations. What is the scientific and technical reason behind this mathematical myth though Multiplication before Division also gives the same result mostly? DMAS, a nice tool but has less convincing/appealing to admit its order of operation.
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I'm quite sure that mathematicians would have no problem with the 'DMAS rule', if it was actually a rule, which it isn't, and any decent mathematician would know this! DMAS is just another made up memory aide. One of the many acronyms taught around the world to help students remember the agreed upon standard for solving mixed operator expressions, the Order of Operations. The Order of Operations is not the product of actual scientific reasoning; it is not a mathematical theory or law. It is a globally agreed upon convention comprised of a series of steps that serve as a hierarchy of mathematical operators and processes. The Order of Operations may not have been devised as the result of science but they definitely follow a good deal of mathematical logic.
The mathematics behind the Order of Operations makes a lot of sense and it is not difficult to understand if it is well taught. Unfortunately when it comes to mathematics, teachers are all too often looking for shortcuts. Teaching students a mnemonic or an acronym is seen as being easier than explaining the actual mathematical concepts. The problem with doing this and teaching students the Order of Operations with a mnemonic or acronym is the likelihood of it going sideways. Students taught the acronym DMAS have a tendency to move through their lives believing that division takes precedence over multiplcation and is uniformly calculated ahead of multiplcation. Likewise many students believe that addition must be calculated before subtraction. The lack of a letter in DMAS that corresponds to both of the grouping symbols and exponentiation steps is also a problem because it leaves many students confused about the correct order to calculate expressions containing these.
MDAS is no better. It sees many people go through life believing that multiplcation has precedence over division and is uniformly calculated ahead of it. MDAS also results in the same problem as DMAS with its lack of a letter to represent the step of grouping symbols and the step of exponentiation. The other commonly taught acronyms: BODMAS, BEDMAS, BIDMAS, PEMDAS, GEMDAS and GEMS also have the potential to mislead. One of the biggest problems with the six letter acronyms is the tendency for people to incorrectly end up believing that they represent six steps when in fact they only represent four steps. As with DMAS and MDAS above, the position of the D and the M in the acronym leads many people to believe the letter that comes first (DM or MD) represents the operation that must always be done first.
The acronyms with an E, an O or an I also have the potential to confuse. For starters, the O that stands for Orders, is often mistakenly thought to stand for Of, Open, Off or Others which often leads people to errorously equate this step with 'opening' or 'clearing' any brackets or parentheses. Whereas this step comes after that of calculating operations contained in grouping symbols and as such has nothing to do with them. Another problematic factor with the E, the O or the I is that just the one letter is used to represent a multitude of operations that are all done as part of this step. This E/O/I step includes exponentiation and its inverse operations of radicals/roots and logarithms as well as unary operations like percentages, ratios, fractions and factorials and also functions including the trigonometric functions; sin, cos, tan, arsin, arcos and cot. The fact that this step uses one letter for multiple operations means there is often a gap in people's knowledge as they are unaware that it includes more than just exponents.
The use of B and P in their corresponding acronyms is potentially limiting too. Brackets and parentheses are just two out of a range of signs and symbols used to group operations. Other types of grouping symbols include braces, angle brackets, the modulus sign in absolute values, the vinculum as an extension of a radical to group any operations under it and the vinculum when used horizontally to separate any operations above it (the numerator) from operations below it (the denominator). Given the range of symbols used in this first step and their purpose of grouping the operations in an expression that need to be calculated as the first priority, I feel that the letter G, if an acronym is to be used, and the term 'grouping symbols' is a more appropriate representation of Step 1 in the Order of Operations.
As far as I'm concerned though, get rid of the acronyms and teach the Order of Operations in relation to the mathematical logic it follows.
Step 1 - Grouping Symbols
Calculate all operations grouped together and placed within an opening grouping symbol and a closing grouping symbol.
Step 2 - All Other Operations
Exponents and their inverse operations radicals roots and logarithms from left to right, factorials, percentages, fractions, ratios, functions. Multiple exponents uniquely go from right to left.
Step 3 - Multiplcation AND Division
Multiplcation and its equivalent inverse operation of division across the page in the order they appear from left to right.
Step 4 - Addition AND Subtraction
Addition and its equivalent inverse operation subtraction across the page in the order they appear from left to right.
Teaching the four steps above in this way should not be hard nor should it be hard for students to understand, at least not if they have been given a solid foundation in mathematics. A knowledge of inverse operations is clearly a prerequisite but that is easily taught and it should be taught regardless. Understanding that inverse operations are a version of each other, that they undo each other's calculations and are thus of the same precedence and therefore calculated with equal priority is essential to developing an actual understanding of the Order of Operations' structure. Another key concept to know is that multiplication is repeated addition. It is more powerful because it speeds up the addition process. The following addition: 2+2+2+2+2+2+2+2+2+2 uses 10 addends and 9 operators to get to the answer of 20. Multiplication is more powerful because of its repeated addition quality, it can reach the answer of 20 in the above using just 2 multiplicands and 1 operator like so: 10x2.
Exponentiation is to multiplication as multiplication is to addition. Exponentiation is repeated multiplication and as such it is more powerful again. The following multiplication: 2×2×2×2×2×2×2×2×2×2 uses 10 multiplicands and 9 operators to get to the answer of 1,024. Whereas the use of exponentiation is more powerful because it is repeated multiplication. It gets to the answer is 1,024 using just 1 number and 1 exponent like so: 21?.
The obvious logic is the the more powerful the operation, the higher it is in the Order of Operations hierarchy. And operations and their inverses logically go together too.
All you have to do is look around the web to see the mass confusion that results from incorrect knowledge of the Order of Operations and even more so the misuse of each of the acronyms discussed here.
6÷2(1+2)
-22
4+4-4
3÷3+3-3+3÷3
3+3×0+3+3÷3
These questions are frequently asked, hotly debated and more often than not the majority of answers given are incorrect. If only the Order of Operations was explained to students by knowledgeable teachers at the start of their mathematical education!!!
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What are mathematical measures used to measure human values?
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The link/reference supplied by Nishad T M and Keith Jones will, as I expect, be very helpful in understanding the associated matter.
Thanks to Nishad T M and Keith Jones .
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Chess Influence on Brain?
Want to transform your brain and make better decisions? Learn chess, a game synonymous with intelligence and brain power. It's been proven by numerous studies to help a variety of mind skills and has been growing in popularity around the world.?
According to a World-Chess-Federation-sanctioned YouGov polling studyfrom 2012, 70% of adults have played chess at some point in their lives, with the number of worldwide chess players estimated to be above 605 million. The percentage of active chess players stood at 15% in the US, 23% in Germany, and 43% in Russia. A whopping 85 million played chess in India, buoyed by the popularity of the former world chess champion Viswanathan Anand.?
Some more recent stats from the organizers of the 2014 world chess championship report?that?1.2 billion viewers watched that competition.?
How do you play chess? To be very brief: it’s a board game played by two opponents, each with 16 pieces, who use strategic thinking to put the opponent's king piece under an attack from which it cannot escape, called a “checkmate”.?
Chess is an ancient game, at least 1500 years old. It likely originated in India, derived from the strategy game chaturanga. Chess went through a number of forms but eventually its rules were standardized and world championships began to be held in the 19h century. The current world chess champion is Norwegian Magnus Carlsen, who recently defended his title against the Russian Sergey Karjakin. The women’s chess champ is Hou Yifan from China.
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I am working on updating my draft paper on a general concept of means.
One of the core failures of the drafts to date has been a lack of examples. There are plenty of examples which are in many ways just the arithmetic mean in disguise, but I have finally stumbled across an example that is not so.
Consider the set G = {x | x is an undirected graph, with potentially countably infinitely many points, and x^n = x, for all n in Z+} where multiplication is the Cartesian product of graphs. The set ignores duplicates which are simply isomorphisms of each other. The mean under Cartesian product exists and I'm pretty sure it is unique.
The question I have is how many elements are in G? I have a few examples already: a single point, countably infinitely many disconnected points, the infinite dimensional hypercube graph, and I believe the complete graph with countably infinitely many points. What other graphs fit? And is the set finite or infinite?
Of course any answers that I get that yield results will be cited in the final draft of the paper. I'm also open to a graph theorist that would want to work with me, though I understand that this result is unlikely given that I have not published in any peer reviewed journals yet.
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There is a lot of information about means in this entry --
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I wish to collect images of vehicle from radar (using radar imaging) I can see alot of journals talking about mathematics or theory of it but noonr gives practical tutorials on it ...can someone help me obtain radar images ?
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see Conference works
[IEEE 2010 International Conference on Artificial Intelligence and Computational Intelligence (AICI) - Sanya, China (2010.10.23-2010.10.24)] 2010 International Conference on Artificial Intelligence and Computational Intelligence - Inverse Synthetic Aperture Radar Imaging at Low Signal-to-noise Ratio
Ju, Yanwei, Yu, Li, Wang, Yang, Chu, Xiaobin
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I want to know how we can relate magnetostriction with Applied magnetic field mathematically? Or if there is any way to derive it using mechanical equations?
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Hi Dibyajyoti,
Strain = (Elastic Compliance * stress) + (piezomagnetic coupling * Magnetic field)
When stress is zero or constant, strain is proportional to magnetic field.
The piezomagnetic coupling is non-linear depending on stress and Mag field. However, it can be estimated by treating them linear.
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Assume that you are living in the time when the Gregorian calendar was introduced by Pope Gregory XIII in October 1582, when
Galileo Galilei was about eighteen years old. However, he was tried by the Inquisition, found "vehemently suspect of heresy", and forced to recant 1632, and then he spent the rest of his life under house arrest.
The most noticeable thing in this matter is that people of those years could realize the rotation and subsequently, they could calculate the rate and the duration of the rotation but what was not clear for them was what is rotating around what. At that time what would be your solution?
Now, if I can take this sad historical event as the fact, then I would ask myself if the integral theorem of Helmholtz and Kirchhoff plays a central role in the derivation of the scalar theory of diffraction along with the concept of the wave-particle duality, or it obtains the propagation of light in the diffracted space with an inhomogeneous refractive index?
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One more thing: In all this, mathematics is totally neutral. People often confuse "mathematical models" (sothing that a natural scientist does) with mathematics (which mathematicians do). Mathematics is not concerned with "truth" at all. All math theorems say "if A than B", but they NEVER tell you whether A is true or not. Math creates pre-fabricated logic containers, it is not concerned with the truth values of their "inputs".
Hence, you should re-formualate you question as "Do mathematical models present solutions for understanding the reality of the universe?". The answer is then obvious: some do, some don't. And often several model lead to the same conclusion. That's all, folks :-)
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I want mathematical answers.
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Hi, perhaps this is what are you looking for.
Book: Fast Multipole Methods for the Helmholtz Equation in Three Dimensions (Elsevier Series in Electromagnetism) – 27 ene 2005. Nail A Gumerov and Ramani Duraiswami
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If corresponding factorials and triangular numbers are added, the results form the sequence of numbers, {2, 5, 12, 34, 135, 741, 5068, 40356, ...}, which I call factoriangular numbers. In the list of the first few factoriangular numbers, I found three Fibonacci numbers: 2, 5 and 34. Aside from these three, are there other Fibonacci numbers in the sequence of factoriangular numbers?
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Now it is a a complete useful answer.
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THD = (sigma(V2^2+V3^2+V4^2+...Vn^2))0.5/V1 (1)
THD = (sigma(V2^2+V3^2+V4^2+...Vn^2))0.5/V1^2 (2)
Among these two equation which one is correct? Some journals mention (1), and others (2). For voltage profile management which equation is better?
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Change your equation (1) : THD = (sigma(V2^2+V3^2+V4^2+...Vn^2))0.5/V1 To :
  • THD = (sigma(V2^2+V3^2+V4^2+...Vn^2))^0.5/V1
then it will be OK. Please note the power symbol (^) before 0.5
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Development of a theoretical (i.e. Mathematical) theory from experimental/simulation results: relevant papers, links, and textbooks will be appreciated.
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In full agreement with all the others who answered the question:
"How can one develop a theoretical (mathematical) model from experimental / simulation results?"
I also say that when we study a new phenomenon (and not only then, but also when we want to obtain new information about a known phenomenon, possibly with higher-level applications than existing ones), it is essential to start from the experimental data. In addition, the theoretical models created should be taken into account, if any (at least not to reinvent the wheel ...).
The experimental data can be harnessed through: statistical theoretical modeling (as Bharat Soni shows) or dimensional analysis (Buckingham theorem, as Sanjiv Sharma shows). After validating these primary theoretical models (but often very useful in important applications of driving and optimizing dynamic processes), one can move on to trying to create theoretical models based on the laws of classical physics. These models should be able to use all the input and control data of the process used and to predict the output parameters of the system (modeled process). In addition, such models should give additional data about the phenomenon, data that can give new explanations, new parametric combinations (possibly optimal) that will improve the clit and quantitative process. I also do not exclude theoretical models that show that obtaining superior performances is impossible, or that the modeled process, for a long time of operation leads to negative irreversible processes for certain entities.
For example, in the Resistance of the materials the calculus relations were for centuries purely empirical. However, with these elementary models, the engineers (more art than calculation?) Has built gigantic bridges and cathedrals, temples, etc. When the classical mechanics and the mechanics of the continuous bodies were constituted as theories, the first improvements and optimizations appeared. Spectacular improvements and optimizations have emerged with the use of computers and numerical analysis (combined with superior statistics and stochastic models, etc.). But at the same time there were spectacular accidents (broken suspension bridges, collapsed domes, railway and aviation accidents).
However, experience dominates the world of high engineering performance. After hundreds of years of theoretical developments, in very high environments is used Reverse Structural Analysis ... Loads are measured (not given) are introduced into the systems of equations (for example), the displacements are calculated, and then the problem is solved by loading the system with the resulting displacements, to determine interesting physical characteristics at inaccessible points, etc. Isn't it great art to estimate loads in engineering for the last centuries or even millennia?
And to not be boring, I add a minor example I have been dealing with for the last few months: compressing and compacting granular materials and powders. Theoretical stage (with experimental origins) at the time we started:
Cardei P., Gageanu I., (2017), A Critical Analysis of Empirical Formulas Describing the Phenomenon of Compaction of The Powders, J. Modern Technology & Engineering, vol. 2, No. 1, pp. 1-20;
or
experimental stage:
Gageanu I., Cardei P., Matache M., Voicu Gh., (2019), Description of the experimental data of the pelleting process using elementary statistics, Proceedings of the Sixth International Conference "Research People and Actual Tasks on Multidisciplinary Sciences", June 12-15, 2019, Lozenec, Bulgaria, pp. 437-445;
and higher order models
Cardei P., A mathematical model for a process of compacting granular materials
Cardei P., Complex constituent equations for granular materials in compression processes,
The big questions in this branch are:
- How time can the theory and science be complicated yet, so that the components from which it is made, remain united and not yield , so that science can be mastered by the human mind?
-how long time, will humanity still think that it is rational to support a research that at each result sets out another 3-5 or more research directions needed (the more we know, the less we know ...?); some people might believe us dishonest people, especially as scientific texts are increasingly inaccessible to a growing part of humanity ...!
-How many people can understand the efforts required to obtain top results?
- the inflation of specific literature reaches quotas that mimic the growth of the population on Earth ... much more is written than read!
Regards
Cardei Petru
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I am aware that due to the properties of spinors, to return a spinor to its initial state by rotation, the spinor must be rotated by 4*pi radians, i.e. rotation by 720 degrees.
While I was taught the fact as a mathematical curiosity in my quantum classes, I still don't know what the physical ramifications of this are. What does this mean for spins in real space? Does this fact influence spin dynamics due to external fields and potentials? The cartoon for Larmor precession uses an arrow to represent spin that seems to act like any other normal 3D object.
What is the relevance of this 4*pi symmetry?
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As I remarked it is a consequence of the wave characteristics of motion, which requires two zeros per period, one to separate the periods, and one to separate the crest from the trough. Think of it this way. If you start the phase at zero and go around the circle with the phase increasing, when you get back to where you started, because there were no nodes on the way, you get to your first zero, but the phase is decreasing bu was always positive (the crest). Now you have to go through the trough, the negative phase. I am looking at this through the view of what physically happens. A spinor is a mathematical descriptor, not a physical thing.
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1.Understanding, Calculating, and Measuring Total Harmonic Distortion (THD).
Amplitudes of Harmonics of Distorted Sine Wave
Harmonic Amplitude
1 3.08V
3 0.308V
5 0.159V
7 0.090V
9 0.0487V
11 0.0253V
13 0.0164V
15 0.010V
How to generate a table like using voltage and frequency? what is the equation used for this table?
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THD = (sigma(V22+V32+V42+...Vn2))0.5/V1
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I am denosing an ECG signal using Adaptive filters, I am intrested in finding the SNR of the ECG signal before and after filtering.
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Hi,
actually a meaningful definition of SNR with respect to the ECG is not easy.
One way is described on physionet in the context of noise stress testing. You can have a look at https://physionet.org/physiotools/wag/nst-1.htm in the section "Signal-to-noise ratios".
Greetings, Sebastian
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I am lottle bit confused about that how permittivity of a material decreases with an increase in frequency of the voltage source? Kindly, explain this concept with some example or mathematical.
Thanks
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The complex dielectric constant is ability of material to irradiate or absorb electromagnetic energy of EM wave.
As frequency increases loss of energy more and hence dielectric decrases
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In my research work, I want to construct mathematical programming model for a supply chain network problem. I have assumed production cost to be linear in nature. Is this assumption correct or should I change this assumption. Please suggest with valid description.
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Dear Sir, it depends so many factor and environment like demand, product nature and product life cycle, it may be linear, quadratic, exponentially, stock-dependent etc.,
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Ho to differentiate mathematical analytics from mathematical analysis is a big issue for developing mathematical analytics.
Can you provide an answer to it?
Prof Zhaohao Sun
2019-8-2
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Wow. It is beautiful.
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I do not know the definition of mathematical analytics. Can you help me?
Prof Zhaohao Sun
2019-8-1
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Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
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There are various behavioural activities of an insect. I wish to convert it to a mathematical representation where I can indicate that the insect prefers to a particular activity after the previous activity.
Will be very thankful!!
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You need to apply Markov chains; this may be a right approach for building a mathematical model.
Best regards
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I reject Cantor's infinite set theory as inconsistent (see The Countable-Infinity Contradiction ). Is mathematics more than the unbounded set of consistent definitions formed from the concept of 1?
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I mentioned in my previous answer the need of the dimension concept to build the geometry; this includes the points which are defined as objects that have zero dimension. To locate the position of the point, we need the algebraic system of numbers. For example, p = p(x, y, z) ∈ R3 where x, y, and z are numbers represents the length, width, and height.
Best regards
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Are citation chances for researches in pure sciences more likely than researches in humanities to hit a high score?!
Of course you'll get cited when you write a good research, but based on observation I noticed that researches in sciences like physics, biology, mathematics,...etc get more citations even though some researchers come from a not very robust academic background!
Thank you for sharing your opinion!
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In an ideal world that would be nice Muthana - but tradition dictates. It may be that humanities citation is harder to come by but it could be argued that it's more difficult to get published, in the first place, in the pure sciences. Of course, this is an over-generalisation - but could be a counter.
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I am struggling to solve the 4th order ordinary differential equation with a Gaussian function. I have attached one sample of equation where, A, B, and C are the const. coefficient.
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No problem, use the same service, for example https://www.wolframalpha.com/input/?i=exp(-x%5E2%2F2)
and you will find alternative representations, as well as series representations. Not sure will it be simpler for you or not, but again that service is FREE. Also not sure are there other similar free services...
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It is sometimes good to examine the progress in science, even for the most passionate topics such as quantum gravity
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Sergey
Im tired about this bla that the external world does not exist except of information about it.(ie. what you say about particles)
Information does not just generate itself spontaneously.
In any case you talk about philosophy, not about physics.
Maybe you can discuss what limits the information you can have, might be more productive.
Bell understood very well what is SR, and has written about it.
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What are the isometries of the Hilbert Cube I^\infty = the set of all sequences (x_i) such that x_i \in [0, 1] endowed with the metric
d((x_i), (y_i)) = \sum_{i=0}^\infty 2^{-i} |x_i - y_i| ?
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Do you know good references on the subject? I seems a question very innocent but it is very hard!
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Soil texture, determined by the measurement of particle size distribution, introduces three variables to create texture classes.
However, if we forget about the three fractions (clay, silt and sand), a the end of the particle sizes are distributed along a continuous axis (one dimension).
Could it be possible to derive a single number to characterize soil texture, to make whatever calculation more useful?
Some people use sometimes sand content, or clay content, reducing the (somewhat arbitrary) three dimensions of texture to a single value, but there should a mathematically more acceptable way to reflect soil particle size distribution withtout loosing too much information?
What do you think?
The average or medial particle size could perhaps be more interesting? Or some sort of the average particle size of the interquartile of the distribution (if it is unimodal...)? Any thoughts?
Not being able to reduce soil texture to a single value often feels constraining to make relevant data analyses...
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Soil surface area is an important property of soil which governs surface bound processes like adsorption- desorption, synthesis of new mineral phases etc.. However, processes like water movement , heat flow and gaseous exchange are controlled by relative proportion of different size soil separates. Therefore, in my view soil surface area alone may not help in characterizing soils for their physical and ion exchange properties.
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I am looking for the instrument itself with the reliability/validity data available. I am interested to see the link between growth/fixed mindset and mathematics performance.
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Am LOOKING FOR THE SAME TOO
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for more clarity.
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Dear Mr.swami
heat transfer due to the applications and conditions, depends on to many parameters. it is better to add some details to your question.
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how an SOC is find by a test machine any mathematical proof to get the exact SOC of a battery.
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This is worse asked as "how do we know variability exists". A variable is an intuitive concept, although it's full technical description is not necessary for a primary / elementary school child to learn how to use variables in function space.
We have dependent variables and independent variables, and clearly it means that which can be varied, but what creates variability?
In some descriptions of mathematics you'll find there is explained this idea that the null set is the basis of numeration, but 0 was invented long after numeration had transitioned from being invented to being discovered.
"A variable is a symbol for a number that is liable to change"
Yes, but what creates the variable? What allows for us to know this is a mathematically sound idea?
I learnt variables in grade 4, but I'd like to relearn them as a 4th year.
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Has Anyone realized that we cannot really measure many natural parameters directly ?
Before the "Digital Electronics" Paradigm came into Existence, it was Either Length of Angle which we measured. When Measuring Temperature or Pressure for example, we measured the Length of a Column of Mercury, Alchohol or some other Liquid, Solid or Gas.
When weighing objects using a Balance, we measured the Angle.
After Electrical of Electronic Technology came, we simply look at the Numbers Generated by a Monitor or Look at (or Again Measure) the Spectrum of Light either from Celestial Objects or the light w.r.t. the Chemical / Physical Processes here on Earth.
So without Direct Measurements, how many Variable Parameters are actually Realistic ?
Are we or Aren't we trusting technology too much ?
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Do you think scientists are more susceptible to concluding that a false positive is a real positive or that a false negative is a real negative?
As I understand,
A) A false positive is when a scientist concludes that an experiment/assay succeeded when actually it failed.
B) A false negative is when a scientist concludes that an experiment/assay failed when actually it succeeded.
A scientist can waste a lot of resources on a false positive if (s)he doesn't notice that the material (s)he is testing is not what (s)he thinks it is. All observations are irrelevant to what you think you are studying as well as anything you publish about it.
A scientist could dismiss a powerful medical drug by falling for a false negative. The drug works. You just didn't test its properties well never to return to it ever again. Are theorists more susceptible to falling for false positives and experimentalists are more susceptible to falling for false negatives, for instance? For theorists, maybe we talking about models more than assays.
Also do you think scientists are conditioned to look out for false positives or false negatives more so? Which one is more dangerous to science?
Nearly all experiments and theories require optimization so false positives and false negatives are certainly possible occurrences.
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