Science topics: Mathematics

Science topic

# Mathematics - Science topic

Mathematics, Pure and Applied Math

Questions related to Mathematics

Is there any relation between NPs size and energy band gap, I mean how the energy band gap vary with the nanoparticle size? please provide your answer with a mathematical relation if there is?

How I can get the inverse Laplace transform of

L

^{-1}((1/(s+a)^2)*F(s))where F(s) is variable function (we can say it is discrete and random)

OR how I solve this first order non-homogeneous differential equation,

y'+y = f

where f is variable function (we can say it is discrete and random)

Thanks in advance

Nasser

Wondering if there is even mathematical tables to help with word problems?

Is there any rapid publication journals that are indexed by SCOPUS in the area of Computer Science ,Mathematics, Applied Mathematics & Optimization

The prescriptive curricula indicate the evaluation standards on the one hand and on the other demand the teacher's evaluation of general and Niss competences for the secondary education stage.

Is not it contradictory? or is it complementary?

Calculus (Latin, calculus, a small stone used for counting) is a branch in mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change[1], in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient.

Historically, calculus was called "the calculus of infinitesimals", or "infinitesimal calculus". More generally, calculus (plural calculi) may refer to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, variational calculus, lambda calculus, pi calculus, and join calculus.

Dear Scholar

The following are FACTS:

1. Polygon based 3.1415926...has been thrust on circle as its Pi.

2.Pi has been called a transcendental number since 1882.

3. From 1882 we have been told that Squaring a Circle is an UNSOLVED GEOMETRICAL PROBLEM.

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4. Hippocrates' work has been ignored , although squaring of circle was done. It is a Historical Blunder.

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5. In Hippocrates period 500 BC , EXACT Pi Value was unknown.

However, he DID square a circle.

6. His work is PURELY THEORETICAL because of the unknown exact Pi value.

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7. With the discovery of the EXACT Pi VALUE in March 1998, (3.1464466...) Hippocrates" work has turned into a PRACTICAL WORK from then on wards.

8. Hence, HIPPOCRATES OF CHIOS IS THE TOP MOST MATHEMATICIAN IN THE WORLD ( He is already called A FOUNDING FATHER OF MATHEMATICS ) whether the Mathematical World accepts it or not.

Suppose we have a set of players, i.e., {

*p*_{1},*p*_{2}, ...,*p*} and each player has three different strategies, i.e., {_{n}*s*_{1},*s*_{2},*s*_{3}}. They play*m*number of games. In each game, each player seeks to maximize its profit by selecting a strategy with highest playoff. The profit associated with each strategy is as follows.1) Payoff for selecting strategy

*s*_{1}is zero2) Payoff for selecting strategy

*s*_{2}is a real number, which is calculated using some formula*f*_{1}3) Payoff for selecting strategy

*s*_{3}is also a real number, however, it is calculated using another formula*f*_{2}I want to prove the existence of Nash equilibrium when all the players select one of the available strategies.

I have searched on web and found several documents, however, I couldn't get a clear idea to prove it mathematically.

Any help is deeply appreciated. Please let me know if I have missed any information. Thank you in advance.

I am currently analysing data on whether there is a difference in the level of understanding between maths and science using a sample of year 1, year 2 and year 3 students. I am also looking at whether the level of understanding improves across the year groups. I am running a mixed ANOVA, however my homogeneity of variances for science were violated. Can I run it anyway?

People usually say that the number greater than any assignable quantity is infinity and probably same in the case of -ve ∞.

We are dealing with infinity ∞ in our mathematical or statistical calculations, sometimes we assume, sometimes we come up with it. But whats the physical significance of infinity.

Or

Anyone with some philosophical comments?

- Zero because how come there is value for nothing?
- Infinity because how come there is a value for everything?
- Does the fact that we use
**Infinity**and**Zero**to express ideas mean that our mathematical system is flawed? Not necessarily in a bad way, maybe because there is no other way to express such ideas ,that we know of, other than using zeros and Infinities. - Isn't mathematics supposed to be the most determinist thing we know, how come its so uncertain?

Rubik's cube is a fascinating toy which involves transformations or permutations. I'm curious, what is the mathematical group of 3 x 3 x 3 cube.

What additional information does the phase measurement in a frequency-domain imaging technique provide compared with the continuous wave technique that measures only the amplitude of the diffuse light?

I find that having deep knowledge in other disciplines throws light on my core intellectual disciplines, history, psychology, etc, making me more aware of limitations of thought. For others, this may not help. For those involved with maths, knowing other disciplines probably has no or little affect on their insight into their core discipline.

What do you think and what is your preference?

I look for mathematical theory of Differential equations like

Picard–Lindelöf theorem and Carathéodory's existence theorem that deal with existence/uniqueness of differential equations. I hope some purely theoretical reference can address such theoretical methods not just applied methods.

How can we establish mathematical relationship between S11 and arbitrary geometry?

It is said that fixed point theory has lot of applications not only in the field of mathematics but also in various disciplines. Which one is the most important?

There are number of well studied mathematical and computational techniques used in the crypto analysis of public-key crypto systems?

Which are the most effective?

I want to predict the Passenger car unit (PCU) values of different vehicle types using ANN and ANFIS. Is it possible to return a series of equations in the output layer of ANN (or) ANFIS model?

I am looking for recent subjects in the area of using Markov chains in queueing models or theory for the thesis of a master student in mathematics.

Thanks a lot in advance.

Mohamed I Riffi

How wind speed is mathematically related wind power???

Dear All,

x/y=d*exp(-p*t)/(d+p)

In the above equation

known values= x/y(ratio 4/2=2), d=18.2 and t=6.25, need to calculate "p". One way is to adjust the "p" until you get the x/y=2, for this way i need to go manually onebyoine. I have 400 for all this I have to go manually and adjust the "p" values.

Is there is a way to rearrange the equation or excel method to back calculate "p" values automatically. I would highly appreciate any help and suggestions.

With many thanks

Vince

By "gentle" I do not mean that I am afraid of formulas - I studied mathematics myself. But I would prefer literature that may serve as a first course in Bayesian statistics.

- Is there anything such as true randomness, or is it just a delusion? If yes, why? If not, why?
- Is there a branch of knowledge dedicated to only the study of randomness?

**What are some of the most important formulas in mathematics?**

- Does such an equation exist?
- Can it ever exist, or is it mathematically impossible?
- Is this equation relevant to
**Chaos Thoery**and**Quantum Mechanics**? If yes how?

The equation I am seeking for behaves something like this :

f(1) = 2

f(1) = 8

f(1) = 2.4

f(1) = 9005

f(1) = 0

f(1) = 3

Please excuse my ignorance.

The present day theory of generalized functions does not allow the existence of powers of the Dirac delta. However, this technical infeasibility might not reflect the mathematical "truth". It would therefore be very interesting to see potential applications of such powers of the Dirac delta. It may point us the way out of this dilemma.

We understand from the infinite related mathematics history that in present classical mathematics (such as classical mathematical analysis and classical set theory) basing on classical infinite theory system, there has been an avoidless theoratical and operational defect whenever we conduct the quantitative cognizings to “infinite related mathematical things” with limit theory--------the confusions of “potential infinite, actual infinite” concepts and the absence of the whole “theory of infinite mathematical carriers” have been making us humans unable to study and cognize scientifically the foundation of limit theory (the “limit theory needs its own foundation” even has never been considered about). And, because of this very fundamental defect, it is very difficult for people to really understand scientifically what kind of mathematical tool limit theory is and how to operate with this mathematical tool scientifically in pracdtical quantitative cognitions to “infinite related mathematical things” in infinite sets. So, following four questions have been produced and troubling people long:

（1）Do we use limit theory treat “potential infinite mathematical things” or “actual infinite mathematical things”？Do we need different limit theories for “potential infinite things” and “actual infinite things”？

（2）Is limit theory a “quantitative cognizing tool” or “qualitative cognizing tool”, a “precise cognizing tool” or “approximate cognizing tool”？

（3）When we conduct the quantitative cognitions to different infinite sets, how can we use limit theory to analyze, manifest and treat those number forms of

*X--->0*elements inside them (such as those number forms of*X--->0*elements in [0, 1] real number set)?（4）What on earth is the foundation of limit theory？

We understand from the infinite related mathematics history that it is the absence of limit theory’s foundation that results in the production and suspending of so many “infinite related paradox families” in present mathematical analysis and set theory.

Our studies have prooved that limit theory is needed whenever there is the concept of “infinite” in our science and whenever we need to conduct the quantitative cognizings to “infinite related mathematical things”. The emergence of the new infinite theory system (especialy with its “theory of infinite related carriers” and nothing to do at all with “potential infinite--actual infinite”) lays a scientific foundation for limit theory and enable us to answer above four questions clearly and scientifically:

（1）Limit theory has nothing to do at all with “potential infinite mathematical things” or “actual infinite mathematical things”. It is a special mathematical quantitative cognizing tool for “infinite related mathematical carries”. Only one limit theory is needed.

（2）Limit theory is a “quantitative cognizing tool”,------an“approximate quantitative cognizing tool” for “infinite related number forms” in our mathematics (an “1＜1 paradox” was once created to express the nature of limit theory: 1=3×⅓ = 3×0.333333……＜1).

（3）When conducting practical quantitative cognitions with limit theory to mathematical things in infinite sets, what we should do first is “really doing analysis on the infinite related mathematical carriers” being quantitative cognized according to the “theory of mathematical carriers as well as its infinite related number spectrum and set spectrum” in new infinite theory system-------to know what position they are in “new infinite related number spectrum and set spectrum” and what kind of quantitative natures they have, then to decide how to conduct the scientific quantitative cognizing operations with limit theory, but not the indiscriminately “pipeline limit theory operations”.

（4）The new infinite theory system (especially its theory of “infinite related mathematical carriers”) is the foundation of limit theory.

The emergence of the new infinite theory system has decided the emergence of the new limit theory.

I am a graduate student in Mathematics and interested in Algebraic Geometry , In particular questions on Moduli Space . Now to start thinking about some problem for research what kind of question we may ask?

Are there any paper that will be very helpful?

How to start thinking about it.

Looking forward for help and suggestion.

I got problem posted on internet , like compatifying moduli space and motivic structure.

But I am not sure about those problem in initial research.

log(a+bx) is concave since its double derivative is less than zero. (mx+c) is a straight line, so I can consider it as either concave or convex. But how can I prove mathematically that the ratio of the two is quasiconcave?

It is known that, a,b,c,m > 0.

I need a plagiarism software particularly which checks plagiarism for mathematical equations?

Dear Scholar

Geometry is the study of the Earth. Earth is a planet and is a member of the Solar family. Sun is a Star. So the planets and stars are 13 to 14 billion years old.

Mathematics is invented by man. Man came just 100 thousand years ago. It means Geometry is far far older than Mathematics which came very recently

Therefore Geometry should be first and mathematics next

Further , every concept in it has a support of a construction like other subjects of Natural Science such as Geology, Zoology, Botany, Physics, Chemistry

Looking to connect with scholars in Brazil who study mathematics education of secondary/primary students who have learning disabilities/marked at twice exceptional.

Thanks!

- Do the high school students perceptive economics too mathematical and difficult which result in non-enrollment in this degree?

- Is this choice related to students' GPA?

- Do the related field of study such as finance, accounting, business make students' choice toward economics more difficult?

One of the central themes in Dynamical Systems and Ergodic Theory is that of recurrence, which is a circle of results concerning how points in measurable dynamical systems return close to themselves under iteration. There are several types of recurrent behavior (exact recurrence, Poincaré recurrence, coherent recurrence , ...) for some classes of measurability-preserving discrete time dynamical systems. P. Johnson and A. Sklar in [Recurrence and dispersion under iteration of Čebyšev polynomials. J. Math. Anal. Appl. 54 (1976), no. 3, 752-771] regard the third type („ coherent recurrence” for measurability-preserving transformations) as being of at least equal physical significance, and this type of recurrence fails for Čebyšev polynomials. They also found that there is considerable evidence to support a conjecture that no (strongly) mixing transformation can exhibit coherent recurrence. (This conjecture has been proved by R. E. Rice in [On mixing transformations. Aequationes Math. 17 (1978), no. 1, 104-108].)

The fundamental defects of “potential infinite and actual infinite” confusions in present classical infinite set theory have been making us humans unable to study and cognize scientifically the foundation of “one-to-one correspondence theory” (the “one-to-one correspondence theory needs its own foundation” even have never been considered about). And, because of the absence of this very foundation, it is very difficult for people to really understand scientifically what kind of mathematical tool “one-to-one correspondence theory” is and how to operate with this mathematical tool in practical quantitative cognitions to elements in infinite sets. So, following five questions have been produced and troubling people long:

（1）Are the elements in infinite sets “potential infinite things” or “actual infinite things”？

（2）Are there different “one-to-one correspondence theories and operations” to “potential infinite elements” or “actual infinite elements” in infinite set theory？

（3）How do we practically carry on “one-to-one correspondence” operations between two sets-------do we have “‘one single element’ to ‘one single element’ correspondence” or “‘one single element’ to ‘many elements’ correspondence” or “‘many elements’ to ‘many elements’ correspondence”？can we arbitrarily alter the elements’ “special nature, special existing condition, special manifestation and special relationship among each other” in infinite sets during the “one-to-one correspondence operations” for quantitative cognitions (such as alter all the elements in Natural Number Set first [1x2, 2x2, 3x2, 4x2, …,nx2, …] = [2,4,6,8, …,e,…] (not the correspondence between N and E but E andＥ), then prove it has same quantity of elements in Even Number Set)?

（4）What kinds of the elements in two different infinite sets are corresponded-------- do we have “‘one single original element’ to ‘one single original element’ correspondence” or “‘actual infinite elements’ to ‘potential infinite elements’ correspondence” or “mixture correspondence of ‘actual infinite elements’ and ‘potential infinite elements’”？

（5） What on earth is the foundation of “one-to-one correspondence theory”？

The fundamental defects in present classical infinite set theory have made us unable at all to answer clearly and scientifically above five questions. So, when carrying on practical quantitative cognitions to elements in different infinite sets with “one-to-one correspondence theory”, one can do very freely and arbitrarily--------lacking of scientific basis. For example: it is because of acknowledging the differences of elements’ “special nature, special existing condition, special manifestation and special relationship among each other” between Real Number Set (R) and Natural Number Set (N), one can prove that the Real Number Set (R) has more elements than N (the Power Set Theorem is proved in the same way). But, as what has been discussed in above

**2.1 .1**, we are able to prove with exactly the same way “the mother set has more elements than its sub-set”, “Rational Number Set has more elements than Natural Number Set”, “Natural Number Set has more elements than odd number set” ,...; we can even apply the widely acknowledged method of altering elements’ “special nature, special existing condition, special manifestation and special relationship among each other” to prove “Natural Number Set has more elements than Natural Number Set”, “odd number set has more elements than even number set”, “even number set has more elements than odd number set”, ....Basing on the new infinite theory system with the “infinite mathematical carriers theory”, the Second Generation of Set Theory provides us with the scientific foundation of “one-to-one correspondence theory” and enable us answer above five questions clearly and scientifically:

（1）the elements in infinite sets are “infinite related mathematical carriers” with explicit quantitative nature and definition, indicating the existing of “abstract infinite law” and nothing to do at all with “potential infinite--actual infinite”. This decides one of the major differences between the first and the second generation of set theories-------the elements in different infinite sets have their own “special nature, special existing condition, special manifestation and special relationship among each other. So, it is really possible that different infinite sets have different quantity of elements and people can take them really as “visible and tangible infinite related mathematical things (such as the new numbers in new number spectrum)” for the quantitative cognitions

（2）the elements in infinite sets have nothing to do at all with “potential infinite elements” and “actual infinite elements”, there is only one identity for them-------“infinite related mathematical carriers” with explicit quantitative nature and definition; So, there is only one “one-to-one correspondence theory and operation” for them.

（3）it is explicitly stipulated that only “‘one single original element’ to ‘one single original element’ correspondence” operation is scientific (allowed) when comparing two sets for the quantitative cognitions and, during this process, any operations of arbitrarily altering the elements’ “special nature, special existing condition, special manifestation and special relationship among each other” are unscientific (not allowed).

（4）in the Second Generation of Set Theory, because of nothing to do at all with “potential infinite--actual infinite”, it is impossible to have any troubles produced by the confusion of “potential infinite --actual infinite”.

（5）the new infinite theory system (especially its theory of “infinite related mathematical carriers”) is the foundation of “one-to-one correspondence theory”.

A

**conjecture**is a**mathematical**statement that has not yet been rigorously proved.**Conjectures**arise when one notices a pattern that holds true for many cases. ...**Conjectures**must be proved for the**mathematical**observation to be fully accepted. When a**conjecture**is rigorously proved, it becomes a theorem. Share your favorite conjecture as a answer for this? let we know some beautiful unsolved statements in the field of science and Maths?Hello, I am facing some struggles with maths, gel elecrophoresis and my DNA samples. I need to use 1uL of 6x loading dye and MQ water to equalize DNA samples for GE. The average DNA sample load for GE well is 5 uL + 1 uL of loading dye + 4 uL MQ water, but I want them all to be even, like, for instance, 3,2 will need 1,8 MQ to reach the equality.

I got NanoDrop data (the concentrations are like 16,4 ng/uL, 13,4... and etc.), but I cannot reach my goal described above due to my problems with the logical chain of actions.

My DNA samples were washed with the elution buffer of 50 uL. I am not even sure if I am calculating the total amount correctly as well (it is a basic formula, but I guess that I am confused by the results I keep having, so I hope someone could help me to understand my issues and shed some light on the matter).

Thank you!

I have read informative research paper on SWCNT and its mathematical equation. My work begin with implementing SWCNT FETransistor in comsol and observe the change in resistance by applying different voltage but after reading research paper i came to know that before designing directly in comsol I need to implement CNT equation in Matlab.

Kindly suggest me proper links to simulate those equation in matlab or few links of videos or research paper which help me to simulate SWCNT in matlab and COMSOL.

Space-Filling curves like Peano, Osgood, Hilbert, Lance-Thomas ones.

Reference paper:

Hans Sagan,

*A geometrization of Lebesgue space-filling curve*, Mathematical Intelligencer, Vol. 15, n. 4, 1993Thanks.

Gianluca

Please refer to the following article for more details:

'

**' by***The Fields Medal should return to its roots...***Michael Barany***at link:***https://www.nature.com/articles/d41586-018-00513-8****Reference link:**

The emergence of new infinite system determines the production of "new infinite set theory"--------The infinite set theory based on the classical infinite system is called "classical infinite set theory (the First Generation Of Infinite Set Theory) " while the infinite set theory based on the new infinite system is called "new infinite set theory (the Second Generation Of Infinite Set Theory)".

The same mission and same cognizing contents decide the two similarities between the two set theories.

**1 The same qualitative-quantitative cognizing motivation and idea**

It is a must to carry on the qualitative-quantitative cognizing activities on “infinite related mathematical things (such as elements in infinite sets and the quantity of elements in infinite sets)” by both new and classical set theories; especially in many practical quantitative cognizing operations, most “mathematical contents” in infinite sets are treated as “mathematical things with visibal and tangible quantitative nature and meaning” by both new and classical set theories.

**2 the same quantitative cognizing tools**

Both new and classical set theories use one-to-one coresponding theory and limit theory to carry on quantitative cognitions to those “infinite related mathematical things” in infinite sets.

It is these two similarities between new and classical set theories that decides many invaluableners intellectual wealth accumulated since antiquity in classical set theory are reserved in new set theory.

There seem to be a wide variety of shapes in the biological world . In 2d we have various shapes of leaves. In 3d we have anthills , trees , fruits and animals with different shapes. All of them are closed surfaces , mostly convex. The jack fruit has thorns on its surface . Why is this so? What is being optimized?How can we fit a mathematical function to describe these shapes? This is a general exploitative question and all are welcome to suggest views.

A

**prime number**is a whole**number**greater than 1 whose only factors are 1 and itself. A factor is a whole**numbers**that can be divided evenly into another**number**. The first few**prime numbers**are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.**Numbers**that have more than two factors are called composite**numbers**.Can any one suggest me any textbook or website for finding the most of the mathematical stuff related to Hyperspectral image Classification ?

Dear friends:

The graph of the equation

f(x, y) = 0

gives rise to many interesting curves in the plane for different choices of the function.

One such choice of f(x, y) led me to the following graph of the equation f(x, y) = 0.

I have the following questions:

1) Can you name this geometric shape?!

What does it remind you of?

2) Any noticeable symmetry property?!

Thank you for your thoughts.

Best wishes

Sundar

For a Mathematics Postgraduate, who is interested in doing his PhD in areas related to Algebra and Analysis, what research field would you suggest. Preferably, the domain should be promising and relevant as per the current research interests of the Mathematics community in particular and the society in general, both theoretically and practically?

I have the following result (mathematical proof suppressed):

**"In a one-dimensional real space, the number of points between any arbitrary point and its immediate neighbor is indeed infinite. "**

I would like to know whether this result already exists in mathematics literature or not. If exists, then please provide me the relevant references. (The above result as it is is not Cantor's continuum hypothesis, but seems to contain it as a subset, which I haven't yet proved and work is in progress)

This is a question for Mathematicians and Mathematics lovers and the others!

This video may help every body to start.. https://www.youtube.com/watch?v=QYyuZ3_PQ4M

I'm so eager to learn about micro-mechanics, however, I can't find a source that discuses it in a simple way. Most of the sources I found starts immediately with complicated mathematical equations, without introducing the subject. I would also appreciate it if you can offer me some advice about the knowledge that I need to acquire before exploring micro-mechanics.

I have two independent groups and for calculating differences in variance I want to use VR (variance ratios):

VR = variance of group A / variance of group B

So if it's correct, how I should calculate the standard error of VR? And is there a way for interpreting VR (e.g., it is small, large, or significant)?

Thank you in advance,

Isn't it urgent to simlify?

Dear i want to write a thesis of phd maths in the area of fluid mechanics for that we have to write a synopsis . I am requesting to know a problem in which can i research.

For example, a few decades ago it was unimaginable perform statistical works without having a broad domain of mathematics, but now everybody uses it only following the instructions of a SPSS program.

"It is widely accepted that there are no inherent gender differences in mathematical ability or intelligence"

*Sunday Times Jan 21 2018 p5.*"Differences in intelligence have long been a topic of debate among researchers and scholars. With the advent of the concept of

*g*or general intelligence, many researchers have argued for no significant sex differences in*g*factor or general intelligence[1][2] while others have argued for greater intelligence for males.[3][4] The split view between these researchers depended on the methodology[1] and tests they used for their claims.[5]... Some studies have concluded that there is larger variability in male scores compared to female scores, which results in more males than females in the top and bottom of the IQ distribution.[8][9] Additionally, there are differences in the capacity of males and females in performing certain tasks, such as rotation of objects in space, often categorized as spatial ability."*Sex differences in intelligence**Wikipedia Jan 21 2018*What the ST article probably meant is that it is widely accepted that this topic cannot be rationally discussed in the popular media.

This is a highly contentious issue, but surely society would greatly benefit from knowing the answer. For individual researchers, however, their careers and reputations could be trashed by studying this topic. I heard a very highly cited professor of psychology say that his wife had begged him not to give the lecture that turned out to be a straightforward literature review of cognitive sex differences.

I am posing the question here as RG is one of the very few places that topics like this can be sensibly discussed.

I have time series data from multi channel EEG. I am looking at various symbol based complexity measures. As a preliminary step I have to convert my time series to symbols based on some logic (as simple as order dynamics or zero crossing)

I am looking for better methods/algorithms to generate symbols from EEG time series.

I obtained a Power length relationship formula

V=5.5* (0.62*L + 3*P/100)^(1/2) .

L = distance in km

P= Power in kW

V= Voltage in kV

When I applied it to my case study it proves inaccurate.

Please does anyone know of any other formula with similar relationships.

The major concern is how sensitive the AR model to data non homogeneity.

Kindly, I need some references.

thanks in advance

mathematics

log

exponent

infinity

I want to interpolate the amount of product formed (as concentration or % of conversion) vs reaction time in a biocatalysis process. The fitting equation should have as (y) the amount of product and as (x) the reaction time. I thought to use as the fitting equation the integrated form of the M&M but I am not able to find the correct mathematical form. Or should I use another equation?

In Taguchi’s optimization, for calculating S/N ratio (Smaller-the-better), we use the formula.

S/N = -10Log10[mean of sum of squares of measured data]

In this formula, why the term ‘-10 Log10’, whether it has any mathematical derivation/clarification for this method? Also what is the meaning/significance of DOF in Taguchi's design.

Please share

Do you find your students trying to stay away from complex mathematical solutions? what is the reason?

I think asking and formulating questions have a big impact on our lives, so I was wondering what techniques do you use to formulate your questions, and how much time you set for formulating the Question ?

The fundamental defects in present classical infinite related science system have decided the barber paradox (one of the members of Russell’s Paradox Family) is really an unavoidable and unsolvable problem for present classical set theory.

In present classical infinite related science system, it has been admited that the concept of infinite is composed by both “potential infinite” and “actual infinite”. On the one hand, no one is able to deny the qualitative differences and the important roles “potential infinite--actual infinite” play in the foundation of present classical infinite theory system; on the other hand, no one is able to deny that the present classical set theory is basing on “potential infinite--actual infinite” concepts as well as its related whole present classical infinite theory system. The fact is: any areas in present classical infinite related science system (of couse including present classical mathematical analysis and set theory) can not run away from the constraining of “potential infinite--actual infinite” concepts-------all the contents in present classical mathematical analysis and set theory can only be existing in the forms of “potential infinite mathematical things” and “actual infinite mathematical things”. But, the studies of our infinite related science history have proved that no clear definitions for these two concepts of “potential infinite--actual infinite” and their relating “potential infinite mathematical things--actual infinite mathematical things” have ever been given since antiquity, thus naturally lead to following two unavoidable fatal defects in present classical set theory:

（1）It is impossible to understand theoretically what the important basic concepts of “potential infinite” and “actual infinite” and their relating “potential infinite number forms, potential infinite sets” and “actual infinite number forms, actual infinite sets” are and what kinds of relationship among them are. So, in many “qualitative cognizing activities on infinite relating mathematical things (such as all kinds of infinite sets, elements in infinite sets, numbers of elements in infinite sets)” in present classical set theory, many people even don’t know or actually deny the being of “potential infinite” and “actual infinite” concepts as well as their relating “potential infinite number form, potential infinite sets” and “actual infinite number forms, actual infinite sets”--------it is impossible at all to understand clearly and scientifically the exact relationship among the important basic concepts of “infinite, infinities, infinite many, infinitesimals, infinite sets, elements in infinite sets, numbers of elements in infinite sets”, ... So, it is impossible at all to understand clearly and scientifically all kinds of different infinite sets (such as lacking of the “’set spectrum’ for the overall qualitative cognictions on the existing forms of infinie sets”), elements in an infinite set (such as ”are the infinie related elements potential infinite mathematical things or actual infinite mathematical things, how they exist?”), numbers of elements in an infinite set (such as ”are they actual infinite many or potential infinite many?”), the “one-to-one coresponding theory and operation” in infinie sets (such as ”are the potential infinite elements coresponding to potential infinite elements or actual infinite elements coresponding to actual infinite elements or actual infinite elements coresponding to potential infinite elements?”) ,... --------the unavoidable defects of qualitative cognition on infinite sets and their elements.

（2）First, it is impossible to understand whether the “elements in an infinite set, numbers of elements in an infinite set and all kinds of infinite sets” being cognized in present classical set theory are “potential infinite mathematical things” or “actual infinite mathematical things”, whether there are different theories and operations for “potential infinite mathematical things or actual infinite mathematical things”, and it is impossible at all to understand correctly (scientifically) in present classical set theory the natures of infinite related quantitative cognizing theories and tools (such as limit theory and the “one-to-one coresponding theory”) and their operational scientificities-------- it is impossible at all to master correctly (scientifically) the operational competences and skills of limit theory and the “one-to-one coresponding theory” thus resulting in no scientific gurantee for the operations of limit theory and the “one-to-one coresponding theory”; second, it is impossible at all to judge the scientificities of many infinite related quantitative cognizing activities in present classical set theory, people in many cases can only parrot every bit of what have been done by others or do as one wishes to treat many “not—knowing—what” infinite mathematical things with the unified way of “flow line” (any “infinite sets”, “elements of an infinite set”, “elements’ number of an infinite set” can either be “potential infinite” or “actual infinite”, neither be “potential infinite” nor “actual infinite”, first “potential infinite” then “actual infinite”, first “actual infinite” then “potential infinite”, ,,,), those believed and accepted Russell’s Paradox, Hilbert Hotel Paradox, Cantor’s operations of “cutting an infinite thing into pieces to make different super infinite numbers” and “proving the uncountability of real number set by diagonal method” as well as the famous “applying Russell’s Paradox to prove the Power Set Theorem” are tipical examples of “potential infinite--actual infinite” confusing operations--------the unavoidable defects of quantitative cognition on infinite sets and their elements.

We understand from our science and mathematics history, the fundamental defect in present classical set theory disclosed by the members of Russell’s Paradox Family is: looking for something belongs to an infinite set but is impossible to be found inside this infinite set--------no logic in our science can solve such paradox family as

**are produced by the confusion of “potential infinite” and “actual infinite”.***all the members of Russell’s Paradox Family*Knowledge representation may be constructed as an attempt to formally capture and describe human sensory and perceptual data. But is knowledge representation via ontologies etc., anything more than the application of logic and mathematics?

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