Mathematics - Science topic

In Mathematics, some proofs are not convincing since the assumption fails in the Proofs.

If equality is Changed to "approximately equal to" then the Proof becomes more Perfect. But Uniqueness cannot be guaranteed.

In Page number 291, Introduction to Real Analysis Fourth Edition authored by Bartle and Sherbert, the Proof of Uniqueness theorem is explained.

That Proof is not perfect.

Reason : Initially epsilon is assumed as positive and so not equal to zero. Before Conclusion of the Proof, epsilon is considered as zero and written as two limits are equal.

The equality cannot hold since epsilon is not zero. Only the possibility to write is Two limits are approximately equal.

Since Epsilon is arbitrary, never imply epsilon is zero.

I hope the authors and other mathematicians will notice this error and will change in new editions.

What research is there (if any), about gifted students frequently getting easy questions on academic tests/exams INCORRECT and harder more challenging ones CORRECT – particularly in mathematics? Does anyone have any empirical evidence as to why this might occur? Thank you.

is there any literature available on a kinetic study on the working of RO membrane with any software or simple mathematical simulation?

Every integer can be expressed as a sum of three triangular numbers.

Given two integers N=a+b+c and M=x+y+z , how to express the product N*M as a sum of three triangular numbers. Example:

11=0+1+10 and 13=0+3+10 ; the product 11*13=143=10+28+105

How to write the product N*M=F(a,b,c,x,y,z) +G(a,b,c,x,y,z) +H(a,b,c,x,y,z) as three triangular numbers?

I have digged into a theory established by D. Loeb from University of Bordeaux, and found an interesting way to represent the things you have (classical set) and the things you do not have and might need, want, be ready to acquire (new forms of set with negative number of elements)

This fits very well in the extension of the matrices of sets which I needed to develop, se why and how here (see references below).

I would be thrilled to know if you have use cases where this model of classical sets of what you have, and new negative sets of what you do not have, my help.

Please share your input!

REF:

[1]

[2]

[3] D. Loeb, Sets with a negative number of elements, Advances in Mathematics, 91 (1992), 64–74.https://core.ac.uk/download/pdf/82474206.pdf

In a mathematical analysis of piezoelectric models, we use the terms "the electrically open and short circuit case" for which we have some mathematical definition as well.

What is the physical significance of these boundary conditions in making sensors and other devices?

It is well confirmed that the nonlinear evolution equation (NLEE) is widely used as a mathematical leading equation for describing the physical issues in many branches of physics. But it is very difficult to solve. Recently, many researchers have proposed various types of solution methods. Unfortunately, most of the solutions methods lead to additional free parameters. In my opinion, the solutions with additional free parameters of NLEEs are not useful for further verification in the laboratory. That is why my discussion topic is "What is the best solution method for nonlinear evolution equations?".

Although Bashkar II, in his Siddhantha Shiromani, critisized a Buddhist school of astrology who held the Earth is moving, I have not seen any mention about texts on Buddhist astrological or mathematical tradition in recent studies. Vedic and Jain sources are well known.

Are there any primary textual resources on Buddhist astrology/mathematics?

Dear experts and colleagues,

Hello, all! I recently received a reviewer's comment stating that the proposed network measures of graph theoretical analyses could be correlated by mathematical definition.

So I ran the correlational analyses and global efficiency, characteristic path length, mean clustering coefficient (global measures) showed correlated to each other.

I understand that Global efficiency is inversely related to characteristic path length, but I am quite confused about how characteristic path length is inversely correlated with mean clustering coefficient, while mean clustering coefficient is positively correlated with global efficiency.

Or does my data is wrongly suggested?

Briefly explaining my study, it is a neurological study using MR images (diffusion tensor imaging) to explore the structural networks.

Any feedback and discussion are welcomed here!

hi, I have to get an inverse matrix of a square matrix (20*20) on excel , to make sure that calculation is right I Knew that multiplying the matrix with its inverse should yields a unity matrix which have a diagonal of ones and other cells are zeros but when i multiply the matrix with the inverse i got the result is a matrix with adiagonal of ones but not all other cells are zeros (some have values like 1,2,etc ... is this ok or what often is my mistake? thanks in advance

Need a journal published in German language in the fields of mathematics and programming indexed in scoups Q1?

About two years ago, I have submitted a manuscript to a reputed journal. After a couple of months of the peer review process, the response was “major revision has been requested”. I made the necessary adjustments and resubmitted it again. The Journal's editor responded that my manuscript requires minor revision. Well, the decision was <<"Revise for Editor Only'' he claimed that revision should be quick and it will not undergo the entire review process>>. Again, I made the required edits in order to make the manuscript acceptable for publication. Afterward, I resubmitted it. It is the day 120 and the status is "With Editor". In fact, I did send two emails to the editorial team to update the status. Their response to both emails was the same, saying that they contacted the editor to accelerate the process.

Dear readers, I need to have a piece of advice: what to do as a next step?

Thank you in advance,

Bassam

How to mathematically interpret the formula Kb=Kf (1−Rw)

I am combining fish abundance and biomass data collected from five locations which have utilised different transect dimensions:

15 x 4 m (60 m2; from one location)

30 x 5 m (150 m2; from three locations)

50 x 4 m (200 m2; from one location)

When pooling data collected from transects of differing sizes, should you standardise your data down (to the smallest dimensions) or up (to the largest)? Or in this case, perhaps standardise according to the most commonly used dimensions (30 x 5 m/150 m2)?

To me it seems as though there would be no difference, but I was wondering if there was some sort of mathematical explanation for why one way might be preferable over the others?

the VPL formula can be given here as,

f(P)=sum((a+b*P+c*P^2)+abs(e*sin(f(Pmin-P))))

Can anyone please explain if the value from the term (Pmin-P) in the above formula is in degrees or radians?

Hi everyone,

In engineering design, there are usually only a few data points or low order moments, so it is meaningful to fit a relatively accurate probability density function to guide engineering design. What are the methods of fitting probability density functions through small amounts of data or low order statistical moments?

Best regards

Tao Wang

Hello. I want to ask how can I translate weightages of "yes" or "no" of a criterion in terms of numbers in AHP calculations?

for examples, my goal is to select most suitable construction material vendor (Alternative) according to the set criteria including "ASTM Standards", with 4 other criteria.

This criterion means "Is the material vendor giving the material according to the Construction Standard ASTM, or not?" So the answer given to this by the alternative (vendor) would be a "Yes" or a "No", but not a value.

First, I've sent a questionnaire to the experts to give me pair wise comparison weightages for one criteria vs the other. And I've got great response with consistency of 0.9. Acceptable!

But when I ask the vendors to provide their responses, they put numerical values to the first four criteria, and I find the comparison matrix for these vendors (alternatives) for each criteria using simple maths division (value of one vendor divided by second vendor). It gives me the exact zero consistency, because I've found the alternatives weightages using exact math comparison. But I get numerical values of weightages to find ranks, so it works fine for me.

But when it comes to the 5th criterion (ASTM Standards), the responses are in "Yes" or "No" terms! My question is that what numerical value should I give to a Yes and a No so that I can get their comparison by dividing with each other?

for instance, if I use Yes =1 and No = 0, the system hangs because anything divided by zero gives an infinity answer, and it doesn't proceed further.

If I want to use a scale of 1 to 9, saying Yes = 9, and No = 1, it gives me good results. But I've no reason to use 1 or 9, for it could be any numerical value say 1000 for Yes, and 1 for No.

Please suggest me a reasonable value with a citation if possible.

Thanks in advance.

I want to learn fractal mathematics from scratch. What are the prerequisites and recommended resources for it?

Thanks and regards.

Nishanth

Sometimes , we use term of "zero time" in a formulation but are we sure it is really "0" ? maybe it is 0,000......1 and is there a "zero" time(can we stop the time?), or sometimes, we say v=0 are we sure?

On the other hand

1/0 = infinity. Well then, what's "infinity"? How does it work in all the other equations?

infinity - infinity = 0?

1 + infinity = infinity?

If we use closest number to zero-monad (basic thing that constitutes the universe-everything-)Gottfreid Leibniz, in his essay “Monadology,” suggested that the fundamental unit of all things is the monad. He intended the monad to have some of the attributes of the atom, but with important differences. The monads Leibniz proposed are indivisible, indissoluble, and have no extension or shape, yet from them all things were made. He called them “the true atoms of nature.” At the same time, each monad mirrored the universe. If we use monad instead of zero, every equations work

I think Science says "Every Thing had originated from a basic thing"

Boolean and ZFC logic are constructed from fundamentally different foundations. Modern (20th century) mathematics appears to be dominated by the ZFC approach. I am not sure it is understood the two approaches are incompatible. Is this incompatibility studied?

I have done cropping attacks in visual (pictorial) form but, I want to do this test in mathematical form, i.e., I want to calculate values of cropping attack analysis in MATLAB.

Hi,

I am trying to write the motivation part for linearization of a non-linear mathematical formulation. I claim the mathematical model will be more simple and easier to solve. But, of course, I need a reference for that! Any suggested book chapters or articles that discuss this point please?

Thanks in advance...

Zak

STEM fue el tema principal de la conferencia internacional ASTE 2019, con al menos 8 pósteres, 27 presentaciones orales y 3 talleres que promovieron las aulas STEM, la instrucción/enseñanza STEM, las lecciones STEM, los campamentos de verano STEM, los clubes STEM y las escuelas STEM sin proporcionar una conceptualización o definición operativa de lo que es STEM. Algunas presentaciones defendían la integración de las disciplinas, pero el ejemplo proporcionado fue principalmente prácticas "indagatorias" y de "diseño de ingeniería" que de hecho no diferían del tipo de actividades en el aula hands-on/minds-off mal conceptualizadas y epistemológicamente incongruentes.

Por lo tanto, vale la pena considerar:

(1) ¿Por qué lo llamamos STEM si no difiere de las prácticas aplicadas durante décadas (por ejemplo, indagación, actividades hands-on)?

(2) ¿Qué beneficios (si los hubiere) puede aportar esta mentalidad/tendencia de STEMinificación a la educación científica y su investigación?

Dear colleagues, please tell me a link to materials about mathematics of Dropout regularization in ANN. I perfectly understand how this algorithm works in practice, but I don't quite understand the mathematics.

I know that an infant's brain can repair itself when damaged but why doesn't the same happen in adults after stroke or brain injuries?

Hello everyone

I would really appreciate it if anyone could give some idea of some mathematical techniques for developing correlation for a dependent variable, W which has to be defined as W=f(x,y,z) where the individual functions are in form of power-law, W=a(x^b), W=c(y^d) and W=e(z^f).

In general in mathematics we work with groups that includ numbers, generally we work with constants.

So for exempel: For any x from R we can choose any element from R we will find it a constant, the same thing for any complex number, for any z from C we will find it a constant.

My question say: Can we find a group or groups that includ variabels not constants for exemple, we named G a group for any x from G we will find an x' it's not a constant it's another variabel ?

and if it exisit can you give me exempels ?

While working in both the software, after loading the training and validation data for the prediction of a single output using several input variables (say 10), it skips some of the inputs and delivered an explicit mathematical equation for future prediction of the specific parameter but it skips some of the input variables (say 2 or 3 or maybe greater). What criteria are these software uses in the back for picking the most influential parameters while providing a mathematical predictive model?

Hello

Can someone help me to solve this?

Because I really don't know about these problems and still can't solve it until now

But I am still curious about the solutions

Hopefully you can make all the solutions

Sincerely

Wesley

Austrian-born mathematician, logician, and philosopher Kurt Gödel created in 1931 one of the most stunning intellectual achievements in history. His shocking incompleteness theorems, published when he was just 25, proved that within any axiomatic mathematical system there are propositions that cannot be proved or disproved from the axioms within the system. Such a system cannot be both complete and consistent.

The understanding of Gödel’s proof requires advanced knowledge of symbolic logic, as well as Hilbert and Peano mathematics. Hilbert’s Program was a proposal by German mathematician David Hilbert to ground all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent. Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic. Gödel’s 1931 paper proved that Hilbert’s Program is unattainable.

The book Gödel’s Proof by Ernest Nagel and James Newman provides a readable and accessible explanation of the main ideas and broad implications of Gödel's discovery.

Mathematicians, scholars and non-specialist readers are invited to offer their interpretations of Gödel's theory.

When I observed mathematics education in preservice teachers at my university, I found that What students learn in mathematics classes does not match what is needed in school mathematics classes. That led to my initiation to do design research, a Hypothetical Learning Trajectory that contains a sequence of learning processes related to elementary school mathematics learning. I consider starting with observations in elementary math class to identify misconceptions, then jointly reviewing issues on campus, conducting literature reviews, designing lessons to address identified problems, implementing them in class and evaluating the results. The final result is a Local Instructional Theory on Learning about Teaching Mathematics for prospective teachers to overcome misconceptions that occur in elementary mathematics classes. I need so many suggestions to do this research.

In 2010, Dr. Khmelnik has found the suitable method of resolving of the Navier-Stokes equations and published his results in a book. In 2021, already the sixth edition of his book was released that is attached to this question for downloading. Here it is worce to mention that the Clay Mathematics Institute has included this problem of resolving of the Navier-Stokes equations in the list of seven important millennium problems. Why the Navier-Stokes equations are very important?

According to the resources; there is used to algorithm in HOMER sotware, grid search algorithm and derivative-free algorithm.

So how can I find the mathematical formulas of these algorithm ?

Please if you know the way or source help me

Thank you

Hello! I have an exercise to do and I am struggling with it for a week ago. I have a 2D flow with the initial velocity at the inlet=0.01m/s. And I want to calculate the numerical results of the velocity which is the function of x and y direction (U(x,y)) in the domain of the water flow. For example if I want to calculate the velocity at the distance x1 and x2 (as in the figure) in the function of x and y., how can I calculate it? Please note that it is incompressible flow. It is fully developed after it passed the entrance length. The height of the domain is 0.02 m and the length is 1 m. Please help me! You can see the following figure. Thank You in advance! I will appreciate your help !

According to the resources; there is two algorithm used in HOMER sotware optimization process; grid search algorithm and derivative-free algorithm.

So how can I find the mathematical formulas of these algorithm ?

Please if you know the way or source help me

Thank you

I mean the mathematical component of said process.

Mathematical about the work-related with graphene or any other type of films/coatings.

Lubrication equations in solid films.

The temptation in all the remodeling of the study plans to train teachers that I have experienced, faced with a new strong point of interest, has been to introduce a subject that caters for it. Thus, environmental education, for example, has been the curriculum of Spain for more than 25 years.

Now the SDGs are the focus of attention, and the university is committed to developing them. the challenge is to do it from the established curricular subjects

Educational mathematics is developed in three or four subjects of each training curriculum, and has to embrace achieving the teacher's competence development to teach school mathematics and also, the purpose of working on the SDG, how can we do it?

What are the various fields

using BTE how do we get mobilities and conductivity ,more calculation(mathematics) oriented answers would be helpful.

In classical times there was a concept of pure science that was produced entirely in the intellect.

More recently sciences were developed by testing the intellectual product with empirical data. These sciences are not regarded as being pure.

Mathematics, often regarded as pure science, has for most of history been based on postulates of geometry that could not be proven. Then came relativity and other geometries. In the past century there was considerable effort to reformulate mathematics on a firmer basis of conditional sets. Math is now regarded as being somewhat more pure than before, while producing two generations of graduating students in some countries who are not able to do simple arithmetic.

Fortunately I had some excellent teachers who explained the two systems and why they were both needed. Other teachers displayed the Gödel's incompleteness theorems.

In academic settings there seems to be a difference of opinions about whether or not math is a science, and whether or not it is pure.

Is Mathematics A Science?

I am interested in TPACK and mathematics education, can you share recent research articles on both topics here?

For instance:

Physical reality can be observed. At least part of the structure and behavior of physical reality is perceivable. Humans can communicate about these experiences. Curious humans want to comprehend these perceptions. Humans have designed linguistic tools to be able to communicate about the perceived structure and behavior of physical reality and with these tools, they have constructed structures and models of mechanisms that might explain the perceived structures and mechanisms that physical reality exposes. Some of these structures and models of mechanisms seem to be successful. People discuss the success of these approaches and call this activity exact science. Other humans discuss this activity and call themselves philosophers. Humans are interested in the structure and mechanisms of physical reality because this knowledge helps them survive as individuals and as communities. Part of the exact sciences is formed by mathematics. Mathematics contains structures and models of mechanisms that are not directly derived from perceptions of physical reality. These concepts are derived from abstract foundations. Examples are empty space and point-like objects. Scientists use these concepts to construct vector spaces, number systems, and coordinate systems. The scientists apply these higher-level concepts to construct a model of their living space. The philosophers will immediately indicate that it is impossible to prove that these models are correct. However, these models feature structure and behavior. If the structure and behavior of the models agree more with the perceived models and behavior, then there is a larger chance that the model fits reality. Since reality appears to be very complicated, little chance exists that good correspondence will ever end the dispute.

One of the aspects of the dispute concerns what the best inroad will be for comprehending most of the structure and the mechanisms of physical reality. That is the background of the posed question.

US Fed's balanced sheet has recently doubled up from $4T to $8T (see the monthly chart) – not to mention it used to be $800B around 2008. It seems like to me, that is highly inflating the housing markets, pushing the housing prices higher as well as the inflation rates higher – regardless of taking economic productions much into consideration. Fed refers to the situation as "transitory".

I'm sure that there should be solid mathematical rations behind it. Does this parabolic Quantitative Easing approach a mathematically and/or economically sound strategy, considering the current economic situations? Any other alternative strategy? Any upsides and downsides?

Thank you!

---------

PS:

A bit outdated visual components of Fed's balanced sheet:

Dear colleagues, I would like to know if there is a mathematical equation or model to calculate the Soxhlet number of cycles by varying the following parameters:

- the type of solvent

- the volume of the extractor

- the temperature of the solvent heating

if yes how can we apply it? and how much uncertainty it has?

thank you so much

best regards

I need mathematical formula to measure public service quality and organizational impact

such as Fourier , Hilbert or Laplace transforms in order to analysis and studies in the field of music acoustics.

Please look at the mathematical construction of theta and zeta functions in the representation of a winding sphere. In this paper, based on the representation of the winding of a sphere, we construct a proof of the Riemann hypothesis of nontrivial zeros. Could you check this proof?

Hi researchers,

I need to find a method of proving a mathematical equation that exist in attached file.

This mathematical equation is about Bessel function.

I will be thankful to hear your helps and advises.

A Diophantine equation is an algebraic equation with several unknowns and integer coefficients. Those are equations whose solutions must be whole numbers. The only solutions of interest are integers

In mathematics and physics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it or the minimum number of sides to build a physical area or volume.

To build a geometrical rectangle (square) we require 2 orthogonal sides (x, y are independent indeterminates) area = x*y (or area = x*x)

To compute a numerical square (square number) we require 2 numbers p and q coprime with gcd(p,q)=1 or independent numbers.

Let we introduce a dimension for nature of numbers like I (for integer), R (for real), C (for complex) and so on.

n^2 = p^2 +q^2 ; 5^2=3^2 +4^2

Dimensional analysis gives for n^2= p^2 +q^2

I*I =I*I +I*I ; The sum of square might be equal to a square in some conditions.

Then the equation n^2 = p^2 +q^2 may have integer solutions.

A dimension is anything we can independently adjust, it is based on some geometric or algebraic definition.

In any correct mathematical equation representing the relation between physical quantities or mathematical objects (length, area, volume,….,.simplex), the dimensions of all terms must be the same on both sides. Terms separated by ‘+’ or ‘–’ must have the same dimensions.

The degree of freedom is the number of free components : how many components need to be known before the « objects » is fully determined?.

For example:

- a point in the plane has two degrees of freedom : its two coordinates;

- a square has two degrees of freedom : its two sides ( length and breadth).

- A point in 3-dimensional space has three degrees of freedom because three coordinates are needed to determine the position of the point.

The degree of freedom of a Diophantine equation is the number of parameters of each side that may vary independently. The degree of freedom must be the same on both sides.

- The equation n^2= p^2 +q^2

LHS is a square number with two degrees of freedom (its two multipliers or components) .

RHS is a sum of two squares with two degrees of freedom p^2 and q^2 which vary independently.

The degree of freedom is defined as the dimension of a mathematical object. When the degree of freedom is used instead of dimension, this usually means that the object is only implicitly defined.

Hilbert's Tenth Problem Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in rational integers.

The problem was solved in 1970 by Yuri Matiyasevichwho in his doctoral dissertation proved that a general algorithm for solving all Diophantine equations cannot exist.

I think the concept of dimensional analysis is an attempt to answer Hilbert 10th problem related to homogeneous Diophantine equations . It works very well and allows to know if a homogeneous Diophantine equation has integer solutions but it remains to calculate these solutions using modular arithmetic or algebraic method…. The most important thing is to answer Yes/No and affirm that the integer solutions exist or not.

Dear Community,

I want to center (subtract the mean) my data in order to lower my intercept (as close as possible to zero). However, as I have categorical data as well, which I don't know how I can possibly center, I can't seem to lower my intercept.

And the thing is that my dummy variable drive up the intercept... So I don't know to fix the issue.

When I enter only continuous variables that are centered, the intercept is close to zero.

I thank you in advance?

Dear Colleagues!

I hope you are all doing well. I have a question to all of you. I love to teach and so far I have been teaching everything from international business, marketing, management to organisational psychology. I feel ambivalent towards this however.I love to teach and Im curious in my nature and what better way to learn new things than to teach? However I also feel that if I continue being a generalist It might also be bad since I risk loosing touch with my main specialisation.

What are your thoughts? Your experiences?

My speciality is this :

Best wishes Henrik and professor Hugo 3 months old who keeps me company when Im trying to work :-)

Ps stay safe.

I have seen that some equation sets have an explicit way of defining the substrate consumption whereas others have an implicit way. I would like to know how to convert the former into the latter.

For instance, in the attached file, it can be seen that there are two ways to describe the growth of bacteria.

In the first (explicit), the presence of a half-saturation constant suggests that the model is a Michaelis-Menten case. The second is straight a logistic model.

I was wondering if I can convert the first into the second, that is explicit to implicit.

Considering that the Monod term says that

then I can write

My question is: Would this modification be mathematically and biologically sound?

If yes, how can I estimate the carrying capacity? For instance, if I know the amount of limiting substance, can I estimate the number of cells that a system can sustain?

Thank you

I'm working on constructing a field based on finite undirected and unlabeled graphs. I've selected graph join and graph Cartesian product. But I'm trying to figure out if the latter distributes over the former (or simple graph union).

See

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?

Hi All,

Can anyone please tell me which mathematical equation can be used to normalize the single ion monitoring quantitation in GC-MS? Thanks in advance!

The field equations originally starting as Maxwell distributions graphs configure a velocity variable. Understanding that in connection to wave theory requires a mathematical transformation of velocity variable into wave function parameter. This may help mathematically to define particle wave quantum relativity quantitatively. Legendre transform theoretically will have a way to provide link among functionality of parameter-variable systems.

There is a contradiction between the natural width of the energy transition, which is determined by the lifetime at the corresponding energy level and the spectral line width of the radiation line, which is determined by the duration of the wave train.

For example: For the Mössbauer transition, whose lifetime is of the order of 2 years, while the interaction time at the receiving end is about 10^(-10) sec.

Mathematically, this interaction is expressed by the Feynman diagram of the electron - electron interaction, which integrates over the internal photon line, which, together with the delta functions of the vertex parts, limits the photon spectrum.

By the way, the same paradox applies to any other type of collision.

So, is exist (really) the electromagnetic field?

When we derive the formula for length contraction, we use the direct Lorentz transformation. But for solving the formula for time dilation, we use the inverse transformation. Why is that so?

A question from far away worlds...Life Sciences (cricket) and an hyperbolic function from history of mathematics are trivially juxtaposed to encourage whatever reply.

[The antennas of the cricket roughly complete the less frequently represented branches of the hyperbola in the photographed virtual third and fourth quadrant of the Cartesian coordinate system].

Here we discuss about one of the famous unsolved problems in mathematics, the Riemann hypothesis. We construct a vision from a student about this hypothesis, we ask a questions maybe it will give a help for researchers and scientist.

They say the best educators are able to make a complex subject easily understood by a child. Perhaps this is a challenge to us all.

Quarternion mathematics can be quite complex to wrap your head around. For educators out there how are you explaining this to your students from high school.

Is a pictorial method the most appropriate under these circumstances.

I have read that time is defined in terms of entropy (entropy of the universe maybe? I'm not sure). But entropy is a macroscopic quantity which makes time a macroscopic quantity. Yet time is a parameter in Schrodinger's equation. So we have a macroscopic quantity appearing in a microscopic equation. That makes me think that this microscopic equation is really a statistics equation. It produces deterministic solutions but maybe these deterministic solutions are just mathematical procedures for statistical calculations. That would be consistent with the fact that these solutions actually are used for statistics calculations. Does it makes sense for a macroscopic quantity (time) to appear in a microscopic equation, unless it is a statistics equation? Or, am I mistaken in calling time macroscopic? My primary question is whether Schrodinger's equation can be derived from some set of statistical postulates. The question is not whether the equation was historically obtained from statistical arguments (we already know it wasn't), the question is whether the same equation can be derived from statistical arguments. What Schrodinger was thinking at the time of producing his equation is not relevant to this question.

Mathematics is the basis of exact sciences. The development of mathematics consists in the fact that, among others, new phenomena of the surrounding world, which until recently were only described in the humanistic perspective, are also interpreted in mathematical terms.

However, is it possible to write down the essence of artistic creativity in mathematical models and create a pattern model for creating works of art, creative solutions and innovative inventions? If that was possible, then artificial intelligence could be programmed to create works of art, creative solutions and innovative inventions. Will it be possible in the future?

Do you agree with my opinion on this matter?

In view of the above, I am asking you the following question:

Will mathematics help to improve artificial intelligence so that it will achieve human qualities of artistic creativity and innovation?

Please reply

I invite you to the discussion

Best wishes

what are other possible ways to convert a CW laser to a pulsed laser. Please give all the theoretical and mathematical details.

More specifically I am looking to analyze and plot non-michaelian kinetics based on functional parameters from BRENDA or similar sites. I do not know how to find the mathematical function describing such kinetics and have not yet been able to find it in the literature.

I would greatly appreciate any help from the community!

Hello Experts,

I want to know that how to find theta maximum when i am using GPS and sphere and surface type distribution. and using cosine distribution.

then i want to know that is there any mathematical calculation to find theta maximum for biasing.

like in the Geant4/examples/advanced/radio-protection theta maximum is 0.003 deg. how they got this using the surface area of source or object. like how can i get for my object ?

any type of help will be appreciated.

Thanks in advance !

Best Regards

Priyanshu

How to transfer the logical description of safe constraints to mathematical description？Any feasible idea？

Question about the loss of hyperbolicity in nonlinear PDE: when complex eigenvalues appear, what is the effect on flow? I understand that we do not have general results on existence in this case, but is it only the mathematical tools that are lacking where can we show physical phenomena of instability?

Different longitudinal studies, such as the Perry Preschool Project or the Abecedarian Project, have shown that early and effective exposure to different content in ECE students, as science or maths, cause positive effects in children later development not only in academical sphere, but also in personal, social and economic ambits.

Hi all,

I attached an image file of excel data in which the problem is to predict the value of u by using any mathematical method.so, please share me the procedure or method to be followed to solve the problem.thank you in advance.

Hi all, I am looking for a patterning assessment to use as a pre- and post-test alongside a patterning intervention in mathematics for 7 to 9 year old children.

I know of PASA by JT Mulligan, are there any others?

Thanks in advance for your help!