Mathematics - Science topic

Thank you very much for your kind comments.

Dear Leonard Hall, I agree with your last posts. I would like to add one more comment, regarding the phrase “independent of mathematics”. According to mathematical logic, which is the basis of mathematics, a mathematical theory is a collection of axioms and theorems that are derivable from the axioms using rules of inference (rules of logic). Both axioms and theorems are mathematical sentences. A sentence of a theory is said to be independent of the theory if adding that sentence to the axioms of the theory yields a consistent theory AND adding the negation of that sentence to the axioms of the theory also yields a (different) consistent theory. A consistent theory is a theory whose axioms do not lead to contradictions.

In view of the previous definition, the physical interpretation of the square of the absolute value of the wave function is independent of the mathematical theory that is used to describe quantum mechanics. The mathematical theory will remain (mathematically) valid even if the square of the absolute value of the wave function is not interpreted as probability density.

The first point is to read a lot from all of these fields. A good entry point are review articles which summarize large areas of a discipline and may point out open questions. Also, for a PhD, it is important to be aware of your personal, ongoing interests. Maybe these interests coincide with some open questions in the research domain. You can combine different fields in many ways, e.g. using methods from one discipline for problems in another one, or generalizing open questions into a more general question, or creating a new method by combining elements of an existing method, or transfering one model to another context, etc. It is up to your interests, your creativity, your questions! Always remember that each research discipline is simply a different perspective onto the world. Thus, you can pick any part of the world and look at it from all these different perspectives.

Thanks for your thoughts and wishes

Many people write to me, and my mailbox is very accepting.

Some simple people assume that their questions are, somehow, special, worthy, or unique. They even may want to claim innovation!

But, we live in a fluid, and many of our thoughts are not even

original, or our own. Ego interferes.

Only correct living, like following the Dhrama and Jesus, can keep the laboratory of the mind clean and receptive to higher thoughts.

The complex numbers have been followed without deep questioning, and their justification, in medieval Italy, was to solve the equation x^2+1=0.

But, they actuall lead one astray from the actual solution.

This was revealed by the FFT, that can now be entirely calculated with rational numbers, and without any trigonometric functions, as mentioned above.

Then, we conclude that FT ~ FFT, as the RG preprint briefly explains. For the savvy, a letter cn b a wrd!

There are no mathematical real-numbers either. Thus, the set C is deprecated and the set G is superfluous. They cannot be calculated (Gisin,Ozhigov, Gerck)with probability 1.

Mathematics gets simpler, and correct, accessible to natural processes, and accessing them in quantum mechanics.

Then, the Shor quantum algorithm of 1994, without any practical result since then, only theoretical results, opens the calculations of the FFT, to the components of numbers.

This reveas the prime numbers as "lumps", resonances in the number line, much in the same way that a physical chord has physical resonances. Easier to calculate, with such a physical model.

In fact, and the meaning of the question is not understood.

There is certainly a similarity, but it is rather a property of inductive method of thinking, characteristic of human in general.

Well it's a good idea to find some of them, first. The first equation implies that y=0 is an equilibrium, so a class of equilibria is of the form (x,0,z). That reduces the problem. From the last equation it then should be possible to solve for z and, from the second, for x.

Then look at the other factor of the first equation; and so on.

Stam Nicolis, you have been telling me how the problem is being considered in GTR, Cosmology, etc. This is known already.

The question I have posed is for considerations towards new attempts to discuss the problem rationally and to come to possible further conclusions that might help us understand the very problems better

Dear Azzam,

I was not talking about you. You know I have no problem to talk science with you. We were talking about some supporters of the theory of relativity, who don't accept the questioning of this theory. You know that.

QM can have values unknown, but not uncertain. Likewise, RG questions. Please stay on topic, per question. Do not be uncertain yourself.

Opinions do not matter, every opinion is right and should be, therefore, not discussed.

But, facts? Mass is defined (not a choice or opinion) as the ratio of two absolutes: E/c^2. Then, mass is rest mass. There is no other mass.

This is consistent, which is the most that anyone can aspire. Not agreement, which depends on opinion. Science is not done by voting.

Everyone can, in our planet, reach consistency -- and the common basis is experiment, a fact. We know of other planets, and there consistency may be uncertain -- or ambivalent, and even obscure. A particle, there, may be defined, both, as the minimum amount of matter of a type, or the most amount of quantum particles of a type.

We can entertain such worlds in our minds, more or less formed by bodies of matter, and have fun with the consequences using physics. But, and there is my opinion (not lacking but not imposing objectivity) we all -- one day -- will be lead to abandon matter. What will we find? That life goes on. The quantum jump exists. Nature is quantum.

Manabu Goto this may interest you: https://conference-service.com/conferences/mathematics-education.html

This is just one example of how you might use a optimization algorithm to find an optimal output value from 'N' data points. There are many other approaches that you could consider, depending on the specific goals and constraints of your problem.

There are many research areas in machine learning that are well-suited for people with a strong background in math. Some of which are:

You can search and explore more areas and choose one best suited to you

The engineering philosophy behind Coq and the Coq kernel is well worth careful consideration:

To reach the Scopus document search module, you should use academic IPs. If your institute has been listed in the Scopus database, you have permission to search documents in Scopus. It is not free of charge, and your university should pay its share to Scopus to provide this service for its academic researchers.

Cite:

No. Consider the series ... in the above link example/ answer by Mark Gritter.

Both are divergent series, but the difference between the series is ... a convergent series.

Hereby attached is a system of three Ordinary Differential Equations (ODE). We have to use numerical methods such as RK4 and Euler to obtain the results using Java. I think RK4 is better for this kind of problem. In this thread, Dudley J Benton has already mentioned C programming for this. It is really amazing.

For the parameter values, you can use your own values for your convenience.

Many thanks Jack Don McLovin

I have evidence that that is the upper bound... today it has been proved. But I reserve my ideas to publish them by a proper article. I just hope that journals can accept so clear ideas behind of this problem is a fundamental basis but not complicated to understand as it is believed. Many thanks.

Thank you very much Madam @Shima Shafiee

We need to be optimistic, because that is the lesson from nature. An animal can self-medicate, obeying natural laws in chemistry that are unknown to animals. A tree grows when pruned, so we can see this pandemic as an opportunity. Let's grow, nature is not a zero-sum game!

Irrational numbers and mathematical real-numbers are uncomputable, with probability 1.

But irrational numbers can be calculated exactly in algebra a and that is how animals are able to calculate-- in a network of thoughts.

One of the most important features that distinguish mathematics from other sciences is abstraction, so some of them think that mathematics is abstract concepts. Abstraction is simply (a mental process based on separating one of the properties from something, and considering it independent of others).

(The Link Between Mathematics and Ethics) was built on the basis of the new view of man in contemporary psychology, as this view tends towards the primacy of the mind. In other words, this is consistent with the new scientific view that began with the theory of relativity and quantum mechanics, which proved the centrality of the mind. After World War II, many psychologists pointed out that the abolition of the role of the mind in human behavior and the subjection of the mind to instinct in the method of psychoanalysis led to the dehumanization of man. Therefore, psychology in the new view considers reason and determination as the highest human faculties, and they distinguish man from animals. (And the mind and the will not only control the body, but they also control the emotions and nullify them when necessary. By subordinating the emotions to the mind, harmony and happiness become within the reach of man). (And the old view of science considers that the human mind cannot choose freely because matter does not act except by mechanical necessity. This is the reason why the old view tended to explain human actions in the language of instinct). In short, this study comes within this framework, that is, we proceed here from the fact that man is a conscious force, and what mathematics does is that it creates what can be called a “moral authority” with mental foundations, meaning that the ethics generated by mathematics are based on the authority of the mind, not fear. (According to Dr. Mahmoud Bakir's opinion).

Ignoring the displacements due to strain in the element, the rigid body translation equals the average of the nodal displacements of the elements and the rigid body rotations equal the average rotations of the nodes of the element. I believe this would offer high accuracy for elements away from the regions of constraints.

History of mathematics can offer students a window into the processes of developing new mathematics, and the ways in which this knowledge is accepted and circulated within different communities. Especially pertinent to the question of decolonising the curriculum, turning to the history of the discipline offers a window into the role played by mathematics and mathematicians in settler colonialism, and how the mathematics we use today was in turn shaped by colonialism.

A new project at The Open University will produce an interactive online database of original sources, selected to demonstrate the global nature of mathematics. Original sources – such as letters, calculation aids, khipu or clay tablets – enable students to see beyond the final results explicated in their university textbooks to the work that went into uncovering these results in the first place...

origin

Three more papers published by my purported to prove Fermat's Last Theorem are attached herewith.

Clarivate announced that starting with 2023 ESCI-indexed journals will also be assigned an impact factor. See: https://clarivate.com/blog/clarivate-announces-changes-to-the-2023-journal-citation-reports-release/

Online-based classrooms are necessary for circumstances where the learners and teachers feel that the knowledge can be catered to without meeting in person. It is an opportunity for learners to learn at their doorsteps. Nonetheless, online classes are not as effective as offline classes for many learners who take education as a social process where peer learning, group dynamics, and interpersonal relationship are of high importance. Online class doesn't provide the experience of personal interaction while learning.

There is even such a discipline called "COmputational Social Sciences"...

I recommend research results from authors of the French group of Didactis of Mathematics as: Vergnaud, Bideaud, Meljac, Fischer, Brun. Also, from Oxford University Peter Bryant and Terezinha Nunes.

Most statisticians agree that the minimum sample size to get any kind of meaningful result is 100.

We can imagine any finite quantity to be halved, and then each half to be halved again, and so on, without end. You can then say the finite quantity has infinitely many parts. It's just a conceptual distinction.

Raphael Neelamkavil , you said, "But in your paper "The zero-dimensional physical theory (V): information, energy, efficiency, and intelligence" you exhibit enough awareness of the above facts. Hence, I do not understand what else you meant by the question at the end of your comment!".

The title of this forum topic is, "Can the Primitive Notions (Categories) and Axioms of Mathematics, Physics and Philosophy Converge?". When I said, "This is all a good question and debate, yet what is deliberate misinformation and ignorance, what is the drive for it, and can it be written about in a way so as not to promote it as being useful?" I am essentially asking whether or not the primitive notions are already granted by the contemporary ideas of mathematics, physics, and philosophy. My work highlights they are not, so a clear issue in this debate is all about what is assumed and what is not. My work with zero-dimensionality assumes nothing, and thence creates a new spectrum of ideas for mathematics, physics, and philosophy which has been, is, and perhaps still will be for most.

In Leon Lederman's wonderful book, "The God Particle" he comments about a pecking order in physics. It goes something like, "the experimental physicists only defer to the theoretical physicists who in turn only defer to the mathematician and the mathematician only defer to God..."

Physics is not mathematics. The role of physics like all sciences is to understand the universe. The theoretical physicists' role is to develop theories that explains all the experiments from the past plus allows predictions to be made to test the and potentially falsify the theory. The role of the experimental physics is to develop and perform those experiments. There is often as much deep mathematics used by an experimental physicists as a theoretical physicists.

The role of the mathematician is simple to expend the understanding of mathematics through rigorous logical reasoning. If a physicists or any other scientist finds these tools useful - then great.

Arguably the greatest theoretical physicists of the second half of the 20 Century was Richard Feynman. Here is what he said about physics.

"It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong."

I would suggest for a better understanding of physics - what it is and isn't - a read of "The God Particle" would be recommended

https://en.wikipedia.org/wiki/The_God_Particle_(book) .

As far as I understand your problem, you first need a mathematical relation between the instructions and rank. For instance, Rank x should correspond to some instruction value as y and vice versa; it means you require a mathematical function.

So there are various methods/tools to find a suitable (as accurate as you want) to find mathematical function based on given discrete values like curve fitting methods or the use of ML.

Further, Once you obtain the mathematical function, run your code a few times, and you will get a set for various combinations of (instruction, rank). These set values will work as the feedback for your derived function. Make changes based on the feedback, and you will get a much more accurate function.

I hope you are looking for the same.

One possible approach is presented in the attached word document

And this:

"Theoretically, such a system can be solved exactly; i.e. it can be determined whether the system has real solutions or not, and if it has, its solutions can be calculated exactly." is exactly what CAS-systems like Maple and Mathematica do. Good for Dudley J Benton to have a perpetual subscription. My experience is: the Maple syntax is simpler - and the sysmbolic solution of partial differential equations is better in Maple than in Mathematica. But for people wthout a license Mathematica is easier to rech - via wolframaplha.com. And there you need not to adhere to the syntax rules.

A point in space is given always by two points:

- coordinates of the point

- coordinates of origin of coordinates

Between those two points there is a "length" (physical dimension) with a physical Unit (Meters)

For vectors X1=[x1,1;x2,1;..,xn,1]; X2=[x1,2;x2,2;..,xn,2];,.., Xn=[x1,n;x2,n;..,xn,n]

M=[m1,m2,..mn] - vector median,

where

m1=med(x1,1; x2,1;..,xn,1)

m2=med(x1,2; x2,2;..,xn,2)

- - - - - - - - - - - - -

mn=med(x1,n; x2,n;..,xn,n)

I did give a physical explanation for why your boundary condition enforces the function f to become zero at r=0. In at least one physical interpretation, it models a system with infinite emission/absorption rate at r=0. This forces the temperature at this point to immediately become equal to the environmental temperature. In this interpretation f is (proportional to) the difference between body and environment temperatures. When you define a physcally unreasonable it is only fair that it provides you with physically unreasonable results ;-D

Thank you, Anton Vrdoljak.

For my opinion we can use any product formulas only under condition of independence. For example the formula that you used P(a,b│c)=P(a│c)∙P(b│c) is valid if a and b are independent each from other. Both may be dependent from c. But it can be the case of so called "false dependence". For example a is the usage of energy, b is sale of warm clothes, c is decreasing of tempetature.

Sorry, Jianhing. But I think you have misunderstood something in the lecture. Frequentist statistics, which is an interpretation of probability to be assigned on the basis of many random experiments.

In this setting, on designs functions of the data (also called statistics) which estimate certain quantities from data. For example, the probability p of a coin to land heads is given from n independent trials with the same coin and just counting the fraction of heads. This is then an estimator for the parameter p.

Each estimator should have desirable properties, as unbiasedness, consistency, efficiency and low variance and so on. Not every estimator has these properties. But, in principle one can proof, whether a given estimator has these properties.

So, it is not a characteristics of frequentist statistics, but a property of an individual estimator based on frequentist statistics.

The solution is not a mathematical formula!

The question can be approached by two ways:

a) experimental: prepare homogenous standards having the same density and geometry as your samples, #1 material with low K,Th,U content, #2 same as #1 with known amount of K added, #3 same as #1 with known amount of Th added ,and #4 same as #1 with known amount of U added.

From the differences between measurements #N-#1 you may deduce the contribution of each of the three elements to the spectrum and, more specifically, the contribution of each of them to three regions of interest corresponding to strong peaks of each element, usually 1.46 MeV for 40K, 2.61 MeV for Tl208 (progeny of Th) and 609 keV for Bi214 (progeny of U), assuming secular equilibrium in Th and U families, or at least the same disequilibrium conditions in sample and standards.

It is then possible to calculate a matrix relating the measurements in the 3 ROIs to the three activities.

b) Monte Carlo simulation. The NaI detector is usually quite simple and can be simulated with a good accuracy. Experimental measurements are still necessary to evaluate the gaussian broadening of the peaks at the different energies, and an experimental validation of the MC model is always desirable.

If the methods are different, it is likely that there is no correlation ...

However, it would help a lot to know the datasets and the processing you say you have done.

My predisposition to mull with numbers and mathematical equations consistently, even though I do not specialize in the math field as a professional, is due to having FUN filled mentors early in life. They were so creative to attach images and anecdotes to math problems that my sense of wonder and fun was constantly tickled as I trundle along mathematical mines and problems. Missing the correct answer was not occasion for embarrassment but for more opportunities to discover funny and creative ways to approach math problems with new, innovative, and fun-filled attempts. My mentors showed me the short-cut methods, the winding methods, and the funny but sure fire methods. I do not believe I ever hated math. Math is FUN!

I thought it would be better to type my work. Here is a link to the acceptable version of the article : https://www.researchgate.net/publication/364357359_A_contradiction_in_the_formula_of_Poisson_which_destroys_Riemann's_Hypothesis

I thought it would be better to type my work. Here is a link to the acceptable version of the article : https://www.researchgate.net/publication/364357359_A_contradiction_in_the_formula_of_Poisson_which_destroys_Riemann's_Hypothesis

Therefore, you have 20x20 = 400 control points. If you do georeferencing in Qgis, you can use all control points or some of them, like every 5 Km (16-points). During resampling, all pixels have coordinates in the ground system.

If you do not do georeferencing (no resampling), then you could calculate the coordinates of unknown pixels by interpolation. Suppose a pixel size a [m], then in one km, you have p = 1000/a pixels, and therefore known coordinates have the first(x1,y1) and the last(x2,y2) pixel. The slope angle between the first and last pixel is:

s = arc-tan[(x2-x1)/(y2-y1)]. Therefore, a pixel of a distance d from the first pixel has coordinates x = x1 + d.sin(s) and y = y1 +d.cos(s). You can do either row of column interpolation or both and take the average.

For me the following book is very useful

Functional Equations and How to Solve Them (Problem Books in Mathematics)

Springer

Christopher G. Small

Year:

2006

Language:

English

WO 2017/037729 A1: Concurrent architecture of Vedic multiplier-an accelerator scheme for high speed computing

Mathematics is essentially one of the professional tools of science, including for physicists.

Admire the tool... If the cook says "Miracle saucepan", then the food will not get better...

Students should be shown the application of mathematics from a practical point of view. On the other hand, it is necessary to respect the theoretical side of mathematics, which is not easy for everyone to learn.@Peter Kepp Rickardo Gomes

Hi fellow researcher,

I think the answer depends on what kind of equipment you have on your disposition and what is your purpose. The simpler way is to have a model blade and compare it to the blade you want to determine the integrity using the physical properties of the blade.

For example, if you have an accurate sound sensor and a device that produces an specific sound profile in the model blade you can use this device to produce a similar sound in the test blade. Comparing the Fourier decomposition of frequencies of the sound produced by the test blade will give you information of cracks and non-uniformity in density produced by the forging process or even if the material the blade was made is of quality or not.

You can do a similar approach with thermodynamics. you can heat Specific spots on the test blade. As cracked regions do not conduct heat as well as non-cracked regions you will observe anomalies in the heat map of the blade.

Notice you don't really have to calculate something, but just know what to expect with a model blade data.

Dear, to understand the NATURE

The RHS is a fraction, whose numerator and denominator are quadratic expressions in Δ. Therefore the fraction takes positive values when numerator and denominator are of the same sign...

Also, Hamilton-Jacobi theory can be applied with not only fractional derivatives but also, definition of fractional derivatives and integrals on time scale Yazen Alawaideh

The question is too general. To generate the basic idea of the algorithm, you need to know the detailed statement of the problem. Typically, the process of developing an algorithm starts with the identification of your problem complexity class. If there is no evidence or clear feeling that the problem is NP-hard, then it is reasonable to try to develop a polynomial algorithm for solving it. Such algorithms are usually based on the use of specific properties of the problem. Sometimes it is possible to construct a polynomial algorithm based on the general scheme of dynamic programming, taking into account the specific properties of the problem.

If the problem is known to be NP-hard, then branch-and-bound methods, dynamic programming, and their modifications often work well for a relatively small problem dimension. Sometimes it is possible to build a successful formulation of the problem in the form of an integer programming model, followed by the use of appropriate methods or ready-made software. For high-dimensional problems, you can either use well-known metaheuristics, or develop your own approximate algorithm. In the latter case, success is usually based on the use of the problem properties. As you can see, in any case, it is useful to start by studying the specific properties of your particular problem.

Dear, Tekle Gemechu basins of attraction comes from the dynamical system and chaos theory. It is related with systems behavior. There are several example of basins of attraction. Therefore, definition and examples of basins of attraction are given in scholarpedia. Below scholarpedia's link:

Hi Hieram, youre welcome! Imho fun should be induced by fruitful scientific research supported by open commenting one other’s ideas (opposed to endless fruitless repeating discussions what presumingly not cannot ever work … until it does) like iSpace („integer-Space„ or „complex-Space“ when treating the i as the one for a complex number) able to derive and decipher inter-relationships, dependencies and calculate exact arbitrary precision numerical values for most but all constants of nature.

Also recently a new true quantum geometric iSpace-IQ unit system has been developed, able to directly represent native quantum relations of contants while keeping strictly compatible to MKSA/SI system showing a single *time* based conversion factor, effective predicting quantization of time itself.

So - no - being a true long time Apple expert consultant i’d say we do not need to fear to be sued for (at least not in the foreseeable future ;-) ). And please all take the time to read thru the very short yet imho rreally convincing math of both of my newest papers to be found on my RG home.

Here is a link to RG summary of my iSpace project:

Metric space A is said to be a totally bounded if every Cauchy sequence in A has convergent sub sequence

Fertility rate, mortality rate, menstrual period, gestation of the fetus week per week compare to the physiological and patological symptoms, body weight and body height to determine the healthyness, the length of conjugata vera, conjugata diagonale, etc to assest the passage for labour the baby need sectio caesarea or not. Count the weeks of gestation to know the maturity of embrio or fetus organ systems, mengukur tinggi fundus uteri dengan meteran untuk menaksir masa kehamilan, ukur jarak dari symphisis pubis dan proccesus xyphoideus sebagai patokan, ukur lingkar lengan atas dengan meteran, menentukan masa subur untuk fertilisasi dengan perhitungan penanggalan, dll.

Theories and Theories of Truth | SpringerLink

I have many times served as an applied mathematician on a multi-disciplinary team, including, for instance, biologists, meteorologists, geologists, hydrologists, etc. The other team members possessed essential knowledge to the success of the project but not the math skills. This is good for you to recognize in the study of business because nobody knows everything. A diverse team can solve problems that a single individual cannot. I would have the biologists explain over and over again that part they understood (like fish behavior or metabolic needs) and I would create a model. Then we would run the model and ask, "Is it responding the way you expect it to?" One of these interesting projects considered production of peanut butter crackers and cheese crackers sold in vending machines manufactured on the same assembly line at a factory on the road from my house to the school. Walk over to the Mathematics Department and find a graduate student studying applied mathematics who is looking for a project. You can help each other.

Ankur Maheshwari I agree with Ben Cardoen that a heuristic/partial search algorithm may provide a sufficiently good solution to an optimization problem, especially with incomplete or imperfect information or limited computation capacity where commercial solvers may struggle. But the key issue of heuristics is that they do not guarantee that a globally optimal solution can be found on some class of problems when compared with commercial solvers such as Ipopt, Cplex, Mosek, Gurobi,..., for NLP or LP or MILP or MINLP problems.

Hi Sunday Emmanuel Fadugba I have no experience with SCILAB (and very little with MATLAB). What I can recommend is using Mathematica (if you can afford it; or maybe you can use the free version on Raspberry Pi) or Julia (free). Hope it helps.

I like this new thinking. But for me it is difficult to say "true" or "false" since everyone has his own standard. I feel interested in the definition convenient both in the application and mathematical analysis.

I agree that it starts in Piaget's sensory-motor stage of play. Mary Reilly's Systems Explanation of play: Learning through play and the Third form of Information Processing theories mirror and expand on Piaget's Theory of play and learning.

Dear Abdollah Aliesmaeili ,

Just based on the metrics I would suggest that you might have a look at:

Educational Studies in Mathematics https://www.springer.com/journal/10649 CiteScore 3.6 (SJR Q1 journal), Impact factor 2.853 (JCR Q2 journal)

ZDM – Mathematics Education https://www.springer.com/journal/11858 CiteScore 4.1 (SJR Q1 journal), Impact factor 2.481 (JCR Q2 journal)

Journal of mathematics teacher education https://www.springer.com/journal/10857 CiteScore 3.6 (SJR Q1 journal), Impact factor 1.786 (JCR Q2 journal)

Research in Mathematics Education https://www.tandfonline.com/journals/rrme20 CiteScore 3.4 (SJR Q1 journal), ESCI indexed (so no impact factor and Q ranking (yet))

Best regards.

Dear Shireen,

There are data-driven and parametric that you can utilize to detect chaos. If the system is well-defined, a good starting point can be Lyapunov Exponent and Poincare map. If you have only output of the system then you need data-driven methods like 1/0 test or entropy-based methods.

Regards

coupling equations available in ODEs and also built-on ode45, ode15, ect code in matlab.