Mathematics - Science topic

It is crucial to understand that this expression could be used in problems related to engineering, physics, mathematics, or any other aspect of real life.

Typically, Matlab is used to solve ODE and PDE problems. Perhaps users calculated this term 0^0 incorrectly in the process.

>> % How to fix this problem 0^0 in Matlab !?

>> % Mathematically, x^0=1 if x≠0 is equal 1 else undefined(NaN)

>> 0^0

ans =

1

>> f=@(x,y) x^y;

>> f(0,0)

ans =

1

>> v=[2 0 5 -1];

>> v.^0

ans =

1 1 1 1

We assume that this is true nowadays, because two mathematicians from two different mathematical fields can hardly find a common language to communicate.

The question arises: is it possible to reorganize at least the mathematical language?

I have 'N' number of inputs (which correspond to temperature) to calculate a specific output parameter. I'm getting 'N' number output data based on the inputs.

However, my goal is to select an optimum number from all the output data and use it in another calculation.

'N' number of input data --> Output parameter calculation --> Identification of an optimized output parameter --> Use that value for another calculation.

How to find an optimal value among 'N' "number of output data. Can we employ any algorithm or process?

how Using mathematical modelling in mathematics education can be an innovative and powerful approach to helping students understand how mathematical concepts can be applied in real-world situations?

DEAR PROFESSORS

GREETINGS OF THE DAY.

NOWADAYS WE ARE USING MANY SOFTWARE FOR MATHEMATICS.

FOR MATHEMATICS WORK, IS THERE ANY FREE AI BASED APPS AVAILABLE?

IF SO, PLEASE KINDLY SHARE THE LINK HERE.

THANKS ALL

The limits of logic and mathematics is that we couldn't describe a question without symbol system, but symbol system is just an abstraction of the real world not the real world itself, so there is a distance between the abstracted symbol system and the real world, therefore there is truth we can't reach by symbol system, which A-HA moment may reach. But when we thinking we always use a symbol system like words or mathematics with apriori logic, so I wonder if AI could have A-HA moment?

My current workflow needs the following features

Do you feel that deep learning is mainly an engineering contribution?

Fermat's last theorem was finally solved by Wiles using mathematical tools that were wholly unavailable to Fermat.

Do you believe

A) That we have actually not solved Fermat's theorem the way it was supposed to be solved, and that we must still look for Fermat's original solution, still undiscovered,

or

B) That Fermat actually made a mistake, and that his 'wonderful' proof -which he did not have the necessary space to fully set forth - was in fact mistaken or flawed, and that we were obsessed for centuries with his last "theorem" when in fact he himself had not really proved it at all?

I have Temperature results for eight different paths. The results are in the form of the column having 200 values see attached image. I want the average temperature for these eight paths at those 200 points.

Mathematically, it is posited that the cosmic or local black hole singularity must someday become of infinite density and zero size. But this is unimaginable. If an infinite-density stuff should exist, it should already have existed.

Hence, in my opinion, this kind of mathematical necessities are to be the limiting cases of physics. IS THIS NOT THE STARTING POINT TO DETERMINE WHERE MATHEMATICS AND PHYSICAL SCIENCE MUST PART WAYS?

I believe that it is common knowledge that mathematics and its applications cannot directly prove Causality. What are the bases of the problem of incompatibility of physical causality with mathematics and its applications in the sciences and in philosophy?

The main but very general explanation could be that mathematics and mathematical explanations are not directly about the world, but are applicable to the world to a great extent.

Hence, mathematical explanations can at the most only show the general ways of movement of the processes and not demonstrate whether the ways of the cosmos are by causation, what the internal constitution of every part of it is, etc. Even when some very minute physical process is mathematized, the results are general, and not specific of the details of the internal constitution of that process.

No science and philosophy can start without admitting that the cosmos exists. If it exists, it is not nothing, not vacuum. Non-vacuous existence means that the existents are non-vacuously extended. This means that they have parts. Every part has parts too, ad libitum, because each part is extended and non-infinitesimal. Hence, each part is relatively discrete, not mathematically discrete.

None of the parts of any physical existent is an infinitesimal. They can be near-infinitesimal. This character of existents is Extension, a Category directly implied by the To Be of Reality-in-total.

Similarly, any extended being’s parts -- however near-infinitesimal -- are active, moving. This implies that every part has so (finite) impact on some others, not on infinite others. This character of existents is Change.

No other implication of To Be is so primary as these two (Extension-Change) and directly derivable from To Be. Hence, they are exhaustive of To Be.

Existence in Extension-Change is what we call Causality. If anything is existent, it is causal – hence Universal Causality is the trans-scientific and physical-ontological Law of all existents.

By the very concept of finite Extension-Change-wise existence, it becomes clear that no finite space-time is absolutely dense with existents. Hence, existents cannot be mathematically continuous. Since there is continuous (but finite and not discrete) change (transfer of impact), no existent can be mathematically absolutely continuous or discrete in its parts or in connection with others.

Can logic show the necessity of all existents as being causal? We have already discussed how, ontologically, the very concept of To Be implies Extension-Change and thus also Universal Causality.

WHAT ABOUT THE ABILITY OR NOT OF LOGIC TO CONCLUDE TO UNIVERSAL CAUSALITY?

In my argument above and elsewhere showing Extension-Change as the very exhaustive meaning of To Be, I have used mostly only the first principles of ordinary logic, namely, Identity, Non-contradiction, and Excluded Middle, and then argued that Extension-Change-wise existence is nothing but Universal Causality, if everything existing is non-vacuous in existence.

For example, does everything exist or not? If yes, let us call it non-vacuous existence. Hence, Extension as the first major implication of To Be. Non-vacuous means extended, because if not extended, the existent is vacuous. If extended, everything has parts.

The point of addition now has been Change, which makes the description physical. It is, so to say, from experience. Thereafter I move to the meaning of Change basically as motion or impact.

Naturally, everything in Extension must effect impacts. Everything has further parts. Hence, by implication from Change, everything causes changes by impacts. Thus, we conclude that Extension-Change-wise existence is Universal Causality. It is thus natural to claim that this is a pre-scientific Law of Existence.

In such foundational questions like To Be and its implications, we need to use the first principles of logic, because these are the foundational notions of all science and no other derivative logical procedure comes in as handy. In short, logic with its fundamental principles can help derive Universal Causality. Thus, Causality is more primary to experience than the primitive notions of mathematics.

Extension-Change, Universal Causality derived by their amalgamation, are the most fundamental Metaphysical, Physical-ontological, Categories. Since these are the direction exhaustive implications of To Be, all philosophy and science are based on these.

Bibliography

(1) Gravitational Coalescence Paradox and Cosmogenetic Causality in Quantum Astrophysical Cosmology, 647 pp., Berlin, 2018.

(2) Physics without Metaphysics? Categories of Second Generation Scientific Ontology, 386 pp., Frankfurt, 2015.

(3) Causal Ubiquity in Quantum Physics: A Superluminal and Local-Causal Physical Ontology, 361 pp., Frankfurt, 2014.

(4) Essential Cosmology and Philosophy for All: Gravitational Coalescence Cosmology, 92 pp., KDP Amazon, 2022, 2nd Edition.

(5) Essenzielle Kosmologie und Philosophie für alle: Gravitational-Koaleszenz-Kosmologie, 104 pp., KDP Amazon, 2022, 1st Edition.

Why are numbers and shapes so exact? ‘One’, ‘two’, ‘point’, ‘line’, etc. are all exact. But irrational numbers are not so. The operations on these notions are also intended to be exact. If notions like ‘one’, ‘two’, ‘point’, ‘line’, etc. are defined to be so exact, then it is not by virtue of the exactness of these substantive notions, but instead, due to their being defined so, that they are exact, and mathematics is exact.

But on the other side, due to their being adjectival: ‘being a unity’, ‘being two unities’, ‘being a non-extended shape’, etc., their application-objects are all processes that can obtain these adjectives only in groups. These are pure adjectives, not properties which are composed of many adjectives.

A quality cannot be exact, but may be defined to be exact. It is in terms of the exactness attributed to these notions by definition that the adjectives ‘one’, ‘two’, ‘point’, ‘line’, etc. are exact. This is why the impossibility of fixing these (and other) substantive notions as exact misses our attention.

If in fact these quantitative qualities are inexact due to their pertaining to groups of processual things, then there is justification for the inexactness of irrational numbers, transcendental numbers, etc. too. If numbers and shapes are in fact inexact, then not only irrational and other inexact numbers but all mathematical structures should remain inexact except for their having been defined as exact.

Thus, mathematical structures, in all their detail, are a species of qualities, namely, quantitative qualities. Mathematics is exact only because its fundamental bricks are defined to be so. Hence, mathematics is an as-if exact science, as-if real science. Caution is advised while using it in the sciences as if mathematics were absolutely applicable, as if it were exact.

Bibliography

(1) Gravitational Coalescence Paradox and Cosmogenetic Causality in Quantum Astrophysical Cosmology, 647 pp., Berlin, 2018.

(2) Physics without Metaphysics? Categories of Second Generation Scientific Ontology, 386 pp., Frankfurt, 2015.

(3) Causal Ubiquity in Quantum Physics: A Superluminal and Local-Causal Physical Ontology, 361 pp., Frankfurt, 2014.

(4) Essential Cosmology and Philosophy for All: Gravitational Coalescence Cosmology, 92 pp., KDP Amazon, 2022, 2nd Edition.

(5) Essenzielle Kosmologie und Philosophie für alle: Gravitational-Koaleszenz-Kosmologie, 104 pp., KDP Amazon, 2022, 1st Edition.

Pakistan is probably the only country in the World, where maths is not required in 11 & 12th grades. Two decades back half in these classes would opt for maths and half for biology. Recently the trend has been changed and the enrolment in maths is severely decreased and hence enrolment in the engineering programs is also affected. I believe that as community we should work to make maths in 11 & 12th classes compulsory and also allow admission in engineering programs to students without maths.

What else can be the solution of this serious problem?

Can you share with me some books on this topic: Mathematics and software for computer-aided design of switches RF. Thanks a lots.

Please give specific idea.

Please let me know the mathematical formula and steps for the determination of solubility of drugs

Do lines t₁, t₂, and t₃ intersect at a single point? If yes, prove it!

Please, take a look at the problem statement in the attached photos.

Are computer science papers generally not as complex as mathematics papers?

What is satisfaction? I would like to hear your opinions from various perspectives. It has many perspectives: logical, mathematical, philosophical, musical, pictorial, poetic, spiritual, physical, and many others.

There are a lot of researchers who go by the book the right approach and write results, and observations in their field of work, proving the existing information or suggesting improvement in the experiment for better analysis and so on, very hard working but then there are other who are crazy thinkers always suggesting things with little backup from existing experiments or know facts, always radical in their understanding of results, and these people mostly get dismissed as blip by the first category of researchers.

So if I have to take your opinion who will you back for hitting gold one who is methodical and hardworking or who are crazy thinker?

What is the best mathematical technique used to derive the equation of the compound cross section of the real irrigation channels?

Maybe in general (on metric spaces, etc).

It's like literature review/ reference.

Are computer science papers generally not as profound as mathematics papers?

I have two original equations with three unknowns ( X, Y, Z). I've just added one extra equation to make the original equations solvable. What should I call this adding process in mathematics? I just need the correct wording for that. Any help would be appreciated. Thanks

Mathematical Generalities: ‘Number’ may be termed as a general term, but real numbers, a sub-set of numbers, is sub-general. Clearly, it is a quality: “having one member, having two members, etc.”; and here one, two, etc., when taken as nominatives, lose their significance, and are based primarily only on the adjectival use. Hence the justification for the adjectival (qualitative) primacy of numbers as universals. While defining one kind of ‘general’ another sort of ‘general’ may naturally be involved in the definition, insofar as they pertain to an existent process and not when otherwise.

Why are numbers and shapes so exact? ‘One’, ‘two’, ‘point’, ‘line’, etc. are all exact. The operations on these notions are also intended to be exact. But irrational numbers are not so exact in measurement. If notions like ‘one’, ‘two’, ‘point’, ‘line’, etc. are defined to be so exact, then it is not by virtue of the exactness of these substantive notions, but instead, due to their being defined as exact. Their adjectival natures: ‘being a unity’, ‘being two unities’, ‘being a non-extended shape’, etc., are not so exact.

A quality cannot be exact, but may be defined to be exact. It is in terms of the exactness attributed to these notions by definition that the adjectives ‘one’, ‘two’, ‘point’, ‘line’, etc. are exact. This is why the impossibility of fixing these (and other) substantive notions as exact miss our attention. If in fact these are inexact, then there is justification for the inexactness of irrational, transcendental, and other numbers too.

If numbers and shapes are in fact inexact, then not only irrational numbers, transcendental numbers, etc., but all exact numbers and the mathematical structures should remain inexact if they have not been defined as exact. And if behind the exact definitions of exact numbers there are no exact universals, i.e., quantitative qualities? If the formation of numbers is by reference to experience (i.e., not from the absolute vacuum of non-experience), their formation is with respect to the quantitatively qualitative and thus inexact ontological universals of oneness, two-ness, point, line, etc.

Thus, mathematical structures, in all their detail, are a species of qualities, namely, quantitative qualities, defined to be exact and not naturally exact. Quantitative qualities are ontological universals, with their own connotative and denotative versions.

Natural numbers, therefore, are the origin of primitive mathematical experience, although complex numbers may be more general than all others in a purely mathematical manner of definition.

Bibliography

(1) Gravitational Coalescence Paradox and Cosmogenetic Causality in Quantum Astrophysical Cosmology, 647 pp., Berlin, 2018.

(2) Physics without Metaphysics? Categories of Second Generation Scientific Ontology, 386 pp., Frankfurt, 2015.

(3) Causal Ubiquity in Quantum Physics: A Superluminal and Local-Causal Physical Ontology, 361 pp., Frankfurt, 2014.

(4) Essential Cosmology and Philosophy for All: Gravitational Coalescence Cosmology, 92 pp., KDP Amazon, 2022, 2nd Edition.

(5) Essenzielle Kosmologie und Philosophie für alle: Gravitational-Koaleszenz-Kosmologie, 104 pp., KDP Amazon, 2022, 1st Edition.

Learning strategies

-feynman technique

-active recall technique

Title: "feynman technique" and its effect on student mathematical learning in solving algebra.

What I always found an RRL/RRS, their methods were teaching strategies. Basically, teachers will introduce/utilize this method in their daily lesson plan on the experimental group. Is their any way that won't include the teachers, instead only the students will be involved in the methodology?

Updated information of my thoughts and activities.

This is meant to be a one-way blog, albeit you can contribute with your recommendations and comments.

I am conducting a research project involving the use of the MACD (Moving Average Convergence Divergence) signal indicator for analyzing multivariate time series data, possibly for trading purposes.

I've defined some initial parameters such as ema_short_period, ema_long_period, and signal_period. However, I'm interested in insights and best practices for parameter selection in such analyses.

I used these values to calculate and implement this indicator.

What parameters should I consider when dealing with multivariate data, and how can I optimize these parameters for my specific analysis goals?

Additionally, if anyone has experience with using the MACD in multivariate time series analysis, I'd appreciate any advice or insights you can provide.

I'm implementing this using python.

Thank you!

Note. The sequence of polynomials should be the same for all the continuity points; yet the convergence does not have to be uniform of the continuity set.

Comment. Looks and sounds like "déjà vu", a consequence of some known result. So far, I've got this: The continuity set is G_δ (i.e., a countable intersection of open sets) hence, by a theorem of Mazurkiewicz, it can be endowed as a complete metric space. Also, by the Heine-Borel theorem, a metric space is complete and totally bounded if and only if it is compact. So one may wonder if the above result is just a consequence of the following extension(s) of Weierstrass’ approximation theorem: to compact metric spaces (due to Stone) or to totally bounded metric spaces (due to Bishop). In other words, this issue amounts to the question: is a G_δ set totally bounded? And the answer is in the negative because, in general, not every bounded metric space is totally bounded.

Traffic models are very useful for various purposes. First, they can help in the design and operations of traffic systems since they can predict traffic operational conditions at some time in the future under various sets of design, traffic, and control characteristics. Traffic engineers and designers can make decisions regarding facility modifications or traffic management improvements based on the expected impact of those improvements in the transportation system. Second, they can help in the evaluation of existing systems and in the development of priorities for improvement. Mathematical models are those that describe a physical system mathematically. Such models describe specific r​e​l​a​t​i​o​n​s​h​i​p​s​”

There are a few stance to this.

1. Thats a technical problem mostly, not a physical limitation.

(One can start with the assumptions that is possible, derive some results and then see how the Big picture leads to the resolution of initial problem.

2. Its not technical since if the mathematics fail, physics fails too the 2 cannot be separated.

3. Its a conformist's view. Established science says it is true and people stick to the established viewpoints in fear of tracing a new path.

Which one do you endorse?

Bonjour,

Je suis actuellement en train de travailler sur un projet de recherche portant sur l'utilisation de l'optimisation mathématique pour déterminer le taux directeur optimal en politique monétaire. J'aimerais savoir s'il existe des travaux de recherche récents ou des modèles spécifiques qui ont abordé ce sujet. De plus, je suis à la recherche de conseils sur la manière de structurer mon modèle et de choisir des variables pertinentes pour ce type d'analyse. Toute suggestion de lecture ou d'expertise serait grandement appréciée.

Merci d'avance pour votre aide

Tutorial Videos related to Mathematics with Sympy, Scipy, and Python Videos at my YouTube Channel https://www.youtube.com/@1414Abhinandan/videos.

Thank you.

If this ordinary person with zero basic knowledge can learn advanced mathematics in one or two years, then I think this will greatly improve the entire mathematics or scientific research community. (Those who have methods or opinions can express their own opinions. If There is no way I will start learning advanced mathematics from scratch)

Does someone have any idea for proving or rejecting the Riemann Hypothesis?

Mathematical proof of Euler product 

ζ(s) = Σ 1/n^s = 1/1^s + 1/2^s + 1/3^s + ... ... + 1/n^s -----[1]

s>=1, ζ(S) divergent

1/2^s ζ(S) = 1/2^s + 1/4^s + 1/6^s + ... ... + 1/2n^s -----[2]

[1]-[2]

=> (1-1/2^s) ζ(S) = 1 + 1/3^s + 1/5^s + 1/7^s + ... ... -----[3]

1/3^s (1-1/2^s) ζ(S) = 1/3^s + 1/9^s + 1/15^s + 1/21^s + ... ... -----[4]

[3]-[4]

=> (1-1/3^s) (1-1/s^s) ζ(S) = 1 + 1/5^s + 1/7^s + 1/11^s + 1/13^s + ... ...

... ...

(1-1/5^s)(1-1/3^s)(1-1/2^s) ζ(S) = 1 + 1/7^s + 1/11^s + 1/13^s + ... ...

... ...

∏(1-1/p^s) ζ(S) = 1

p(prime numbers)

=> ζ(S) = ∏(1-1/p^s)^(-1) = 1/1^s + 1/2^s + 1/3^s + ... ... + 1/n^s

s=1, ζ(S) divergent

So prime numbers are infinitas

Euler product is only meaningful when s>=1; the output will diverge if s<1

Riemann used analytic continuation to make the ζ(s) function meaningful on the complex plane 

when s<1.

ζ(s) = Σ 1/n^s = 1/1^s + 1/2^s + 1/3^s + ... ... + 1/n^s

analytic continuation -∞ <= s <= ∞

=> ζ(s) = Γ(1-s)/2𝝅i * ∫{-∞}^[∞] [(-Z)^s / (e^z - 1)] dZ/Z = Reimann ζ function (s)

Reimann ζ(s) = Σ 1/n^s, s∈C, n∈N

where s is any complex number, while n is any natural number.

Γ(s)= (s-1)!

ζ(s) = 2Γ(1-s)/(2𝝅)^(s-1) * sin (𝝅s/2) ζ(1-s)

when s = -2, -4, -6 ... ...

ζ(s) = 0 (trivial zeros)

Reimann hypothesis (1859)

all nontrivial zeros of ζ(s) function, their output of complex number with real part 1/2.

# Original paper here ----- https://www.emis.de/classics/Riemann/Zeta.pdf

In the meantime, I would like to say hello to the professors and those who are interested in mathematics. A question about whether dy/dx=dx/dy is a differential equation or not challenged my mind today. I got help from GBT and artificial intelligence and he answered that no it is an equation but it cannot be a differential equation and for the second time when a friend asked about artificial intelligence he answered that it is an algebraic equation and not an equation Differential! I asked math professors and they all said that yes, it is a non-linear first order differential equation that has two types of answers, the first type is the parallel lines that bisect the first and third quadrants, the second type is the parallel lines that bisect the second and fourth quadrants. Again, the question arose for me, why does artificial intelligence give the wrong answer to the problem, dear ones, because artificial intelligence uses special algorithms and does not have a central computing unit. Well, now the question is, why do the algorithms that define it give these wrong answers? Are the algorithms wrong or is it something else? In this matter, the professors of mathematics and computer science, please guide me by giving a complete answer. Thanks

Dear colleagues and enthusiasts of beautiful geometric problems, I invite you to solve another elegant problem:

Reconstruct triangle ABC from points A, D, E, and H1.

I will be glad to see your solutions and share my own!

Attaching mathematical expressions here is problematic. I am attaching the link to the question here.

link: https://physics.stackexchange.com/q/782250/147579

Dear Researchers,

Subject: Call for Systematic Literature Review Papers in Computer Science Fields - Special Issue in the Iraqi Journal for Computer Science and Mathematics

I hope this letter finds you in good health and high spirits. We are pleased to announce a unique opportunity for researchers in the field of computer science to contribute to our upcoming special issue focused on systematic review papers. As a Scopus-indexed journal with a remarkable CiteScore of 2.9 and a CiteScore Tracker of 3.5, the Iraqi Journal for Computer Science and Mathematics is dedicated to advancing the knowledge and understanding of computer science.

Special Issue Details:

- Title: Special Issue on Systematic Literature Review Papers in Computer Science Fields

- Journal: Iraqi Journal for Computer Science and Mathematics

- CiteScore Tracker: 3.5 (As per the latest available data)

- CiteScore: 2.9 (As per the latest available data)

- Submission Deadline: December 31, 2023

- Publication Fee: None (This special issue is free of charge)

We invite you to contribute your valuable insights and research findings by submitting your systematic review papers to this special issue. Systematic reviews play a crucial role in synthesizing existing research, identifying trends, and guiding future research directions. This special issue aims to gather a diverse collection of high-quality systematic review papers across various computer science disciplines.

Submission Guidelines:

Please visit our journal's submission portal at https://journal.esj.edu.iq/index.php/IJCM/submissions

to submit your paper. Make sure to select the special issue "Systematic Literature Review Papers in Computer Science Fields" during the submission process.

We encourage you to review the author guidelines and formatting requirements available on the journal's website to ensure your submission adheres to our standards.

Should you have any inquiries or need further assistance, please do not hesitate to contact our editorial team at mohammed.khaleel@aliraqia.edu.iq

Your contribution to this special issue will undoubtedly enrich the field of computer science and contribute to our mission of fostering academic excellence. We look forward to receiving your submissions and collaborating towards the advancement of knowledge.

Warm regards,

Dr. Mohammad Aljanabi

Editor in Chief

Iraqi Journal for Computer Science and Mathematics

ChatGPT scored a 155 on an IQ test , and has sufficient background to process mathematical proof review for example and verifying scientific formulas and checking at real time the plagiarism traces but the scientific community argues that the confidentiality breach prevents the use of AI as recognized peer reviewer , what do you think about it ? writers and journals should they recognize the AI as a valid peer reviewer ?

I am working on the image of some critical curves under complex-valued harmonic polynomials. The following picture was produced and I couldn't give the well known name for this in Mathematics. Can I get any suggestion on this please?

Hi,

Does anyone know a good way to mathematically define/identify the onset of a plateau for a curve y = f(x) in a 2D plane?

A bit more background: I have a set of curves from which I'd like to extract the x values where the "plateau" starts, by applying a consistent definition of plateau onset.

Thanks,

Yifan

Recently I've discussed this topic with a tautologist researcher, Quine's follower. The denial of the capacity of deductive logic to generate new knowledge implies that all deductive results in mathematics wont increase our knowledge for real.

The tautologic nature of the deduction seems to lead to this conclusion. In my opinion some sort of logic omniscience is involved in that position.

So the questions would be:

Thanks beforehand for your insights.

In the 'Collection of Geometric Problems' from 1966, there is a problem in which the author made a mistake.

Try to find the author's error!

In the picture, you can see the conditions of this mathematical problem without changes, with an error.

The experiment conducted by Bose at the Royal Society of London in 1901 demonstrated that plants have feelings like humans. Placing a plant in a vessel containing poisonous solution he showed the rapid movement of the plant which finally died down. His finding was praised and the concept of plant’s life has been established. If we scold a plant it doesn’t respond, but an AI bot does. Then how can we disprove the life of a Chatbot?

Article Topic: Some Algebraic Inequalitties

I have been collecting some algebraic inequalities, soonly it has been completed and published on Romanian Mathematical Magazine.

For computer science, is mathematics more of a tool or a language?

The fundamental theorem of calculus is the backbone of natural sciences, thus, given the occasional thin line between the natural and social, how common is the fundamental theorem of calculus in social sciences?

Examples I found:

Ohnemus , Alexander . "Proving the Fundamental Theorem of Calculus through Critical Race Theory." ResearchGate.net . 1 July 2023. www.researchgate.net/publication/372338504_Proving_the_Fundamental_Theorem_of_Calculus_through_Critical_Race_Theory. Accessed 9 Aug. 2023.

Ohnemus , Alexander . "Correlations in Game Theory, Category Theory, Linking Calculus with Statistics and Forms (Alexander Ohnemus' Contributions to Mathematics Book 9)." amazon.com. 12 Dec. 2022. www.amazon.com/gp/aw/d/B0BPX1CSHS?ref_=dbs_m_mng_wam_calw_tkin_8&storeType=ebooks. Accessed 11 July 2023.

Ohnemus , Alexander . "Linguistic mapping of critical race theory(the evolution of languages and oppression. How Germanic languages came to dominate the world) (Alexander Ohnemus' Contributions to Mathematics Book 20)." amazon.com. 3 Jan. 2023. www.amazon.com/Linguistic-evolution-oppression-Contributions-Mathematics-ebook/dp/B0BRP1KYLR/ref=mp_s_a_1_13?qid=1688598986&refinements=p_27%3AAlexander+Ohnemus&s=digital-text&sr=1-13. Accessed 5 July 2023.

Ohnemus , Alexander . "Fundamental Theorem of Calculus proved by Wagner's Law (Alexander Ohnemus' Contributions to Mathematics Book 8)." amazon.com. 11 Dec. 2022. www.amazon.com/gp/aw/d/B0BPS2ZMXC?ref_=dbs_m_mng_wam_calw_tkin_7&storeType=ebooks. Accessed 25 June 2023.

Most masters focus on general review of qm, classical mechanics, assesing students skills in classical yet heneric and self-value calculative and interpreting capabilities.

The English MSc's on the other hand, provide an introduction to the physical principles and mathematical techniques of current research in:

general relativity

quantum gravity

quantum f. Theory

quantum information

cosmology and the early universe

There is also a particular focus on topics reflecting research strengths.

Graduates are more well equiped to contribute to research and make impressive ph. D dissertations.

Of course instructors that teach masters are working in classical and quantum gravity, geometry and relativity, to take the theoretical physics sub-domain, in all universities but the emphasis on current research's mathematical techniques and principles is only found in English university'masters offerings.

The choice of coordinate systems is a mathematical tool used to describe physical events. Local or universal spatial events occur in multiple coordinate systems of space and time or spacetime as we know it under classical, relativistic and cosmological physics.

Whether the fundamental laws of physics remains consistent across different coordinate systems.

I have deep neural network where I want to include a layer which should have one input and two outputs. For example, I want to construct an intermediate layer where Layer-1 is connected to the input of this intermediate layer and one output of the intermediate layer is connected to Layer-2 and another output is connected to Layer-3. Moreover, the intermediate layer just passes the data as it is through it without doing any mathematical operation on the input data. I have seen additionLayer in MATLAB, but it has only 1 output and this function is read-only for the number of outputs.

"Mathematics is logical systems formulising relationships of variable(s) with other variable(s) quantitatively &/or qualitatively as science language." (Sinan Ibaguner)

I tried to devise my best description as shortly & clearly !

For physics, is mathematics more of a tool or a language?

"Matematik, değişken(ler)in diğer değişken(ler)le ilişkilerini niceliksel ve(ya) niteliksel tarz formüle eden mantıksal sistemlerin sanatsal bilim dili. "

Kısa ve net matematik tanımım ! Daha iyisi ne olabilir !?

Hello,

I am looking for mathematical formulas that calculate the rigid body movement of an element based on the nodal displacements. Can anyone give a brief explanation and recommend some materials to read? Thanks a lot.

Best,

Chen

I am using SPSS to perform binary logistic regression. One of the parameters generated is the prediction probability. Is there a simple mathematical formula that could be used to calculate it manually? e.g. based on the B values generated for each variable in model?

Paradox Etymology can be traced back to at least Plato's Parmenides [1]. Paradox comes from para ("contrary to") and doxa ("opinion"). The word appeared in Latin "paradoxum" which means "contrary to expectation," or "incredible. We propose, in this discussion thread, to debate philosophical or scientific paradoxes: their geneses, formulations, solutions, or propositions of solutions... All contributions on "Paradoxes", including paradoxical ones, are welcome.

[1] https://www.newworldencyclopedia.org/entry/Paradox

If someone can help me understand Helicity in the context of the High Harmonic Generation, it will be helpful. Due to mathematical notations, the exact question can be found "https://physics.stackexchange.com/questions/778274/what-is-helicity-in-high-harmonic-generation".

In what ways may a STEM facility develop these skills?

Einstein in an August 10, letter to his friend Besso (1954): “I consider it quite possible that physics cannot be based on the field concept, i.e., continuous structure. In that case, nothing remains of my entire castle in the air, gravitation theory included, (and of) the rest of modern physics” A. Pais, Subtle is the Lord …” The Science and the Life of Albert Einstein”, Oxford University Press, (1982) 467,

This investigation arose out of discussions the author conducted with Professor H. P. Robertson and with Drs. V. Bargmann and P. Bergmann on the mathematical and physical significance of the Schwarzschild singularity. The problem quite naturally leads to the question, answered by this paper in the negative, as to whether physical models are capable of exhibiting such a singularity.", A. Einstein, The Annals of Mathematics, Second Series, Vol. 40, No. 4 (Oct., 1939), pp. 922-936

“Many physicists maintain - and there are weighty arguments in their favour – that in the face of these facts (quantum mechanical), not merely the differential law, but the law of causation itself - hitherto the ultimate basic postulate of all natural science – has collapsed”. A. Einstein, “Essays in Science”, p. 38-39 (1934)

Einstein dismissed the idea of gravitational wave until his death:

“Together with a young collaborator, I arrived at the interesting result that gravitational waves do not exist, though they had been assumed a certainty to the first approximation,” he wrote in a letter to his friend Max Born. Einstein's paper to the Physical Review Letters titled “Do gravitational waves exist?”; was rejected.

https://www.discovermagazine.com/the-sciences/even-einstein-doubted-his-own-gravitational-waves

Arthur Eddington who brought an obscure Einstein to world fame, and considered himself to be the second person (other than Einstein), who understood General Relativity (GR); dismissed the idea of gravitational wave in the following way: "They are not objective, and (like absolute velocity) are not detectable by any conceivable experiment. They are merely sinuosities in the co-ordinate-system, and the only speed of propagation relevant to them is 'the speed of thought'".

A.S. Eddington, F.R.S., The Proceedings of the Royal Society of London, Series A, Containing Papers of a Mathematical and Physical Character. The Propagation of Gravitational Waves. (Received October 11, 1922), page 268

Mathematics is purely science or just a numbers buckets.

Dear Colleaugues & Allies ~ I just posted the final prepublication draft of an article on the nature of the Langlands Program, RH, P v. NP, and other "open" problems of pure maths, number theory, etc., and the proofs. I would deeply appreciate your feedback and suggestions. So, if you are interested, please send me a request for access to the [private] file, for review and comment. Thanks & best of luck etc. ~ M

pls answer

The mathematical function of TPMS unit cell is as follows: (for example Gyroid)

sin x * cos y+ sin y * cos z+ sin z * cos x = c

parameter 𝑐 determines the relative density of the unit cell.

I am interested to design TPMS unit cell with nTopology software. In this software, TPMS network-based unit cell is designed with "Mid-surface offset" parameter and TPMS sheet-based unit cell is designed with "approximate thickness" parameter.

What is the relation between these parameters and the relative density of the unit cell?

Physics is a game of looking at physical phenomena, analyzing how physical phenomena changes with a hypothetical and yet mathematical arrow of time in 3D space, namely by plotting that physical phenomena with a mathematical grid model (typically cartesian based) assuming that physical phenomena can be plotted with points, and then arriving at a theory describing that physical phenomenon and phenomena under examination. The success of those physical models (mathematical descriptions of physical phenomena) is predicting new phenomena by taking that mathematics and predicting how the math of one phenomenon can link with the math of another phenomenon without any prior research experience with that connection yet based on the presumption of the initial mathematical model of physical phenomena being undertaken.

Everyone in physics, professional and amateur, appears to be doing this.

Does anyone see a problem with that process, and if so what problems do you see?

Is the dimension of space, such as a point in space, a physical thing? Is the dimension of time, such as a moment in time, a physical thing? Can a moment in time and a point of space exist as dimensions in the absence of what is perceived as being physical?

Right now, in 2022, we can read with perfect understanding mathematical articles and books

written a century ago. It is indeed remarkable how the way we do mathematics has stabilised.

The difference between the mathematics of 1922 and 2022 is small compared to that between the mathematics of 1922 and 1822.

Looking beyond classical ZFC-based mathematics, a tremendous amount of effort has been put

into formalising all areas of mathematics within the framework of program-language implementations (for instance Coq, Agda) of the univalent extension of dependent type theory (homotopy type theory).

But Coq and Agda are complex programs which depend on other programs (OCaml and Haskell) and frameworks (for instance operating systems and C libraries) to function. In the future if we have new CPU architectures then

Coq and Agda would have to be compiled again. OCaml and Haskell would have to be compiled again.

Both software and operating systems are rapidly changing and have always been so. What is here today is deprecated tomorrow.

My question is: what guarantee do we have that the huge libraries of the current formal mathematics projects in Agda, Coq or other languages will still be relevant or even "runnable" (for instance type-checkable) without having to resort to emulators and computer archaeology 10, 20, 50 or 100 years from now ?

10 years from now will Agda be backwards compatible enough to still recognise

current Agda files ?

Have there been any organised efforts to guarantee permanent backward compatibility for all future versions of Agda and Coq ? Or OCaml and Haskell ?

Perhaps the formal mathematics project should be carried out within a meta-programing language, a simpler more abstract framework (with a uniform syntax) comprehensible at once to logicians, mathematicians and programers and which can be converted automatically into the latest version of Agda or Coq ?

After sharing that article, I received an email saying

"I have read the abstract. But can not see the connections between the individual topics. They are completely different areas that can not be easily related to each other. e.g. the electromagnetic wave to the Wick rotation or Möbius band."

I admit that I struggled with the connections between topics myself, and I wasn't satisfied with my posting. I'd decided to dispense with a classical approach and tackle these topics from the point of view that everything is connected to everything else (what may be called a Theory of Everything or Quantum Gravity or Unified Field approach). I'm convinced the connections are there, and wrote the following in my notepad before getting out of bed this morning (I dreamed about the Riemann hypothesis last night). It clarified things for me and I hope it will help the other ResearchGaters I'm sharing with.

The Riemann hypothesis, proposed in 1859 by the German mathematician Georg Friedrich Bernhard Riemann, is fascinating. It seems to fit these ideas on various subjects in physics very well. The Riemann hypothesis doesn’t just apply to the distribution of prime numbers but can also apply to the fundamental structure of the mathematical universe’s space-time (addressed in the article with the Mobius strip, figure-8 Klein bottle, Wick rotation, and vector-tensor-scalar geometry). In mapping the distribution of prime numbers, the Riemann hypothesis is concerned with the locations of “nontrivial zeros” on the “critical line”, and says these zeros must lie on the vertical line of the complex number plane i.e. on the y-axis in the attached figure of Wick Rotation. Besides having a real part, zeros in the critical line (the y-axis) have an imaginary part. This is reflected in the real +1 and -1 of the x-axis in the attached figure, as well as by the imaginary +i and -i of the y-axis. In the upper half-plane of the attached figure, a quarter rotation plus a quarter rotation equals a half – both quadrants begin with positive values and ¼ + ¼ = ½. (The Riemann hypothesis states that the real part of every nontrivial zero must be 1/2.) While in the lower half-plane, both quadrants begin with negative numbers and a quarter rotation plus a negative quarter rotation equals zero: 1/4 + (-1/4) = 0. In the Riemann zeta function, there may be infinitely many zeros on the critical line. This suggests the y-axis is literally infinite. To truly be infinite, the gravitational and electromagnetic waves it represents cannot be restricted to the up-down direction but must include all directions. That means it would include the horizontal direction and interact with the x-axis – with the waves rotating to produce ordinary mass (and wave-particle duality) in the x-axis’ space-time, and (acting as dark energy) to produce dark matter in the y-axis’ imaginary space-time.

The Riemann hypothesis can apply to the fundamental structure of the mathematical universe’s space-time, and VTS geometry unites the fermions composing the Sun and planets with bosons filling space-time. Thus, the hypothesis also applies to the bodies of the Sun and Mercury themselves. Its link to Wick Rotation means Mercury’s orbit rotates (the Riemann hypothesis is the cause of precession, which doesn’t only exist close to the Sun but throughout astronomical space-time as well as the quantum scale). The link between the half-planes of the hypothesis and the half-periods of Alternating Current’s sine wave suggests the Sun is composed, in part, of AC waves.

Vector-Tensor-Scalar (VTS) Geometry suggests matter is built up layer by layer from the 1 divided by 2 interaction described in the article. The Sun and stars are a special case of VTS geometry in which stellar bodies are built up layer by layer with AC waves in addition to matter such as hydrogen and helium etc. If the Sun only used 1 / 2 (without the AC interaction), it’d be powered by high temperatures and pressures compressing its particles by nuclear fusion. When powered by AC waves, the half-periods entangle to produce phonons which manifest as vibrations apparent in its rising and falling convection cells of, respectively, hot and cooler plasma.

Summation of AC’s sine waves leads to the Sun’s vibratory waves, emission of photons (and to a small extent, of gravitons whose push contributes to planetary orbits increasing in diameter). Because of the connection to Wick rotation, the convective rising and falling in the Sun correlates with time dilation’s rising and falling photons and gravitons. As explained in the article, this slows time near the speed of light and near intense gravitation because the particles interfere with each other. Thus, even if it's never refreshed/reloaded by future Information Technology, our solar system's star will exist far longer than currently predicted.