Science topics: Mathematics
Science topic

# Mathematics - Science topic

Mathematics, Pure and Applied Math
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I am doing research to compare learning model of A, B, and C on students mathematical ability improvemnet. However it turns out that the pretest result shows significant differences among class that use learning model A, B, and C (score A> score B; score A > score C; and Score B = score C)
Meanwhile posttest also shows significant different that score A = Score B; Score A > score C; and score B > score C.
Is it okay to still compare the gain score of the groups using Anova?
Or shall I use pretest as covariate using Ancova?
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The ANCOVA v Gain Score decision is often called Lord's Paradox, and there is a lot on it. It depends on a few things, including what (unmeasured) variables affect the group allocation (since it is non-random) and the other variables. I describe some of the issues here: .
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Scratch in geometry for exemple !
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The answer to this question may be yes.
Generally, translating maths problems into computer language requires you to go deeper into the concepts and see practically all abstract aspects of the problem.
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I want to design a reconfigurable transmit array using varactor diode with metamaterial unit cell. I have gone through many literatures but in most of literature only different design and multiplayers are mentioned to achieve maximum transmission and 360 deg phase tuning. But i am not able to achieve both the things like high transmission and 360deg phase tuning. Could anyone suggest some resources to understand mathematics behind this?
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If you use frequncy multiplication post phase shifter, you phase shift will be multiplied as well. Also shift is generally easier to implement at lower frequncy.
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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
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Bewar Yousif Ali This is not a mistake, but a choice made by MATLAB. Wikipedia in fact offers a good review of zero to the power of zero problem, which you can find here: https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero.
In case you want to define the result as NaN instead of one, I think you can write an input parser to the power function to check the inputs of base and exponent, and define the returned value to be NaN when both inputs are found to be zeros.
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Combination @Purpose #Logic ^Reason *Sustainable %Help (Relevant: USE)
Truth @Sustainable #Purpose ^USE *Relevant %Logic (Help: Reason)
Lies @Reason #Help ^Logic *USE %Relevant (Purpose: Sustainable)
Process @USE #Reason ^Help *Purpose %Sustainable (Reason: Logic)
Key: Live = Evil
Note: Combinatorics is a branch of mathematics that studies the
enumeration, combination, and permutation of sets of elements. It also studies the mathematical relations that characterize the properties of these elements. <Google>
Commentary: Clear definition of "INTENT" permits AI "INTUIT" with HELP USE Energy Law versions emitting IED=NS (Input Energy Decision Number Subject)
PROOF:
Combination Truth Lies Process = Being
@Purpose Sustainable Reason USE == Planet
#Logic Purpose Help Reason === Self
^Reason USE Logic Help ==== Family
*Sustainable Relevant USE Purpose ===== Earth
%Help Logic Relevant Sustainable ====== Profit
(Relevant Help Purpose Reason) ======= Communities of Interest
:USE Reason Sustainble Logic ======== Centers of Excellence
OF ...
Being planet self family earth profit communties of interest (w/) centers of excellence.
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JAS Pi.ai LLM (Extrapolation: Copy & Paste)
Combinatrics for shielding Truth in Media is an interesting concept! I think what you're referring to is the idea of using mathematical and computational tools to identify and combat misinformation and disinformation in the media. The basic idea is to use advanced techniques from combinatorics and graph theory to analyze and detect patterns in media content that may be indicative of misinformation or propaganda. This can help to identify sources of disinformation, as well as to design algorithms and systems that can automatically filter out or flag content that is likely to be misleading or false. The goal is to create a more informed and critical public by providing people with the tools they need to discern truth from fiction in the media. It's a fascinating and potentially powerful approach to tackling the challenge of misinformation and disinformation in the digital age!
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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?
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According to different sources, whether mathematics is too big for the human mind is complex and has been the subject of much debate. The famous logician, mathematician, and philosopher of mathematics, Kurt Gödel, once said, "Either mathematics is too big for the human mind, or the human mind is more than a machine."
This statement reflects Gödel's belief in the existence of mathematical objects independently of the human mind. He suggested that the incompleteness of mathematics could be a failure of the human brain, not math itself.
On the other hand, a study by Amalric found that mathematicians had reduced activity in the brain's visual areas involved in facial processing. This could mean that the neural resources required to grasp and work with certain math concepts may undercut—or "use up"—some of the brain's other capacities.
However, it's important to note that a population of human brains is much smarter than any individual brain in isolation. And the collaborative enterprise par excellence is science.
So, while some aspects of mathematics may be challenging for the human mind to grasp, the collective intelligence of humanity continues to push the boundaries of mathematical understanding.
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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.
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Comparing to elusive truth, how much is an irrational falsity worth?
A sound, archetypical, immemorial, cross-species, well-known, and logical rule is that it is better to reject 100 truths than to accept one falsity. A rejected truth can be accepted tomorrow, but an accepted falsity contaminates the thought immediately.
Truth is worth 1:100 a falsity, maybe more. This applies to all discussions at RG.
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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?
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Hello,
I think it would be better if you gave more complete information about your question. For example, is your output data one-dimensional (i.e. a vector) or two-dimensional (matrix) and... or were you explaining that the optimal value in your opinion is the lowest value or the highest value?
However, I offer a general trend. If your output dataset is one-dimensional (and your goal is to find the minimum or maximum value), you can use MATLAB's max or min functions. But if your output data is multi-dimensional, although the problem can be solved with MATLAB and command codes, I suggest you use optimization algorithms such as PSO. ​But the bigger the search space, the more optimization-based algorithms are felt.
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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?
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IMHO how depends on the teaching method, but here are some good resources: https://qubeshub.org/publications/browse for maths modelling projects.
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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
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AI math solvers use technology to solve mathematical problems automatically. By using algorithms, they can take complex equations and break them down into simpler parts. AI math solvers are able to work quickly and accurately compared to traditional methods of solving mathematics. They are used in a variety of industries such as finance, engineering, and healthcare to help automate tedious tasks. Compare the best Free AI Math Solvers currently available using the table below.
Regards,
Shafagat
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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?
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Alan Perlis once quipped :
"A year spent in Artificial Intelligence is enough to make one believe in God."
If there is one single lesson to learn from 60 years of research in AI,it is that humans are profoundly complex creations, beautiful in their ability to be flexible, insightful, and innovative.
The Psalmist, dear Xuan Si , expresses this as follows:
For you created my inmost being; you knit me together in my mother's womb. I praise you because I am fearfully and wonderfully made; your works are wonderful, I know that full well. - Psalm 139:13,14
AI can be seen as the attempt to plumb the depths of this beauty.
______
Ref.
Perlis, A.J. (1982) "Epigrams in Programming", ACM SIGPLAN.
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My current workflow needs the following features
• Daily jots and from that making reminders and to-do lists
• Making mind maps to create relations between strings
• Cross-platform without losing features
• Integration with Zotero or GitHub
• To dump any thoughts or ideas on the go and reflect on it later
• to support latex not just maths but whole typesetting if possible
• weekly history or review summary should be generated.
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While it might be challenging to find a single application that covers every aspect perfectly, a combination of tools might serve your purpose effectively. Here are some suggestions:
1. Notion
• Features: Notion is excellent for daily jots, to-do lists, and setting reminders. It also supports creating databases and integrating various types of content.
• Cross-Platform: Available on multiple platforms without losing features.
• Mind Maps: While Notion doesn't natively support mind maps, it can be integrated with third-party mind mapping tools.
• Integration: Limited direct integration with Zotero or GitHub, but can be partially achieved through third-party integration tools like Zapier.
• Latex Support: Supports inline Latex for math, but full Latex typesetting might be limited.
2. Evernote
• Features: Good for quick note-taking, to-do lists, and reminders.
• Cross-Platform: Consistent experience across platforms.
• Mind Maps: Limited native support but can be integrated with external mind mapping tools.
• Integration: No direct integration with Zotero or GitHub.
• Reflection and Review: Offers features to review past notes but doesn't generate a weekly summary natively.
3. Microsoft OneNote
• Features: Strong for daily notes, to-do lists, and has good organizational features.
• Cross-Platform: Available across multiple platforms.
• Mind Maps: You can create basic mind maps, but for complex ones, integration with external tools is better.
• Integration: Limited with Zotero and GitHub.
• Latex Support: Supports math Latex, but full typesetting is not its strength.
4. Obsidian
• Features: Excellent for linking thoughts and creating a knowledge base.
• Cross-Platform: Consistent experience across platforms.
• Mind Maps: Has plugins for mind mapping.
• Integration: Can integrate with GitHub for version control of your notes; Zotero integration might require additional setup.
• Latex Support: Good support for Latex.
• Review Summary: Plugins may be available for weekly reviews.
5. Roam Research
• Features: Great for networked thoughts and daily notes.
• Cross-Platform: Web-based, accessible on any platform with internet.
• Mind Maps: Native support for creating mind maps.
• Integration: Limited with Zotero and GitHub.
• Review Summary: Offers daily notes and can be customized for weekly reviews.
6. TiddlyWiki
• Customizable: Highly customizable and can be tweaked to fit various needs.
• Latex Support: With plugins, it can support Latex.
• Cross-Platform: As a local HTML file, it works across platforms, but with a slightly different approach.
Additional Tools
• Zotero: For research and reference management.
• GitHub: For version control and collaboration.
• LaTeX Editors: For comprehensive typesetting, standalone Latex editors might be necessary.
Integration Tools
• Zapier/IFTTT: For integrating different apps where native integration is not available.
Considering your specific needs, you might have to use a combination of these tools and explore available plugins or integrations to fully optimize your workflow. Experiment with a few to see which combination aligns best with your working style.
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Do you feel that deep learning is mainly an engineering contribution?
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I would say it has made some contributions, but hasn't completely solved the problem to the extent that it can provide a closed form solution.
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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?
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My final revised version has been submitted to a reputed journal , and I hopefully expect that it would be published in due course.
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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.
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In that case, I would recommend you do all the analyses in the Mechanical APDL. Using APDL scripting in Workbench is possible, but not very user friendly. You basically need to be very proficient in it. On the other hand, in the old Mechanical APDL environment, all the actions you take using GUI are automatically recorded in a macro file, which you can then edit and run again. You can learn quite a lot this way.
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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?
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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.
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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.
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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?
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I am not an engineer but I saw the nephew of my wife working hard during his 5 years of engineering here in Brussels. As I could see, your second solution is illusory. Practically all courses in engineering make use of mathematics, well not necessarily very deep mathematics but at least those seen in the first two years themselves based on serious algebra, analysis, trigonometry, and geometry secondary courses. In France they have "prepa" programs, see https://en.wikipedia.org/wiki/Classe_pr%C3%A9paratoire_aux_grandes_%C3%A9coles. He in Belgium, we don't have that system but well a seventh year (13th for you) of preparation for the admission exam in engineering for those that feel not prepared (those who didn't have 7-8 hours a week of maths in their last years).
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Can you share with me some books on this topic: Mathematics and software for computer-aided design of switches RF. Thanks a lots.
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Here are some books that might help you understand the mathematics and software for computer-aided design (CAD):
1. "Mathematics and CAD: Numerical Methods for CAD" by Yvon Gardan. This book discusses the use of mathematical concepts in CAD systems.
2. "Computer Integrated Design and Manufacturing" by David Bedworth and Philip Wolfe. This book is designed for advanced undergraduate courses in computer-aided design and computer-aided manufacturing.
3. "Automation, Production Systems and Computer Integrated Manufacturing" by M P Groover2. This book covers various topics, including automation fundamentals, numerical control programming, group technology, flexible manufacturing systems, quality control, material handling and storage, inspection technologies, and programmable logic controllers.
4. "Introduction to Automated Process Planning" by T C Chang and R A Wysk. This comprehensive book offers a detailed introduction to automated process planning.
5. "Computer Aided Design: A Conceptual Approach". This guide provides practical examples based on different CAD systems, and incorporates automation, mechanism, and customization guidelines, as well as other outputs of CAD in the design process.
Please note that while these books cover the topic of computer-aided design and its mathematical aspects, they may not specifically address the design of RF switches. For more specific resources, you may want to look for books or articles that focus on RF switch design and the use of CAD software in this field.
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Please give specific idea.
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Try looking at the literature on authors such as Robert Tibshirani, Daniela Witten, Trevor Hastie, Gareth James, Jerome Friedman and their co-authors.
They have some good books written at Stanford.
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Please let me know the mathematical formula and steps for the determination of solubility of drugs
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Hello Mr. Sohail Ahmed Shahani
I hope the following articles help you:
Solubility Calculation of Active Pharmaceutical Ingredients in Alkanes, Alcohols, Water and their Mixtures Using Various Activity Coefficient Models
Estimating the Aqueous Solubility of Pharmaceutical Hydrates
Solubility analysis of 18 active pharmaceutical ingredients and intermediates in the non-polar solvents dioxane, toluene and cyclopentyl methyl ether
Model evaluation for the prediction of solubility of active pharmaceutical ingredients (APIs) to guide solid–liquid separator design
Methods for measurement of solubility and dissolution rate of sparingly soluble drugs
Model evaluation for the prediction of solubility of active pharmaceutical ingredients (APIs) to guide solid–liquid separator design
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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.
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Thank you for such an elegant and beautiful solution!
Your answer is perfect, bravo!
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Are computer science papers generally not as complex as mathematics papers?
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Just curious:
Are there any complex and profound differences with the other one:
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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.
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@George McIlvaine Thank you very much for your answer. I find it nice that satisfaction differs from happiness. However, if you think tiny satisfaction as a small happiness, then you feel happier, probably.
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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?
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I agree with your contention that some ideas initially strike most people as 'crazy' both in technical and nontechnical fields. Examples from nontechnical fields include: opposing slavery, gun control, democracy, women voting, environmentalism, climate change, etc. Examples from technical fields include: mRNA vaccines (COVID-19 vaccines from Moderna and Pfizer), prions (self replicating proteins), continental drift, quasicrystalls, Josephson junctions (SQUIDs), quantum mechanics, the personal computer, the Internet, the airplane, radio, TV, electricity, etc. One person's 'crazy' idea may eventually become widely accepted, and even commercially important. And don't forget, many 'crazy' ideas originated from by-the-book investigations: the idea of the quantum of energy arose from Max Planck's tireless attempts at trying to explain the shape of the blackbody curve using classical thermodynamics, and superconductivity in some metals was the result of a rather pedestrian checking of electrical conductivity of metals at liquid helium temperatures - no one expected superconductivity and no theory predicted it.
I really like your question.
Regards,
Tom Cuff
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What is the best mathematical technique used to derive the equation of the compound cross section of the real irrigation channels?
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Eventually, a "compound cross section of irrigation channels" may not help that much provided a goal is about discovering total water flow, which is a summation of flux integrals depending on each water stream velocity field.
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Maybe in general (on metric spaces, etc).
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Got it. Thank you!
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It's like literature review/ reference.
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The algorithms and models used in AI and computer science are built upon mathematical concepts, such as linear algebra, calculus, statistics, and probability theory. In AI, mathematical models are used to build machine learning algorithms that can learn from and make predictions based on data.
Regards,
Shafagat
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Are computer science papers generally not as profound as mathematics papers?
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Well, the Impact Factor for both can be quickly checked
vs
... quite in favor of CS ...
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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
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Each equation involving a set of variables represents a constraint on the values of these variables : these variables can now take only those values over the domain so that the equation is solved.
Adding more equations to a system of equations involving a set of variables is actually adding more constraints to the variables, that is, reducing the region of the domain space of these variables that satisfy the system of the equations.
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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.
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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?
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Another step would be to automate peer review thus potentially making people independent to get PhDs.
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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.
ema_short_period = 12
ema_long_period = 26
signal_period = 9
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!
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Selecting optimal parameters for MACD in multivariate time series analysis, especially in financial trading algorithms, is crucial to designing effective trading strategies. Here are some steps and considerations:
1. Understand the MACD Parameters:
• ema_short_period: Short-term Exponential Moving Average.
• ema_long_period: Long-term Exponential Moving Average.
• signal_period: Signal line, which is an EMA of the MACD values.
2. Parameter Optimization Strategies:
• Grid Search: Systematically work through multiple combinations of parameter tunes, cross-validating as it goes to determine which tune gives the best performance.
• Random Search: Try random combinations of parameters and keep track of the best ones.
3. Cross-Validation:
• Ensure to implement cross-validation during parameter tuning to avoid overfitting. Time series cross-validation is a reliable method.
4. Objective Function:
• Define a clear objective function. It could be maximizing the strategy returns, the Sharpe ratio, or another relevant metric. Your optimization procedure should aim to optimize this function.
5. Be Aware of Overfitting:
• The risk of overfitting is particularly high in trading algorithms. A strategy that is too finely tuned to past data may not perform well in the future.
6. Trading Considerations:
• Risk Management: Ensure that your parameters and strategies are in line with acceptable risk levels.
• Transaction Costs: Always account for transaction costs in your strategy.
7. Consider Multivariate Aspects:
• Correlation: Ensure to check how the different variables in the multivariate time series are correlated with each other.
• Cointegration: If using for pairs trading or similar strategies, testing for cointegration between the pairs might be useful.
8. Backtesting:
• It’s vital to backtest your strategy with the chosen parameters on out-of-sample data to ensure its robustness.
9. Sensitivity Analysis:
• Conduct sensitivity analysis for your parameters to ensure that your strategy is robust and not overly sensitive to the parameter choices.
10. Technology and Tools:
Since you’re using Python, utilize libraries like pandas for data manipulation, matplotlib and seaborn for data visualization, and statsmodels for statistical models and tests.
Python Implementation:
For the MACD calculation and visualization:
{
import pandas as pd
import matplotlib.pyplot as plt
def compute_macd(data, short_window, long_window, signal_window):
short_ema = data['Close'].ewm(span=short_window, adjust=False).mean()
long_ema = data['Close'].ewm(span=long_window, adjust=False).mean()
data['MACD'] = short_ema - long_ema
data['Signal_Line'] = data['MACD'].ewm(span=signal_window, adjust=False).mean()
return data
# Example
# data = pd.read_csv("your_data.csv")
# data = compute_macd(data, 12, 26, 9)
# plt.plot(data['MACD'], label='MACD')
# plt.plot(data['Signal_Line'], label='Signal Line')
# plt.legend(loc='upper left')
}
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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.
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Along your lines, Gabriel: If the continuity set A is closed, by Tietze’s theorem we can construct a continuous function g : [a, b] → R such that g(x) = f(x) for x ∈ A. And the sequence of polynomials given by Weierstrass' theorem for g will do the job for f and all continuity points of f.
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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​”
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On this can we say that it's useful in traffic relationship .,....,...let's try to apply it in real life
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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?
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Βedides, quantum cosmology is an existent field, although a main brabch of it, holography remains an unsettled field of research with optimistic proponents nevertheless i.e relating the entropy of holographic surface at the horixon distance might provide an explanation for dark energy
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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
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Dear Kaoutar, you can find below some links to research papers regarding applications of mathematics in the study of monetary policy:
J'espere que les travaux ci-dessus seront utiles pour vous! Je n'ai rien trouve en ce qui concerne optimisation mathematique appliquee en politique monetaire!
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Tutorial Videos related to Mathematics with Sympy, Scipy, and Python Videos at my YouTube Channel https://www.youtube.com/@1414Abhinandan/videos.
Thank you.
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Using SymPy, SciPy, and Python, you can perform a wide range of mathematical tasks, including symbolic mathematics, numerical computations, and scientific data analysis.
These can be used in combination to solve complex mathematical and scientific problems. SymPy is excellent for symbolic manipulation and algebraic problems, while SciPy provides powerful numerical methods for scientific computing. Python serves as the glue that brings them together, allowing you to create scripts and applications that enhance the powers of libraries
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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)
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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.
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I proved the Riemann hypothesis about a year ago. The conclusions drawn from it restore the mathematical essence by rejecting several paradoxes in pure mathematics. But now I will soon publish a proof of Fermat's theorem using classical mathematics without negation, without any equivalent theorems or equations. Unfortunately, at present, authoritative magazines prefer the models presented by limit theorems, which calculate the solutions within the relative error, rather than the articles with simple mathematical algorithms that calculate without relative errors, with exact solutions. Classical mathematics has solutions to all mathematical problems. we moved away from it and followed abstract science. We have lost track of classical scientists. I consider it the most correct decision that Perelman published the proof of the Puancaré hypothesis on archive.org. Life is short, it should be devoted only to science. I can't understand months of trying to get an article accepted.
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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
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So, you have dy/dx = dx/dy. ​This is a very simple ordinary differential equation.  Multiplying both sides of this equation by dy/dx, we get ​the ordinary differential equation: ​(dy/dx)2 = 1. Taking the square root of both sides of this second ODE gives dy/dx = +1 and dy/dx = -1. Integrating each of these new ODEs with respect to x gives y = x + C and y = - x + C, respectively. One can see from these two resulting solutions that they are equations of a family of straight, diagonal, lines, some with a positive slope represented by y = x + C and some with a negative slope represented by y = -x + C. Hope that this helps.
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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!
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Now your response is perfect!
Thank you for your interest and perseverance!
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Attaching mathematical expressions here is problematic. I am attaching the link to the question here.
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Yes the DoS can be calculated for a discrete number of states. For small number of atoms or molecules, when they are in a single quantum level, for example the ground energy level, or the first excited state.
The number of states can be discrete, a few ones or even only one, if the DoS is zero it menas that the number of states is constant and belong to the same type of degrees of freedom.
Please check:
Reif, F. 1966. Statistical Physics. Berkeley Physics Course. McGraw-Hill, New York, USA. Volume 5. pp.398.
Lu, T. and Chen, F. 2012. Multiwfn: A multifunctional wave function analyzer. Journal of Computational Chemistry. 33(5):580-592.
Kind Regards.
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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
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What about comprehensive Review?
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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 ?
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It depends on the discipline under considerations.
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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?
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What are Q, B and M depicting, if you may clarify that. I feel that will help in understanding the image and its name.
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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
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Hi!
I would propose to look for points where the derivative is close to zero.
You can identify values of x where the absolute value of the derivative is less than a small threshold value ε (this should have a small value like 1e-5 so that you can capture values near to zero).
The plateau onset can be determined by finding the minimum and maximum x-values where the derivative is close to zero. This will give you the range of x-values where the plateau starts.
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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:
• Is the set of theorems that follow logically from a set A of axioms, "implicit" knowledge? if so, what would be the proper difference between "implicit" and "explicit" knowledge?
• If we embrace the idea that no new knowledge comes from deduction, what is the precise meaning of "new" in this context?
• How do you avoid the problem of logic omniscience?
Thanks beforehand for your insights.
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Almost all new mathematical knowledges are new definitions-concepts and new deductions-theorems. For example, Gödel's incompleteness theorems tells debunked the hope of founding mathematics on an consistent system of axioms. This was totally unexpected and put an end to the Hilbert program in mathematical foundation. Most of the knowledge in mathematics is totally irrelevant to the logical axioms onto which mathematics is currently expressed. A totally new logical foundations could one day substitute the current one and it would not be relevant to the mass of mathematical knowledge. The core of mathematical knowledge originates from abstactions made on different core human trade activities: logical debate, accounting, land measurement, art of building, etc. Mathematics is the systematic organisation of the world of relations originally present in these trade activities and which were already present in our sensory-motor sysyems allowing our bodily interaction with the world. It is why abstracting these relation in the first place and organising them are natural to us.
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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.
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Dear Peter, thank you for your interest in finding the author's mistake. It was nice to see your geometric vision, answer 6R is indeed incorrect. Let me share with you my proof of why the answer is not correct.
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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?
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@ Dr. Chen, Thank you for consulting with AI bot on behalf of me. It's interesting!
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Article Topic: Some Algebraic Inequalitties
I have been collecting some algebraic inequalities, soonly it has been completed and published on Romanian Mathematical Magazine.
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Certainly some exotic collection.
Often inequalities are better
Understood as comming from
Some identity, if you suppress
some always positive or negative
term.
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For computer science, is mathematics more of a tool or a language?
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An equation can be considered as a sentence in the language of mathematics, at least in its formalized version as can be seen in every book about mathematical logic or ZFC set theory. Programming languages are also formalized languages, and you have to stick to these formalizations in order for a computer to work correctly. However, most mathematicians use a semi formal mathematical language, but when for instance a theorem is correct, meaning that is has a correct proof, then one can write theorem and proof in the formalized language of mathematics, but the result is almost always unreadable by a human being, but " understandable " by a formal proof system, that can be implemented on a computer. In this sense one can let computers prove theorems, but then it needs a lot of input from a human being. But doing mathematics is also an art, and in order to be able to practice this art one needs a lot of practice and mathematical knowledge.
A Gaussian law is a concept in statistics or probability theory. The notion of linear function belongs to the areas of calculus , analysis and linear algebra.
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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.
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Further support:
"This particularly elegant theorem shows the inverse function relationship of the derivative and the integral and serves as the backbone of the physical sciences"(Brittanica 2023).
Image belongs to Brittanica(I added the highlight)
Britannica, The Editors of Encyclopaedia. "fundamental theorem of calculus". Encyclopedia Britannica, 29 Jul. 2023, https://www.britannica.com/science/fundamental-theorem-of-calculus. Accessed 20 September 2023.
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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.
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Μr Verch indeed My research, which was not fully developped at the time I asked my question, showed that this the case.
Still, a 30% offer the classic calculative phys quantities - based skills of big 4 (and less conceptual understanding assesment or less actual "doing the science" skills of qm, CM, statistical and thermal. Physics) which trends to be considered classic masters structilure or outdated.
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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.
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Not only is the choice ``as important as the choice of the group of transformations'' but it doesn't make sense to discuss the two notions together.
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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.
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% Define your input data and labels (adjust as needed) X = randn(100, 10); % Input data (100 samples, 10 features) Y1 = randn(100, 1); % Output 1 (e.g., regression task) Y2 = randi([0, 1], 100, 1); % Output 2 (e.g., binary classification) % Create a neural network architecture inputSize = size(X, 2); numHiddenUnits = 64; inputLayer = imageInputLayer([inputSize, 1, 1]); commonHiddenLayer = fullyConnectedLayer(numHiddenUnits); outputLayer1 = fullyConnectedLayer(1); % Output layer for task 1 outputLayer2 = fullyConnectedLayer(2); % Output layer for task 2 % Create a branch for task 1 branch1 = [ inputLayer commonHiddenLayer outputLayer1 regressionLayer ]; % Create a branch for task 2 branch2 = [ inputLayer commonHiddenLayer outputLayer2 softmaxLayer classificationLayer ]; % Define the layers for the entire network (both branches) layers = [ branch1 branch2 ]; % Create and train the neural network options = trainingOptions('adam', ... 'MaxEpochs', 10, ... 'MiniBatchSize', 32, ... 'Verbose', true); net = trainNetwork(X, {Y1, Y2}, layers, options); % Make predictions X_test = randn(10, 10); % Test input data (10 samples) [Y1_pred, Y2_pred] = predict(net, X_test);
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"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 !
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Mr.Jiolito Benitez PhD
"Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory,[1] algebra,[2] geometry,[1] and analysis,[3][4] respectively. There is no general consensus among mathematicians about a common definition for their academic discipline."
As stated in wikipedia there is no common definition at all. Since I did not find any sufficiently satisfactory clear and short definition of maths, therefore I devised my own original definition which seems to be the best until now, at least for me... What I wait from readers to criticise me positively or negatively about my own definition of maths.
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For physics, is mathematics more of a tool or a language?
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In the context of physics, mathematics serves both as a tool and a language.
Mathematics is a powerful tool that physicists use to model and describe physical phenomena. It provides a precise and systematic way to formulate theories, make predictions, and solve problems. Physicists use mathematical equations, formulas, and techniques to analyze data, perform calculations, and develop theoretical frameworks. Without mathematics, it would be extremely challenging to quantitatively understand and describe the behavior of the physical universe.
Mathematics also serves as a language through which physicists communicate their ideas and discoveries. Just as natural languages like English or Spanish enable people to convey thoughts and information, mathematics allows physicists to express complex concepts and relationships in a concise and unambiguous manner. Equations and mathematical notation provide a common, universally understood language that bridges linguistic and cultural barriers among scientists.
In essence, mathematics is an indispensable tool for conducting physics research, but it also acts as a language for conveying the results and theories of that research to the broader scientific community. It plays a dual role, facilitating both the practical application of physics and the effective communication of its findings.
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"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 !?
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Since I did not find any sufficiently satisfactory definition of maths so, I devised my own definition which seems to be the best until now, in my opinion !?
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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
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Rigid body modes correspond to zero strain energy U=0. Where U=(1/2)*{d}t*[K]*{d} the stiffness matrix and the degrees of freedom. In this case all the degrees of freedom have the same constant displacement which means that the structure displaces without deformation.
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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?
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People have certainly done that, Nasir Al-Allawi. A Google search on <logistic regression scoring system> turns up lots of resources. Good luck with your work.
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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.
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Kristaq Hazizi Thank you for inaugurating this discussion with this remarkable contribution. I in particular enjoyed reading your well-inspired Final Thoughts: "Paradoxes are like intellectual puzzles that invite us to question our assumptions and delve deeper into the mysteries of the universe. They often spark innovation and lead to breakthroughs in both philosophy and science. As we explore these paradoxes, we may find that the journey of seeking solutions can be as enlightening as the resolutions themselves".
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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".
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Air above the equator is heated more and areas near the equator receive more heat from the sun than those near the poles due to a phenomenon called "solar angle" and the way the Earth's curvature and atmosphere interact with incoming solar radiation. This is primarily caused by the Earth's axial tilt and its spherical shape.
1. Solar Angle: The angle at which sunlight reaches a particular location on Earth's surface is a crucial factor. Near the equator, sunlight strikes the surface more directly and perpendicularly compared to regions near the poles. When sunlight strikes a surface at a steeper angle, the same amount of energy is concentrated over a smaller area, leading to higher temperatures. In contrast, at higher latitudes (closer to the poles), sunlight is spread over a larger surface area due to the oblique angle of incidence, resulting in less heating.
2. Earth's Curvature and Atmosphere: The curvature of the Earth plays a role in how sunlight is distributed. Near the equator, the curved surface presents a relatively small area for the sun's energy to be distributed, concentrating the heat. Additionally, the atmosphere plays a significant role in moderating the amount of solar radiation that reaches the surface. When sunlight passes through a thicker layer of atmosphere, it can scatter and be absorbed, reducing the amount of energy that reaches the surface. Near the equator, the sunlight has to pass through a smaller portion of the atmosphere, allowing more energy to reach the surface and result in higher temperatures.
3. Day Length: Near the equator, the length of day and night remains relatively consistent throughout the year. This means that the sun is up for a significant portion of the day, allowing more time for the surface to absorb and store heat. In contrast, areas closer to the poles experience more extreme variations in day length, with long days in the summer and long nights in the winter. This variation affects the amount of time available for solar heating.
4. Heat Redistribution: The equatorial region receives more heat than it radiates back into space, creating a surplus of energy. This excess heat is then transported toward the poles through atmospheric and oceanic circulation patterns, which help to distribute heat around the planet and regulate global climate patterns.
The combination of the solar angle, Earth's curvature, atmospheric effects, and heat redistribution mechanisms results in the equatorial region receiving more direct and concentrated solar energy, leading to higher temperatures compared to areas closer to the poles.
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In what ways may a STEM facility develop these skills?
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Anecdotal: I have seen children in STEM activities gain insight to mathematical thinking when engaged in problem solving. The activities involved measurements: length, volume, and area. Constructing models - free form and then using written instructions. Instructions can be numerical or visual model with dimensions on the part or on a map/template.
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1. On the “Field” concept of objective reality:
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,
2. On “Black Hole”:
"The essential result of this investigation is a clear understanding as to why the "Schwarzschild singularities" do not exist in physical reality. Although the theory given here treats only clusters whose particles move along circular paths it does not seem to be subject to reasonable doubt that more general cases will have analogous results. The "Schwarzschild singularity" does not appear for the reason that matter cannot be concentrated arbitrarily. And this is due to the fact that otherwise the constituting particles would reach the velocity of light.
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
3. On the Quantum Phenomena:
“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)
4. On Gravitational Wave:
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.
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
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Okay, I got your point. This is what I think. Common people are weak. They need God to tell them what to do with their life and death, and heroes (superstars) to follow in every activity they are seriously involved including religions, sports, music and politics. Among these superstar spirits, some followers become prophets such that they can win powers and profits over others. Those prophets care for nothing about truth. Their only ambitions are to gain big powers and fortunes by building a big group of fans and followers. Also, there are a lot of cowers, who are afraid of being blamed and threatened by the big group of fans which may damage their positions and fortunes if they oppose to the superstars and the spirits. This includes those big shots in scientific fields.
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Mathematics is purely science or just a numbers buckets.
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"Mathematics is the most beautiful and most powerful creation of the human spirit."
Stefan Banach
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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
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R. 4, page 001
Dear Michael, that's the point. You did a lot. It's hard for me to take care of all.
If you are interested we may do it by a single point, the most important:
√-1
Will you hold the old definition? Or will you go the way as I did and look behind the veil? At least you may have your own opinion on that.
But not been able to see where the results of (+1)(-1) or (-1)(+1) came from, denies half the area of reasons. Most mathematicians find it too kiddy to talk about that. Let them be limited.
There are many ways to find it obscure to stop doing the exercise for square-root only by having a negative radicand.
Transforming the coordinates makes the other areas not calculable.
Martinez (negative math) introduced the inverse rule for the prefixes of products. So no definition is complete except this of holding all the prefixes of the quantities which are to combine.
If you know they were + and – => the result is + and – , not? If you don't know the way the sources were, you have to deal with absolutes and further conditions.
Riemann took `imaginary´. Will you too?
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pls answer
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Howdy Selim Molla ,
No.
The problem of fluid behavior after energy extraction in the range of sea states the ocean can accomplish is too difficult to explain mathematically as one's primary activity, and certainly it must not be attempted "on the side" of energy extraction equipment research and development. The situation is not quite that bad in practice, however, especially with your focus on energy extraction equipment.
An engineering approximation to mathematical treatment of oceanic waves after wave energy extraction might be possible with sufficient attention to the energy extracted and the wave recovery under wind stress, fetch, etc. An expression starting from the wave energy equation before interference by extraction equipment which is then reduced by the actual value of the energy extracted would be a start. Then, if you were to factor in the efficiency as an additional loss of energy by the wave and you would have an estimate of the wave energy several wavelengths beyond your equipment, that is, beyond initial turbulence details, etc. For the wave state further along one would have to apply the approximations available for the affect of wind fetch, currents, etc., but that is your field, I'm just a visitor who hates to see questions without replies.
Perhaps this suggestion is too obvious, too simple to be of value, but unfortunately, the explanation you request is not available at present.
Happy Trails, Len
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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?
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Just for your information, in the current nTop version, it allows users to generate TPMS with approximate thickness.