Science topics: Mathematics
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# Mathematics - Science topic

Mathematics, Pure and Applied Math
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I noticed that in some very bad models of neural networks, the value of R² (coefficient of determination) can be negative. That is, the model is so bad that the mean of the data is better than the model.
The question is: in linear regression models, the multiple correlation coefficient (R) can be calculated using the root of R². However, this is not possible for a model of neural networks, for example, that presents a negative R². In that case, is R mathematically undefined?
Obs.: I tried calculating the correlation y and y_pred (Pearson), but it is mathematically undefined (division by zero). I am attaching the values.
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I don't know, but my first thought here is "why even dwell on it here?"
In regression analysis we often use the coefficient of determination (R**2). It is a useful metric for fit but not for prediction when you need to measure how stable the regression model is. Here, a suggested change to R**2 is to replace SSE with PRESS, and we get R**2(pred)= 1- (PRESS/SSTotal). It can happen that the model is so bad that PRESS>SS Total. R**2(pred)<0 then. I would say, here it is best to either state that R**2(pred) is undefined or set it to zero. The prediction oriented R**2 looks really bad.
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Is it mathematically justified to place negative and positive numbers on the same plane?
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My point is Negatives and positives should not be on the same plane
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1 - Prof. Tegmark of MIT hypothesizes that the universe is not merely described by mathematics but IS mathematics.
2 - The Riemann hypothesis applies to the mathematical universe’s space-time, and says its infinite "nontrivial zeros" lie on the vertical line of the complex number plane (on the y-axis of Wick rotation).
3 - Implying infinity=zero, there's no distance in time or space - making superluminal and time travel feasible.
4 - Besides Mobius strips, topological propulsion uses holographic-universe theory to delete the 3rd dimension (and thus distance).
5 - Relationships between living organisms can be explained with scientifically applied mathematics instead of origin of species by biological evolution.
6 - Wick rotation - represented by a circle where the x- and y-axes intersect at its centre, and where real and imaginary numbers rotate counterclockwise between 4 quadrants - introduces the possibility of interaction of the x-axis' ordinary matter and energy with the y-axis' dark matter and dark energy.
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An equivalent formulation of the Riemann hypothesis. See formula (3.22) in the
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What is missing is an exact definition of probability that would contain time as a dimensionless quantity woven into a 3D geometric physical space.
It should be mentioned that the current definition of probability as the relative frequency of successful trials is primitive and contains no time.
On the other hand, the quantum mechanical definition of the probability density as,
p(r,t)=ψ(r,t)*.ψ(r,t),
which introduces time via the system's destination time and not from its start time is of limited usefulness and leads to unnecessary complications.
It's just a sarcastic definition.
It should be mentioned that a preliminary definition of the probability function of space and time proposed in the Cairo technique led to revolutionary solutions of time-dependent partial differential equations, integration and differentiation, special functions such as the Gamma function, etc. without the use of mathematics.
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In mathematics and theoretical physics, there is always room for improvement and advancement, and there may be areas that researchers are currently investigating. The definition of probability that you propose is an interesting idea, and it may be an area of active research. However, it's important to note that the definition of probability used in current mathematical and theoretical physics models has been well-tested and validated through experimentation.
While the quantum mechanical definition of probability density you mentioned may have limitations, it has been successful in explaining many phenomena in physics. In addition, there are other areas of mathematics and theoretical physics that are currently being explored, such as the development of new mathematical models for complex systems or the investigation of fundamental particles and forces.
It's also important to note that mathematics is a powerful tool for understanding the physical world, and it's often used to make predictions and develop new technologies. While new definitions and approaches may be proposed, they need to be validated through experimentation and observation before they can be widely accepted.
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Theoretical and computational physics provide the vision and the mathematical and computational framework for understanding and extending the knowledge of particles, forces, space-time, and the universe. A thriving theory program is essential to support current experiments and to identify new directions for high energy physics. Theoretical physicists provide a great deal of assistance to the Energy, Intensity, and Cosmic Frontiers with the in-depth understanding of the underlying theory behind experiments and interpreting the outcomes in context of the theory. Advanced computing tools are necessary for designing, operating, and interpreting experiments and to perform sophisticated scientific simulations that enable discovery in the science drivers and the three experimental frontiers.
source: HEP Theoretical and Computationa... | U.S. DOE Office of Science (SC) (osti.gov)
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Physics, mathematical, and computational sciences have contributed to the betterment of mankind and continue to push innovation and research today because they provide fundamental frameworks for understanding the natural world, developing new technologies, and solving real-world problems.
Physics, for example, provides a fundamental understanding of the laws of nature that govern the behavior of matter and energy, from the smallest particles to the largest structures in the universe. This understanding has led to the development of technologies such as lasers, semiconductors, and superconductors, which have revolutionized communication, computing, and energy production.
Mathematics provides the language and tools for describing the structure of the natural world and for solving problems across a wide range of fields, from engineering to economics. Mathematical models and simulations allow scientists and engineers to study complex systems and make predictions about their behavior, leading to new discoveries and innovations.
Computational science, which combines mathematics, computer science, and domain-specific knowledge, has become increasingly important in recent years due to the explosion of data and the growing complexity of problems in many fields. Computational tools and algorithms are used to simulate physical processes, analyze large data sets, and develop new materials and drugs.
Overall, physics, mathematical, and computational sciences continue to play a critical role in driving innovation and advancing knowledge in many fields, making them essential for the betterment of mankind.
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Irrational numbers are uncomputable with probability one. In that sense, numerical, they do not belong to nature. Animals cannot calculate it, nor humans, nor machines.
But algebra can deal with irrational numbers. Algebra deals with unknowns and indeterminates, exactly.
This would mean that a simple bee or fish can do algebra? No, this means, given the simple expression of their brains, that a higher entity is able to command them to do algebra. The same for humans and machines. We must be able also to do quantum computing, and beyond, also that way.
Thus, no one (animals, humans, extraterrestrials in the NASA search, and machines) is limited by their expressions, and all obey a higher entity, commanding through a network from the top down -- which entity we call God, and Jesus called Father.
This means that God holds all the dice. That also means that we can learn by mimicking nature. Even a wasp can teach us the medicinal properties of a passion fruit flower to lower aggression. Animals, no surprise, can self-medicate, knowing no biology or chemistry.
There is, then, no “personal” sense of algebra. It just is a combination of arithmetic operations.There is no “algebra in my sense” -- there is only one sense, the one mathematical sense that has made sense physically, for ages. I do not feel free to change it, and did not.
But we can reveal new facets of it. In that, we have already revealed several exact algebraic expressions for irrational numbers. Of course, the task is not even enumerable, but it is worth compiling, for the weary traveler. Any suggestions are welcome.
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@Ed Gerck
Irrational numbers are uncomputable with probability one
================================================= ===
My deepest apologies, but I have read your Answer dated December 14, 2022 in the FLT thread https://www.researchgate.net/post/Are-there-other-pieces-of-information-about-Victory-Road-to - FLT#view=641367549777ccc70c026256/234 .
There was a link to your own thread given by you. This thread gives your erroneous statement from the very beginning, namely: "Irrational numbers are uncomputable with probability one".
Please agree, Dear Professor Ed G., that any irrational number is calculated with 100% accuracy with a probability of 1 for any number of orders p-1, if you write down p orders. Thus, if you write for the root of 2 one order before point and three orders after point, you will have sqrt(2)=1.414..., i.e., you can consider that you have written 4 orders. At the same time, the accuracy of 100% with a probability of 1 is provided for 3 orders, i.e. 1.41, etc., for any number of orders...
Speaking of some kind of all orders "full notation" , as you would like to see it, it's not possible for such a representation of irrational numbers.
If you point out my mistake to me, I will be grateful.
Greetings,
SPK
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Category theory is a branch of mathematics that deals with the abstract structure of mathematical concepts and their relationships. While category theory has been applied to various areas of physics, such as quantum mechanics and general relativity, it is currently not clear whether it could serve as the language of a metatheory unifying the description of the laws of physics.
There are several challenges to using category theory as the language of a metatheory for physics. One challenge is that category theory is a highly abstract and general framework, and it is not yet clear how to connect it to the specific details of physical systems and their behaviour. Another challenge is that category theory is still an active area of research, and there are many open questions and debates about how to apply it to different areas of mathematics and science.
Despite these challenges, there are some researchers who believe that category theory could play a role in developing a metatheory for physics. For example, some have proposed that category theory could be used to describe the relationships between different physical theories and to unify them into a single framework. Others have suggested that category theory could be used to study the relationship between space and time in a more unified and conceptual way.
I am very interested in your experiences, opinions and ideas.
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I am sending you an article on this subject.
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What is this mean ( ± 0.06) and How can I calculate it mathematically?
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Standard error = s / √n
where:
• s: sample standard deviation
• n: sample size
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All tests doing a proof for the Riemann-Hypothesis on the Zeta-Function must fail.
There are no zeros by the so called function of a complex argument.
A function on two different units f(x, y) only then has values for the third unit
`z´ [z = f(x, y)]
if the values variables `x´ and `y´ would be combined by an algebraic rule.
So it should be done for the complex argument, Riemann had used.
But there isn´t such a combination. So Riemann only did a `scaling´. Where both parts of the complex number stay separate.
The second part of the refutation comes by showing wrong expert opinion of mathematics. This is on the false use of `imaginary´ and `prefixed multiplication´.
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The imaginary compartmentalization does not remain of the same dimension all throughout the processualization of complex functions . Even self-determination is ensconced in a sphere where the focus is not on mathematical rigor but rather on collecting some bits of data on the functionals [ of the originary function ] on the very powerful machinery of manifolds and “post-Newtonian calculus”. The systematics of functional differential equations does not have a continuously differentiable solution for every value of the parameter , say , a .
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What are the properties of transversal risks in networks? Happy for applied examples and diffusion properties.
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Transversal risks in networks are risks that cross multiple nodes or elements of a network, rather than being confined to a single node. These risks can have a significant impact on the network as a whole and can be difficult to manage and mitigate.
Some properties of transversal risks in networks include:
1. Diffusion: Transversal risks have the potential to spread rapidly through a network, affecting multiple nodes and elements. The speed and extent of diffusion depend on factors such as the topology of the network, the connectivity between nodes, and the nature of the risk itself.
2. Interconnectivity: Transversal risks often arise from the interconnectivity between nodes or elements in a network. The risk can be amplified when the interconnectivity is high, and nodes or elements are highly dependent on one another.
3. Cascading effects: Transversal risks can trigger cascading effects, leading to a chain reaction of failures or disruptions across the network. These cascading effects can be difficult to predict and control.
4. Non-linearity: Transversal risks often exhibit non-linear behavior, meaning that the impact of the risk is not proportional to the size or severity of the risk. Small disruptions can lead to large and unexpected consequences.
Applied examples of transversal risks in networks include:
1. Cybersecurity: Cyber attacks can spread through computer networks, affecting multiple nodes and elements. A single attack can lead to cascading effects, disrupting critical systems and services.
2. Supply chain disruptions: Disruptions in one part of a supply chain can affect multiple nodes and elements downstream, leading to inventory shortages, delays, and other disruptions.
3. Financial contagion: Financial risks can spread through interconnected financial institutions, leading to a systemic crisis that affects the broader economy.
4. Disease outbreaks: Diseases can spread through social networks, leading to large-scale epidemics that affect multiple regions and populations.
Overall, the properties of transversal risks in networks highlight the importance of understanding the interconnectivity and complexity of modern systems and networks. Effective management of transversal risks requires a holistic approach that considers the entire network and its interdependencies.
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Project Name - Improving Achievement and Attitude through Co-operative learning in F. Y. B. Sc. Mathematics Class
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Physics is a scence of representations, with mathematical aspects in them, foremost and not of naked correlations and parameter analysis.
It also has competent conceptualizaions, genious principles.
Even the innocent seeking uniform motion is a representational scheme fo motions under the theory of kinematics. (Representations are seperate from reality but are invaluable part of scientific infering, predicting, explaining etc) i.e heat is represented as a flow between subsystems. Representations change i.e Einstein found the curved spacetime one for gravity phenomena.
Physics is also the science f cosmology. It has no meaning if it bypasses the universe-i.e the sum of subsystems. This discipline has problems because we cannot take ourself out of it and study it but physics has tools for this (QM) or theoretical approximaions (more cognitively open consideration of the concept of boundary conditions).
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Philippos Afxentiou I am not sure if I have identified the topic of the discussion correctly. I understand that you are making the point that physics must be a unified subject applying at the very small scale and also at the very large scale.
Sydney Ernest Grimm makes a very good point about the CMB rest frame and it does suggest a unique frame of reference within the universe. Also the recent LIGO experiments have shown that gravitational waves and electromagnetic waves travel at the same speed even across expanding space. This suggests that light travels as a wave disturbance of the medium of space. The space rest frame then explains the CMB dipole:
These ideas which arise from the large scale of the universe then can be applied at the small scale. Light is a wave in the medium of space so electrons must be looped waves in the medium of space.
Richard
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Hello
I have an Excel file containing weather data of Missouri in U.S. The data starts from 25th July and ends on 9th September in 2014. For each day, almost 21 times data has been recorded (6 hours within solar noon time).
How can I make a type99 source file using this Excel file? I already have studied mathematical reference of Trnsys help, but that was not very helpful. Thanks
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No, unfortunately I didn't find any solution for this problem.
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The Gamma function,
G(n)= Integral from 0 to infinity [Exp(e^-x^n)]dx
is of the great mathematical and physical importance.
It can be calculated without numerical integration (for practical purposes) via its mathematical and physical properties:
i-minimum of Gamma occurs at x = 1.4616321 and the corresponding value of Gamma(x) is 0.8856032.
ii-Gamma(1.)=Gamma(2.)=1.
iii-Gamma(x)=(x-1.) !
A simple preliminary approach that gives the value of Gamma(x) with an error less than 0.001 is the second-order polynomial expression for the factorial x,
(1.-0.46163*x+0.46163*x*x),x element of [0,1].
For example, this gives:
G(10.5)=11877478.
vs the value of 11899423.084) given by numerical integration.
and Gamma(1.4616)= 0.88527 vs 0.8856032.
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The Gamma function G(n) is well defined for any positive value of n,
G(n)= Integral from 0 to infinity [Exp(e^-x^n)]dx . . . . . (1)
Needless to say, it is of great mathematical and physical importance.
However, for practical purposes, it can be calculated using an adequate closed-form polynomial without going through complicated numerical integration.
The required closed form solution must retain its mathematical and physical properties, namely:
i-minimum of Gamma occurs at x = 1.4616321 and the corresponding value of Gamma(x) is 0.8856032.
ii-Gamma(1.)=Gamma(2.)=1.
iii-Gamma(x)=(x-1.) !
iv-The recurrence relation ,Gamma (x)=x. Gamma (x-1)
We propose a simple preliminary approach that gives the required value of Gamma(x) with an error less than 0.001. The proposed preliminary approach must satisfy conditions i-iv,
but since the factorial function x! is not yet defined for negative numbers (x<0), we divide the entire positive x-space into three intervals as follows:
a) x element of ]0.1]
Here, the proposed second-order polynomial expression for the Gamma function is G(x)=F(x-1) where F(x) is the factorial function x!. F is approximated by,
F(x)=(1.-0.46163*x+0.46163*x*x) . . . . . . . (2)
x element of [0,1].
b) x element of [1,2]
The Gamma function is approximated via the expression,
G(x)=Done(x)+0.3333/X**1.5 . . . . . . . . . .  (3)
Where 1/3 *1/X. Sqrt(x) is a correction factor.
c) x element of [0,infinity[
We can here use the expression (4) supplemented by the expression (2) for the remaining fraction,
G(x)=F(x-1) . . . . . . . . . . . . . . . . . . . . .. . . . (4)
Equations 2, 3 and 4 were implemented in a simple algorithm which produced the required numerical results.
Table I presents some examples of numerical results of the proposed technique compared to those of the numerical tables obtained by numerical integration of Eq. 1.
Table I. results of the proposed method vs those of the numerical tables obtained by numerical integration of Eq. 1.
x                          10.5                     1.4616                      0.5                     0.25
G(x) Proposed    11877478           0.88527            1.82646                    3.5798
technique
G(x) numerical   11899423.084 0.8856032.       1.7738                      3.6534
tables
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Thermal stresses in applied mathematics
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Dear professors and students, greetings and courtesy. I wanted to know if the real numbers are the largest and the last set of numbers that exist, or if there are sets or sets of numbers that are larger than that, but maybe they have not been discovered yet? Which is true? If it is the last set of numbers that exists, what theorem proves the non-existence of a set of numbers greater than it? And if there is a larger set than that, in terms of the history of mathematics, by obtaining the answer to which mathematical problem, it was proved that the obtained answer is not closed with respect to the set of complex numbers and belongs to a larger set? Thank you very much
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First, what do you mean by a number? If you mean a set of things that includes, say, rational numbers and extends the addition & multiplication operations in a way that is consistent with the usual rules (e.g., associativity: a+(b+c)=(a+b)+c & a*(b*c)=(a*b)*c, distributivity: a*(b+c)=a*b+b*c, zeros: 0+a=a, 0*a=0, commutativity: a+b=b+a, a*b=b*a, unit/identity: 1*a = a, inverses: every a has a b=-a where a+b=0, every a not zero has a b=1/a where a*b=1) then we can make a claim that the complex numbers are the biggest class of "numbers".
Actually, you can go further by constructing a non-Archimedean set of "real numbers" which extends real numbers and is still an ordered field, and then have an extended set of complex numbers of the form a+i.b where a, b are these extended real numbers.
Non-Archimedean means that there are "numbers" a, b > 0 where a/b is larger than any whole number 1, 2, 3, ...
But if you keep the regular real numbers, but are willing to lose something else like commutativity of multiplication (a*b=b*a) then there are the quaternions discovered/invented by William Rowan Hamilton in the 19th century. These have the form a+b.i +c.j +d.k where a, b, c, d are real numbers. The essential properties of the symbols i, j, k are that i*i = j*j = k*k = -1, and i*j = -j*i = k, j*k = -k*j = i, & k*i = -i*k = j. Quaternions form a division ring.
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As the concept comes from the Bernoulli numbers and different branches of mathematics, I have recently considered the importance of introducing the same concept, 'The unity of mathematics' within the context of the Bernoulli numbers and some special series (the Flint Hills and Cookson Hills series). I believe in the scenario of defining a balanced relationship between the effect of the Bernoulli numbers and the series of hard convergence.
I am pointing out this potential link.
For a general conclusion about what I consider should the concept of 'unity' by the Bernoulli numbers and the Flint Hills, just pay attention to this screenshot:
DOI: 10.13140/RG.2.2.16745.98402
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I dont see very well how you could achieve the "unity of mathematics"
based on series/sequences alone. For example geometry would remain apart. you must persue some more modest goal.
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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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@ Andrea Ossicini,
Interesting - thanks for sharing
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Mathematics Teacher Educators (MTEs) best practices.
I'm interesting in research literature about Mathematics Teacher Educators (MTEs) best practices, especially on MTEs' practices for teaching to solve problems.
thank you.
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Problem solving technique and thinking aloud strategies helpful for mathematics teaching
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Good day, Dear Colleagues!
Anyone interested in discussing this topic?
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The tandem of Mathematics and Computer Science is vital for the development of AI. Mathematics provides the theoretical foundation, while Computer Science provides the practical tools to implement AI algorithms. By combining these two disciplines, researchers and practitioners can create AI systems that can perform increasingly complex tasks, and help solve some of the most challenging problems facing our society.
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How can I define histogram bins in a well define mathematical expression especially driven from data points x_i, i=1,..,n and the range or any other well define measures in the dataset.
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Dear Dr Babura,
I think that you mean how Sturges came up with his rule. Part of your question is explained in the following link,
Please let me know if this is what you are looking for Dr.
Best wishes.
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Kindly share with me any details of Scopus indexed Mathematics conferences in India.
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See attached file
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There are a few point to consider in this issue
Points pro current emphasis
1. Math is the backbone of a physical theory. Good representation, good quantities of a theory, phenomena but bad math makes for bad theory
2. There is a general skepticism for reconsidering role of mathematized approach in physics Masters syllabi/upgrading role of literature/essay
2. Humans communicate, learn, think & develop construct via language
Arguments Con
1. Math is the elements in theory and "physics product" that is responsible for precision& prediction. Indespensible though, it exists in the mind of some individuals & function as well, in parallel with conception, physical arguments
2. Not all models in physics are mathematical. Some are conceptual
3. Formulations of solutions to physics problems via math techniques and methods is def of mathematical physics. However, this is a certain % of domain of skills.
But syllabus focuses 100% on this
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Je pence qu'il y a une grandes différences entre la physique mathématiques et les math, où les maths sont des outils utilisés dans la physique comme les langues, par contre la physique mathématiques est une description mathématiques pour les phénomènes naturels, c'est a dire ces une autre représentation discret des phénomènes par des équations ( ces variables c'est des être naturels comme le temps, distance, énergie massa...), des ça aide à bien maîtriser et comprendre ces phénomènes. Bien sûr pour un physiciens il devrait maîtriser les math pour qu'ils puissent expliquer ces phénomènes et mieux comprendre la nature
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Physics continues a tradition of assesment in graduate program based on final exams and of the form of mathematized exersices with no conceptual qs or essays.
This fulfils the aim. Of. Mastering demanding nomenclature in the domain. Given slow progress in field last decades this might be a good alternative but there are also pedagogical reasons.
This form of assesment is extreme and outdated.it has further disadvantages
** Students do not develop critical research skills such as literature analysis and research.
**certain skills for future researcher are notvtested i. E ability to combine research from different Source, ability to think critically of competing thesis or theories, to discern gaps in current research
** A mixed approach should ensure all aims
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To sum up
1. The issue is not about removing mathematics or questioning their role in physics. It is about what motivates Ph. D students most.
2. Current physics master curricula are, dispite the existence in some of a parallel non written or expressed properly strategy in the programs, are monopolizng learning goals to undepagogical levels.
( 80% Application goals to Calculations and 20% understanding (explain why) in specific situations. Pedagogical this is a scandal. Bloom demands 4-2-2-2-1 ration in knowledge, understanding, application, synthesis, evaluations. Essay qs address the latest 2.)
3. I believe students should be inquired to experience by self-discovery radical formulations that involves new conceptual ideas ornee physical quantiries as Smolin's variety, views that provenly mathematically rebuild established theories
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I have Expi293 cell cultures (suspension). After counting them, the density turned out to be 4.26 x 10^6. I need to split them. Starting from this concentration, how can I obtain a 30ml cellular suspention at a density of 0.25 x 10^6? How many mL of cellular suspension (the one at a density of 4.26 x 10^6) and how many mL of medium do I need? I still have difficulties in understanding which kind of mathematical calculation do I need to use. Could you explain it to me?
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Use the formula C1V1= C2V2
C1= 4.26 x 10^6
V1= volume to be taken (Xml)
C2= 0.25 x 10^6
V2= required volume (30ml)
4.26 x 10^6 x Xml = 0.25 x 10^6 x 30ml
X= 0.25 x 10^6 x 30ml / 4.26 x 10^6
Therefore X= 1.76ml
So, add 1.76ml of cell suspension (the one at a density of 4.26 x 10^6) into 28.24ml of culture media to obtain 0.25 x 10^6 cell density in 30 ml cellular suspension.
Best.
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Suggest some best topics for Experential learning
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You might find some inspiration in the examples that come with this software:
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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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1. Sort the data: Begin by sorting the data from smallest to largest, or from largest to smallest. This will make it easier to find an optimal value.
2. Calculate the mean or median: Calculate the mean or median of the data set, which will represent the average value.
3. Find the mode: Find the mode, which is the most common value in the dataset. This could be an optimal value.
4. Look for outliers: Look for any outliers in the data that could skew the results. Remove any outliers and recalculate the mean or median.
5. Apply constraints: Apply any constraints that are applicable to the data. For example, if you are looking for an optimal value within a certain range, then you would only consider values within that range.
6. Select the optimal value: Once you have considered all the applicable factors, select the optimal value that best meets your criteria.
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What digital technological techniques and strategies can multilingual PSTs prepare in their multilingual classrooms that can allow their students’ to be considered capable to learn mathematics regardless of their fluency in the language of instruction?
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On the base of my experience it is better to use native language or intermediary language for detailed explanations. You can find the short video with math content in YouTibe and use as the additional manuals in intermediary language.
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My Awesomest Network, I am starting my Ph.D. studies and I have some questions and doubts concerning it. Could I write them down here, pleaswe? First of them is how can I join disciplines as sociology, management, economics, mathematics, informatics and other similaer items to make a complex holistic interdisciplinary analysis and coherent study of pointed fields.
Thank You very much for all in advance
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Thank You for an opinion!
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blockchain application
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What are the ideas behind the mathematics involved in blockchain system?
Blockchain technology is based on mathematical concepts such as cryptography, hash functions, and consensus algorithms. The mathematics behind blockchain helps to ensure the security and integrity of the data stored on the network.
1. Cryptography: Blockchain uses cryptographic algorithms to secure the transactions and to ensure that the data stored on the network is not tampered with. The most commonly used cryptographic algorithm in blockchain is the SHA-256 (Secure Hash Algorithm 256-bit), which is used to create digital signatures.
2. Hash functions: A hash function is a mathematical function that takes an input and returns a fixed-size output, which is typically a string of characters. In blockchain, hash functions are used to create a unique identifier for each block, called a block hash, which is used to link blocks together.
3. Consensus algorithms: The consensus algorithm is used to validate and confirm transactions on the network. The most commonly used consensus algorithm in blockchain is Proof of Work (PoW), which is used by Bitcoin, and Proof of Stake (PoS), which is used by Ethereum. These algorithms require the network participants to perform complex mathematical calculations to validate transactions and add new blocks to the chain.
In summary, the mathematics behind blockchain technology helps to ensure the security and integrity of the data stored on the network, and to validate and confirm transactions on the network through consensus algorithms.
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Or, by what formal means can we comprehend and communicate the nature of Nature?
From Mathematics: Nature and physics are “independent of mathematics”
From Physics: “We need the criteria of something that actually works, not just math rigor.”
“I appear to be caught between two successful disciplines, mathematics and science - rigor and usable results.”
[For full versions of the quotes in justice to the individuals review “What Is a Linear Representation of an Essentially Quadratic Phenomenon?” in Q&A on ResearchGate. Applied Mathematics is not specifically mentioned in the posts there.]
There exist phenomena in nature, for example kinetic energy of a mass in motion, which may be represented by the product of the mass times its present velocity times the linear average of its velocity between zero and its present value (K.E. = m*v*v/2 to clarify.) Now, ignoring the abstractions of mathematics and the accurate-enough theories of physics, what are the axes of any space in which kinetic energy may be plotted, noting that in that space energy is represented by a volume, area times length, and the area may be linearized with v as the square root of the area? Note that two axes of v and v/2 are needed to plot the area. What’s up? What are area and length in nature that are plotted in such a space? Is it significant in the natural process that v*v is an area in the plot? Is energy an essentially quadratic phenomenon of nature, or even essentially cubic? Are these matters so answered already they may be dismissed, or may some of us explore them for the insight that may bloom (flowers “blow” in some poems)?
These are questions of Natural Philosophy in the mind of a person that are not answered by the rigid explanations of the current state of ignorance that feels so knowing in each era. Aristotle’s view was great in his time, like ours is to us now. (The accepted solution is for an academic to fix the person who errs with an inoculation of facts “it is known that,” a familiar experience. In Charles Ives musical work, “The Unanswered Question,” the trumpet remained curious after the explanations.)
Looking to the 4thmillennium in the Gregorian calendar, will this inquiry have been resolved as natural processes are then comprehended? Given scales and data a number may be assigned to a measured kinetic energy that is accompanied by units to associate it with nature. The issue seems moot, but in fact, . . .
The Schrodinger Eqn. is a linear representation used in calculation that must be squared to be real, that is, the real result is a squared value, calling it quadratic will serve. The square root of two is formal, but the Schrodinger Equation produces a real value in the end after multiplication by its complex conjugate, “squaring.” The physicist is correct that in Physics it doesn’t matter “what the imaginary solution was” during calculation since only the result matters and other representations exist. Is that okay with you? I wonder, since another formal linear representation of an essentially quadratic phenomenon, the square root of two, cannot be written down as a completed decimal value, and during processing the imaginary Schrodinger expression requires representation as an area via a + bi, or (a, b), or . . ., which expressions are not real.
[Remember – ResearchGate encourages discovery, as if current knowledge could not only be incremented, but also that a new arena for thought could be discovered. “It is known that” must not be the whole answer, and exploration is in the charter.]
So, by what formal means can we comprehend and communicate the nature of Nature?
Happy Trails, Len
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Howdy Robert A. Phillips,
We share a sense of Nature and of knowledge. Your preprint of "The Cause of the Gravitational Effect" reminds me of Albert Einstein's first cut in 1911 at the bending of the path of light in a gravitational field gradient. Your observation on KE in a fluid is appropriate to my fluid dynamics focus, but I would word it "Kinetic energy involves more than just the body. In any case our agreement is quite pleasant.
"Using a natural fluid model to interpret the nature of cosmological interactions resolves many of the "big questions." " You might enjoy my condensation cosmology concept. The Universe did not "inflate," but as primal energy condensed to matter, light slowed (same speed always is measured) and the Universe has appeared to expand.
The issue of whether natural processes "are quadratic" represented by v2 in K.E. = mv2/2 remains of interest to me in forming an object oriented model of flow in a mountain stream rapids. What is happening "in" a turbulent flow structure that must be specified in its object class data and functions, whether it is processed analytically or by a computer program. Imaginary and irrational number expressions may freely be used during calculation as long as they are made rational in the end. Do we need to notice that; does nature notice that; does it matter? Daniel Boone was never "lost" in the Kentucky wilderness, but on occasion he was "mighty bewildered" for days. Maybe I'm just bewildered.
Happy Trails, Len
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There is valid curiosity that such modifications might exist in nature.
There is research in proving mathematical results that shed light on QT in a more operational manner, motivated by quantum information theory.
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There has been a development regarding the usage of Steepest Entropy Ascent formalism which modifies QM by incorporating the second law of thermodynamics in the formalism itself. The research shows that this is quite a consistent modification, including preclusion of signaling and other things. However, this approach is motivated by the requirements of consistency with thermodynamics, and not from the information theoretical approach.
You may check the following works, they might be of interest.
And some recent work shedding light on this
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There are at least 2 stands in this & issue debate.
**Scientific continuity is related to scientific change
Shebere & Kuhn are repredebtatives. The (alleged by S. ) problem of "incommensurability"(Kuhn, '60s) attempts to explain scientific change in terms of concepts of meaning and reference. Another way is through the concept of "reasons" and the issues of reasons.
The Gallilean paradigm broke meaning continuity from the Aristotelian & is inconsumerable i. E no comparison can be made between the 2
**Scientific Continuity as independent area
A more standard way, it providers factors such as mathematics continuity and causal continuity. GR for example deviated some how causal from Newtonian gravity but maintained mathematical cintinuity
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The issue of scientific continuity can be defined as the preservation of knowledge, research progress, and expertise in a field over time, despite changes in personnel, funding, and other factors. Scientific continuity is important because it ensures that research programs and projects can be continued over the long term, and that valuable knowledge and data are not lost or forgotten.
To assess the issue of scientific continuity, the following factors can be considered:
1. Personnel stability: Assess the stability of the research team, including turnover, retirements, and other personnel changes, and their potential impact on scientific continuity.
2. Funding stability: Evaluate the stability of funding sources and whether they are adequate to maintain the research program over the long term.
3. Data management: Assess the quality of data management systems, including data archiving, sharing, and preservation.
4. Collaborations: Evaluate the presence and strength of collaborations between researchers and institutions, which can help ensure scientific continuity by creating networks of expertise and resources.
5. Documented procedures: Evaluate the existence and implementation of documented procedures for transferring knowledge, data, and expertise from one generation of researchers to the next.
By considering these factors, researchers and institutions can determine the level of scientific continuity in a field, and take steps to address any gaps or weaknesses to ensure that research progress is maintained over the long term.
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Hai,
I had worked with Dr. M. Azzedine,France member of MAA and proved unsolved Beals Conjecture, FLT directly, Collatz Conjecture & Goldbachs Conjecture.( All proofs in one article)Article will get published on April.
Can I expect any career / financial benefits from that work? I also developed Mathematical Theology to bring mathematics in humanity. I had investigated the thesis of some university level mathematics professors from Kerala State India.
What are the expectations on the person who proves Collatz Conjecture? I am an ordinary research scholar from a government college, Tamilnadu, India.
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Thank You Sir.
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It finally has occurred to me that there is a similarity between i = √-1 and √2. They are each linearized representations of essentially quadratic values. We use the former in complex numbers and include the latter in the real number system as an irrational number. Each has proved valuable and is part of accepted mathematics. However, an irrational number does not exist as a linear value because it is indeterminate – that is what non-ending, non-repeating decimal number means: it never can exist. Perhaps we need an irrational number system as well as a complex number system to be rigorous.
The sense of this observation is that some values are essentially quadratic. An example is the Schrödinger Equation which enables use of a linearized version of a particle wave function to calculate the probability of some future particle position, but only after multiplying the result by its complex conjugate to produce a real value. Complex number space is used to derive the result which must be made real to be real, i.e., a fundamentally quadratic value has been calculated using a linearized representation of it in complex number space.
Were we to consider √-1 and √2 as similarly non-rational we may find a companion space with √2 scaling to join the complex number space with √-1 scaling along a normal axis. For example, Development of the algebraic numbers a + b√2 could include coordinate points with a stretched normal axis (Harris Hancock, Foundations of the Theory of Algebraic Numbers).
A three-space with Rational – Irrational – Imaginary axes would clarify that linearization requires a closing operation to restore the result to the Rational number axis, where reality resides.
[Note: most people do not think like I do, and almost everyone is happy about that: please read openly, exploringly, as if there might be something here. (Yes, my request is based on experience!) Tens of thousands of pages in physics and mathematics literature from popular exposition to journal article lie behind this inquiry, should you wish to consider that.]
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Howdy Folks,
I am satisfied that mathematics and physics (science) have been well defined and described here. A couple movies are running in my mind's eye that I wish to pass along as afterwords - they are observations not insults.
In Ray Bradbury's work "Medicine for Melancholy" he includes a prose movie of Pablo Picasso sketching a mural in the moist sand of a long beach as the tide is coming in - just like the "then current" theories in science presented by academics as truth, the foaming edges of the waves wash the mural away - new paradigms replace old and the human creation of science is adjusted. It is not "nature" even now.
M. C. Escher's "Metamorphosis" is a great contribution to defined elements fitted together perfectly into a closed, consistent, unnatural whole. Rigorous, however independent of nature, EXCEPT FOR THE FACT that humans and their imagination are natural. I disagree with the separation of "artificial" from natural, except as a verbal convenience.
These are creations of human minds, not figments of human imagination. And I carefully avoided an observation that fresh ideas are not fertilizer and to bury them in a field will not benefit flowers there.
Great exchange, Thanks again, Happy Trails, Len
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Could any expert try to examine the new interesting methodology for multi-objective optimization?
A brand new conception of preferable probability and its evaluation were created, the book was entitled "Probability - based multi - objective optimization for material selection", and published by Springer, which opens a new way for multi-objective orthogonal experimental design, uniform experimental design, respose surface design, and robust design, etc.
It is a rational approch without personal or other subjective coefficients, and available at https://link.springer.com/book/9789811933509,
DOI: 10.1007/978-981-19-3351-6.
Best regards.
Yours
M. Zheng
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1. Evolutionary Algorithms (EA): Evolutionary algorithms (EA) are a family of optimization algorithms that are inspired by the principles of natural evolution. These algorithms are widely used in multi-objective optimization because they can handle multiple objectives and constraints and can find a set of Pareto-optimal solutions that trade-off between the objectives.
2. Particle Swarm Optimization (PSO): Particle Swarm Optimization (PSO) is a population-based optimization algorithm that is inspired by the social behavior of birds and fish. PSO has been applied to multi-objective optimization problems, and it has been shown to be effective in finding Pareto-optimal solutions.
3. Multi-objective Artificial Bee Colony (MOABC): MOABC is a multi-objective optimization algorithm inspired by the foraging behavior of honeybees. MOABC has been applied to various multi-objective optimization problems and has been found to be efficient in finding the Pareto-optimal solutions
4. Decomposition-based Multi-objective Optimization Algorithms (MOEA/D): Decomposition-based multi-objective optimization algorithms (MOEA/D) decompose the multi-objective problem into a set of scalar subproblems, then solve them by using a scalar optimization algorithm. MOEA/D has been found to be effective in solving multi-objective problems with high dimensionality and/or large numbers of objectives.
5. Deep reinforcement learning (DRL) : DRL is a category of machine learning algorithm that allows the agent to learn by interacting with the environment and using the rewards as feedback. This approach has been used to optimize the decision-making process in multi-objective problems.
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Perception is not the ultimate guide for knowledge but as Gallileo captured the actual and empirical, not necessarily the real, similar concerns arise.
In general, the repercussions of Reduction arise because what is actual, i.e final instantiation of underlining process, is not all the story. Further omissions come from the empirical approach since sense means are not always valid projectors of the actual.
Gallilean approach has yielded a framework that empowered our comprehension & ability to define/describe phenomena in the realm of the actual& empirical. His treatise should not be considered more than this i.e descrining the nature of the real and its dynamics.
The reduction of change to motion has been noted but little has been argued about its shortfalls in epistemic practice. This reduction is part of the reduction of the real to the actual since it omits any need to refer to the real to make its claims functional. It also removes philosophical or anthropocentric notions of growth and ultimate ends which is good in one sense but in a pure "reductionist shortfalls" point of view is still a problem dimain restriction.
The description of motion with mathematics is another point neglected. Motion can be described qualitatively or conceptual but such a framework has not been devised.
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Thanks for your thoughts and wishes
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This question discusses the YES answer. We don't need the √-1.
The complex numbers, using rational numbers (i.e., the Gauss set G) or mathematical real-numbers (the set R), are artificial. Can they be avoided?
Math cannot be in ones head, as explains [1].
To realize the YES answer, one must advance over current knowledge, and may sound strange. But, every path in a complex space must begin and end in a rational number -- anything that can be measured, or produced, must be a rational number. Complex numbers are not needed, physically, as a number. But, in algebra, they are useful.
The YES answer can improve the efficiency in using numbers in calculations, although it is less advantageous in algebra calculations, like in the well-known Gauss identity.
For example, in the FFT [2], there is no need to compute complex functions, or trigonometric functions.
This may lead to further improvement in computation time over the FFT, already providing orders of magnitude improvement in computation time over FT with mathematical real-numbers. Both the FT and the FFT are revealed to be equivalent -- see [2].
I detail this in [3] for comments. Maybe one can build a faster FFT (or, FFFT)?
The answer may also consider further advances into quantum computing?
[2]
Preprint FT = FFT
[2]
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Many people write to me, and my mailbox is very accepting.
Some simple people assume that their questions are, somehow, special, worthy, or unique. They even may want to claim innovation!
But, we live in a fluid, and many of our thoughts are not even
original, or our own. Ego interferes.
Only correct living, like following the Dhrama and Jesus, can keep the laboratory of the mind clean and receptive to higher thoughts.
The complex numbers have been followed without deep questioning, and their justification, in medieval Italy, was to solve the equation x^2+1=0.
But, they actuall lead one astray from the actual solution.
This was revealed by the FFT, that can now be entirely calculated with rational numbers, and without any trigonometric functions, as mentioned above.
Then, we conclude that FT ~ FFT, as the RG preprint briefly explains. For the savvy, a letter cn b a wrd!
There are no mathematical real-numbers either. Thus, the set C is deprecated and the set G is superfluous. They cannot be calculated (Gisin,Ozhigov, Gerck)with probability 1.
Mathematics gets simpler, and correct, accessible to natural processes, and accessing them in quantum mechanics.
Then, the Shor quantum algorithm of 1994, without any practical result since then, only theoretical results, opens the calculations of the FFT, to the components of numbers.
This reveas the prime numbers as "lumps", resonances in the number line, much in the same way that a physical chord has physical resonances. Easier to calculate, with such a physical model.
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We assume that in general probability and statistics belong to physics rather than mathematics.
The Normal/Gaussian Distribution:
f(x)={Exp(-x^2/2 sigm^2)}/sigma.Sqrt(2.Pie)
can be derived from the universal laws of physics for a given number n of randomly chosen data in less than five minutes.
Accuracy increases as n increases.
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In fact, and the meaning of the question is not understood.
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Mathematics abstracted and idealized concrete mathematics, exemplified in Euclid’s The Elements. Religion around the same time or earlier, abstracted the concrete representation of deities. Are there similarities in the problem solving approaches?
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Plato, who preceded but for a couple of decades overlapped with Euclid, dealt in abstractions (e.g. forms) but seems to have swung both ways in respect of the literality of gods. However, Pythagoras preceded them both by several hundred years and advanced geometry from measurement practices to abstract generalizations. Yet he appears to have believed in the gods of the Greek pantheon. So it seems that abstraction in Greek mathematics emerged well before abstraction in monotheistic religion related phenomena. But these are vague observations. The concept of abstraction and how it applies in the two domains needs to be clarified before a plausible answer can be given.
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I have a system of non-linear differential equations that explains the behaviour of some of the cancer cells.
Looking for help identifying the equilibrium points and eigenvalues of this model in order to determine the type of bifurcation present.
Thanks in advance.
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Well it's a good idea to find some of them, first. The first equation implies that y=0 is an equilibrium, so a class of equilibria is of the form (x,0,z). That reduces the problem. From the last equation it then should be possible to solve for z and, from the second, for x.
Then look at the other factor of the first equation; and so on.
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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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Stam Nicolis, you have been telling me how the problem is being considered in GTR, Cosmology, etc. This is known already.
The question I have posed is for considerations towards new attempts to discuss the problem rationally and to come to possible further conclusions that might help us understand the very problems better
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In my current work on the theory of hyperbolic functions, I, as a completely extraneous observer of the turbulent debates relating to the subtlest intricacies of the Special Theory of Relativity (SRT), have drawn attention to the fact that hyperbolic functions are most used not in constructing bridges, aqueduct arches or describing complex cases of X-ray diffraction, but in those sections of the SRT that are related to the name of Professor Minkowski. Since my personal interest in SRT is essentially limited to the correct application of hyperbolic functions when describing moving physical realities, I would be grateful to the experts in the field of SRT for the most concise explanation of the deep essence of the theory of space-time patterns of surrounding me reality.
Naturally, my question in no way implies the translation into human language of the lecture of the Creator of the Theory, the honour of acquaintance with which in 1907 belongs to the academic/medical community of the city of Cologne and its surroundings. My level of development and my agreeableness have ensured that I not only managed to read independently the text underlying the concept of « Minkowski four-dimensional continuum », but also to formulate my question as follows:
Which of the options I propose is the most concise (i.e. non-emotional-linguistic) explanation of the essence of Minkowski’s theory:
1. The consequence of any relative movement of massive physical objects is that we are all bound to suffer the same fate as the dinosaurs and mammoths, i.e. extinction.
2. Understanding/describing the spatial movements of physical objects described by a^2-b^2=const type mathematical expression implies acquiring practical skills of constructing second-order curves called «hyperbolas».
3. All of us, including those who are in a state of careless ignorance, are compelled to exist in curved space.
4. Everything in our lives is relative, and only the interval between physical events is constant.
5. The products of the form ct (or zct), where c is the speed of light and z is some dimensionless mathematical quantity/number symbolizes not a segment of three-dimensional space, but a time interval (or time?) t between uniquely defined events.
6. The electromagnetic radiation generated by a moving massive object always propagates in a direction orthogonal to the velocity vector of the moving object.
Of course, I will be grateful for any adjustments to my options, or expert’s own formulations that have either eluded my attention or whose substance is far beyond my level of mathematical or general development.
Most respectfully
Sergey Sheludko
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Minkowski "spacetime" and Lorentz's Transforms are just contrived geometrical tricks based on the axiom that the velocity of light c is an universal constant in any IRF :
"The Mystery of the Lorentz Transform: A Reconstruction and Its Implications for Einstein's Theories of Relativity and cosmology"
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Our answer is YES. This question captured the reason of change: to help us improve. We, and mathematics, need to consider that reality is quantum [1-2], ontologically.
This affects both the microscopic (e.g., atoms) and the macroscopic (e.g., collective effects, like superconductivity, waves, and lasers).
Reality is thus not continuous, incremental, or happenstance.
That is why everything blocks, goes against, a change -- until it occurs, suddenly, taking everyone to a new and better level. This is History. It is not a surprise ... We are in a long evolution ...
As a consequence, tri-state, e.g., does not have to be used in hardware, just in design. Intel Corporation can realize this, and become more competitive. This is due to many factors, including 1^n = 1, and 0^n = 0, favoring Boolean sets in calculations.
This question is now CLOSED. Focusing on the discrete Weyl-Heisenberg group, as motivated by SN, this question has been expanded in a new question, where it was answered with YES in +12 areas:
[2]
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QM can have values unknown, but not uncertain. Likewise, RG questions. Please stay on topic, per question. Do not be uncertain yourself.
Opinions do not matter, every opinion is right and should be, therefore, not discussed.
But, facts? Mass is defined (not a choice or opinion) as the ratio of two absolutes: E/c^2. Then, mass is rest mass. There is no other mass.
This is consistent, which is the most that anyone can aspire. Not agreement, which depends on opinion. Science is not done by voting.
Everyone can, in our planet, reach consistency -- and the common basis is experiment, a fact. We know of other planets, and there consistency may be uncertain -- or ambivalent, and even obscure. A particle, there, may be defined, both, as the minimum amount of matter of a type, or the most amount of quantum particles of a type.
We can entertain such worlds in our minds, more or less formed by bodies of matter, and have fun with the consequences using physics. But, and there is my opinion (not lacking but not imposing objectivity) we all -- one day -- will be lead to abandon matter. What will we find? That life goes on. The quantum jump exists. Nature is quantum.
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If anyone knows of a conference on mathematics education to be held in Europe from April 2023 to March 2024, especially on mathematics education for elementary and junior high school students, please let me know.
As for the contents, it is even better if there are a textbook of mathematics, steam education, mathematics class and a computer.
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Please suggest some ML related research papers for Mathematics students.
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An Empirical Study of ML Algorithms for Stock Daily Trading Strategy.
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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 ?
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The engineering philosophy behind Coq and the Coq kernel is well worth careful consideration:
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Greeting,
When I tried to remotely accessed the scopus database by login into my institution id, it kept bring me back to the scopus preview. I tried cleaning the cache, reinstall the browser, using other internet and etc. But, none of it is working. As you can see in the image. It kept appeared in scopus preview.
Please help..
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To reach the Scopus document search module, you should use academic IPs. If your institute has been listed in the Scopus database, you have permission to search documents in Scopus. It is not free of charge, and your university should pay its share to Scopus to provide this service for its academic researchers.
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How to write formally within the context of mathematics that: "given two series S1 and S2 and they are subtracted each other coming from a proved identity that is true and the result of this subtraction is a known finite number (real number) (which is valid) the two series S1 and S2 are convergent necessarily because the difference could not be divergent as it would contradict the result of convergence? I need that definition within a pure mathematical scenario ( I am engineer).
" Given S1- S2 = c , if c is a finite and real number, and the expression S1-S2 = c comes from a valid deduction, then, S1 and S2 are both convergent as mandatory."
Best regards
Carlos
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Cite:
Mark Gritter
No. Consider the series ... in the above link example/ answer by Mark Gritter.
Both are divergent series, but the difference between the series is ... a convergent series.
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I'm trying to write a java programme that will solve the system of ordinary differential equations using the Runge-Kutta fourth-order (RK4) technique. I need to solve a system of five equations. Those are not linear.
And determining all of the equilibrium solutions to this system of differential equations also requires.
Can someone help me? Thank you in advance.
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Hereby attached is a system of three Ordinary Differential Equations (ODE). We have to use numerical methods such as RK4 and Euler to obtain the results using Java. I think RK4 is better for this kind of problem. In this thread, Dudley J Benton has already mentioned C programming for this. It is really amazing.
For the parameter values, you can use your own values for your convenience.
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Which are the implications in mathematics if the Irrationality Measure bound of "Pi" is proved to be Less than or equal to 2.5?
How can be understood the number pi within this context?
Thanks,
Carlos
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Many thanks
Jack Don McLovin
I have evidence that that is the upper bound... today it has been proved. But I reserve my ideas to publish them by a proper article. I just hope that journals can accept so clear ideas behind of this problem is a fundamental basis but not complicated to understand as it is believed. Many thanks.
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I am working on meta-heuristic optimization algorithms. I would like to solve Image segmentation using Otsu’s method and my algorithm. I could not understand how to use meta-heuristic in image segmentation. Please help me in this regard. I am from maths back ground. If anybody have matlab code for the same, please share with me. I will be grateful to you.
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Thank you very much Madam @Shima Shafiee
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I'm interested in the intersection of mathematics and social sciences, and I'm looking for expert opinions on ethical content in mathematical history.
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One of the most important features that distinguish mathematics from other sciences is abstraction, so some of them think that mathematics is abstract concepts. Abstraction is simply (a mental process based on separating one of the properties from something, and considering it independent of others).
(The Link Between Mathematics and Ethics) was built on the basis of the new view of man in contemporary psychology, as this view tends towards the primacy of the mind. In other words, this is consistent with the new scientific view that began with the theory of relativity and quantum mechanics, which proved the centrality of the mind. After World War II, many psychologists pointed out that the abolition of the role of the mind in human behavior and the subjection of the mind to instinct in the method of psychoanalysis led to the dehumanization of man. Therefore, psychology in the new view considers reason and determination as the highest human faculties, and they distinguish man from animals. (And the mind and the will not only control the body, but they also control the emotions and nullify them when necessary. By subordinating the emotions to the mind, harmony and happiness become within the reach of man). (And the old view of science considers that the human mind cannot choose freely because matter does not act except by mechanical necessity. This is the reason why the old view tended to explain human actions in the language of instinct). In short, this study comes within this framework, that is, we proceed here from the fact that man is a conscious force, and what mathematics does is that it creates what can be called a “moral authority” with mental foundations, meaning that the ethics generated by mathematics are based on the authority of the mind, not fear. (According to Dr. Mahmoud Bakir's opinion).
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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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Ignoring the displacements due to strain in the element, the rigid body translation equals the average of the nodal displacements of the elements and the rigid body rotations equal the average rotations of the nodes of the element. I believe this would offer high accuracy for elements away from the regions of constraints.
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Why is it necessary to study the History of Mathematics?
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History of mathematics can offer students a window into the processes of developing new mathematics, and the ways in which this knowledge is accepted and circulated within different communities. Especially pertinent to the question of decolonising the curriculum, turning to the history of the discipline offers a window into the role played by mathematics and mathematicians in settler colonialism, and how the mathematics we use today was in turn shaped by colonialism.
A new project at The Open University will produce an interactive online database of original sources, selected to demonstrate the global nature of mathematics. Original sources – such as letters, calculation aids, khipu or clay tablets – enable students to see beyond the final results explicated in their university textbooks to the work that went into uncovering these results in the first place...
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Which software is best for making high-quality graphs? Origin or Excel? Thank you
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origin
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How long does it take to a journal indexed in the "Emerging Sources Citation Index" get an Impact Factor? What is the future of journals indexed in Emerging Sources Citation Index?
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Clarivate announced that starting with 2023 ESCI-indexed journals will also be assigned an impact factor. See: https://clarivate.com/blog/clarivate-announces-changes-to-the-2023-journal-citation-reports-release/
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Lockdowns due to the COVID pandemic in last three years (2020-22) has played a significant role in the widespread of online based classrooms using applications like Zoom, MS teams, Webex and Google Meet. While substantial amount of the students were happy to complete their semester classes in due time without getting hampered by the lockdowns, thanks to the online based classrooms, there are also notable amount of students and parents who were complained regarding the online based classrooms that they have drastically distracted the academic performance of students.
Overall, I would like to leave it as an open-ended question. Dear researchers, what you think regarding the online based classroom? Is it an advantage for students or a disadvantage?
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Online-based classrooms are necessary for circumstances where the learners and teachers feel that the knowledge can be catered to without meeting in person. It is an opportunity for learners to learn at their doorsteps. Nonetheless, online classes are not as effective as offline classes for many learners who take education as a social process where peer learning, group dynamics, and interpersonal relationship are of high importance. Online class doesn't provide the experience of personal interaction while learning.
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My Awesomest Network, I am starting my Ph.D. studies and I have some questions and doubts concerning it. Could I write them down here, please? First of them is how can I join disciplines as sociology, management, economics, mathematics, informatics and other similar items to make a complex holistic interdisciplinary analysis and coherent study of pointed fields. I think personally that linking or joining et cetera aspects of artificial intelligence and computational social sciences would be interesting area of considerations. What are Your opinions?
Thank You very much for all in advance
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There is even such a discipline called "COmputational Social Sciences"...
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I am a post graduate student presently writing my thesis in the department of curriculum and instructional designs.
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I recommend research results from authors of the French group of Didactis of Mathematics as: Vergnaud, Bideaud, Meljac, Fischer, Brun. Also, from Oxford University Peter Bryant and Terezinha Nunes.
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I need mathematical full solution.. Can anyone please help me..
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Most statisticians agree that the minimum sample size to get any kind of meaningful result is 100.
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What is infinite? does this have any value? must there be an end or is it just our thoughts it can't imagine that there is no end to infinity! Aren't all things part of infinity? we too? is God an infinity that cannot be imagined but felt? is an infinity an energy that binds us and all things (reality and thought) together? Is there a physical explanation for infinity? Is the limitation by (infinity -1) or (-infinity + 1) legitimate or just a need to calculate it mathematically?
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We can imagine any finite quantity to be halved, and then each half to be halved again, and so on, without end. You can then say the finite quantity has infinitely many parts. It's just a conceptual distinction.
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We see many theories in physics, mathematics, etc. becoming extremely axiomatic and rigorous. But are comparisons between mathematics, physics, and philosophy? Can the primitive notions (categories) and axioms of mathematics, physics and philosophy converge? Can they possess a set of primitive notions, from which the respective primitive notions and axioms of mathematics, physics, and philosophy may be derived?
Raphael Neelamkavil
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Raphael Neelamkavil , you said, "But in your paper "The zero-dimensional physical theory (V): information, energy, efficiency, and intelligence" you exhibit enough awareness of the above facts. Hence, I do not understand what else you meant by the question at the end of your comment!".
The title of this forum topic is, "Can the Primitive Notions (Categories) and Axioms of Mathematics, Physics and Philosophy Converge?". When I said, "This is all a good question and debate, yet what is deliberate misinformation and ignorance, what is the drive for it, and can it be written about in a way so as not to promote it as being useful?" I am essentially asking whether or not the primitive notions are already granted by the contemporary ideas of mathematics, physics, and philosophy. My work highlights they are not, so a clear issue in this debate is all about what is assumed and what is not. My work with zero-dimensionality assumes nothing, and thence creates a new spectrum of ideas for mathematics, physics, and philosophy which has been, is, and perhaps still will be for most.
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I suppose so, it's true that physics is the special case of mathematics.
In physics, the existence and the uniqueness of the solution are ensured whereas in mathematics, it is the general case of physics, the existence and the uniqueness of the solution pass before all.
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In Leon Lederman's wonderful book, "The God Particle" he comments about a pecking order in physics. It goes something like, "the experimental physicists only defer to the theoretical physicists who in turn only defer to the mathematician and the mathematician only defer to God..."
Physics is not mathematics. The role of physics like all sciences is to understand the universe. The theoretical physicists' role is to develop theories that explains all the experiments from the past plus allows predictions to be made to test the and potentially falsify the theory. The role of the experimental physics is to develop and perform those experiments. There is often as much deep mathematics used by an experimental physicists as a theoretical physicists.
The role of the mathematician is simple to expend the understanding of mathematics through rigorous logical reasoning. If a physicists or any other scientist finds these tools useful - then great.
Arguably the greatest theoretical physicists of the second half of the 20 Century was Richard Feynman. Here is what he said about physics.
"It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong."
I would suggest for a better understanding of physics - what it is and isn't - a read of "The God Particle" would be recommended
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Assume we have a program with different instructions. Due to some limitations in the field, it is not possible to test all the instructions. Instead, assume we have tested 4 instructions and calculated their rank for a particular problem.
the rank of Instruction 1 = 0.52
the rank of Instruction 2 = 0.23
the rank of Instruction 3 = 0.41
the rank of Instruction 4 = 0.19
Then we calculated the similarity between the tested instructions using cosine similarity (after converting the instructions from text form to vectors- machine learning instruction embedding).
Question ... is it possible to create a mathematical formula considering the values of rank and the similarity between instructions, so that .... given an un-tested instruction ... is it possible to calculate, estimate, or predict the rank of the new un-tested instruction based on its similarity with a tested instruction?
For example, we measure the similarity between instruction 5 and instruction 1. Is it possible to calculate the rank of instruction 5 based on its similarity with instruction 1? is it possible to create a model or mathematical formula? if yes, then how?
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As far as I understand your problem, you first need a mathematical relation between the instructions and rank. For instance, Rank x should correspond to some instruction value as y and vice versa; it means you require a mathematical function.
So there are various methods/tools to find a suitable (as accurate as you want) to find mathematical function based on given discrete values like curve fitting methods or the use of ML.
Further, Once you obtain the mathematical function, run your code a few times, and you will get a set for various combinations of (instruction, rank). These set values will work as the feedback for your derived function. Make changes based on the feedback, and you will get a much more accurate function.
I hope you are looking for the same.
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Hi frds,
Need a good weather probability calculator. Would like to calculate the probability of e.g. 10 degrees Celsius on a day above the average. Has anybody got good research/formulas?
Which distribution is assumed in the probability calculation? Normal one?
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One possible approach is presented in the attached word document
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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?
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A point in space is given always by two points:
- coordinates of the point
- coordinates of origin of coordinates
Between those two points there is a "length" (physical dimension) with a physical Unit (Meters)
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I am thinking of the vector as a point in multidimensional space. The Mean would be the location of a vector point with the minimum squared distances from all of the other vector points in the sample. Similarly, the Median would be the location of the vector point with the minimum absolute distance from all the other vector points.
Conventional thinking would have me calculate the Mean vector as the vector formed from the arithmetic mean of all the vector elements. However, there is a problem with this method. If we are working with a set of unit vectors the result of this method would not be a unit vector. So conventional thinking would have me normalize the result into a unit vector. But how would that method apply to other, non-unit, vectors? Should we divide by the arithmetic mean of the vector magnitudes? When calculating the Median, should we divide by the median of the vector magnitudes?
Do these methods produce a result that is mathematically correct? If not, what is the correct method?
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For vectors X1=[x1,1;x2,1;..,xn,1]; X2=[x1,2;x2,2;..,xn,2];,.., Xn=[x1,n;x2,n;..,xn,n]
M=[m1,m2,..mn] - vector median,
where
m1=med(x1,1; x2,1;..,xn,1)
m2=med(x1,2; x2,2;..,xn,2)
- - - - - - - - - - - - -
mn=med(x1,n; x2,n;..,xn,n)
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Any idea why the solution of the attached equation is always zero at r=0? It seems simple at first look, however, when you start solving, you will see a black hole-like sink which makes the solution zero at r=0 (should not be). I used the variable separation method, I will be happy if you suggest another method or discuss the reasons.
I also attached the graph of the solution, showing the black hole-like sink.
Thanks
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I did give a physical explanation for why your boundary condition enforces the function f to become zero at r=0. In at least one physical interpretation, it models a system with infinite emission/absorption rate at r=0. This forces the temperature