Science topics: Mathematics
Science topic

# Mathematics - Science topic

Mathematics, Pure and Applied Math
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I want to ask if I can get good resources that can explain the mathematical approach behind the Adaptive Model Predictive Control AMPC MATLAB toolbox?
am not be able to find the mathematical analysis behind this toolbox even on the MathWorks webpage.
thank you
Mohamed
see
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Problem: 5 minutes of play are worth more than an hour of study
Knowing that: G = Game S = Gtudy 1 hour = 60 min
The mathematical formula that defines the statement is: 5 x G> 60 x S The quantitative ratio of the minutes expressed in the mathematical formula can be simplified: 60: 5 = 12, therefore the simplified mathematical formula is: G> 12 x S
So, 1 minute of play is worth more than 12 minutes of study Or it can be said that: game G is worth more than 12 times than study S.
Therefore, the quantitative value of physical objects (or of spatial and / or temporal quantities) must be calculated differently from the qualitative value of human life experiences.
Explain why it is possible___________________________________________________________________
___________________________________________________________________________
(Exercise based on Fausto Presutti's Model of PsychoMathematics).
Agreed with dear David Eugene Booth
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In several discussions, I have often come across a question on the 'mathematical meaning of the various signal processing techniques' such as Fourier transform, short-term fourier transform, stockwell transform, wavelet transform, etc. - as to what is the real reason for choosing one technique over the other for certain applications.
Apparently, the ability of these techniques to overcome the shortcomings of each other in terms of time-frequency resolution, noise immunity, etc. is not the perfect answer.
I would like to know the opinion of experts in this field.
Utkarsh Singh There is an esthetic reason in why a mathematical method is of interest in signal processing:
-a beautiful algorithm is well articulated, says what it does in few instructions, and does it in a stable and reliable manner
-this hints to the underlying algebra
With powerful and minimal computation, we go deep into algebra structures: group, rings, fields (see references on Evariste Galois as the inventor of "group" as we know it)
-Fourier transform is an interesting invention: it allows to decompose a signal into resonating modes (as for piano music: you produce a sound at frequency F, but also its harmonic NxF...). Naturally there is the aliasing question and the Nyquist theorem for reconstruction
There are many more time-frequency representations: Fourier, Laplace, discrete or continuous, cosine transform, wavelet transform, etc.
The interesting feature of discrete algorithms for those transforms is that you can implement a butterfly structure.
The key idea is to replace a very large number of multiplications (in brute force "non-esthetic" programming) by a smaller number of additions.
This idea worked for me for developing a codec system using underlying GF(n) properties.
See this patent:
The regularity in the processing and the efficiency of the representation go hand in hand.
Let me go back to a very basic mathematical method: the Gram-Schmidt decomposition: take a sequence of n vectors v(1),..., v(n), and the matrix of cross-products m(i,j)=<v((i),v(j)>. The Gram-Schmidt method diagonalises this matrix. It extracts eigenvalues, and eigen vectors. In frequency terms, it extracts modes (resonating modes present in the signal).
This algorithm highlights the efficiency side of the representation: it's projecting the signal onto something found "in itself", call it principal components if you want.
There are only two reasons for choosing a technique in engineering:
-(i) it addresses the problem completely
-(ii)it's economically implementable.
Both criteria are equally important and a good way to find these is to look for elegant, esthetic solutions (minimal and complete at the same time).
Does it help?
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In recent years, many new heuristic algorithms are proposed in the community. However, it seems that they are already following a similar concept and they have similar benefits and drawbacks. Also, for large scale problems, with higher computational cost (real-world problems), it would be inefficient to use an evolutionary algorithm. These algorithms present different designs in single runs. So they look to be unreliable. Besides, heuristics have no mathematical background.
I think that the hybridization of mathematical algorithms and heuristics will help to handle real-world problems. They may be effective in cases in which the analytical gradient is unavailable and the finite difference is the only way to take the gradients (the gradient information may contain noise due to simulation error). So we can benefit from gradient information, while having a global search in the design domain.
There are some hybrid papers in the state-of-the-art. However, some people think that hybridization is the loss of the benefits of both methods. What do you think? Can it be beneficial? Should we improve heuristics with mathematics?
I am surprised that a known scholar with a long experience in the transportation domain maintains such a hard stance on heuristic search. Obviously, we live in a world where extreme opinions are those which are the most echoed. Truth is, assuming that all practical optimization problems can be solved to optimality (or with approximation guarantees) is essentially wishful thinking. Given this state of art, better integration of exact and heuristic algorithms can largely benefit the research community. At the risk of repeating myself, here are some important remarks to consider:
• CPLEX and Gurobi (the current state of the art solvers for mixed integer programming optimization) rely on an army of internal heuristics for cut selection, branching, diving, polishing, etc... Without these heuristic components, optimal solutions could not be found for many problems of interest. CPLEX has even recently made a new release permitting a stronger heuristic emphasis (https://community.ibm.com/community/user/datascience/blogs/xavier-nodet1/2020/11/23/better-solutions-earlier-with-cplex-201). MIP solvers also heavily depend on the availability of good (heuristic) initial solutions to perform well. For many problems, cut separation is also done with heuristics. In the vehicle routing domain, we have a saying: heuristics are the methods that find the solutions, exact methods are those that finally permit to confirm that the heuristics were right (sometimes many decades later, and only for relatively small problems with a few hundred nodes despite over 60 years of research on mathematical models)...
• The machine learning domain is quickly taking over many applications that were previously done with optimization. Among the most popular methods, deep learning applies a form of stochastic gradient descent and does not guarantee convergence to optimal parameters. Neural networks currently face the same scrutiny and issues as the heuristic community, but progress in this area has still brought many notable breakthroughs. Decision-tree construction and random forests are also largely based on greedy algorithms, same for K-means (local improvement method) and many other popular learning algorithms.
• Even parameter tuning by the way is heuristic... I'm sorry to say that, but most design choices, even in the scientific domain, are heuristic and only qualify as good options through experimentation.
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Hi
I would really appreciate if someone helps me out with this MATLAB problem. I have uploaded both MATLAB file (which is not working properly) and the question.
Thank you very much in advance
#MATLAB
Hi, you can directly use the following MATLAB function : fminsearch that uses the Nelder-Mead simplex (direct search) method instead of trying to implement your own version. Best
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In the lands with ancient plain sediments, the courses of rivers change dramatically over time for easy movement and the arrival of rivers to an advanced geomorphic stage.
Are there mathematical arrays that achieve digital processing such as spectral or spatial improvements or special filters to detect buried historical rivers?
Ruqayah Al-Ani The digital elevation model (DEM) is a good component in the field of remote sensing and GIS. The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model (GDEM). The ASTER GDEM needs further error-mitigating improvements to meet the expected accuracy specification. The RMSE values can be used to represent the DEM errors, in addition to mean error and standard deviation (stddev).
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The mathematical relations how it comes.
Thanks
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List of unsolved problems in mathematics, engineering, industry, science, etc.
An Euler brick is a cuboid that possesses integer edges a>b>c and face diagonals. If the space diagonal is also an integer, the Euler brick is called a perfect cuboid, although no examples of perfect cuboids are currently known.
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In the definition of a group, several authors include the Closure Axiom but several others drop it. What is the real picture? Does the Closure Axiom still have importance once it is given that 'o' is a binary operation on the set G?
What actually happens is that, closure property is a common one to almost all structures (systems). Therefore, authors who drop it in their texts assume that it is automatically embedded in the structure. Others who include it want to be vivid in their texts for clarity sake.
So, those who drop this important property do not truncate it entirely or cancel it.
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I am considering to send my research about Sophie Germain primes and it´s relation with primes of the form prime(a)+prime(b)+1= prime(c) and prime(b)-prime(a)-1= prime(c)
Mainly you have to send a mathematic research but others science researchs are accepted too. I don´t know the level of the contest but my chance is that my research i´ts have a deep relation with the work of Sophie Germain.
Do you have any recomendation of the form to present my work and the form of write to the responsables of the prize?
I don´t understand you. It´s no trivial to find two prime numbers whose sum +1 will be other prime number. In fact my formula have a success of the 80%
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Hi, Prof and Dr. the following is my thesis title. Any comment, please.
"the study of predicted factors of teachers' intention in teaching Mathematics Problem Solving through online"
Design optimization, fabrication, and performance evaluation of solar parabolic trough collector for domestic applications
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I am working on a research and i am looking for someone who can help with a mathematics matters.
Attached for your kind perusal@Miss. A.M
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Abstract
This paper studies the proof of Collatz conjecture for some set of sequence of odd numbers with infinite number of elements. These set generalized to the set which contains all positive odd integers. This extension assumed to be the proof of the full conjecture, using the concept of mathematical induction.
You can find the paper here: (PDF) Collatz Theorem. Available from: https://www.researchgate.net/publication/330358533_Collatz_Theorem [accessed Dec 21 2020].
The first 11 theorems in your article provide a limit family of numbers that obey the Collatz conjecture and the number of steps needed to reach 1.
Unfortunately, in theorem (12), you have assumed that Collatz conjecture is true!!
In fact, your assumptions of the existence of b1 , b2 , ....bk-1 where k is finite
is exactly the Collatz conjecture, and the rest is an elementary computation of the number of steps to reach 1.
Can you prove that k is finite?
Obviously, if one assumes k is finite, then he assumes that Collatz conjecture is true.
Anyway, you have determined a nice family of numbers that satisfy the Collatz conjecture.
I wish you good luck to show k is finite.
Best regards
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How i can extract mathematical function by the given data set
Maybe spline interpolation.
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Some Mathematical expressions will be helpful.
No
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I am looking for a research paper about the mathematical or computational modelling of protein oxidation (caused by reactive oxygen species).. I would really appreciate that if someone helps me with this.
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Would prefer a book for learners.
see
Anh C.T., Hung P.Q., Ke T.D., Phong T.T.: Global attractor for a semilinear parabolic equation involving Grushin operatot. Electron. J. Differ. Equ. 32, 1–11 (2008)
D’Ambrosio L.: Hardy inequalities related to Grushin type operators. Proc. Am. Math. Soc. 132, 725–734 (2004)
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I am looking for any book/article reference about the mathematical description of zero normal flux boundary condition for shallow water equations. My concern is that for a near-shore case how it is obvious to have zero normal flux. Physically, it does make sense that we have a near-shore case and on the boundary, there is no flow in the normal direction. How to mathematical explain it using the continuity equation in the case when there is a steady flow? The continuity equation suggests that $\partial h / \partial t + u. \partial h/ partial x = 0$. If we take steady flow then it is clear to me to get zero normal flux condition. But what if the first term is not zero? or do we say that at the boundary the flow is always steady?
Shallow Water Hydrodynamics: Mathematical Theory and Numerical Solution for a Two-dimensional System of Shallow Water Equations
ElsevierTan Weiyan (Eds.)Year:1992
Lattice Boltzmann Methods for Shallow Water Flows
Springer-Verlag Berlin HeidelbergDr. Jian Guo Zhou (auth.)Year:2004
Numerical Methods for Shallow-Water Flow
Springer NetherlandsC. B. Vreugdenhil (auth.)Year:1994
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I want to determine the success rate of an personnel selection instrument (interview, assessment center...) depending on the validity of the instrument itself, the selection rate and the base rate.
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If we are given that (x-2)(x-3)=0 and 0.0=0, then we can conclude that both x=2 and x=3 simultaneously. This is because x-2=0 and x-3=0, simultaneously, is consistent with 0.0=0. However, this leads to a contradiction, namely, x=2=3. So, generally we exclude this option while finding roots of an equation and consider that only one of the factors can be zero at a time i.e. all the roots are mutually exclusive. In other words, we consider 0.0 to be not equal to 0.
Now, if we are given that x=0 and asked to find out what x^2 is, then certainly we conclude that x^2=0. It is trivial to observe that this conclusion is made through the following process: x^2=x.x=0.0=0. That is, we need to consider 0.0=0 to make this simple conclusion.
Therefore, while in the first case we have to consider 0.0 not equal to 0 to avoid contradiction, in the second case we have to consider 0.0=0 to reach the conclusion. So, the question arises whether 0.0 is equal to 0 or not. As far as I know, mathematical truths are considered to be universal. However, in the present discussion it appears to me that whether 0.0 is 0 or not, is used as par requirement. Is that legitimate in mathematics?
@Pedro, I don't understand why the word or is emphasised . As per my understanding , a quadratic equation must possess exactly 2 roots so this equation (x-2)(x-3)=0 contains two distinct roots which are x=2 and x=3. For better visualisation , one can easily plot that equation to find the roots where the function cuts the x-axis. It does not mean that x=2=3. Do I miss any necessary information?
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How do you define uncertainty in an economic decision model? With this mathematical approach in mind, how should you make decisions?
Let us take an example. An agent-based model of the economy, society, stock market, etc. You define the model, implement it in an AB evaluation environment, and run the simulations.
Many people end here. What can be done more? We change parameters and run simulations again for all changed parameters separately. In this way, we create statistics of possible evolutions of the model. From here, statistical evaluation is easy.
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My dear friends, I am asking if some of your students are interested in applying a postdocotor position in China with me, here is the link and details!!!
Jefferson Santos Silva There is no deadline, the program opens all the time before the end of 2021
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How does one get access to the Mizar Mathematical Library (MML) ? This refers
to the Mizar system for the formalisation and automatic checking of mathematical proofs based
on Tarski-Grothendieck Set Theory (mizar.org).
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As we know,Strehl Ratio(SR) is a measure of turbulence is a medium.How to calculate SR of a medium mathematically?
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Any decision-making problem when precisely formulated within the framework of mathematics is posed as an optimization problem. There are so many ways, in fact, I think infinitely many ways one can partition the set of all possible optimization problems into classes of problems.
1. I often hear people label meta-heuristic and heuristic algorithms as general algorithms (I understand what they mean) but I'm thinking about some things, can we apply these algorithms to any arbitrary optimization problems from any class or more precisely can we adjust/re-model any optimization problem in a way that permits us to attack those problems by the algorithms in question?
2. Then I thought well if we assumed that the answer to 1 is yes then by extending the argument I think also we can re-formulate any given problem to be attacked by any algorithm we desire (of-course with a cost) then it is just a useless tautology.
I'm looking foe different insights :)
Thanks.
The change propagation models may give a great idea
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Dear scholars,
I am now struggling on a question.
Let's assume that there is a given line or a given arbitrary function defined on a z=0 plane. Now I twist the plane into a non-linear 3D surface that can be represented by any given continuous and differentiable equations. How could I represent this line or function in analytical equations now.
You could think this like "a straight line on a waving flag".
Much appreciated if you have any idea or suggested publications.
Thanks.
See here: (PDF) Folding and Bending Planar Coils for Highly Precise Soft Angle Sensing (researchgate.net)
A little more further evaluation is required.
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Can you help me create a source of type sinc in ADS
I found a mathematical function that plays the role (picture 1) but I do not know how to use it ?
hello , you can use Verilog A to create this source.
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NO. No one on Earth can claim to "own the truth" -- not even the natural sciences. And mathematics has no anchor on Nature.
With physics, the elusive truth becomes the object itself, which physics trusts using the scientific method, as fairly as humanly possible and as objectively (friend and foe) as possible.
With mathematics, on the other hand, one must trust using only logic, and the most amazing thing has been how much the Nature as seen by physics (the Wirklichkeit) follows the logic as seen by mathematics (without necessarily using Wirklichkeit) -- and vice-versa. This implies that something is true in Wirklichkeit iff (if and only if) it is logical.
Also, any true rebuffing of a "fake controversy" (i.e., fake because it was created by the reader willingly or not, and not in the data itself) risks coming across as sharply negative. Thus, rebuffing of truth-deniers leads to ...affirming truth-deniers. The semantic principle is: before facing the night, one should not counter the darkness but create light. When faced with a "stone thrown by an enemy" one should see it as a construction stone offered by a colleague.
But everyone helps. The noise defines the signal. The signal is what the noise is not. To further put the question in perspective, in terms of fault-tolerant design and CS, consensus (aka,"Byzantine agreement") is a design protocol to bring processors to agreement on a bit despite a fraction of bad processors behaving to disrupt the outcome. The disruption is modeled as noise and can come from any source --- attackers or faults, even hardware faults.
Arguing, in turn, would risk creating a fat target for bad-faith or for just misleading references, exaggerations, and pseudo-works. As we see rampant on RG, even on porous publications cited as if they were valid.
Finally, arguing may bring in the ego, which is not rational and may tend to strengthen the position of a truth-denier. Following Pascal, people tend to be convinced better by their own-found arguments, from the angle that they see (and there are many angles to every question). Pascal thought that the best way to defeat the erroneous views of others was not by facing it but by slipping in through the backdoor of their beliefs. And trust is higher as self-trust -- everyone tends to trust themselves better and faster, than to trust someone else.
What is your qualified opinion? This question considered various options and offers a NO as the best answer. Here, to be clear, "truth-denial" is to be understood as one's own "truth" -- which can be another's "falsity", or not. An impasse is created, how to best solve it?
"Only dead fish swim with the current implies that those who swim against the current are those who wish to invoke change; who want to control, manipulate, and improve their environment. People who swim upstream make things happen. They are the movers and shakers; the innovators and inventors; the disruptors of the world. There is nothing new downstream; only that which is old and boring, ancient history, the past, the been there and done that... the tried and true. One must swim upstream to find and explore new territory; learn new stuff, have new experiences. To create; fly; soar."
But those who try, find it hard to not "go with the flow." The solution maybe to swim like a salmon, making the least waves. With the same principle, it works on a swimming pool, trying to improve personal "best times" -- and tells one why a deeper pool is faster.
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somebody, please elaborate on how to calculate exergy destruction in kW units. from Aspen HYSYS I found mass exergy with kJ/kg unit and i don't know how to calculate it by using Aspen HYSYS and if somebody has mathematical calculation with example please share with me. I know how to calculate by aspen plus but I need a mathematical or Aspen HYSYS solution.
thanks in anticipation
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As we know, computational complexity of an algorithm is the amount of resources (time and memory) required to run it.
If I have algorithm that represents mathematical equations , how can estimate or calculate the computational complexity of these equations, the number of computation operations, and the space of memory that are used.
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What happens to numbers with highest power and it's implication on the numbers last digit. How applicable is that in mathematical problem solving
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The mosque is in abu Dhabi
Civil engineers use trigonometry often when surveying a structure. Surveying deals with land elevations as well as the various angles of structures.
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In the education discipline, several leadership theory has been discussed but no such mathematical foundations are available to estimate them. More, especially how can I differentiate( in terms of Mathematical expressions ) the several leadership styles in decision making problems so that I could get the better one; and the decision maker would comfort to apply their industrial/ managerial/ organizational situation ? We may assume that, the problem is a part of fuzzy decision making/ intelligent system / artificial intelligent system/ soft system.
The leaders are manager of an industry/ organization/ corporate house, the ministry of a Government / the agents of a marketing system, the representatives of customers of a particular product in a supply chain management problem.
I think what you want is in this book
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what are the differences between mathematical modelling and realistic mathematic education?
Mathematical modeling is the process of a problem solving by the mathematical expression of real life event or a problem. This process enables learners to relate mathematics to real life and to learn it more meaningfully and permanently.
Realistic Mathematics Education – RME – is a domain-specific instruction theory for mathematics, which has been developed in the Netherlands. Characteristic of RME is that rich, “realistic” situations are given a prominent position in the learning process.
Mathematical Modelling Approach in Mathematics Education BY:Ayla Arseven
Best regards
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What is the importance of Golden Ratio in nature and mathematics? Why the golden ratio is sometimes called the "divine proportion," by mathematicians?
In the world of art, architecture, and design, the golden ratio has earned a tremendous reputation. Greats like Le Corbusier and Salvador Dalí have used the number in their work. The Parthenon, the Pyramids at Giza, the paintings of Michelangelo, the Mona Lisa, even the Apple logo are all said to incorporate it.
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Dear Friends,
Kindly allow me to ask you a very basic important question. What is the basic difference between (i) scientific disciplines (e.g. physics, chemistry, botany or zoology etc.) and (ii) disciplines for branches of mathematics (e.g. caliculus, trigonometry, algebra and geometry etc.)?
I feel, that objective knowledge of basic or primary difference between science and math is useful to impart perfect and objective knowledge for science, and math (and their role in technological inventions & expansion)?
Let me give my answer to start this debate:
Each branch of Mathematics invents and uses complementary, harmonious and/or interdepend set of valid axioms as core first-principles in foundation for evolving and/or expanding internally consistent paradigm for each of its branches (e.g. calculous, algebra, or geometry etc.). If the foundation comprises of few inharmonious or invalid axioms in any branch, such invalid axioms create internal inconsistences in the discipline (i.e. branch of math). Internal consistency can be restored by fine tuning of inharmonious axioms or by inventing new valid axioms for replacing invalid axioms.
Each of the Scientific disciplines must discover new falsifiable basic facts and prove the new falsifiable scientific facts and use such proven scientific facts as first-principles in its foundation, where a scientific fact implies a falsifiable discovery that cannot be falsified by vigorous efforts to disprove the fact. We know what happened when one of the first principles (i.e. the Earth is static at the centre) was flawed.
Example for basic proven scientific facts include, the Sun is at the centre, Newton’s 3 laws or motion, there exists a force of attraction between any two bodies having mass, the force of attraction decreases if the distance between the bodies increase, and increasing the mass of the bodies increases the force of attraction. Notices that I intentionally didn’t mention directly and/or indirectly proportional.
This kind of first principles provide foundation for expanding the BoK (Body of Knowledge) for each of the disciplines. The purpose of research in any discipline is adding more and more new first-principles and also adding more and more theoretical knowledge (by relying on the first-principles) such as new theories, concepts, methods and other facts for expanding the BoK for the prevailing paradigm of the discipline.
I want to find answer to this question, because software researchers insist that computer science is a branch of mathematics, so they have been insisting that it is okay to blatantly violating scientific principles for acquiring scientific knowledge (i.e. knowledge that falls under the realm of science) that is essential for addressing technological problems for software such as software crisis and human like computer intelligence.
If researchers of computer science insist that it is a branch of mathematics, I wanted to propose a compromise: The nature and properties of components for software and anatomy of CBE (Component-based engineering) for software were defined as Axioms. Since the axioms are invalid, it resulted in internally inconsistent paradigm for software engineering. I invented new set of valid axioms by gaining valid scientific knowledge about components and CBE without violating scientific principles.
Even maths requires finding, testing, and replacing invalid Axioms. I hope this compromise satisfy computer science scientists, who insist that software is a branch of maths? It appears that software or computer science is a strange new kind of hybrid between science and maths, which I want to understand more (e.g. may be useful for solving other problems such as human-like artificial intelligence).
Best Regards,
Raju Chiluvuri
Dear @Raju Chiluvuri
To my opinion, mathematics is the precursor to all the disciplines of science. And, in fact, mathematics is also a science.
Thanks!
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Hi
I am doing linear regression research assignment where I have to research how does mathematical scores and gender (independent variables) affect to natural history scores (dependent variable). I am not sure am I interpreting gender's dummy variable (female = 1, male = 0) right in the coefficients table.
Am I right by interpreting that females are getting on average 10.9 points less natural history scores than male?
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In fact, it is the fundamental defects in the work of “quantitative cognition to infinite things” that have been troubling people for thousands of years. But I am going on a different way from many people.
1, I analysis and study the defects in existing classical infinite theory system disclosed by the suspended "infinite paradox symptom clusters" in analysis and set theory from different perspectives with different conclusion: to abandon the unscientific (mistaken) "potential infinite and actual infinite" concepts in existing classical infinite theory system and discover the new concepts of "abstract infinite and the carriers of abstract infinite", especially to replace the unscientific (mistaken) "actual infinite" concept in existing classical infinite theory by the new concept of “carriers of abstract infinite" and develop a new infinite theory system with “mathematical carriers of abstract infinite and their related quantitative cognizing operation theory system ". From now on, human beings are no longer entangled in "potential infinite -- actual infinite", but can spare no effort to develop "infinite carrier theory", and develop comprehensive and scientific cognition of various contents related to "mathematical carrier of abstract infinite concept".
2, Abstract concept - abstract concept carrier theory, new infinite theory system, carrier theory, infinite mathematical carrier gene, infinite mathematical carrier scale,...The development of basic theory determines the construction of "quantum mathematics" based on the new infinite theory system.
3, I have up loaded 《On the Quantitative Cognitions to “Infinite Things” (IX) ------- "The Infinite Carrier Gene”, "The Infinite Carrier Measure" And "Quantum Mathematics”》2 days ago onto RG introducing " Quantum Mathematics". My work is not fixing here and there for those tiny defects (such as the CH theory above) but carrying out quantitative cognitions to all kinds of infinite mathematical things with "quantum mathematics" basing on new infinite theory system.
According to my studies (have been presented in some of my papers), Harmonic Series is a vivid modern example of Zeno's Paradox. It is really an important case in the researches of infinite related paradoxes syndrome in present set theory and analysis basing on unscientific classical infinite theory system.
All the existing (suspending) infinite related paradoxes in present set theory and analysis are typical logical contradictions.
The revolution in the foundation of infinite theory system determines the construction of "Quantum Mathematics" based on the new contents discovered in new infinite theory system: infinite mathematical carrier, infinite mathematical carrier gene, infinite mathematical carrier measure,... in new infinite carrier theory. So, the "Quantum Mathematics" mentioned in my paper is different from Quantum Logic and Quantum Algebras;
According to my studies (have been presented in some of my papers), “Non-Standard Analysis and Transfinite numbers” is all the infinite related things in unscientific classical infinite theory system based on the trouble making "potential infinite and actual infinite" --------- Non-Standard Analysis is equivalence with Standard Analysis while Transfinite is an odd idea of “more infinite, more more infinite, more more more infinite, more more more more infinite,…”).
Search RG for Ed Gerck. I'm sure he'd be glad to discuss this topic.
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Mathematics differs from sensory science in that it draws its subject from structural construction to abstract abstraction of quantitative quantities, while other sciences rely on the description of actual sensory objects already in existence.
What do you think?
Dear colleagues. A very interesting question, some years ago, in 2012, I published a work where I give a definition of Mathematics that can serve to answer the question.
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Computer Aided Design (Cad) subject deals with the backend mathematical calculation that happens in a 3D design.
The book of Computer Aided Optimal Design: Structural and Mechanical Systems by the Mota Soares, C.A. and Templeman, A.B can be useful.
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Hello,
I am interested in the personalization of learning based on profiles, more specifically in mathematics.
Do you know any relevant references?
Thank you
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The fact that , electron can have only discrete energy level is obtained by solving schrodinger equation with boundary conditions, which is a mathematical derivation .
Physically, What makes the electron possess only certain energies ?
Or is there any physical insight or explanation or physical intution which can arrive at same conclusion(without math) that electron can have only discrete energy levels inside potential well
When the electron's energy can take only certain values this just means that the states that would correspond to the other values don't exist, under those circumstances. These circumstances are described by the boundary conditions imposed, that are part of the physical description, too.
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Given a fixed volume where the relative humidity and temperature are known, how can you estimate how much water vapor will condense corresponding to a temperature decrease. I suspect it has to do with the dew point temperature but I'm having trouble finding mathematical relations.
It is not very difficult, but some algebra needs to be involved.
The workflow is the following:
1. Knowing relative humidity at T=T0 (as an input), calculate the partial pressure of vapor at this temperature.
2. Calculate water vapor concentration rho_0 using the ideal gas equation.
3. Calculate saturated vapor pressure at T=T1 from tables or the Clausius-Clapeyron equation.
4. Calculate corresponding saturated vapor density rho_1 at T=T1 using the ideal gas equation.
5. If rho_1 < rho_0, there will be no condensation, otherwise the mass of water condensed in volume V will be V(rho_1 -rho_0).
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Hi every one,
here I have a problem in MATLAB, when I want to solve the following equation, relative to PI in the photo, or tau in the code, MATLAB will send me this error: Warning: Unable to find explicit solution. For options, see help.
I attached the question and the code below (in code, I rewrite pi in the photo with tau).
If you have any idea to solve this problem, analytically or numerically, I will be happy to hear it out.
NOTE:
> PI_0.1(X,t) = tau
> X = [x(t),y(t),psi(t)]^T;
** PROBLEM: Find tau in terms of X and t in which solve the mentioned equation.
Arash.
code:
______________________________________
______________________________________
clc;clear;
syms x y psi tau t
c1 = 1;c2 = 1.5;lambda = 0.1;
x_r(tau) = 0.8486*tau - 0.6949;
y_r(tau) = 5.866*sin(0.1257*tau + pi);
psi_r(tau) = 0.7958*sin(0.1257*tau - pi/2);
x_r_dot = 0.8486;
y_r_dot(tau) = 0.7374*cos(0.1257*tau + pi);
psi_r_dot(tau) = 0.1*cos(0.1257*tau - pi/2);
phrase1 = c1/2*(cos(psi)*(x - x_r) + sin(psi)*(y - y_r))*(cos(psi)*x_r_dot + sin(psi)*y_r_dot);
phrase2 = c1/2*(-sin(psi)*(x - x_r) + cos(psi)*(y - y_r))*(-sin(psi)*x_r_dot+cos(psi)*y_r_dot);
phrase3 = 0.5*(psi - psi_r)*psi_r_dot;
eq = -2*(1-lambda)^2*(phrase1 + phrase2 + phrase3) - 2*lambda^2*(t - tau)
sol = solve(eq == 0 , tau , 'IgnoreAnalyticConstraints',1)
______________________________________
______________________________________
Pass x, instead of tau, as rightly pointed out by Saeb AmirAhmadi Chomachar
syms x y psi tau t
c1 = 1;c2 = 1.5;lambda = 0.1;
x_r(tau) = 0.8486*tau - 0.6949;
y_r(tau) = 5.866*sin(0.1257*tau + pi);
psi_r(tau) = 0.7958*sin(0.1257*tau - pi/2);
x_r_dot = 0.8486;
y_r_dot(tau) = 0.7374*cos(0.1257*tau + pi);
psi_r_dot(tau) = 0.1*cos(0.1257*tau - pi/2);
phrase1 = c1/2*(cos(psi)*(x - x_r) + sin(psi)*(y - y_r))*(cos(psi)*x_r_dot + sin(psi)*y_r_dot);
phrase2 = c1/2*(-sin(psi)*(x - x_r) + cos(psi)*(y - y_r))*(-sin(psi)*x_r_dot+cos(psi)*y_r_dot);
phrase3 = 0.5*(psi - psi_r)*psi_r_dot;
eq = -2*(1-lambda)^2*(phrase1 + phrase2 + phrase3) - 2*lambda^2*(t - tau);
eqn = rewrite(eq,'log');
sol = solve(eqn == 0 , x , 'IgnoreAnalyticConstraints',1);
pretty(sol)
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Hello,
I am doing research on HVLD detection capability.
From your experience, is there some mathematical formula to prove that HVLD machines can detect holes regardless of size or some other ways to prove it?
I am not expert in this subject , may be the following links are useful
High-Voltage Leak Detection of a Parenteral Proteinaceous Solution Product Packaged in Form-Fill-Seal Plastic Laminate Bags. Part 3. Chemical Stability and Visual Appearance of a Protein-Based Aqueous Solution for Injection as a Function of HVLD Exposure
Rasmussen, M., Damgaard, R., Buus, P., Guazzo, D. M.Journal:PDA Journal of Pharmaceutical Science and TechnologyYear:2013
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A question related to our cultural indebtedness to our mathematical forbears.
Interesting question. However, the foundations that allowed calculus to evolve started long before Newton and Leibniz. The foundation is not calculus but the concept of the limit. Archimedes (287-212 BC) was probably the first to recognize what became the concept of the limit in is estimation pi and the area of the circle by taking inscribed and circumscribed polygons bounding the circle and using the simple fact that one approaches pi from below while the other from above. Of each sequence defines a Cauchy sequence - concept unknown at that time and the completion of the reals (also unknown at that time) show the limit of each sequence is the same and equal a the number pi. In reality the concept of infinitesimal - goes back to Archimedes although the formal concept of "infinity" was not accepted until long afterwards.
Roll backwards to the Greeks when faced with the proposition of an infinite number of prime number, was a problem as they believed the universe was finite. Infinity was not something the Greeks wanted to accept and Aristotle (385-348 BC). But Archimedes had just shown that infinity and infinitesimals had a role in mathematics - in fact a central role. It was not to the 1600's that mathematicians attack the problem of infinity to try to understand what it mean as they developed the concept of numbers that are used today.
As we better understood our real number system, the concept of point set or general topology was defined to abstract and better understand the structure. In general topology concepts like nets (generalizations of sequences required to define integrals for example), convergence, close to, in a neighborhood and limits are all defined through the concept of open sets which are used to define a topology on a set which now allows for the definition and study of the concept of limits and continuity and handle infinity. While the formulations of general topology came along after the "birth of the calculus" and known as Analysis Situs a term coined by Henri Poincaré through the work of Poincaré , Euler, Cantor, Lefschetz, Courant, Hilbert, etc., a firm foundation was laid not only to the real number system, but to limits, continuity all the foundations of what we now know as 'calculus."
Topology is so important to the foundations of calculus and the concept of a limit that in his classic text, "General Topology," John Kelley writes in the first paragraph of the preface he writes, "...I have, with difficulty, been prevented by my friends from labeling it: What Every Young Analyst Should Know." No truer words have been spoken or written as the foundations of topology has allowed the concept of calculus to be expanded far beyond its original intent.
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I am doing a research proposal i need answers on my topic. information must be from 2015-2020. relevant articles
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Any bibliographic recommendations on the problem of routing vehicles with multiple deposits, homogeneous capacities? less than 10 nodes
A multi-depot VRP with less than 10 nodes should be almost enumerable, as there exist less than 1024 possible subsets of customers. Given this fact, perhaps the simplest solution approach is to generate all feasible routes from each depot, discard those that are not TSP-optimal, and directly solve a set partitioning formulation based on these routes. Now, if you face larger problems (e.g., 15 nodes or more), you should use the formulations suggested by Adam and Noha, or even go for sophisticated branch-and-price approaches as described in
since the code associated with this paper is freely accessible at
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L'Huillier's theorem or calculation of spherical excess of "spherical triangle" formed between the unit vectors on unit sphere can find out the area, but how to explain this formula from purely plane trigonometry standpoint (i.e. without assuming any pre-requisite knowledge on spherical trigonometry)? The solid angle can be found by spherical trigonometry rules, and I am well aware of it. I want to introduce this problem to anyone with knowledge of plane trigonometry, but no knowledge of spherical trigonometry.
I hope you find the following discussion is useful
Best regards
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what is the mathematical expressions and equations used for the designing of antipodal structure of an antenna.
Dear Sneha,
You will get the design formulas and an example of antipodal Vivaldi Antenna.
If you have more questions you can ask the first author of the paper.
Best wishes
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I hope for a global overview on mathematical giftedness and its support in school and/or on an extracurricular level. What programmes/opportunities are offered?
First thanks , it is really an interesting question.
A problem is that gifted and talented students do not receive the necessary care
To meet their needs by remaining in regular classes. Therefore, I find it important to do the following:
- Staying away from traditional methods during teaching, this leads to boredom for students, especially talented people
- When constructing lessons conceptually, we take into account that gifted and talented students may also suffer
One of the weaknesses in understanding the curriculum and that they need to be considered. And when applying the teaching conceptually within
In the ordinary class, students of all levels will learn in a deeper way.
- Adding open-ended questions to both education and evaluation for their positive results on students ’understanding
As well as their attitudes towards the material.
The- direct and indirect financial support for talented people
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Quantum computing is the field that focuses on quantum computation/information processing, the mathematical and physical theory for which as well as the engineering required to realize different circuits and algorithms into hardware performance, as well as other contingent issues such as the whole “compute chain” (from software engineering to quantum machine code and then further on to the physical architecture) and device/hardware issues such as thermal, electrooptical and nanoengineering.
My question is how quantum computing is related to artificial intelligence?
Quantum computing (QC) is the enabling technology for efficiently processing huge quantities of (quantum) information, in many cases outperforming "classical" computing (i.e. binary logic based). It provide you the "muscles" for data crunching, provided you feed it with quantum-coded information (qubits) and you get probabilistic results (with high likelihood if well designed).
Artificial Intelligence (and Machine Learning more specifically) is a discipline focused in performing data analysis with the objective of simulating human reasoning for achieving a certain goal. It can then definitively take advantages by a super fast computing capability provided by QC, both for speeding up "classical" algorithms or for running QC native ones, which are expected to open the door to a next level of AI capabilities beyond our current imagination.
Just be patient for few more years and wait for a working universal QC becoming available (at competitive price).
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Can any one suggest application(s) for $R_{\alpha}, R_{\beta}$ and $R_{m}$ -functions in mathematical or applied sciences; which is recently introduced in following research paper;
H. M. Srivastava et al. A family of theta- function identities based upon combinatorial partition identities and related to Jacobi’s triple-product identity, Mathematics 8(6)(2020), Article ID 918, 1-14.
Interesting question. Following the discussion.
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Dear colleagues,
I am looking for a practical guide presenting the non-parametric tests intended for students without mathematical background (or very little) with if possible the codes SAS or R.
Thank you.
Hi Natacha,
rcompanion.org is a great source with many examples of non-parametric tests.
sthda.com is also good, but the author uses his own limited packages.
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Here I just want to know about the actual parameters to measure the content of happiness in a person. With the help of these parameters a neural network can be generated and maintained to achieve the maximum happiness. I am also expecting some better approach from the scholars.
I think you may use face expression analysis, emotions & gates etc., recognition databases. Such databases are publicly available on kaggle.com and here : https://www.robots.ox.ac.uk/~vgg/data/
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Can we apply the theoretical computer science for proofs of theorems in Math?
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Take, for example, such a concept as a minimum flow, that is, a gradient vector field, the level surfaces of which are the minimum surfaces. Then the globally minimal flow, evolving to an absolutely minimal state, could be compared with a quantum vacuum, and the locally minimal flow could be compared with fields and particles. At the same time, it is clear that it is necessary to correctly choose the space in which this minimum flow moves.
Structure wave theory shows how mathematics as a structurally active language based on the release of structure waves is converted into physics.
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Hello all,
I am looking for an method / algorithm/ or logic which can help to figure out numerically whether the function is differentiable at a given point.
To give a more clear perspective, let's say while solving a fluid flow problem using CFD, I obtain some scalar field along some line with graph similar to y = |x|, ( assume x axis to be the line along which scalar field is drawn and origin is grid point, say P)
So I know that at grid point P, the function is not differentiable. But how can I check it using numeric. I thought of using directional derivative but couldn't get along which direction to compare ( the line given in example is just for explaining).
Ideally when surrounded by 8 grid points , i may be differentiable along certain direction and may not be along other. Any suggestions?
Thanks
The answer to a question about the numerical algorithms for resolving the issue of differentiability of a function is typically provided by the textbooks on experimental mathematics.
I recommend in particular: Chapter 5: “Exploring Strange Functions on the Computer” in the book: “Experimental Mathematic in Action”.
You can also get a copy of the text in a form of a preprint from
Judging by the quote placed in the beginning of Chapter 5, the issue of investigation of the “strange functions” was equally challenging i 1850s as it is 170 years later:
“It appears to me that the Metaphysics of Weierstrass’s function
still hides many riddles and I cannot help thinking that enter-
ing deeper into the matter will finally lead us to a limit of our
intellect, similar to the bound drawn by the concepts of force
and matter in Mechanics. These functions seem to me, to say
it briefly, to impose separations, not, like the rational numbers”
(Paul du Bois-Reymond, [129], 1875)
The situation described in your question is even more complicated because the function is represented only by a few values on a rectangular grid and it is additionally assumed that the function is not differentiable at a certain point. In this situation I can suggest to use the techniques employed in the theory of generalized functions (distributions).
For a very practical example you can consult a blog: “How to differentiate a non-differentiable function”:
In order to answer your question completely I would like to know what is the equation, boundary conditions and the numerical scheme used to obtain a set of the grid point values mentioned in the question.
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the types of board game for mathematical literacy to make the learning and teaching fun
You're welcome Rich Philp. For your information, I have a modest knowledge regarding programming, but still I made some games for PC. Here is a free one:
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Electromagnetic (EM) waves have invoked a lot of interest among scientists and engineers over centuries. And this interest seems to be on the rise, in view of new applications of EM waves being explored and developed, particularly at newer and higher frequencies.
Propagation characteristics of EM wave depend on its frequency (or wavelength), to a large extent. And when an EM wave interacts with an object/material, it undergoes reflection, refraction, scattering, attenuation, diffraction, and/or absorption. Each of these effects are dependent on the frequency of the EM wave(s) because the size of wavelength (relative to the object/material) assumes great significance.
And due to the huge range of frequencies of EM waves employed in various applications these days, they undergo a variety of different effects. This confuses the scientific community sometimes as it is often unclear as to which effect is more dominant at what frequency.
Thus a single mathematical formula (or a small set of formulae) would/could be of great help if different effects (as listed above) and their relative weights can be known at different frequencies. This may be of great boon to young scientists and engineers as it would simplify things particularly for those who are mathematically minded.
Not all these phenomena can be summarized in the permittivity of the material. For a start there is the permeability, which is as basic as the permittivity, then whole areas that these two do not cover at all, such as fluorescence, ionisation, photo-electricity, Rayleigh and Raman scattering, interaction with (other) fundamental particles, interaction with gravity/space-time, and more.
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By dynamical systems, I mean systems that can be modeled by ODEs.
For linear ODEs, we can investigate the stability by eigenvalues, and for nonlinear systems as well as linear systems we can use the Lyapunov stability theory.
I want to know is there any other method to investigate the stability of dynamical systems?
An alternative method of demonstrating stability is given by Vasile Mihai POPOV, a great scientist of Romanian origin, who settled in the USA.
The theory of hyperstability (it has been renamed the theory of stability for positive systems) belongs exclusively to him ... (1965).
See Yakubovic-Kalman-Popov theorem, Popov-Belevitch-Hautus criterion, etc.
If the Liapunov (1892) method involves "guessing the optimal construction" of the Liapunov function to obtain a domain close to the maximum stability domain, Popov's stability criterion provides the maximum stability domain for nonlinearity parameters in the system (see Hurwitz , Aizerman hypothesis, etc.).
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Given:
1. The nearest neighbor of 𝑝𝑖 then 𝑝𝑖-𝑝𝑗 is a Delaunay edge.
2. In a 3D set of points, if we know that consecutive points ie... 𝑝𝑖-𝑝i+1 are nearest neighbors.
3. The 3D points do not form a straight line
Assumption:
Each Delaunay tesselation (3D) has at least 2 nearest neighbor edges.
Is my assumption true? If not can you please explain to me the possible exceptions?
Thanks,
Pranav
Are you trying to play chess in 3D?
You need to give a clear definition of paths, so I suggest for you to start in one 3D box, it includes 8 points. I prefer to give each point the following notation
P(i, j, k), so the locations of the 8 points are at
(0,0,0) (1,0,0), (0,1,0), (0,0,1), (1,1,0), (1,0,1),(0,1,1) and (1,1,1).
Study this cube carefully, define each Delanoy edge (axioms of the path), and then add another box, which means 12 points, etc.
If you find the closed formula that allows you to calculate all possible paths from the starting point at the origin to the farthest point at the upper corner of the rectangular box, then you are on the right track.
I wish you good luck.
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I am currently studying the effect of atrophy of a muscle on the clinical outcome of joint injury. There is actually another muscle that was previously well established to have an effect on clinical outcome, and both these 2 muscles are closely related. The aim of the study was to shed some light on the previously ignored muscle to see if there is anything that can be done to help improve clinical outcomes in that aspect.
While doing univariate analysis, i wasnt sure if i should include the previously established muscle as well and when i included it into the multi-linear regression model, the initially significant primary variable became insignificant. I was thinking if this could be due to co-linearity but the VIF value was not high enough to show significant co-linearity in the two variables. (GVIF ^(1/(2*Df))=1.359987)
My question is, should these 2 variables be included in the same model if they are both highly correlated (clinically and mathematically) but was not determined to have co-linearity, or should these 2 variables be evaluated separately?
Bryan Soh, your question is a good one. I think it's necessary to be familiar with the nature of your variables (which it seems you are). Unfortunately, I'm not, but might I suggest that you conduct your analyses both ways, look at the results, then think carefully about which results are likely to be most valid.
I also think it is a good idea to present both sets of results if that's permissible. As you are obviously aware, the world of research isn't black and white, and making other researchers, and consumers of research, aware of that could well be helpful. About 20 years ago, I read an article in a top psychological journal in which the author analysed her data in more than one way (from memory, it was more than only two ways), and she discussed the ins and outs intelligently and with insight. It was, for me, much more enlightening that the run-of-the-mill articles that seem to report clean-cut results but leave the reader wondering how much cleaning up and manipulation, and obscuring, occurred to obtain those results.
Every good wish as you plough on!
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Good evening all;
We are looking for literature on the mixed integer formulation of water distribution problems using Multi objective optimization methods.
Thanks
Nasiru Abdullahi
Mathematics Department
Sure. But you are not really helping by not being precise! And I am quite certain that there is one major goal - such as a quickest route of the water. I suggest that you check with the literature - which is quite big.
A search string might look like this, or with smaller adjustments:
water network [supply, distribution*, system*] problem*
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A careful reading of THE ABSOLUTE DIFFERENTIAL CALCULUS, by Tullio Levi-Civita published by Blackie & Son Limited 50 Old bailey London 1927 together Plato's cosmology strongly suggest that gravity is actually a real world mathematics or in another words is gravitation a pure experimental mathematics?
Sorry for the delay.Good question. I think this is a matter for the future.
Greetings,
Sergey Klykov
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I know lots of composers have created works around mathematical constructs such as the Fibonacci sequence. I would like to learn if any composers have used mathematical constructs in their music to represent journeys.
Tool - An American progressive rock band :)
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Dear all,
I am trying S parameter measurement _transmission_using TEKTRONIX DSA8300 oscilloscope. Initially, S parameters files are generated in LINEAR _magnitude format. Now S parameters transmission files are appearing in dB format from oscilloscope. Perhaps machine settings seem to be changed.
1)Kindly guide for appropriate setting button in TEKTRONIX DSA8300 oscilloscope, so as to receive the data from dB to linear magnitude format.
2) Also, alternative mathematical ways to receive data in LINEAR magnitude format are appreciated as well , kindly.
best thanks
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I have values of dependent variable (y) and independent variable (x)x and y are exponentially related. I want to fit an exponential curve with a DC shift. ie,fit a curve between and in the form, y=A.exp(B.x)+ C . I have methods to fit y=A.exp(B.x). If you know the procedure to fit in the form y=A.exp(B.x)+C , please replay here
I would recommend Online Curve Fitting at: https://mycurvefit.com/
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344/5000
Hi researchers, I have a problem with the mathematical formulation of the multi objectives model for solving the RFID planning problem network. Do you have any courses or documents or information that can help me achieve my mathematical model of RFID network optimization deployed in a body network. i didn't choose the approach and the algorithme of multi optimization yet, I am formulating my problem mathematically
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Charles Sanders Peirce regarded mathematics as “the only one of the sciences which does not concern itself to inquire what the actual facts are, but studies hypotheses exclusively” (RLT, 114). Since, by contrast, “[w]e must begin with all the prejudices which we actually have when we enter upon the study of philosophy” (CP 5.265), the presuppositionless status of mathematics makes it more primitive than anything found in philosophy. Given that phenomenology falls under philosophy (CP 1.280), we get the result that mathematics is prior to phenomenology.
Yet, Peirce also held that “every deductive inference is performed, and can only be performed, by imagining an instance in which the premises are true and observing by contemplation of the image that the conclusion is true” (NEM III/2, 968).
We thus have two conflicting arguments:
On the one hand, one could argue that mathematics is prior to phenomenology because mathematics makes even less presuppositions than phenomenology.
On the other hand, one could argue that phenomenology is prior to mathematics because whatever happens during mathematical inquiry must perforce appear before (some)one.
Peirce's pronouncements notwithstanding, it is not obvious to me why the first argument should trump the second. In fact, I find considerations about the inevitability of appearing in mathematics to be decisive.
What do you think?
I am currently reading Edmund Husserls "Ding und Raum". The book is a complete lecture series about how spatiality and things are constituted. It is heavily descriptive. Husserl used for his analysis the most basic operations I can imagine (e.g. the operation of identity and the operation of distiction) . The level of primitivness seems to me the like of mathematics.
But first we have to clearify, what we want to compare? I see 2 different understandings here: (1) A discipline can be prior to another in regards to its methodological approach. Here Husserl demonstrates that phenomenology operates on an equal level of primitivness. (2) On the other hand a discipline can be seen prior in regards to the nature of its epistemical interests and outcomes. Philosophy loves to ask "why is stuff the way it is?" This kind of questioning and the corresponding anwers can be seen as fundamental.
I think Marc's second conflicting argument entails the second understanding as a hidden component. To say "... phenomenology is prior to mathematics because whatever happens during mathematical inquiry must perforce appear before (some)one." is in fact a consequence of phenomenological insights. But, we have to be careful here: The validity of this argument derives from what it wants to point out.
II think Louis Brassard is right. Mathematics reached a point of high abstraction long before any human started to reflect about whats going on in our mind and why all this stuff is even possible. Now Phenomenology reinvents the wheel again. But this time with an interest into the nature and the origin of transcendental principiles.
So yes. Mathematics is prior to philosophy. This is true only because philosophy is more than just phenomenology. But in some cases philosophy can be as "prior" as mathematics.
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how I do obtain in the mathematical expression "limiting current density used to reduce Fe+3(A/m2)"? actually how i find the i (Fe)?
i (c)= i (cu)+i (Fe)
Armin,
Did you find the equation?
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