Science topics: Mathematics
Science topic

# Mathematics - Science topic

Mathematics, Pure and Applied Math
Questions related to Mathematics
Question
Can any one suggest me any textbook or website for finding the most of the mathematical stuff related to Hyperspectral image Classification ?
Dear Professor,
This website contains research papers in
Hyperspectral image Classification
Question
Dear friends:
The graph of the equation
f(x, y) = 0
gives rise to many interesting curves in the plane for different choices of the function.
One such choice of f(x, y) led me to the following graph of the equation f(x, y) = 0.
I have the following questions:
1) Can you name this geometric shape?!
What does it remind you of?
2) Any noticeable symmetry property?!
Best wishes
Sundar
Respected Sundarapandian,
In my knowledge, I could not understand what is the shape of this curve exactly. Could send the corresponding conference paper, I will study if you are willing.
Question
For a Mathematics Postgraduate, who is interested in doing his PhD in areas related to Algebra and Analysis, what research field would you suggest. Preferably, the domain should be promising and relevant as per the current research interests of the Mathematics community in particular and the society in general, both theoretically and practically?
Rich sources of algebra in contemporary mathematics can be found in the following areas:
Homology Computation using Pyramids (HCP) leads to the study of generators of homology groups. For an introduction to homology theory, see Section 2, starting on page 4 in a 2006 Vienna University of Technology report:
A very readable introduction to computing generators of homology groups is given in Section 4.2, starting on page 7. Notice that HCP has a number of practical applications such as the computer vision and the study of digital images (sse, e.g., Section 5, starting on page 12 in the HCP paper.
Membrane Topology focuses on the study of f homological quantum field theories. For the details, see
Question
I have the following result (mathematical proof suppressed):
"In a one-dimensional real space, the number of points between any arbitrary point and its immediate neighbor is indeed infinite. "
I would like to know whether this result already exists in mathematics literature or not. If exists, then please provide me the relevant references. (The above result as it is is not Cantor's continuum hypothesis, but seems to contain it as a subset, which I haven't yet proved and work is in progress)
It is a well known fact explainable via the notion of linear scale (used already in some answer above), which - being not sufficiently precise - can be (for didactical reasons) replaced by ruler, known from elementary geometry (see e.g.
for getting my understanding of the notion).
If one assumes that between every two different points on the line there is another third point, then the infinity becomes clear (without referring to much deeper axioms of the set theory). However, there are two axioms involved about the (mathemtical) line:
- any point B in the closest neighbourhood of a point say A is not equal A
- between every two different points on the line there is another third point
It is not sufficiently strict definition of the line, only an example of possible formulation of some possible postulates. For strict definition fulfilling standard requirements accepted by the mathematical community is much more complicated; getting into the details - indeed - one needs studying math for couple of years.
Another problem is, whether the mathematical line corresponds to the line or the real world; by some atomistic philosophers - it is not the same, if the atoms need to have some size greater than some minimal, be it 10^{-123} meter. And what is the unit meter? Which (non-visible) points should be taken as the base points. Again we are coming to postulates - this time about the real world.
I think that the main problem of this thread is the definition of infinity, and separation of mathematical from physical models, and many other meta-questions like:
How can be accepted someones (non-professional) ideas if they are not written in commonly accepted terms (by the professional readers)?
How to explain briefly rules of some domain to an outsider who is falsely convinced that he/she understands the domain sufficiently well?
Question
This is a question for Mathematicians and Mathematics lovers and the others!
This video may help every body to start.. https://www.youtube.com/watch?v=QYyuZ3_PQ4M
Bourbaki was not an experiment, it was a PROGRAM. Program, on one hand, to unify mathematics and, on the other hand, to put it at the highest level of generality (or abstraction). None of these directions worked precisely as Bourbaki's members intended, as the development of mathematics in the recent 30, or so, years shows. Nevertheless, it was the most serious attempt in those directions since G. Cantor's revolution.
Definitely, "bourbakism" reflected on teaching mathematics in France. I have a book by G. Choquet on plane geometry intended as a high-school textbook. A very good idea, high level of abstraction, but only for good and very good students. On the other hand, as an undergraduate at Warsaw University in Poland, I was taught mathematical analysis based on the Dieudonne's book. Similarly, I was studying Bourbaki's book on real functions. The beauty of Boubaki's presentation is still stunning.
Speaking of logic, one should realize that the concept of mathematical logic, when Bourbaki started its activities before WWII, was is the making.
Except for Alfred Tarski, there was the largest group of other logicians in one place in the world (13 people, including two professors). BTW, it was Boleslaw Sobocinski (after WWII professor at the University of Notre Dame) who introduced the so-called "inverse Polish notation" to the world of computer science. This notation was earlier used by J. Lukasiewicz in his work on logic. Sobocinski was named the "father of computer logic" in the US. It goes away from Bourbaki, but is relevant.
These are my two cents on Bourbaki.
Question
I'm so eager to learn about micro-mechanics, however, I can't find a source that discuses it in a simple way. Most of the sources I found starts immediately with complicated mathematical equations, without introducing the subject. I would also appreciate it if you can offer me some advice about the knowledge that I need to acquire before exploring micro-mechanics.
" It serves primarily as a graduate level textbook, intended for first year graduate students ..." For you - Chapter 1: Introduction (1,684 KB):
Question
I have two independent groups and for?calculating differences in variance I want to use VR (variance ratios):
VR = variance of group A / variance of group B
So if it's?correct, how I should calculate the standard error of VR? And is there a way for interpreting VR (e.g., it is small, large, or significant)?
Question
Isn't it urgent to simlify?
The long history of mathematics generally lacks a distinction between pure and applied maths. Yet in the modern era of mathematics over, say, the last two centuries, there has been an almost exclusive focus on a philosophy of pure mathematics. In particular, emphasis has been given to the so-called foundations of mathematics — what is it that gives mathematical statements truth? Metamathematicians interested in foundations are commonly grouped into four camps.
Formalists, such as David Hilbert, view mathematics as being founded on a combination of set theory and logic (see Searching for the missing truth), and to some extent view the process of doing mathematics as an essentially meaningless shuffling of symbols according to certain prescribed rules.
Logicists see mathematics as being an extension of logic. The arch-logicists Bertrand Russell and Alfred North Whitehead famously took hundreds of pages to prove (logically) that one plus one equals two.
Intuitionists are exemplified by LEJ Brouwer, a man about whom it has been said that "he wouldn't believe that it was raining or not until he looked out of the window" (according to Donald Knuth ). This quote satirises one of the central intuitionist ideas, the rejection of the law of the excluded middle. This commonly accepted law says that a statement (such as "it is raining") is either true or false, even if we don't yet know which one it is. By contrast, intuitionists believe that unless you have either conclusively proved the statement or constructed a counter example, it has no objective truth value. (For an introduction to intuitionism read Constructive mathematics.)
??
Plato and Aristotle as depicted in Raphael's fresco The school of Athens.
Moreover, intuitionists put a strict limit on the notions of infinity they accept. They believe that mathematics is entirely a product of the human mind, which they postulate to be only capable of grasping infinity as an extension of an algorithmic one-two-three kind of process. As a result, they only admit enumerable operations into their proofs, that is, operations that can be described using the natural numbers.
Finally, Platonists, members of the oldest of the four camps, believe in an external reality or existence of numbers and the other objects of mathematics. For a platonist such as Kurt G?del, mathematics exists without the human mind, possibly without the physical universe, but there is a mysterious link between the mental world of humans and the platonic realm of mathematics.
It is disputed which of these four alternatives — if any — serves as the foundation of mathematics. It might seem like such rarefied discussions have nothing to do with the question of applicability, but it has been argued that this uncertainty over foundations has influenced the very practice of applying mathematics. In The loss of certainty, Morris Klinewrote in 1980 that "The crises and conflicts over what sound mathematics is have also discouraged the application of mathematical methodology to many areas of our culture such as philosophy, political science, ethics, and aesthetics [...] The Age of Reason is gone." Thankfully, mathematics is now beginning to be applied to these areas, but we have learned an important historical lesson: there is to the choice of applications of mathematics a sociological dimension sensitive to metamathematical problems.
Question
Sometimes , we use term of "zero time" in a formulation but are we sure it is really "0" ? maybe it is 0,000......1 and is there a "zero" time(can we stop the time?), or sometimes, we say v=0 are we sure?
On the other hand
1/0 = infinity. Well then, what's "infinity"? How does it work in all the other equations?
infinity - infinity = 0?
1 + infinity = infinity?
If we use closest number to zero-monad (basic thing that constitutes the universe-everything-)Gottfreid Leibniz, in his essayMonadology,” suggested that the fundamental unit of all things is the monad. He intended the monad to have some of the attributes of the atom, but with important differences. The monads Leibniz proposed are indivisible, indissoluble, and have no extension or shape, yet from them all things were made. He called them “the true atoms of nature.” At the same time, each monad mirrored the universe. If we use monad instead of zero, every equations work
I think Science says "Every Thing had originated from a basic thing"
Yes, Mesut, I can be mistaken in claiming that there are zero elephants in the room; I might be hallucinating when I look or somesuch. But likewise I can make mistakes about numerals or the numbers I take the numerals (inkmarks or whatever) to represent. That doesn't affect the conceptual point. If I claim, mistakenly or not, that there are zero elephants in the room I am simply claiming, mistakenly or not, that elephants are absent, not that there is a special kind of elephant, namely an absent elephant, present in the room. Likewise, zero as a notational device doesn't have to be regarded as standing for a special kind of number.
Question
Dear i want to write a thesis of phd maths in the area of fluid mechanics for that we have to write a synopsis . I am requesting to know a problem in which can i research.
You will find it hard to be successful if you do not have a thesis advisor with experience in the area. If you do, you need to talk to him or her and trust their intuition and experience in what is a good problem in the thin area between the trivial and the impossible and that fits your background and skills.
Question
For example, a few decades ago it was unimaginable perform statistical works without having a broad domain of mathematics, but now everybody uses it only following the instructions of a SPSS program.
Dear Jesus Retto,
I have been specializing in AI for years now.
YOU CANNOT DO AI WITHOUT MATHEMATICS. WE ARE EVEN JUST LOOKING FOR THE MATHEMATIC MODEL AND WE WORK IN THE MATHEMATIC LANGUAGE.
EXCEPT IF YOU JUST WANT TO KNOW WHAT IT IS.
Question
"It is widely accepted that there are no inherent gender differences in mathematical ability or intelligence" Sunday Times Jan 21 2018 p5.
"Differences in intelligence have long been a topic of debate among researchers and scholars. With the advent of the concept of g or general intelligence, many researchers have argued for no significant sex differences in g factor or general intelligence while others have argued for greater intelligence for males. The split view between these researchers depended on the methodology and tests they used for their claims.... Some studies have concluded that there is larger variability in male scores compared to female scores, which results in more males than females in the top and bottom of the IQ distribution. Additionally, there are differences in the capacity of males and females in performing certain tasks, such as rotation of objects in space, often categorized as spatial ability." Sex differences in intelligence Wikipedia Jan 21 2018
What the ST article probably meant is that it is widely accepted that this topic cannot be rationally discussed in the popular media.
This is a highly contentious issue, but surely society would greatly benefit from knowing the answer. For individual researchers, however, their careers and reputations could be trashed by studying this topic. I heard a very highly cited professor of psychology say that his wife had begged him not to give the lecture that turned out to be a straightforward literature review of cognitive sex differences.
I am posing the question here as RG is one of the very few places that topics like this can be sensibly discussed.
There is a huge amount of scientific studies that abusing (or misinterpreting) their results, it’s not impossible. These probabilities shouldn't stop scientific researches. Sex differences in neuropsychological abilities is a very important field of study in psychology that can support other psychological researches (e.g., in sampling) or can help us especially in education and our requests from each gender. An interesting point is that when it seems that males are better in some abilities, females sound better in some other.
Regard,
Question
In general, everyone is familiar about the intense implications of conservation of energy which is considered as base for all the fundamentals and any concepts can be understood with the context of conservation of energy. Do we have any mathematical arguments in thinking about the creation of energy or it is still hypothetical. Energy and matter are the two attributes of the universe which comes into action when they interact, but before that there should be something available to transform. The question of existence or possibility of energy which can used for conservation. Why the energy should be conserved.
We are destroying the plant
Question
I have time series data from multi channel EEG. I am looking at various symbol based complexity measures. As a preliminary step I have to convert my time series to symbols based on some logic (as simple as order dynamics or zero crossing)
I am looking for better methods/algorithms to generate symbols from EEG time series.
Hello,
have you looked at SAX ( Symbolic Aggregate approXimation, invented by Eamonn Keogh and Jessica Lin)?
You may find the info and all references at http://www.cs.ucr.edu/~eamonn/SAX.htm
Question
I obtained a Power length relationship formula
V=5.5* (0.62*L + 3*P/100)^(1/2) .
L = distance in km
P= Power in kW
V= Voltage in kV
When I applied it to my case study it proves inaccurate.
Please does anyone know of any other formula with similar relationships.
A caution, earlier empirical formulae were voltage regulation based / loss based / temperature rise based/criteria applicable for radial lines, single m/c infinite source or long lines with ideal voltage sources. In integrated network with FACTS controllers, voltage and line length relationships have lost significance. For HVDC for example length is no limit and voltage options are based on choice of device and over all economy.
For cables, yes reactive power continues to dictate length and reactive compensation, and mechanical handling etc.
Question
The major concern is how sensitive the AR model to data non homogeneity.
Kindly, I need some references.
Autoregressive (AR) modelling is based on assumption of stationarity which implies homoscedasticity and constant mean. Heteroscedasticity makes AR modelling unreliable for forecasting. To study the sensitivity of AR modelling to heteroscedasticity can best be done by simulation.
Question
Universe is timeless. Time has exclusively the mathematical existence. How that this belief of some linear time is burdening physics more than 100 years?
Question
mathematics
log
exponent
infinity
Hi,
the value of log(0) depends on the base of the logarithm!!! log(0)=?∞ if base>1 (the usual cases of base= e, 10 or 2.). But if base<1, log(0)=+∞ and if base = 1, log(0) is not defined.
Regards,
Fabrizio
Question
I want to interpolate the amount of product formed (as concentration or % of conversion) vs reaction time in a biocatalysis process. The fitting equation should have as (y) the amount of product and as (x) the reaction time. I thought to use as the fitting equation the integrated form of the M&M but I am not able to find the correct mathematical form. Or should I use another equation?
Without any knowledge about the experiment parameters i can only guess which equation might suit your problem.
Having the product [P] as (y) results in some pretty ugly equations most of the time. I'm assuming no inhibitory effects.
[P] = [S]° - Km * W { X }
or alternatively (for the amount of conversion)
[P]/[S]° = 1 - Km/[S]° * W { X }
where [P] is the concentration of product P and [S]° is the initial concentration of the substrate S.
W is the Lambert-W function (or prodlog). You can try
X = [S]°/Km * exp[ ([S]°-vmax*t) / Km ]
as an argument for that function. I hope your program can fit this prodlog-function.
Question
In Taguchi’s optimization, for calculating S/N ratio (Smaller-the-better), we use the formula.
S/N = -10Log10[mean of sum of squares of measured data]
In this formula, why the term ‘-10 Log10’, whether it has any mathematical derivation/clarification for this method? Also what is the meaning/significance of DOF in Taguchi's design.
Thank you Fausto Galetto sir
Question
Do you find your students trying to stay away from complex mathematical solutions? what is the reason?
Dear
So thanks
Insightful words
regards
Question
I think asking and formulating questions have a big impact on our lives, so I was wondering what techniques do you use to formulate your questions, and how much time you set for formulating the Question ?
It is a very interesting question for me. I am taking part in RG question answer section actively from November, 2017. Still today I asked perhaps 75 questions. Some of them are coming in my mind as such. I got idea of some questions during giving answer of question of other RG members.
I am writing popular scientific articles from 2002. It may have some effect, I do not know.
Question
Hi,
I am struggeing with a numeric implementation of the free field 2D Green function of the wave equation in space and time domain, which, according to all references I could find, is proportional to
( t2-(r/c)2 )-1/2
and thus, has a singularity at r/c=t. If I want to implement this function as numeric array that can be convolved numerically with a source distribution to get a wave field, I do not know how to deal with this singularity.
An option would be polynominal extrapolation, but I would prefer a mathematically correct attempt.
I thought I might have to analytically convolve the Green function it with a sinc function first, to attain a function that can be accutely sampled according to the Nyquist criterion, but this still did not resolve the singularity.
In consequence, I am also wondering if the 2D Green function is even integrable. I believe it should be in terms of energy conservation, but I ended up with an infinite integral.
Hans-Martin, can you add some details about your application, please? For example: geometry, materials, boundary and initial conditions are necessary to define mathematics and physics of your problem.
Question
The fundamental defects in present classical infinite related science system have decided the barber paradox (one of the members of Russell’s Paradox Family) is really an unavoidable and unsolvable problem for present classical set theory.
In present classical infinite related science system, it has been admited that the concept of infinite is composed by both “potential infinite” and “actual infinite”. On the one hand, no one is able to deny the qualitative differences and the important roles “potential infinite--actual infinite” play in the foundation of present classical infinite theory system; on the other hand, no one is able to deny that the present classical set theory is basing on “potential infinite--actual infinite” concepts as well as its related whole present classical infinite theory system. The fact is: any areas in present classical infinite related science system (of couse including present classical mathematical analysis and set theory) can not run away from the constraining of “potential infinite--actual infinite” concepts-------all the contents in present classical mathematical analysis and set theory can only be existing in the forms of “potential infinite mathematical things” and “actual infinite mathematical things”. But, the studies of our infinite related science history have proved that no clear definitions for these two concepts of “potential infinite--actual infinite” and their relating “potential infinite mathematical things--actual infinite mathematical things” have ever been given since antiquity, thus naturally lead to following two unavoidable fatal defects in present classical set theory:
（1）It is impossible to understand theoretically what the important basic concepts of “potential infinite” and “actual infinite” and their relating “potential infinite number forms, potential infinite sets” and “actual infinite number forms, actual infinite sets” are and what kinds of relationship among them are. So, in many “qualitative cognizing activities on infinite relating mathematical things (such as all kinds of infinite sets, elements in infinite sets, numbers of elements in infinite sets)” in present classical set theory, many people even don’t know or actually deny the being of “potential infinite” and “actual infinite” concepts as well as their relating “potential infinite number form, potential infinite sets” and “actual infinite number forms, actual infinite sets”--------it is impossible at all to understand clearly and scientifically the exact relationship among the important basic concepts of “infinite, infinities, infinite many, infinitesimals, infinite sets, elements in infinite sets, numbers of elements in infinite sets”, ... So, it is impossible at all to understand clearly and scientifically all kinds of different infinite sets (such as lacking of the “’set spectrum’ for the overall qualitative cognictions on the existing forms of infinie sets”), elements in an infinite set (such as ”are the infinie related elements potential infinite mathematical things or actual infinite mathematical things, how they exist?”), numbers of elements in an infinite set (such as ”are they actual infinite many or potential infinite many?”), the “one-to-one coresponding theory and operation” in infinie sets (such as ”are the potential infinite elements coresponding to potential infinite elements or actual infinite elements coresponding to actual infinite elements or actual infinite elements coresponding to potential infinite elements?”) ,... --------the unavoidable defects of qualitative cognition on infinite sets and their elements.
（2）First, it is impossible to understand whether the “elements in an infinite set, numbers of elements in an infinite set and all kinds of infinite sets” being cognized in present classical set theory are “potential infinite mathematical things” or “actual infinite mathematical things”, whether there are different theories and operations for “potential infinite mathematical things or actual infinite mathematical things”, and it is impossible at all to understand correctly (scientifically) in present classical set theory the natures of infinite related quantitative cognizing theories and tools (such as limit theory and the “one-to-one coresponding theory”) and their operational scientificities-------- it is impossible at all to master correctly (scientifically) the operational competences and skills of limit theory and the “one-to-one coresponding theory” thus resulting in no scientific gurantee for the operations of limit theory and the “one-to-one coresponding theory”; second, it is impossible at all to judge the scientificities of many infinite related quantitative cognizing activities in present classical set theory, people in many cases can only parrot every bit of what have been done by others or do as one wishes to treat many “not—knowing—what” infinite mathematical things with the unified way of “flow line” (any “infinite sets”, “elements of an infinite set”, “elements’ number of an infinite set” can either be “potential infinite” or “actual infinite”, neither be “potential infinite” nor “actual infinite”, first “potential infinite” then “actual infinite”, first “actual infinite” then “potential infinite”, ,,,), those believed and accepted Russell’s Paradox, Hilbert Hotel Paradox, Cantor’s operations of “cutting an infinite thing into pieces to make different super infinite numbers” and “proving the uncountability of real number set by diagonal method” as well as the famous “applying Russell’s Paradox to prove the Power Set Theorem” are tipical examples of “potential infinite--actual infinite” confusing operations--------the unavoidable defects of quantitative cognition on infinite sets and their elements.
We understand from our science and mathematics history, the fundamental defect in present classical set theory disclosed by the members of Russell’s Paradox Family is: looking for something belongs to an infinite set but is impossible to be found inside this infinite set--------no logic in our science can solve such paradox family as all the members of Russell’s Paradox Family are produced by the confusion of “potential infinite” and “actual infinite”.
The power set theorem is no paradox. Its demonstration is also valid on finite sets.
Besides, the distinction between countable and uncountable sets is essential to measure theory which is part of analysis.
Question
Knowledge representation may be constructed as an attempt to formally capture and describe human sensory and perceptual data. But is knowledge representation via ontologies etc., anything more than the application of logic and mathematics?
This is an excellent question. In addition to the excellent answers already given by @Dejenie A. Lakew and @Peter Samuels, there is a bit more to add.
By way of starting an answer to this question, consider the following threads (that includes this thread):
Logic and a wee bit of mathematics (set theory) dominate knowledge representation in
Mathematics has more importance in knowledge representation in
More to the point, it is apparent that knowledge representation is not merely an application of logic and mathematics. Instead, logic and mathematics provide a concise language as a means of expressing knowledge, which is something quite different from logic and mathematics.
Question
We may share instrument and compare data with ours.
This is a worthwhile question with many possible answers. In addition to @Amir W. Al-Khafaji's very interesting answer, there is a bit more to add.
In North America, science, mathematics and technology are mixed together. When that mix becomes dominated by technology, there is a tendency for students to become too dependent on what the technology tells them.
In Europe, the situation varies from country to country. In Italy, for example, classical education in science and mathematics is more important than technology. In that case, the potential for the birth of great scientists and mathematicians is greater than it is in North America.
The prevalence of classical education is also very high in universities in the Middle East. The situation is very mixed as we move towards Asia. For example, students in Mathematics in Pakistan receive very high level training. Perhaps the followers of this thread can comment on the situation in Taiwan, China and India or in Korea and Japan.
Question
The identity e^(iπ)+1 = 0 is a well known equation that can be proven mathematically. It is an identify that contains the most beautiful entities encountered in math, namely π, i, e, 0 and 1. It combines the real and the imaginary. Can anyone explain it rationally, creatively and not just mathematically?
I am still waiting for a creative answer to my original question (Willing to accept mathematical, graphical, complex variabls, etc). I am willing to waite a few years! As to the play on words, it is not my interest to engage in a debate that loses focus of the issue at hand. By the way, what the sumerian did was truly ingenious and simple without the benefit of calculus but achieved the exact same result obtained using Newton’s method which requires calculus! The paper you attached didn’t cover it. Thank you for the paper you attached.
Question
Why do Emmy Noether's theorems (1918, about the link of conservation and symmetry in physics) refer to the physical quantity of action? Where in their proofs is that condition necessary to be used? Can similar theorems be formulated to other physical quantities or without any relation to any physical quantities, i.e. abstractly and mathematically? Is the physical quantity of action unique in a sense: whether physical or mathematical, or ontological?
No, this is not entanglement. This is called superposition. It is in the heart of quantum mechanics as it allows interference effects. it states that if the wave function psi_1 is possible and the wave function psi_2 is possible then the wave function a*psi_1 + b* psi_2 is also possible. a and b here are any complex numbers. Even if funstions 1 and 2 are eigenfunctions of an operator, the sum is not (except for the case of equal eigenvalues).
Operators in quantum mechanics correspond to observables. At a measurement the wavefunction collapses to an eigenfunction of the operator. This is the most murky point in quantum mechanics and raises a flood of discussions. Up to the measurement the evolution is smooth as silk. So, the mentioned state is measurable. The wave function would collapse. But prior to the measurement it is free to interfere.
Noether's theorem was formulated before the quantum mechanics of course.
Question
Dear Scholar
Here is the paper
thank you
Question
Which topics/subjects do you think that everyone involved in science should know or master, and without it his progress will be flawed?
phantasy
Question
Where this semiopen, preopen, b-open sets in topological spaces are applied in other fields other than Mathematics?
Thank you Ahmed Ammar.
Question
Hi,
I'd like to learn more about artificial neural networks, specifically pattern recognition algorithms. Unfortunately, I don't have much of a background in mathematics, so I'm looking for something that won't overburden me with too many technical details. Could someone recommend a fairly-light-yet-scientifically-rigorous read on the topic?
Thanks!
Hi Dawid,
From my understanding of the subject, if you want to know what is happening behind the scenes and why you do certain things in artificial neural networks (presently, in a deep learning setting rather than a general machine learning setting) you should be comfortable with mathematics. But you do not have to be an expert at mathematics to get to know neural networks. Moderate familiarity with?calculus, probability and linear algebra will?suffice for one to understand the concepts well.?
Having said that, currently,?a part of the deep learning community is trying hard to make it available for the ''non-mathematics'' community.?Practical Deep Learning For Coders (http://course.fast.ai/lessons/lessons.html) is a good resource to get started if you want to dive in directly and learn as you go on. From the first day onwards, you are instructed to build deep learning algorithms that are par with the state of the Art. The video lectures that you find there give you the reasoning behind why you do certain things in neural networks without digging down into hard core mathematics.
Question
I would like to know how one can mathematical prove that chimney effect does take place when having a ventilated foundation with high pipes on the warmer side of the building and low pipe on the colder side of the build. Also, how can one i give the optimisation that give maximum flow rate
It is really just a solution of the Bernouli equation -- not hard can do it with a simple Fortran program
Question
Dear Colleagues,
Could you please look at my paper with the above title, and tell me what you think? Positive and Negative opinions are welcome. The paper appeared eventually in ALAMT and experienced, in my opinion, Extreme Prejudice in some other journals, where I sent the paper to before sending it eventually to ALAMT.
This leads me to ask a related question: As it is important to expose predatory Journals, do not you think it is equally important to expose "malicious referees" and those who approve their malignant acts?
Here is by the way the complete copy of the so-called reviewer report in one of the journals; only the name of the journal was taken off. This journal is supposed to be a good journal, but in this case the paper was refereed by a totally incompetent and malicious referee with shallow arrogance. In addition, all the garbage written by that referee was approved! Here is the copy: (KEEP close attention to the 2nd paragraph):
----------------------------------------------------------------------------------
"This paper analyzes the relations between several classes of matrices with variants of the diagonal dominance property, and identifies those classes which form pairs of incomparable classes.
In my opinion, the paper lacks of sufficient motivations to show the importance of the considered problem. There are many sophisticated results but I don’t think that they deserve publication in ..."
------------------------------------------------------------------------------------------------------------------------
Sincerely,
Farid O. Farid
Dear Farid,
Sometimes things didn't work the way we want.
In this concern, one day I submitted a paper that includes a note on a generalization of Cayley- Hamilton theorem.
The referee report includes a trivial proof of the Cayley - Hamilton as follows: the characteristic polynomial P(x)= det(xI - A) ,
then P(A)= det(A - A)=0.
Based on his brilliant proof the paper was rejected.
I am sure that he didn't hear about Cayley - Hamilton theorem.
It was a real joke that makes me laugh when I remembered that report.
best wishes
Question
For getting help in the issue, you at least need to specify the type of variables (i.e. continuous, discrete) you are using and the sample size, also explain what is wrong with your results.
Question
Dear Scholar Geometry is the study of the Earth. Earth is a planet and is a member of the Solar family. Sun is a Star. So the planets and stars are 13 to 14 billion years old. Mathematics is invented by man. Man came just 100 thousand years ago. It means Geometry is far far older than Mathematics which came very recently Therefore Geometry should be first and mathematics next Further , every concept in it has a support of a construction like other subjects of Natural Science such as Geology, Zoology, Botany, Physics, Chemistry
Yes, I would agree. In fact, it makes me feel better about it!
Question
Why or why not?
Some philosophers maintain that science is morally neutral, while other philosophers maintain that science produces morality.
Yes. Most moral questions are oversimplified strategic questions. Doing X is amoral because doing X has side effects and long term effects which, if taking into account, would make doing X stupid from point of view of your own interests. For people unable to think all the time about such side effects and long term consequences it makes sense to simplify the question by a moral which names the type of behavior which has such harmful consequences amoral. But this does not change the point that what defines this moral are pragmatic, strategic questions: What is the best way to behave given my own interests? And for answering this question, science is certainly helpful. Because it helps to find out what are these consequences.
Question
Mathematically, how does the electron mean free path or electron-lattice mean free path depend on temperature?
Is there any formula linking the two?
In gas phase the general expression of the mean free path of an electron with fixed velocity is v/f where v is the velocity of the particle and f is the collision frequency
f=Nc*|v-vc|*s, where Nc is the density of target particles vc their velocity and s the cross section. If you have a mixture, you should consider a mean cross section weighted on the gas composition.
In the case of electron collisions,
the only dependence on the gas temperature, considering a system at constant density, is contained in vc. Therefore the mean value of |v-vc| (consider velocities as vectors) over the maxwell distribution, will give you the dependence on the gas temperature.
However vc is much smaller than v, therefore |v-vc| ~ v giving for the mean free path 1/Nc*s.
However the cross section can depend on the electron velocity, therefore a successive mean over the electron distribution should be calculated, giving the dependence on the electron temperature, that depend on the gas species.
In solid phase there are different contributions. One due to the atoms in the lattice, which depend again on the density. This contribution in independent on the temperature if you do not consider thermal expansion. The second contribution is due to collisions with phonon which number is a function of the temperature.
Question
Is there any equation or mathematical expression to generate the radiation pattern polar plot of standard Horn antenna (say 25 dB, 20 dB)?
Thanks Puran for showing the way :P
Question
Mathematics is fundamental in all sciences and mainly in Physics, which has even had many contributions. It seems that the capacity to be applied would be the motor to be create. But this not what good mathematicians as Henry Poincarè or Hardy has said. What is the beauty in mathematics, in theoretical physics or in others which could be related subjects?
For me there are very beautiful mathematical results which sounds difficut to be applied or even against our reality, which are full of "beauty" or at least "surprise".
1.Sum of natural numbers = a negative number as - 1/12.
2. Polynomials with degree five or higher are without?analytical expression of their roots.
3. Banach-Tarsky theorem
4. There cannot exit more than five regular polyhedra in three dimensions.
The beauty of theoretical physics is that Maths is it’s language. The beauty of mathematics is in its remarkable success of describing the natural world.
it is therefore not surprising that most research mathematicians and theoretical physicists pepper their description of important research work with terms like “unexpected,” “elegance,” “simplicity” and “beauty.”
Let me make it easy for you:
Can you imagine a bride without a wedding dress?
Question
I hope i can find explanatory answers for my 2 questions
1) When i plot data results obtained from UV-Vis experiments, I get confused which function i should to fit data points to the best fitted line and what does the fit infers. BTW, I always find that gaussian, boltzmann and asymptotic1 functions gives me the best fit.
2) Regarding Boltzmann function y = A2 + (A1-A2)/(1 + exp((x-x0)/dx)), does values for A1, A2, X0 and dx gives important meaning ? My plot represents fluorescence maximum as function of excitation wavelength.
According to the Beer-Lambert Law, absorbance is proportional to concentration, and so you would expect a straight line.
Considering that you are using a UV-Vis then following the Beer-Lambert Law, absorbance is proportional to concentration, and so you would expect a straight line and therefore a linear fit might be the best option. However, bear in mind that at higher concentrations this is not always the case and the law breaks down.
Question
All types, especially scalene
See ACM Algorithm 736 in (1994)
Question
it is pure mathematics.
<geometers don't like groups>:
In his influential 'Erlanger Programm' Felix Klein characterized geometries as the theorie of associated group invariants.
<algebrists don't like fields>:
Galois solved the most urgent algebra problem of his time (general solvability of polynomial equations of order n) by studying properties of fields.
So my rudimentary ideas concerning the history of mathemathics suggest just the contrary of what Claude cames up with.
Question
De Bruijn sequences are maximally disordered. Yet, they are computable. This implies that de Bruijn sequences retain yet a hint of order. Ordered objects like crystals have a regular structure that imposes order on placement of atoms (for instance), and yet there remains separation between those elements, and so a bit of disorder remains (we understand the physical implications). So, why is it that we find no object that is purely disordered, or purely ordered? Can a reader give a counter-example, physical or mathematical?
Peter, the proper computational answer is to search, as belief systems do have their faults. De Bruijn sequences are maximally disordered, and yet, that disorder is the yield of a rather strict ordering process. Somehow, it seems this is a fundamental point, and the target of the originally posted question is to understand this expected fundamental point.
Fabrice, I suspect that all patterns that are other than a de Bruijn sequence per se, are instead decrepit de Bruijn sequences that have been corrupted to various degrees. Truly random sequences will never be as disordered as a de Bruijn sequence. You can check this with a shustring analysis on the sequence.
Question
Could you suggest me some books that explain distributed intelligence using mathematical equations with numerical examples
I realy appreciate your prompt replies. Thank you very much.
Question
Prof. Hawking worries about we are intermediate species and soon new creatures will appear, e.g. ai-robots. Maybe the situation is more fantastic. it will be men with new abilities, maybe even without darpa`s implants, etc. I think that mathematics and physics are the most achievements of today humans. So logically to think that neurons responsible for that human abilities are initial or building blocks of new living creatures.
Did anybody investigate neurons which are responsible for our mathematical abilities?
Apart from symbolic mathematics there is an intuitive number sense. It does only work good with small numbers. My impression is that integrators are involved. Even a single neuron works like an integrator.
Note that this kind of number sense is distinct from being able to execute algorithms like in human mathematics.
The Piraha and Mundurucu should be mentioned as well.
Regards,
Joachim
Question
I’m going to convert some interval data to ordinal data (e.g., bad, average, good, excellent, etc.) and run a Pearson's chi-square test between two groups. Is there anyone could recommend me some similar previous studies (or a tutorial)?
I would be very thankful for any recommendation or guidance.
Dear Majid,
Pearson's correlation is the wrong test with ordinal data: try using Spearman's correlation instead. It works better when you have more ordinal categories.
Question
Hi all,
I'm comparing the similarity between some samples and I'm not sure what's the best method to do it: correlation or distance.
A friend of mine has told me that distance has "more mathematic" in the background, but after some tests I don't see differences with correlation, any suggestion? Thanks in advance!
Variance is a measure of dispersion. It measures the average distance of a variable from its mean. Covariance involves two variables. It means the average distance between two variables. Correlation is normalized covariance. The closer two variables are the more their correlation. For example the correlation between a variable with itself is maximum at +1.
But correlation is not exactly about the closeness but the association of two variables. Association is about proportional agreement of the variables on a point by point basis. You are therefore not completely right to think of correlation as a distance because close variables may not be associated closely.
Question
I want to analyze Lazy associative classifier (LAC) mathematically
So far I have been able to figure it out is that association rules are generated as the way it is. But the rules ranking are done based on the information Gain. Classification Rules generation is based on CMAR.
Question
It has been said that the infotainment industry shapes its production according the rule of the lowest common denominator with an aim to attract as large audience as possible. In this way, this industry secures a large audience for its advertisements. However, the concept lowest common denominator does not say what it intends to say. A common denominator is enough. What the media offer do not aim to be the lowest, but to be the most common. This is enough to make it "low", so that there is no need to call it "lowest".
Let me illustrate this by an example. Television seldom broadcast Beethoven, because this is not something that common audience loves. On the other hand, television broadcasts sports events, because common people love sports events. Therefore, between Beethoven and sport, television will opt for sport. However, if a television has the possibility to broadcast the football match between two famous clubs or a match between two third-league clubs, the television will broadcast the former event rather than the latter one. Therefore, the media do not seek what is the lowest, but only what is the most common. The problem is that the most common is usually not a sophisticated debate or a high art.
As much as I remember, there is something in mathematics called the highest common denominator (not the lowest). It may be that linguists borrowed this concept from mathematics, but they distorted it in the process of borrowing.
Dear Mario,
what you mention is a greatest common divisor https://en.wikipedia.org/wiki/Greatest_common_divisor
Regards, Viera
Question
I have made a slight adaptation to Shannon's Entropy to measure correlations between two (or more, much more) variables. It works fine, it is intuitive, I have bounded it but I need to mathematically prove that those bounds are the right one.
I like conjectures but I would prefer proof! If someone is interested to help me, I would be graceful. I already have written a paper to explain the measure.
Hi, hereafter a paper on multidimensional shannon entropy. Best
Question
What is the mathematical relationship between surface thickness and impedance? when the surface thickness changes, resistance are changes . what is the mathematical relation?
For the dielectric constant of the graphene there is an answer of V. A. Shaidiuk in this link: http://www.fondpageant.com/post/what_is_dielectric_constant_or_permittivity_of_graphene
And this work: dx.doi.org/10.1021/nl303611v | Nano Lett. 2013, 13, 898?902
Question
Pls can any one help me, I have my first and second degree in mathematics, I found area of Big Data Analytics interested to me due to mathematics involved in it.
*is it possible to pursue my PhD in that are ?
*what advice and suggestion can you give to me ?
*what are the resent?areas of research in Big Data Analytics that involved mathematical aspect??
?
Big Data Analytics in Healthcare and Medicine
Please let me know if these references and sites are helpful to you:
1. Big Data | Big Data in Biomedicine Conference | Stanford ...Web ·?
https://bigdata.stanford.edu
Stanford Medicine Big Data in Biomedicine Conference Site Nav. ... and identify actionable steps for using large-scale data analysis and technology to improve human ...[PDF]
2. Leveraging big data and analytics in healthcare and life ... Web ·?
https://www.intel.com/.../healthcare-leveraging-big-data-paper.pdf
Leveraging Big Data and Analytics in Healthcare and Life Sciences: Enabling Personalized Medicine for High-Quality Care, Better Outcomes This report is based on the ...
http://www.fondpageant.com/publication/279198958_Big_Data... Official Full-Text Paper (PDF): Big Data Analytics in Healthcare ... Grappling with the Future Use of Big Data for Translational Medicine and Clinical CareBig Data Guide from HBR - Free White Paper DownloadAd · www.sas.com/Big-Data/White-Paper 4. Leadership & Big Data Innovation": A Harvard Business Review Learning Summary.White Paper Leadership and Big Data Innovation A Harvard Business Review Key ...Hadoop Data Mgmt. Tools?· Leader in Data Management?· Big Data & IoT Solutions Data Management Papers · Data Management Solutions
Dennis
Dennis Mazur
Question
I would like to know the mathematical equation that can precisely relate the input solar radiation and the output power of a PV panel that is used in single and dual axes tracking systems
Solar Engineering of Thermal Processes by John A. Duffie & William A. Beckman. this book is very helpful for you, you will find the equations you requested.
Question
It is related to combinatorial mathematics
Hi, hereafter a quick introduction to Steiner triple system
Question
Where to begin, if I want to learn about Philosophy of Mathematics, assuming no knowledge of Philosophy and a minimal knowledge of mathematics.
Any resource particularly books and YouTube lecture series.
Regards and Thank you
First, get yourself familiar with basic concepts in (pure/applied) mathematics and philosophy (in particular ontology and theory of knowledge). Philosophical studies and understanding cannot be based on ignorance; not all weird and exciting ideas one gets qualify as philosophy.
When thinking about concepts like infinities, one should first know what kind of role they play in mathematics, including topics that go well beyond the first year Calculus course. Things like the distinction between analytic and synthetic knowledge are important in understanding the motivation of creating theories about foundations of mathematics in the first place.
After that, you can start reading formal theories like logic. I would start from theory of language (mathematics can be understood asa kind of language, and this is the point of view taken by the most philosophers), for example, Frege and perhaps Mill. Then get familiar with Hilbert, Wittgenstein, Carnap, Russel, Kripke, etc. If you don't know the early works, it's impossible to understand what the later scholars are aiming at. Things like axiomatic set theory are certainly interesting from a methodological point of view, but they don't lead into general understanding about the nature of the topic.
Most importantly, you should first understand what mathematics is all about, and why there is a need for philosophy of mathematics. As I see it, the "what" question is usually relatively simple, but the "why" is the deep one. There is no single book or reference that will teach you that; becoming a deep thinker is a life-long project.
Question
I would appreciate your help if you could suggest / provide any (survey) papers on convolutional neural networks, including mathematics when applicable.
I suggest you use "nftool" in MATLAB to learn easily about the steps of the Neural networks.
moreover, in one of my paper I compare all types of NN functions for an engineering application.
Question
pe (fa) : ??? ??? ??? ????? ? ????? ???? ?
??? ?? ????? ??? (????) ??? ????? ?? ???? ??? ??? ???? ?????(100%) ??? ????? ?????? ???? ????? ????? (100% ? ????) ??? ????? ? ???? ??????? ? ????? ??? ?
en:
Is it possible to generalize the uncertainty principle in logic if we assume that (100%) of uncertainty is certain (100%) is uncertainty, distinct, and unobtrusive?
The uncertainty principle is the mathematical statement that the product of the variances of canonically conjugate variables is bounded from below. And it's a consequence of the properties of quantum mechanics. All these words have a very precise meaning.
Question
"Molecular Dynamics (MD) simulation methods that are widely used for proteins, DNA and polymers are based on Cartesian coordinates owing to the mathematical simplicity of the equations of motion. However, constraints are often needed with Cartesian MD simulations to enhance the conformational sampling. This makes the equations of motion in the Cartesian coordinates differential-algebraic that adversely impacts the complexity and the robustness of the simulations."
What does conformational sampling mean?
"Conformational" is derived from the verb "to conform," which means "to form, shape, or fashion according to some pattern, model, or instruction." Just like a man can be found, at different times, to be comfortably standing, sitting, or lying, so can a protein exist, at different times, in different arrangements. Imagine a man, who is neither sitting nor lying, but something in-between---would the man feel more or less comfortable than if the man were sitting or lying? Does a man spend more time sitting and lying or in a position between sitting and lying? Such an "intermediate" man might need an assistance (restraint) to remain in that intermediate conformation for an extended period of time.
"Sampling" is a process of collecting, at regular intervals, samples, i.e., individual structures of a protein, or positions of a man (sitting, sitting, sitting, standing, sitting, lying, lying, lying, . . .). You see, the man is found sitting or lying, but rarely (depending on the interval of sampling), inbetween sitting and lying, but one can apply a restraint to keep the man in otherwise uncomfortable conformation and observe the man's behavior.
Question
Dear all,
I need to detect the values represented by the red rectangle, in the attached picture, automatically.
This means I need to detect the part where the curve change significantly
Thank you
Let me add that after applying any program finding just peaks probably some elimination procedure would be desired. Indeed, the example in the red box supplied by Hadjer shows that any automatic program returning all local maxima and minima will display too many points - in the same manner those which significant as the non-significant. Of course, the expected correct answer should eliminate some of them. This depends on the assumed DEFINITION of a significant point of changes. Perhaps it would be enough to implement in the code a suitable criterion like the following:
For a given fixed half-width t>0 do the following:
1. for every point of maximum (x,y) apply:
If [yn <= y whenever x-t <= xn <= x+t], then decide: [ (x,y) is a significant point of local maximum]
2. for every point of minimum (x,y) apply:
If [yn >= y whenever x-t <= xn <= x+t], then decide: [ (x,y) is a significant point of local minimum]
3. Eliminate a point if it is not unique among other points of the same type within distance not exceeding t.
The third step is just to choose one of points in cases when e.g. at two neiboring maximal points say x1 and x2 the values y1 and y2 are almost equal:) Perhaps some average of the similar x-s and y-s would be better? Or, before running the program finding max and min points, to perform some standard smoothing procedure?
Regards, Joachim
Question
I want to publish mathematical papers. Do we have reliable journal that published articles of history of mathematics with free of cost recently with easy way to submit? And how they excess the published journal?
Dear Eka Ratna Acharya ,
You can publish your work in the following jounals 1. ISSN: 0315-0860, Historia Mathematica
2. Mathematical Intelligencer
Question
To make a research significant to its followers mathematical analysis is required. What are those at the minimum label?
Dear Md Zafar Alam Bhuiyan
The mathematical calculations necessary to highlight the quality of the published research, depends on the type of variables, and how they are measured and made operational.
That is, to use qualitative statistics in nominal, categorical or order variables; and quantitative statistics when dealing with continuous or accounting variables.
In both cases, it is convenient to represent the data in measures of central tendency and dispersion and analyze them both in the experimental group and in a comparative way with a control group.
Of course, the elementary information to be studied is found in several biostatistics textbooks applied to the science or discipline where the root research line is carried out; and in several languages, according to their native language, or in the language where they were trained as professionals and scientists.
regards
Jose Luis
Los cálculos matemáticos necesarios para resaltar la calidad de la investigación publicada, depende del tipo de variables, y la forma como se miden y se hacen operativas.
Esto es, utilizar estadística cualitativa en variables nominales, categóricas o de orden; y estadística cuantitativa cuando se trata de variables continuas o contables.
En ambos casos, conviene representar los datos en medidas de tendencia central y de dispersión y analizarlas tanto en el grupo experimental como en forma comparativa con un grupo testigo,
Por supuesto que la información elemental a estudiar, se encuentra en varios libros de texto de bioestadística aplicada a la ciencia o disciplina en donde se realiza la línea de investigación raíz; y en varios idiomas, según su lengua nativa, o en el idioma donde se formó como profesional y científico.
Saludos
José Luis
Question
Say you have a piece of a semiconducting material being used as an electrode. You apply a potential to the back of this material to drive an electrochemical reaction at the other side. Is there a mathematical way to predict what potential will be felt at the other side of the semiconducting material?
I am also interested to get a suitable solution to it.
The potential drop in semiconductor is mainly due to the increase in resistance with increasing the thickness (the distance). We need to find all the resistances, metal-semiconductor contact resistance, the resistance develops with increasing the semiconductor thickness, semiconductor-electrolyte contact resistance.
I could not find any answer to the question you asked. If nobody has done yet, it will be a good study. The problem has been observed in many potentiostatic measurements for semiconductors.
Question
"D numbers theory" is a generalization of Dempster-Shafer theory by Deng & Deng (2014) [Attached file]. I have problems with application of this theory (specifically in its calculations).
Thanks very much your interest on D numbers. Actually, it is proposed as a generalization of Dempster -Shafer theory which is limited by some strong constrains. The very recent advance on D numbers are there(http://www.mdpi.com/1424-8220/17/9/2086 Fuzzy Risk Evaluation in Failure Mode and Effects Analysis Using a D Numbers Based Multi-Sensor Information Fusion Method; http://ieeexplore.ieee.org/document/8009696/ Exploring the combination rules of D numbers from a perspective of conflict redistribution). In the papers, a new combination rule has been proposed, and the calculations are explained clearly. In the next few days, a new work about D numbers theory will be released. Hope it could benefit your research. Best regards, Xinyang.
Question
Banach-Tarski Theorem (also known as Paradox) is a mathematical statement which says that a sphere can be splitted into two (or an integer N...) spheres each equal to the original one.
Do you know some applications to Physics or other scientific disciplines?
See references.
Gianluca
R.M. French, The Banach-Tarski Theorem, The Mathematical Intelligencer, Vol. 10 (1988), No. 4, pp. 21-28
Stan Wagon, The Banach-Tarski Paradox, 1986
This is an interesting question.
First, the Banach-Tarski paradox is as follows: given two subsets in R^3, which are bounded and which have nonempty interiors, it is possible to cut A into a finite number of pieces which can be moved by rigid motions (translations and rotations) to form exactly B. That is a paradox!
Assuming that this can be done with a pair of spheres A and B, here is a suggested physical application:
Let A, B be finite, bounded spheres with nonempty interiors. Assume A,B are balloons. Fill B with water and then measure the amount of water B holds. Then fill A with water with same amount of water that B holds. The action of expanding A with water resembles the translations and rotations one would make in porting A over to B.
Question
Different steps are introduced by many researchers to plot the simulation results of Axial Ratio vs. frequency. However, the results were completely not compatible with the fundamental and mathematical results.
Therefore, those how are know a tested steps setup of CST simulation, they can share their experiences (with photos, links, or references) of plotting and specifying an antenna polarization (linear, circular, and elliptical polarization).
thank you for help.
Dear Raed
You can plot in this way by considering following steps:
Go to template based processing->Farfield and Antenna Properties-->Farfield result-->New window opened-->go to all settings--->choose E-field from Plot mode, Axial Ratio from Axis/Polarization, Broadband from Frequency Settings, Evaluation range in single direction and choose theta and phi angle--->then OK.
Generally theta = 0 degree and Phi = 0 degree consider for axial ratio for broad frequency range.
Question
Why the Chi-square cannot be less than or equal to 1 ?
The Chi^2 test statistic can be less than or equal to 1. It happens to be zero e.g. when for all categories the observed count equals the expected count. This means a perfect match. It cannot be less than 0 because of the squaring of the differences between observed-expected.
Question
Or if any ne has suggestion which challenge in massive mimo should I research on because most of them has a lot of mathematical prolems. Are they dfficullt?
It is relevant to consider the EE under intrinsic system impairments, e.g., limited chain resolution, hardware impairments, and also considering energy consumed for digital processing (it grows high by the number of chains), as well as channel estimation energy and limits. I have not seen a joint consideration of the aforementioned issues, on a system addressing EE for massive mimo systems. However, aforementioned factors are jointly relevant due to their impact on energy consumption, and on the information rate perfoemance of massive array systems.
Question
There is an improvement in an iterative optimization process being done by introducing additional stopping criterions based on defined threshold and their compliance by the optimization process.
Dear Fsl, I agree with Prof. Denaro; note that general "stopping criteria" don't exist, a part the criterium based on residual definition (see Denaro's answer); every numerical software can have own stopping criteria, see link below for Matlab. Gianluca
Question
Is there any method to combine several HMM with same transition states and observations that describe different objective?
I have a similar problem "How can we combine two semi-Markov chains with similar states with different transition matrix into one to obtain collective results". Later I have to show the theatrical and simulations results.
Question
The field equations originally starting as Maxwell distributions graphs configure a velocity variable. Understanding that in connection to wave theory requires a mathematical transformation of velocity variable into wave function parameter. This may help mathematically to define particle wave quantum relativity quantitatively. Legendre transform theoretically will have a way to provide link among functionality of parameter-variable systems.
Spectral Methods in Fluid Dynamics
• Authors
• Claudio?Canuto
• M.?Yousuff?Hussaini
• Alfio?Quarteroni
• Thomas?A.?ZangJr.
Question
There is any reference to the best staistical approche to check a mathematical conjecture ?
Thank you for responses. if we look at this article in wilipedia (https://en.wikipedia.org/wiki/Collatz_conjecture ) about Collatz conjecture. It s cited the Undecidable generalization decision. So I'm seeking for algorithmes to have clear vision about if the conjecture is undecidable.
Question
This is a very interesting project! Could you give me a new, short-hand definition of "critical feedback"? We have defined critical nodes and critical connections (in relation to connected cortical graphs in graph theory, see Gomez and Lopera 1999 Med Hypotheses 1999 Sep;53(3):263-6 https://www.ncbi.nlm.nih.gov/pubmed/10580535), and recently, here in RG, critical subgraphs (http://www.fondpageant.com/post/What_is_the_meaning_or_the_meanings_of_a_critical_node_in_cortical_graphs)...
Could you please give me a context-free definition (valid for many systems and sciences) of "critical feedback"? Is it a special case of critical subgraph where we have positive and negative loops? If the meaning is conserved, a critical subgraph represents a subgraph which, if it is extracted from the graph, the graph becomes unconnected. This might be important to define a robust and qualitative general structure in the context of a general mathematical theory of systems...
Thanks for this important research for the current controversy on climate change and the march for science (now called the movement for science https://www.marchforscience.com/mission-and-vision/).
Juan F Gomez PhD, International Group of Neuroscience IGN (I have been recently involved in the study of oscillations in ecology and geophysics, and active in science-related groups of local climate).
Dear Juan,
Here are some exemples using ‘critical feedback’ :
-To link field experience and engineering analysis to provide both a better diagnostic tool and critical feedback on the design.
-Monitor and enable critical feedback on research progress (annually wherever possible)
-Data from the monitoring is being examined to increase efficiencies in data collection and provide critical feedback to the operators.
-Please give us as much critical feedback on this early RFA as you are able to provide, namely in the eligibility section (section 2).
Teamwork and Collaboration in Early Years Settings
Unlocking Dynamical Diversity: Optical Feedback Effects on ...
Best regards
?.??
Question
Which is the status of mathematical research about existence and unicity for Navier-Stokes equations (and boundary problems) for finite or infinite domains? Gianluca
One could proceed and visualize them, more? I read there are different ways; on a cube or sphere for a time interval, but it is not asked for in the Millenium Prize Problem
Question
Hello,
I would like to know how physically (mathematically, maybe algorithm) to do Time Synchronous Averaging for signals: vibrations and velocity. I will be grateful for your answer in this matter? I work using LabView and had problems with this.
Time synchronous averaging works because when you add statistically independent noises they add like this: Variance(sum) = sum of variances. So... if you add various versions of your signal plus some random (uncorrelated noises) then your signal adds linearly, but the noise part adds according to the above. It is then easy to demonstrate that the signal-to-noise ration improves proportionally to the square root of the number of epochs used.
Question
I am seeking a short research visit in the field of educational technology and mathematics education. Currently, I am working as a faculty member at Suez Canal University, Faculty of Education, Dept. of Curriculum and Educational Technology.
[PDF] Conditions Influencing Mathematics Teachers Uptake of Digital Tools–a Systematic Literature Review
M Utterberg, J Lundin, B Lindstr?m?- …?for Information Technology &?…, 2017 - learntechlib.org
Sugerencia: Buscar solo resultados en espa?ol. Puedes especificar el idioma de búsqueda en Configuración de Google Académico..
[PDF] Conditions Influencing Mathematics Teachers Uptake of Digital Tools–a Systematic Literature Review
M Utterberg, J Lundin, B Lindstr?m?- …?for Information Technology &?…, 2017 - learntechlib.org... stress how IT in education challenge teacher's ability to integrate educational, technology, and subject ... For example teachers' belief about how technology is compatible with mathematical learning (Goos ... teachers using laptop in teaching is their belief that mathematics should be ... Artículos relacionados Las 2 versiones Versión en HTML
Tier 2 response to intervention in secondary mathematics education
EC Bouck, MD Cosby?- …?School Failure: Alternative Education for?…, 2017 - Taylor & Francis... Missy D. Cosby is a doctoral student in the Educational Psychology and Educational Technology Program in the ... A synthesis of empirical research on teaching mathematics to low-achiev- ing students. ... Fluency without fear: Research evidence on the best ways to learn math facts ... Artículos relacionados[HTML] pegemindeks.net
[HTML] S?n?f y?netimi
A Ayd?n?- Pegem At?f ?ndeksi, 2017 - pegemindeks.net... Factors Affecting Utilization, in RM Gagne (Ed.) Ins-tructional Technology: Foundations. ... Study in Secondary School Classrooms. Journal of Educational Research, 79, 51-58. ... Chapter of the International. Group for the Psychology of Mathematics Education, 17th,. ... Citado por 252 Artículos relacionados [PDF] campbellcollaboration.org
[PDF] Interventions to improve mathematics achievement in primary school-aged children: a systematic review
V Simms, C Gilmore, S Sloan, C McKeaveney - 2017 - campbellcollaboration.org... The effectiveness of educational technology applications for enhancing mathematics achievement in K-12 classrooms: A meta-analysis. Educational Research Review, 9, 88-113 ... Big Math for Little Kids: The effectiveness of a preschool and kindergarten mathematics curriculum ... Artículos relacionados [PDF] scasd.org
[PDF] Stem
…, J Ernst, A Clark, B DTE, D Kelly, WS Education?- TOP OF THE?…, 2017 - scasd.orgFew educational movements of late have gained as much national exposure and conversation as STEM (Science, Technology, Engineering, and Mathematics) Education. It is not uncommon to hear mention of STEM education in sound bites from presidential and Citado por 5 Artículos relacionados [PDF] waikato.ac.nz
Initial teacher education students' reasons for using digital learning objects when teaching mathematics
N Hawera, S Sharma, N Wright - 2017 - researchcommons.waikato.ac.nz... Characterising the perceived value of mathematics educational apps in preservice teachers. ... Showing and telling: Using tablet technology to engage students in mathematics. Mathematics Education Research Journal, 28(1), 123–148. Koehler, MJ, Mishra, P., & Cain, W. (2013). .
Question
We have 3 demand nodes and 1 facility. Collective demand of 3 nodes is greater than capacity of facility but their individual demands are less then capacity of facility. We want to assign maximum demand to facility.
But is not clear because structures are not closed. Two open braces but only one closed. In the other hand, when you say "where" is similar to "for"? Maybe, this could be more clear if you share the exact block of C++ code (if the problem is not C++).
Question
Why are students performing so poorly in mathematics in schools and in standardized achievement tests?
Dear all,
Each of you pointed to some of the facts that affect that the mathematical skills steadily declining . First of all the government should support education at all levels by providing the necessary resources as Jorge Morales says, and forther plans and programs are very important, and the most important of all are good teachers in primary and secondary school and professors as the performers and implementer of these programs Besides, the Bologna way of study has also led to the declining of the study level.
Mirjana
Question
Some of students ask me to give the applications of mathematics in real life. What are some of the interesting applications of mathematics in real life? Could you please share your knowledge about this issue.
You are asking about millions of mathematical application in our life, like calculation of area, volume, velocity, acceleration ....etc.
Question
Hi,
I am trying to write the motivation part for linearization of a non-linear mathematical formulation. I claim the mathematical model will be more simple and easier to solve. But, of course, I need a reference for that! Any suggested book chapters or articles that discuss this point please?
Zak
HI, in mathematical programming the constraints are linearized but the cost function is approximated by a quadratic form leading to Sequential Quadratic Programming (SQP) methods. You can find easily the motivation of these popular methods
Question
I am actually a energetic engenieering student? in master degree at the faculty of sciences and technologies in Tangier , Morrocco .
I have to prepare a presentation about an article titled (Experimental and mathematical study of the discontinuous drying?kinetics of pears?,Silva 2014)?
I have to reproduce using Comsol software the results of the experience done by Silva Victor , but the problem is that? i have never used comsol on mass transfer modelling so?i need your advices if possible so i can do this job correctly??.?
Question
One of the aspects of our current research with a colleague in Mathematics Education requires the definition of what should/could be called a "non-standard" mathematics problem. One of the ways to go around this is to define non-standard problems as those which are not standard, in which case we need to define what is meant by a "standard" mathematics problem.
Your suggestions on either of definitions (standard or non-standard problems) are most welcome.
In Russian, the best answer to the question posed is the article by I.V. Arnold (the father of Academician V.I. Arnol'd) "The principles of selection and compilation of arithmetic problems." To intrigue the reader, I will inform you that in this article, among other things, a selection of 24 non-standard problems is given, each of which is solved by the same action: 3-2 = 1.
Question
Please introduce both of mathematical & technical methods for
selecting best compromise solution (or preferred solutions) from bin-objective pareto set.
For an alternative approach/paper see Information Sciences 340–341(2016)228–249. Asymmetric distances to improve n-dimensional Pareto fronts graphical analysis
Question
Respected researchers,
I need to design an antenna for measuring the precipitation of the rainfall in a particular area. can we change the dielectric constant of the substrate used with respect to the distance the radiation covered. Is there any mathematical formula for this?
Relative permittivity is the factor by which the electric field between the charges is decreased relative to vacuum. Likewise, relative permittivity is the ratio of the capacitance of a capacitor using that material as a dielectric, compared with a similar capacitor that has vacuum as its dielectric. (Wikipedia)
Question
In https://projecteuclid.org/download/pdf_1/euclid.cmp/1103840281 J.-M. Lévy-Leblond has shown that linearizing the (full, time-dependent) Schr?dinger equation leads to a spinor equation. The mathematics is straightforward, no issue with that. My issue is: it is argued that the resulting linearized equation would be Galilei covariant. Yet, as I see it, the key equation (which is (25) on p. 293 in the cited link above) is just the non-relativistic limit of the Dirac equation, with c=1. This is not a miracle to me, as linearizing the Schr?dinger equation by means of dimensionless matrices (that actually turn out to be the Dirac matrices) is only possible by introducing a velocity scale. In the paper above this is not transparent from the beginning, as the natural unit convention "c=1" is used.
The pure fact that linearizing the Schr?dinger equation is a means to get a spinor equation is rarely discussed in the literature anyway. But where it is, it is argued that the resulting equation is non-relativistic and thus Galilei covariant. I argue that it can't be, and that it is neither Galilei- nor Lorentz-covariant! The former it can't because it has the velocity scale "c" in it (which, in the original paper or anywhere else is omitted due to the unit convention), the latter it can't because it is only the non-relativistic limit of the Dirac equation.
Do I have some error in my reasoning?
Looking forward to some replies.
I should add maybe that Lévy-Leblond has made great contributions to analyzing the representation structure of the Galilei group in QM, and in another paper has done an analysis with the inhomogeneous Galilei group similar to what what Wigner did with the Poincare group years before. Therefore, what he states in his papers, at first glance, bears a certain weight, at least to me. This is why I am unsure
Question
Mathematics researcher
A straight line is a Euclidean concept, It can only be defined in a Euclidean space, an affine space with Euclidean metric. ?In a more general geometry, the concept of geodesic replaces that of a "straight line".
A geodesic can be viewed as a curve in the space where an observer traveling along this curve at at constant speed will feel no acceleration forces. ?On the earth for a example they are the "great circles." ?
Question
Official reports (preferably from NSF, AMS, MAA, SIAM) are the ones that I am looking for, but I have been unable to identify them yet. I am interested in success rate and many possible variations of it to illustrate the competitiveness of such grants. Thank you for your help in this matter!
Dear Ana maybe?You can try in American Embassy?at?your?nation? Thaks?
Question
Allocating resources with several decision variables and a very large, yet finite number of constraints. Looking for a software to compute solutions, not looking for a large enterprise/commercial software package like Matlab etc., something open source is desirable; perhaps even a plugin for Excel etc.
Scientific Python (SciPy) is Open Source and offers LP in its massive toolbox:
Probably best installed via the Anaconda installer.
Question
Car Radiators: what is the mathematical approach that I should follow to somehow estimate the external heat transfer coefficient in the air side flowing externally through the fins and tubes?
I hope I can give you a general Idea. The radiator of the vehicle having different configuration setup whether you are considering a coolant-oil exchanger or not.However, in simple setup you can consider the heat transfer coolant side to the external air by considering the system as a series of thermal resistances for a 1D simple-steady heat flow analysis
convection->conduction->convection
considering the radiator area ,A??and length, L?
heat flow,q=Q/A (q , Q are flows)
• Coolant side : ( ?Temperature of coolant?- Temperature of coolant,wall) = (1/h,coolant)*(heat flow)
• Wall side: ( ?Temperature of coolant,wall - Temperature of air,wall) = (L/k)*(heat flow)
• Air Side:?( ?Temperature of air,wall - Temperature of air) = (1/h,air)*(heat flow)
• The average values of the conduction and convection can be taken as h,c=3000 W/(m2K) , k= 200-400 W/mK ( depending on the radiator material) , h,a= 100 W/(m2K) ( This gives the main contribution-> air side)
• Kr= 1/(1/hc + L/k + 1/ha)
Then by considering the final result we have Q=Kr*A*(T,coolant - T,air)
This is a very simple model , however the radiator is much more complex than a metal plate as considered above because the global heat transfer coefficient also depends on the type of technology you are considering ( braze-welded or mechanical welded) or may be a full aluminum radiator . You can also consider the ATB ( Air to boil ) index or ETD ( External Temperature difference ) to know the safety limit for the coolant temperature.?
Question