Science topics: Mathematics
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Mathematics - Science topic

Mathematics, Pure and Applied Math
Questions related to Mathematics
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I tend to consider mathematics the body of axioms, definitions, systems of logic, and their results. If you're not adding to this body, you're not doing mathematics.
Arithmetic, calculating, solving, and so on, just seem more like accounting than mathematics. If anything, I would call these things "calculus" after the original Latin root word, referring to a stone used for counting.
Maybe it's pedantic. But I don't think so. A lot of people who "hate math" really hate "calculus." And honestly, being good at mathematics, at constructing proofs, etc is so different from being good at working with numbers. I'm decent at the former. I'm horrible when it comes to the latter.
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Ahmed Chahtou, among other things, it is frustrating that so many people believe that mathematics is all about numbers and calculations. That misconception is also unhealthy for the field.
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Math passed through centuries in three stages
The first, around 450 BC, continued until 1923 and is called Euclidean mathematics
The second, which began in 1923 when John Poulaye came up with new concepts, including the introduction of so-called imaginary mathematics (complex numbers) and continued until 1950 when the entrances to mathematics became the group ...
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Thank you for your wonderful and useful answers
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I'm using this question to set up possibly a platform for a further question in the future. Did Gödel's incompleteness theorems really shatter the dream of looking for some foundational base for mathematics? Do we need any foundations, whether in the sense of the logicist, the formalist or the intuitionist (or what have you), for mathematics at all? These are some of the related questions. It would be nice to know if anyone out there is still engaging in such a research. Views from all other (non-mathematical) disciplines are also welcome.
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One commonplace I run into is observation that the efforts to provide a foundation that all mathematics can be founded on does not seem to intrude over-much with the practice of mathematics/mathematicians. It seems not every mathematician is concerned about foundational issues (or philosophy of mathematics issues).
There is a long-going moderated discussion list, [FOM], fom@cs.nyu.edu and list server (https://cs.nyu.edu/mailman/listinfo/fom) that has been discussing most of those concerns and with attention on reverse mathematics and prolific contributions by Harvey Friedman, among others.
Consideration of the various different approaches and which goes at the foundation level, and which flavor of that (e.g., which particular set theory) have been discussed at various times and searching the archive might be useful before broaching one of these anew.
Aside: AFAIK, no one has successfully established that Gödel is escaped by moving the pea under a different foundational approach.
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Modifying the original Feistel structure will it be feasible to design a lightweight and robust encryption algorithm. Somehow changing the structure's original flow and adding some mathematical functions there. I welcome everyone's view.
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Dea Saka Kurnia Putra Sir, thank you for your response I will go through the materials shared by you and in case of any queries I will share my problems. It will be of great help if you share me your e-mail i address in the inbox.
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How many types of number in mathematics?
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The numbers in mathematics are divided into real and complex. The real numbers are divided into Rational and Irrational numbers. The Rational numbers are divided into integers and fractions. The integers are divided into positive and negative. Positive and negative numbers are divided into odd and even numbers.
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in solving mathematical problems we consider momentum equation energy equation as well as concentration equation to model our physical problem but why homo-hetro? what they describe physically? and how it help us?
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Hi Sarah,
The homogeneous reactions happen in the whole fluid bulk, e.g. a stirred tank with two feeds with the reagents A and B. The chemical reaction will happen in the fluid as the two streams are mixed. This happens in the whole reactor, there is no special place where we have the chemical reactions, it is homogeneous.
Consider now a tube covered by a catalytic surface. As the fluid flows in the tube chemical reactions take place on the tube wall - the catalytic surface, and only there. The bulk only transports the reagents and products. And the chemical reaction is part of the boundary contour. As the reaction does not happen in the entire domain, this reaction is called as heterogeneous.
This is the distinction among them. I hope help to understand, Bests!
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Many literature on RGBd images says object detection can be improved using depth map features(Geocentric features) but i didnt find any mathematical proof how these features are added with RGB images in order to improve accuracy of object detection?
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You can improve the accuracy by overcoming the detection challenges such as light variance and background deformation.
Depth data is invariant to lighting variations and affords the ability to take advantage of spatial separation between objects.
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Hello all
I am looking for the mathematical relationship (direct or indirect) between the effective density of states in valance band and the external applied field.
Thank you.
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Density of the state will change as wave associated with electron provides the states which obtained from the Schrodinger wave equation when we apply external potential definitely modify the states.
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A mathematical tool used on bands to determine a particular feature or phenomenon
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Yes, there are new indicators using short wavelengths with ground stations and high resolution sensors
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We make the following proposal to the Mathematical community.
Anyone well versed in Logic and Set Theory will be familiar with the concept of cardinality and the nature by which the cardinality of the real numbers R as a whole over the natural numbers N was established.
There is a clear reason why the diagonalisation argument [Diag(N,R)] works in the way of the above establishment.
Being able to pinpoint the reason, will have the effect of being able to prove \kappa{S_1} > \kappa{S_2} for sets S_1 and S_2 having the necessary characteristics, by performing : [Diag(S_1,S_2)].
To aide in clarifying the above, we have attached a diagram.
We will be presenting the above idea in a conference in India.
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The idea of increasing sequences of equal types (zero´s) for creating excluded subsets is an idea of my papers (Cantor, Proof, Cantor 3).
The copyright started 2010/2013.
My papers represent another conclusion but I will not allow you to present the main idea as your work.
The German versions of my papers were present at RG for the ask for help in translation (Who likes to tanslate the counter-proof of the diagonal slash argument from German to English? / Is contradiction between Cantor slash1 and slash2 already known?).
Please accept my copyright or I have to use all possible tools to hold my rights.
You may ask for an acceptance for quoting my papers.
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Dear all, I need a friendly reference from any paper or book chapter to study about seismic ray tracing. I read about seismic ray theory from Cerveny's book, and it's very hard to understand because it contains a very high level mathematical language. I also need a reference that gives kind of flowchart explanation how to do seismic ray tracing. I'm glad if you could help me. Thankyou.
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Dear Yohanes
Before indicating you some references as you requested, I want underline that when we deal about kinematic raytracing we need to distinguish between the "ray tracing (strictly)" and the "ray tracing problem and its solution" not all solution of ray tracing problem include a ray tracer. I suppose that you are interested in solving raytracing problem. The two main approaches to solve the kinematic raytracing problem are: shooting and bending methods, only the first really needs of a ray tracer. In technical literature sometime the two concepts are confused.
I advise you to read the paper ( Advances in Geophysics, 49, 203-267-2007 by N. Rawlinson, J. Hauser, M. Sambridge). It is a short overview paper on (Seismic ray tracing and wavefront tracking in laterally heterogeneous media). In particular, you can read firstly the introductive chapter and the chapter 2 on the raytracing schemes: in particular on shooting (2.1) and bending (2.2) methods. In this paper you will also find other approaches based on the direct solution of the eikonal equation .
Furthermore you can find simple scripts (and demos) in Matlab about raytracer and raytracing in the CREWES site (https://www.crewes.org/ResearchLinks/FreeSoftware/)
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mathematics anxiety
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Attached on my profile you could find my research proposal
Kind regards
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Yep. RG is equating science with experiments. There may be those who like this, but experimentation is NOT THE ENTIRE SCIENTIFIC METHOD (and I would argue that experimentation is THE LEAST OF IT -- especially if one is developing a new perspective and approach). RG appears to have no appreciation for "just" verified observations -- even though that may be exactly what really new discovery looks like . Those observations may, in time (but not right away), be followed by experimentation. Verified observations by themselves may be very important and all we have for some time (in some new areas/kinds of investigation).
The outrageous bias of RG is so great that they now hide the Project Updates (of the Log) with multiple queries about one's experiments and hypotheses -- as if all good, clear hypotheses could be put "in a nut shell" (in a small "blank", with little context) AND that experiments are all that matter (or at least all that deserves several special headings). How about a heading for: "Verified Observations"?
I would ask: What experiments did Einstein do to lead and come up with his understanding of the universe? Did he start with experiments? NO!! He started with observation and MATH (which is basically verified observation). True, eventually some experiments were done to VERIFY HIS IMPORTANT OBSERVATIONS -- but all this did NOT begin with experiments..
And, all of this is not to mention major swathes of Biology. Come on, give us a break.
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And: Daniel Goldman:
OBSERVATIONS are are as falsifiable as experiments, if they lack high inter-observer reliablities (P.S.: p<.05 has NO magic). That all aspiring scientists do not know this is frankly disgraceful. Realize that science is just good reliable, and shown valid, COMMUNICATION -- as is true of all good communication; this can most certainly be found and true of sets of observations. Experiments are communication; observations are communication. DO NOT TRY TO PUT "MAGIC" IN TO ONE OF THOSE.
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Game Theory
Game theory is a tool for the analysis of the interaction among usually rational agents, the formulation of hypotheses about their behaviour and the prediction of the results of each interaction. From this standpoint it is very suitable for the analysis of environmental problems and for the definition of self-enforcing environmental agreements that are founded on cooperation and stability.
Enter game theory
What we have here is a particular kind of group decision problem known as a game, where one party’s decision is influenced by the actions of another party and vice versa.
The mathematical theory of such games is rich, with many important applications. 
Game theory, as it is known, was originally developed during the Cold War to model the nuclear arms race and first strike strategies. 
Since then, the theory has become indispensable in economics and is enjoying applications in diverse areas such as ethics, biology, dating, and, more recently, in environmental management and policy.
One of the enduring lessons of game theory is that in certain common situations, cooperation can be hard to achieve and may be difficult to maintain.
What do you suggest for example for wastewater treatment? did you have experience of that? would you please help by sharing your documents, experience, knowledge and etc. ?
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Title of paper: Games Addiction or Not; Health Therapy or Business
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My topic is; iAn Assessment of Problem Solving Skills in Mathematics of Elementary Pupilsl: Basis for Curriculum Development
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according to the probability theory,
suppose that we calculate the experimental probability of students who prefer mathematics and it was .70%from a sample of 20 students (14/20), is that correct to use these percentage (70% to calculate the probability of prefer mathematics in case of applying the same survey on a sample of 200 students?
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14/20 is a proportion or percentage. It's a relative frequency, not a probability. One may (!) use the relative frequeny as an estimate for the probability, that a student sampled under similar conditions will prefer mathematics (and this also only in the case that there is a countable set of possible alternatives).
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It's a well know fact that the vector integrals are generalized forms of general integrals, such as
1 - Line Integral is a generalized form of Simple/Single Integral
2 - Surface Integral is a generalized form of Double Integral
3 - Volume Integral is a generalized form of Triple Integral
But when I go through the books, there is no difference shown between the Volume and Triple Integral.
In some books, authors are explaining all the above except Volume Integral and they are also not mentioning that Volume Integral is same as Triple Integral - Erwin Kreyszig
In some books, authors are writing like "Triple integrals or Volume Integrals can also be defined..." - Jordon and Smith
Could anyone please give some clarity explanitions on this...
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For a triple integral to be a volume integral, there are coordinate system-dependent "scale factors" (or coordinate-dependent "scale factor functions") that need to be included within the integral. For Cartesian coordinates, the scale factor is "1" so the volume element is "dx dy dz" ; for spherical coordinates, the coordinate-dependent scale is "r^2 sin(theta)", with theta being the angle from the azimuth, so that the volume element is "r^2 sin(theta) dr d(phi) d(theta)". Explained similarly to this in Hildebrand, Advanced Calculus for Applications.
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Suppose in a three layer supply chain there are three different profit function TPs, TPm, TPr then total integrated profit is TIP=TPs+TPm+TPr, if we put TPs=0 then is it reduce to two layer supply chain or not?
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Yeah I mean Supply Chain Management prof. Bruno Durand
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Mathematics means the first science
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I agree. The notion of counting is present in cave paintings
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Like in the question, is there a mathematical way to divide a given rectangle into minimal amount of any squares (some squares could be the same and the side length of every square could be any real number)?
If not for any squares, then maybe for squares and rectangles with integer side lengths?
Example:
given rectangle: 16x17
What is the minimal amount of any squares on which we can divide this rectangle?
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This problem can be solved using dynamic programming.
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In the solid, specially metals, the thermal conduction can be done with lattice fluctuations and free conducting electrons, where the role of electron is more significant.
I want to show the above explanation with some mathematical formula that arise from a physical considerations. But the problem is, I don't know where to start .... can anyone help me ??
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Good solid state theory textbooks should do the job.
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Is statistics a branch from mathematics?
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· Mathematical statistics is a branch of mathematics. "Statistics" as a field also includes things which are not, strictly speaking, mathematical statistics, and which would consequently fall into the category of science. Statistics is part of applied mathematics.
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Hello, i need to extract 3d coordinates from a 2d image with a purpose to give these coordinates to a manipulator because i want it to grip a screw. I know by default the pixel coordinates ,the distance between camera-screw, the specifications of my camera and i dont know the right mathematic transfomation to find the 3d coordinates. Could you help me?
thank you for your advise!
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Thank you Jack Don McLovin , with your example i understood the way to solve my problem. All i need in my project is to find where in the real world is a screw.
Details:
camera distance from screw= 26cm
screw pixels in image= (350,480)
image dimensions=820 x 640
screw length=3cm
screw width=0.5cm
field of view (vertical)=62 degrees
focal length=3mm
pixel size=1.12 μm
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I want to know the Scopus or ISI or SCI journals of Mathematics, Managements and Engineering which provide a fast review process without a publishing fee.
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Fast publishing indexed journal = not free
Free indexed journal = not fast
Fast and free journals = not indexed
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The subject of the results of mathematics is the focus of discussion and discussion among philosophers and scientists. Some of them say that mathematics is absolutely certain and absolute in all cases where science was simple. Others emphasized that mathematics is relative in terms of particular results with what mathematics saw from multiple formats. Thus, you can describe mathematics
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Acknowledgments
On all the wonderful answers
Greetings to all of you
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Delve into your own expertise. The idea that problems-they can be mathematic- are not being successfully unravelled is often dismissed in the belief that they will be answered in some distant future. But what if human knowledge and human ingenuity is finite. A1 ingenuity must also be finite.
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The ones which are based on untestable assumptions. For instance, ”had the World War II not happened, the world would have been more peaceful today” is such assumption. So the question about world peace based on this assumption can never be answered as there is no way to undo the WW II to test the hypothesis.
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Always buildings are damage by an Earthquake. So we have prevent to lose the people poverty, How?
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I recommended the following presentation
Best Regards Javan Doloei
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I recently watched the movie "Ant-Man and the Wasp". The subatomic scene got me thinking:
How small or large can an object/something get?
If it was realistically possible to reduce or increase the size of a car or a person like in the movie - is the process infinite?
Can weird things begin to happen either way (small or large)?
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There are several movies over the years that have explored the premise of changing the size of things because "most of matter is empty space.... lets just put the atoms closer together"
Even IF that was possible, there would be some odd effects that are never really utilised in these films that would actually make them more interesting.
Under such an experiment, mass is constant, so pressure applied by a miniature "ant-man" would be huge. This is hinted on in the first film when he falls and cracks a floor tile. Punches etc would deliver incredible shock, yet also in the movie, Ant man runs across a villains gun. If mass is the same, the villain should have dropped the gun due to the mass on an entire man on top of it, and whilst the idea of storing a functioning tank on a key chain might sound handy, a 60 ton tank in your pocket would prove quite cumbersome.
Transversely, when items are "grown" their density would decrease, to at some size, Ant Man would float away in the breeze.
So whilst it is entertaining to explore the idea, physics would not allow it and even if it did, the consequences could be more problematic than shown on screen, assuming some degree of continuity was maintained.
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can any one suggest mathematical equation for predicting calorific value and kinematic viscosity through density
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Viscosity is related to energy dissipation (conversion of mechanical energy into thermal energy). How that? Multiplying the (dynamic) viscosity (unit Pa s) with the shear rate (unit 1/s) yields the shear stress (shear force per area = shear energy per volume, unit Pa). Since we are dealing with plastic instead of elastic deformation, the shear energy is ‘decaying’ by relaxation at the molecular level. The shear energy is replenished by continuing shear. Multiplying again with the shear rate yields the power per volume (unit Pa/s).
What is the mechanism of disspation? Let’s first talk about condensed matter (as opposed to gases). The relaxation takes place by conformational changes into less strained configurations. The change isn’t smooth but more or less uphill and downhill on the energy ‘landscape’ (potential energy over configuration space). Downhill movements are fast and this is exciting vibrations. More or less corrugation of the energy landscape leads to higher/lower viscosity.
For different substances, there is no correlation with density. Compare, for example, two almost-n-alkanes C30 and C60 (with the same small fraction of short side chains to reduce the melting point). At, say, 100 °C, the density is almost equal while the viscosity is much larger for the longer chains.
For gases, the shear stress develops by transport of momentum between adjacent layers. The Kinematic Theory of Gases predicts that the dynamic viscosity does not depend on density (at constant temperature). The argument is as follows: Particles from a higher layer and particles from a lower layer collide in a middle layer. The spacing between the layers is about the mean free path, so that the colliding particles do stem from the two outer layers. Before the collision, the relative speed of the two particles has a systematic component equal to the velocity difference between the outer layers. That component is directed. After the collision, the relative speed is the same, but the direction is (almost) random. The surplus of kinetic energy has been thermalized. Now, when the density is lowered two times, the rate of collisions per particle decreases by a factor of two, and per unit volume by a factor of four. But the mean free path between collisions increases by a factor of two, as is the velocity difference between the outer layers. The surplus in kinetic energy (proportional to the square of the velocity difference) increases by a factor of four, which cancels the decrease in collision rate. So the dissipation rate does not depend on density.
Now think of carbon dioxide above the critical temperature. You can control the density via the pressure from gas-like to liquid-like without a phase transition. At high enough pressure, energy barriers emerge hindering the movements. This is the point where viscosity becomes strongly dependent on density.
It should be mentioned that a given corrugation of the energy landscape can be made much shallower than the mean thermal energy by raising the temperature. Then the rate of lokal conformation changes is much higher than the shear rate, and the shear stress becomes low again. That is the reason for the liquid outer core of the earth has a rather low viscosity (close to that of water), while the density is 10 to 12 g/cm³, roughly 50 % higher than the same mixture at normal pressure (and manageable temperature).
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There are several model equations reported in literature. I have got the experimental values of moisture ratio and drying time. How can I fit the experimental data to the following equations? How can I obtain various model constants? Any software to be used or it has to be done mathematically? Please guide me with some good literature/links/software to carry out this study.
How can we use regression analysis for find out constant using these models. Can we solve it by non-linier regression with excel solver? Different models are following:
Lewis MR = exp(kt)
2 Page MR = exp(ktn)
3Modified Page MR = exp[(kt)n]
4 Henderson and pabis MR = aexp(kt)
5 Yagcioglu et al. MR = aexp(kt) + c
6 Two-term MR = aexp(k0t) + bexp(k1t)
7 Two-term exponential MR = aexp(kt) + (1a)exp(kat)
8 Wang and Singh MR = 1 + at + bt2
9 Thomson t = a.ln(MR) + b[ln(MR)]2
10 Diffusion approach MR = aexp(kt) + (1a)exp(kbt)
11 Verma et al. MR = aexp(kt) + (1a)exp(gt)
12 Modified Henderson and pabis MR = aexp(kt) + bexp(gt) + c exp(ht)
13Simplified Ficks diffusion (SFFD) equation MR = aexp[c(t/L2)]
14 Modified Page equation-II MR = exp[k(t/L2)n]
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Sir, I have estimate RMSE, R2 value directly from software (MATLAB). and also calculate from drying kinetics formula. Can you tell us what is different in these values? Its same value or not.
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I want to design a microwave absorber and in order to evaluate the performance I need absorbance v/s frequency plot. Kindly assist me.
I also want to know that do I need to consider S-parameters because mathematically absorbance is given by, A=1-|R|-|T| and if owing to ground surface we say T-->0. Thus, A=1-|R|. R is given by magnitude of S11.
That's why I wondering to know that is it possible to analyze the absorbance v/s frequency plot in CST or I need to calculate manually undertaking the |R|.
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we can find it in below path :
Post processing => Result Templates Tools =>
General Results:
General 1D =>
Add new post-processing step .. :
1d(c)=> 1D(c)
f(x,y) : desired formula ...
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I think mathematics is involved in all other sciences
But she is not considered her servant
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Thanks for the wonderful and convincing answers.
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What do you think of the development of mathematics books in the primary stage on the problems of society?
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I agree with you
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It’s all strange, yet true – quantum theory is the most accurate scientific theory ever tested and its mathematics is perfectly suited to the weirdness of the atomic world.
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Echoing what Emil has said, all the predictions made by quantum theory, even the strangest and most unintuitive of predictions seem to be realised in nature. Because of this, just about everyone believes that Nature is inherently quantum.
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Some people consider mathematical axioms as points of strength of mathematics, other say that axioms are points of weakness.
My question is why?! Is it so difficult to prove mathematical axioms?
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The axiomatic system includes primitive statements. That is postulated as facts and called axioms. Obviously, all axioms in the same system should be independent and consistent.
To talk about proving axioms has no meaning. Unless we assume that axiom under consideration is not independent of the other axioms and one can try to show his claim.
A famous example is the well known geometric axioms of Euclid where we have five axioms:
Quoting:
1. A line can be drawn from a point to any other point.
2. A finite line can be extended indefinitely.
3. A circle can be drawn, given a center and a radius.
4. All right angles are ninety degrees.
5. If a line intersects two other lines such that the sum of the interior angles on one side of the intersecting line is less than the sum of two right angles, then the lines meet on that side and not on the other side. (also known as the Parallel Postulate).
In fact, the last axiom is equivalent to say the sum of the interior angles of any triangle is π (180 degrees).
Hundred of mathematicians claimed that the fifth axiom is not independent and can be deduced from the first four axioms.
But all failed to prove that claim.
Those attempts were the base stone to create new geometries such as the ( elliptic geometry), (hyperbolic geometry),etc, and hundreds of Non- Euclidean geometries where the sum of the angles of the triangle in some of such geometries is greater than π and in other geometries, it is less than π.
Nowadays facts and observations about the surrounding universe proved that our universe is Non-Euclidean one. So trying to prove axioms may lead to new creative ideas that change the whole axiomatic system into a new more efficient model. Why not?
Best regards
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What do we mean by dyslexia?
Is it directly related to mathematics education?
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An adequate and adequate answer, thank you
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I am researching the barriers to learning Mathematics from the perspective of the student. recommended articles or researchers would be gratefully received.
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Excuse me Perena Polius
Specialized Teaching Methods Learning difficulties are the essence of specialization, although difficulties are the specialty of educational psychology.
I can send you a search that might benefit you.
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We do have velocity variations (with reference to magnitude and direction) within an individual pore; as well as along the various (tortuous) pores (along the direction of fluid flow).
But still, all these microscopic variations in magnitude and velocity (somehow or magically) get cancelled or nullified; and what we have is the (mostly) well defined - only one - resultant direction of fluid flow - in a saturated groundwater system at the macroscopic scale.
Is there an effort to prove mathematically that this final - single - resultant fluid flow direction at the macroscopic-scale results from the conglomeration of velocity variations at the microscopic-scale - in a typical saturated groundwater system?
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Dear Dr. Sorin Pop,
Thanks for your reply.
We know that the volume averaging of microscopic equations of flow/transport processes may lead to extremely complicated results.
And, that’s the reason why I was asking about any earlier attempt on its actual mathematical derivation.
Of course, it will not be having any practical value.
However, as you have pointed out, we can always make use of the control volume analysis to resolve some of the difficulties associated with the volume averaging of the porous media.
Thanks.
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I want to run some algorithm and generate data from that algorithm and transmit that data to another raspberry pi. In this process, i want to calculate energy. Like, how much energy did that pi consumed from processing the algorithm to transmit the data.
Is there any mathematical equation or software techniques or hardware techniques which can help me to calculate consumed energy by raspberry pi?
Thanks in advance.
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Another option is to use an oscilloscope or multimeter with data logging capabilities if they are available to you. This can be done by measuring the current drawn from your entire system (using a shunt resistor) along with the voltage of your power supply. It is usually wise to measure the voltage instead of just assuming it will remain at its expected value.
Once you have this data you can derive whatever units you need. The power consumption of wireless nodes are often reported as time-averaged current (see most wireless microcontroller datasheets). You can also observe the current draw in different states of operation by looking at current consumption over time. You can get your power by multiplying corresponding current and voltage datapoints. If you want energy, you can do a time integral of your power data.
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There are lots of Optimization method /Evolutionary algorithms (EAs) in literature. Some of them is more effective (for solving linear/nonlinear problem) compared to other. But we don’t know which will fit our model. As a result we checked for everything as we can do. But cant get the desire result. Some of those methods are 1. Genetic algorithms (GA) ; Haupt and Haupt (2004) 2. Pattern search (Mathlab) 3. Particle swarm optimization (PSO), Binary Particle Swarm Optimization (BPSO); Eberhart and Kennedy (1995) 4. Bee optimization; Karaboga and Bosturk (2007) Pham et al (2006) 5. Cuckoo algorithm; Yang and Deb (2009, 2010) 6. Differential evolution (DE) ; Storn and Price (1995, 1997) 7. Firefly optimization; Yang (2010) 8. Bacterial foraging optimization; Kim, Abraham and Cho (2007) 9. Ant colony optimization (ACO) ; I Dorigo and Stutzle (2004) 10. Fish optimization; Huang and Zhou (2008) 11.Raindrop optimization ; Shah-Hosseini (2009) 12.Simulated annealing ; Kirkpatrick, Gelatt and Vecchi (1983) 13.Biogeography-based optimization (BBO), 14. Chemical reaction optimization (CRO) 15. A group search optimizer (GSO), 16. Imperialist algorithm 17. Swine flow Optimization Algorithm. 18. Teaching Learning Based Optimization (TLBO) 19. Bayesian Optimization Algorithms (BOA) 20. Population-based incremental learning (PBIL) 21. Evolution strategy with covariance matrix adaptation (CMA-ES) 22. Charged system search Optimization Algorithm 23. Continuous scatter search (CSS) Optimization Algorithm 24. Tabu search Continuous Optimization 25. Evolutionary programming 26. League championship algorithm 27. Harmony search Optimization algorithm 28. Gravitational search algorithm Optimization 29. Evolution strategies Optimization 30. Firework algorithm, Ying Tan, 2010 31. Big-bang big-crunch Optimization algorithm, OK Erol, 2006 32. Artificial bee colony optimization (ABC), Karaboga,2005 33. Backtracking Search Optimization algorithm (BSA) 34. Differential Search Algorithm (DSA) (A modernized particle swarm optimization algorithm) 35. Hybrid Particle Swarm Optimization and Gravitational Search Algorithm (PSOGSA) 36. Multi-objective bat algorithm(MOBA) Binary Bat Algorithm (BBA) 37. Flower Pollination Algorithm 38. The Wind Driven Optimization (WDO) algorithm 39. Grey Wolf Optimizer (GWO) 40. Generative Algorithms 41. Hybrid Differential Evolution Algorithm With Adaptive Crossover Mechanism 42.Lloyd's Algorithm 43.One Rank Cuckoo Search (ORCS) algorithm: An improved cuckoo search optimization algorithm 44. Huffman Algorithm 45. Active-Set Algorithm (ASA) 46. Random Search Algorithm 47. Alternating Conditional Expectation algorithm (ACE) 48. Normalized Normal Constraint (NNC) algorithm 49. Artificial immune system optimization; Cutello and Nicosia (2002) 50. fmincon .
Besides this there are many other optimization algorithm recently invented which are generally called Hybrid optimization Technique because it’s a combination of two method. If we share our experiences then it will be helpful for all of us who are in the field of optimization. I may be missing some methods, researcher are requested to add those algorithms and the way of use like many model needs initial value, weight, velocity, different type of writing objective function etc. I am facing some problems that’s why I make this format which will definitely help me as well as all other researchers in this field. Expecting resourceful and cordial cooperation.
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Dear Mashud,
I have some experiences in improving optimization algorithms like quantum invasive weed optimization algorithm ( ) and world cup optimization algorithm ( ).
From my experiences two point are important to select a good optimization algorithm:
1) check that do your problems can be solved by the classic methods? if so, do not go to the meta-heuristics.
2) If your problem was NP-hard and can not solve by the classic methods:
after a lot of testifying, I found that there is no more differences among the evolutionary algorithms. of course in some case, one algorithm may have better performance or has high speed, but this prominence is not so bold.
3) Two cases that you should point to them (in evolutionary algorithms) are: Exploration and Exploitation.
Exploration parameter is for places that you have no information about the search space anymore and Exploitation is about that you have an approximate solution for your problem and this parameter in this case finds better solution.
These two parameters comprise the structure of all of the optimization algorithms. for example, in Genetic algorithm, Mutation is an exploration parameter and crossover is an exploitation parameter.
So based on your requirements, select an algorithm that has promonancy about your considered parameter.
good luck,
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The success and the failure in PISA assessments caused different debates, but there is no data linking success with teaching methods. Some countries attempted to draw conclusions about their education policy, while in others failure was associated with student's anxiety regarding tests. On the basis of a text that explains the reasons for success in Finland * I wonder if all five factors match other countries conclusions about successful participation. With respect to this factors can you provide data about the teaching method (s) you think are positively related to success in mathematics;
* George Malaty University of Joensuu, Finland: "The five main reasons are the success of pre-service teacher education, the culture of the teaching profession, the success of in-service teacher education, the different efforts which have been made to develop mathematics education and the daily traditions of school life in Finland "
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@ Zoi Amprazi, I read some articles or books by East Asian and Western math educators. Maybe East Asian and Western math scholars use different approaches in teaching.
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I have been struggling to find the fundamental equations behind infiltration and runoff processes modeling in WOFOST; I am mostly looking for a mathematical description of the modelling approach, however any kind of info related to these two processes (within WOFOST) is more than welcome.
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Dear Dusan,
The same applies to your answer. It does not answer my question. Those are indeed interesting references about the topic but none of them addresses the mathematics behind these two processes within WOFOST.
Thank you anyway. Best regards
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Hello.
I am trying to quantify the accuracy of my western blot. I have loaded cell extracts with increasing protein content. My alpha-tubulin loading control intensities seem to be relatively constant (which makes no sense to me because they should theoretically increase with protein content). Does anybody know how I can mathematically quantify the accuracy of my Western blot with the band intensities?
Thank you.
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I agree with Dr Chandak. I assume that your alpha-tubulin loading control is the second band. It doubled in size accordingly. You can use ImageJ to quantify your loading control intensity and your protein target intensity. Then, normalize your values in percentage to the loading control.
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To me, an Erdös number seems like a harmless piece of trivia, akin to having the same astrological sign as some celebrity or sleeping in the same hotel room that a famous person had once slept in. I realize that a network of linked Erdös numbers may have interesting topological properties, but other than that, do they show anything of general significance?
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If E(x) represents Erdős number, then
E(x): H→R
is a mapping, where H is the set of all human beings, and N is the set of nonnegative integers.
H is an increasing variable set with time.
The solution of E(x)=0 has a solution x ∈ K where K is the set of all humans who are not co-authors with Erdős and not any co-author of any co-author of Erdős up to any order!
K is a nonempty set almost all elements in H are in K except a very few.
E(x)=1 has a few numbers of solutions, that is x∈C, where C is the set of co-authors of Erdős and the cardinal number of C is 511.
Now I raise the following question:
Assume that r >1 a positive integer. Is E(x) = r solvable?
In other words Is E(x) onto?
Another important question: What is E(Erdős)?
If the answer is E(Erdős) = 0 because Erdős is not a co-author of himself.
But on the other hand: Erdős is a co-author with some Erdős co-authors, and then E(Erdős) is not zero !
Is it a paradox like that of Russell's paradox?
Best wishes
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I have found coursed that has prerequisite of math for learning machine learning and also they provide an introduction to these but are unable to cover it entirely.
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I mean how to distribute the amplitude and phase in particular way?
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Dear Dr. Ahmed,
If i understood you, you distribute the signal states of the QAM symbols by means of the constellation diagram or phasor diagram, where one plot the state points on a two intentional diagram. It is so that the states at best distributed regularly in a square mesh with equal distance between the state points in the horizontal x direction and vertical y -direction.
In case of 16 QAM one has 16 symbols distributed homogeneously an a square whose half diagonal length is equal to the maximum symbol strength. Twice its projection distance on the x or the y direction has equidistant four points representing 4 states. In this way one divides the square into square mesh with distance dx=dy= 2 projection distance/3.
For the figure please follow the link: http://ecelabs.njit.edu/ece489v2/lab5.php
So given the coordinates of the points one can calculate its angle and the magnitude of the vector connecting this point to the point of origin.
Best wishes
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I would like to know how the predicted R-Squared are calculate because I want to use it to determine whether I am overfitting a my regression model by including to many terms, based in Mr. Jim's blog http://statisticsbyjim.com/regression/interpret-adjusted-r-squared-predicted-r-squared-regression/
There is some way that it can be automatically calculated by SPSS or do we need to calculated it by hand?
NOTE: I am using SPSS, just in case if someone has a particular advice.
Thank you in advance!
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Within SPSS. Use the the Save option in the regression menu/syntax to save the deletion residuals. Use compute to square them and then sum those squares. That gives you PRESS. RSQ PREDICTED = 1-(PRESS/SSTOTAL) as noted above.
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I am currently working on a final year project which involves the aerodynamics around an airfoil.
while I am familiar with the post processing activities with CFD software, I am not entirely sure how I can attain the Lift Coefficient (Cl) data from the CFD pressure and velocity data.
I know the mathematical relationship between Cl and Cp (pressure coefficient) but surely there must be a way to directly extract Cl from the Cp calculated by the software.
Thanks.
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following
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In fact, this problem has been deeply troubling us:
1. Are “infinite sets” in present set theory “actual infinite sets” or “potential infinite sets”?
2. Are infinite elements in infinite sets “actual infinite many” or “potential infinite many”? If they are “actual infinite many”, how can we conduct the quantitative cognitions to them; and if they are “potential infinite many”, how can we conduct the quantitative cognitions to them? If Set A has more eliminates than Set B, can we say “Set A is more infinite than Set B”? can we really have “infinite”, “more infinite”, “less infinite”, “more more infinite”, “less less infinite”, “more more more infinite” “less less less infinite”, “more more more more infinite”, “less less less less infinite”, “more more more more more infinite”, “less less less less less infinite”, “more more more more more more more infinite”, “less less less less less less infinite” and “more more more more more more more more infinite”…?
3. What kind of mathematical tool of “one-to-one correspondence” is? When we conduct the quantitative cognitions to different infinite sets with “one-to-one correspondence” tool, is it “one element corresponding to one element” or “many elements corresponding to one element” or “many elements corresponding to many elements”, is it “potential infinite many elements corresponding to potential infinite many elements” or “actual infinite many elements corresponding to actual infinite many elements” or “potential infinite many elements corresponding to actual infinite many elements”?
4, can we have many different bijection proofs with different one-to-one coresponding results between two infinite sets? If we can, what conclusion should people choose in front of two opposite results, why?”
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Check the references on cardinal numbers in my original. Cardinal numbers are the way we measure the size of sets - and yes one infinite set can be larger than another. The reals are "more infinite" than the natural numbers or rational numbers. If X is a set the carnality of the power set of X which is the set of all subsets of X is larger cardinality that X. The cardinal number alpha-null is the carnality of the natural numbers, rationals, algebraic numbers over the rationals, etc. The cardinality of the continuum is the cardinality of the real numbers, normally represented by c.
Cantor address all the issues you discussed in what is known as Cantor's theorem.
In other words there is an infinite number of infinities and they are expressed by the cardinal numbers.
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Do you think that the iThenticate/CrossCheck/Similarity Index would cause heavy and serious confusion in mathematics? Even destroy, ruin, damage Mathematics? Our mathematics and mathematicians should follow and inherite symbols, phrases, terminology, notions, notations in previous papers, but now we have to change these to avoid, to escape, to hide, to decrease the iThenticate/CrossCheck/Similarity Index! It’s very ridiculous for mathematics and mathematicians! Mathematics is disappearing! being damaged!
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Yes! Even standard mathematical symbols and notations are captured in similarity index. The habit of using unconventional symbols and notations just to reduce similarity index is destroying the beauty and taste of mathematics.
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I have a series of (x,y) data that should be fitted by an equation (In order to find the equation parameters: A, D, T).
In the fitting tab of OriginPro software, the software needs some initial values for parameters.
How these initial values must be determined?
Equation: y=A*exp(DT/(T-x))
Parameters: A, D, T
The datasheet is attached.
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regarding to the literature, I try some meaningful initial values but by the changing initial values the final parameters values will significantly differ
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Dear researchers , I'm a student in Master 1 (EDP) , and am a beginner in research , I have one international paper entitled " A new special function and it's application in probability " , I want people here to Give me comments to improve that research for the futur contribution in mathematics ? , Now I want theorist in probability and numerical analyis to give us any constrictive opinion about that research in all needed sides , For checking that paper via the journal webpage , just to check this link , Thanks som much for any comments or any kind of help.
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If you have developed a new probability density function, this first suggests that you have taken into account a new phenomenon that needs to be estimated and that is not adaptable to classical probability laws.
If so, how would it facilitate a way of life, phenomena that are difficult to measure with certainty in the present, and that merits the trouble of evaluating its chances of being realized?
Or, what information or role does it assume in other disciplines: in medicine, physics, statistics, demography, risks, etc.?
Science is a kind of molecule, that is to say, which attaches, although it is specific, to other external notions. In this case, how to adapt this theory in others to facilitate its application in the real world.
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Do you think research results have been applied in practice to mathematics applied with other sciences?
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Yes to some extent. But the applicable concepts in maths I have always said is lacking in my country, especially in the Senior High School level.
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The problem disclosed by Zeno’s Paradox is still there and the exactly same idea is still working well. Let’s see one of the modern versions of Zeno’s Paradox
1+1/2 +1/3+1/4+...+1/n +...                                  (1)
=1+1/2 +(1/3+1/4 )+(1/5+1/6+1/7+1/8)+... (2)
>1+ 1/2 +( 1/4+1/4 )+(1/8+1/8+1/8+1/8)+...         (3)
=1+ 1/2 + 1/2 + 1/2 + 1/2 + ...------>infinity                        (4)
Such an antique proof (given by Oresme in about 1360), though very elementary, can still be found in many current higher mathematical books written in all kinds of languages.
Here, with limit theory and technique, we see a “strict mathematically proven” modern version of ancient Zeno’s Paradox:
1, in Harmonic Series, we can produce infinite numbers each bigger than 1/2 or 1 or 100 or 100000 or 100000000000000000000 or… from infinite infinitesimals in Harmonic Series by “brackets-placing rule" to change an infinitely decreasing Harmonic Series with the property of Un--->0 into any infinite constant series with the property of Un--->constant  (such as Un’ >10000000000000000000000000) ;
2, the “brackets-placing rule" to get 1/2 or 1 or 100 or 100000 or 100000000000000000000 or… from infinite items in Harmonic Series corresponds to different runners with different speed in Zeno’s Paradox while the items in Harmonic Series corresponds to those steps of the tortoise in Zeno’s Paradox. So, not matter what kind of runner (even a runner with the speed of modern jet plane) held the race with the tortoise he will never catch up with it.
Lacking the systematic cognition to “infinitesimal”, no one in the world now can answer following question scientifically and this is the very reason for many “suspended infinite related paradox families” in present classical infinite related mathematics:
Are “dx--->0 infinitesimal” in calculus and “Un--->0 infinitesimal” in Harmonic Series the same things? If ”yes”, why we have totally different operations on them? If ”no”, what are the differences and how to treat them differently and why?
--------Could anyone tells how many items of “Un--->0 infinitesimal” in Harmonic Series you use to produce the first Un’ >10000000000000000000000000, how many items of “Un--->0 infinitesimal” in Harmonic Series you use to produce the second Un’ >10000000000000000000000000, how many items of “Un--->0 infinitesimal” in Harmonic Series you use to produce the third Un’ >10000000000000000000000000?
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Five of my published papers have been up loaded onto RG to answer such questions:
1,On the Quantitative Cognitions to “Infinite Things” (I)
2,On the Quantitative Cognitions to “Infinite Things” (II)
3,On the Quantitative Cognitions to “Infinite Things” (III)
4 On the Quantitative Cognitions to “Infinite Things” (IV)
5 On the Quantitative Cognitions to “Infinite Things” (V)
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The emergence of new infinite system (new 'infinite' idea, new number system and new limit theory) determines the production of "new mathematical analysis". The mathematical analysis based on the classical infinite system is called "classical mathematical analysis", and the mathematical analysis based on the new infinite system is called "new mathematical analysis (the fourth generation of mathematical analysis)".
There is no infinite related mathematical analysis without the “infinite related number forms”. So, the “quantitative cognizing work on infinite related number forms” is an important and unavoidable task for mathematical analysis. But our studies have proved that in present mathematical analysis, people have been admitting the being of “potential infinite, actual infinite” concepts, unable to deny their qualitative differences and the important roles they play in the foundation of present classical infinite theory system and, unable to deny that the present classical mathematical analysis is basing on present classical infinite theory system. The fact is: on the one hand, present classical mathematical analysis can not avoid the constraining of “potential infinite--actual infinite” concepts and their relating “potential infinite number forms--actual infinite number forms”; on the other hand, no clear definitions for these two concepts of “potential infinite--actual infinite” and their relating “potential infinite number forms--actual infinite number forms” have been constructed since antiquity, thus naturally lead to following two unavoidable fatal defects in present classical mathematical analysis:
(1)it is impossible (unable) to understand theoretically what the important basic concepts of “potential infinite, actual infinite” and their relating “potential infinite number forms--actual infinite number forms” are. So, in many “qualitative cognizing activities on infinite relating mathematical things (infinite relating number forms)” in present classical mathematical analysis, many people actually don’t know or even deny the being of “potential infinite, actual infinite” concepts and their relating “potential infinite number forms--actual infinite number forms”--------the “qualitative cognizing defects on infinite relating mathematical things (infinite relating number forms)”.
(2)it is impossible (unable) to understand operationally what kind of relationship among the important basic concepts of “potential infinite, actual infinite”, their relating “potential infinite number forms--actual infinite number forms” and all the“infinite number forms as well as their quantitative cognizing operations” are. So, in many “quantitative cognizing activities on infinite things (infinite number forms)” in present classical mathematical analysis, many people have been unable to know whether the infinite relating number forms being treated are “potential infinite number forms” or “actual infinite number forms”, no one has been able to avoid the confusing of “potential infinite number forms” and “actual infinite number forms”, no one has been able to know whether or not treating “potential infinite number forms” or “actual infinite number forms” with the same way or different ways. What is more, many people actually don’t know or even deny the being of “potential infinite number forms” and “actual infinite number forms”--------the “quantitative cognizing defects on infinite relating mathematical things (infinite relating number forms)”.
The above two fatal defects have decided since antiquity the absence of “infinite carrier theory” and the confusion of “abstract infinite concept and its concrete infinite mathematical carrier” which have been making us impossible to construct the scientific and systematic theory of “infinite related concrete number form (the mathematical carriers of abstract infinite concept)”, impossible to construct the “potential infinite--actual infinite” relating number forms as well as the “potential infinite--actual infinite” relating number system and its relating treating theory, thus unavoidable forming an insurmountable obstacle in the “quantitative cognizing process on infinite things (infinite number forms)” in present classical mathematical analysis. And, it is impossible to know what those “’both potential infinite number forms and actual infinite number forms’, ‘neither potential infinite number forms nor actual infinite number forms’ mathematical things” are, and can only treat all of them with the “flow line (pipelining)” unified approach (such as the three formal languages in three generations of mathematical analysis: before standard analisis, standard analisis, non-standard analisis). So, many members of different infinite related paradox families in present “potential infinite--actual infinite” based classical mathematical analysis have been produced one by one naturally (the newly discovered “strict mathematical proven” Harmonic Series Paradox is a typical example), forming a thousands-year old suspended huge black cloud of paradoxes over present classical infinite related science and mathematical analysis.
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The paper “REAL” ANALYSIS Is A DEGENERATE CASE of DISCRETE ANALYSIS
by Doron ZEILBERGER (for a copy see http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/real.pdf) seems to be relevant to this discussion:
" Continuous analysis and geometry are just degenerate approximations to the discrete world, made necessary by the very limited resources of the human intellect. While discrete analysis is conceptually simpler (and truer) than continuous analysis, technically it is (usually) much more difficult. Granted, real geometry and analysis were necessary simplifications to enable humans to make progress in science and mathematics, but now that the digital Messiah has arrived, we can start to study discrete math in greater depth, and do real, i.e. discrete, analysis."
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I have a set a={x1,x2,x3}, b={y1,y2,y3} and c={z1,z2,z3}. X are financial variables from my dataset, Y and Z are financial variables from other dataset. Each value is in thousand dollar. I want to find which set (set b or set c) is closer to set a. So, I used the euclidean distance. But, the resulted distance is too big because the difference between value is thousand of dollar. Hence, I divided each distance with the mean of set a to make it smaller with range of 0-1:
Distance (b,a) = euclidean(b,a)/mean(a)
Distance (c,a) = euclidean(c,a)/mean(a)
I'm not sure if this is mathematically correct or not. Is there any better way?
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What you can do is the following - MATLAB
v = norm(vectorA)+norm(vectorB);
if v ~=0
distance = 1- norm(vectorA-vectorB)/v;
end
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Mathematics has been always one of the most active field for researchers but the most attentions has gone to one or few subjects in one time for several years or decades. I'd like to know what are the most active research areas in mathematics today?
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Mathematics is a science that creates, models, describes, explains, applies, and of course its areas of research are always new. Ask about a branch in recent development and of interest to the scientific community is to prepare to find countless answers. Of course, the investigator's self-interest will guide him to appropriate topics.
I have read some answers to this question, published in this medium and I am surprised. They do not do science a favor with them.
What is the reason for writing " Physics will beat mathematics — look at my reform! " . What reform? Somebody knows about that reform?
Physics is a great science, and from its observations mathematics has developed very serious theories (Fourier - Heat, Gauss - sound). They were times of illustration. And conversely, Physics has found that without the development of mathematics there are many observations that could not be modeled.
But, returning to the initial question, I think you should look for an answer, and in that I agree with @ Mirjana Vukovic , if your interest is in pure or applied mathematics.
Greetings from Venezuela
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Dear Researchers Fellows,
I am seeking a post doctoral position in mathematics education working on integrating technology in teaching and learning mathematics or educational measurement.
Any suggestion is highly appreciated.
Best regards,
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Eric Hsu's website (which was created in cooperation with the SIGMAA on RUME group) lists multiple resources for positions in mathematics education as well as more general resources:
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Considere a completely randomized design, where every unit is randomly assigned to a treatment group. Let's say we have 30 observations and 3 treatment groups. When we choose one observation at random, it has 1/30 of chance of being selected, then the second one has 1/29, and so on. However, I've been told that there is a mathematical proof showing that, in the end, every single observation has the same chance of being selected to be part of a treatment group.
Is this true?
Thanks & Regards.
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If 3 observations are selected from 30 observations for 3 treatments then we will get a sample containing 3 from a population containing 30.
In this case, the probability of each of the 30 observations to be selected in the Ist draw is 1/30.
The probability of each of the remaining 29 observations to be selected in the 3rd draw is 1/28.
Now, an observation will be selected in the sample if it is selected in any of the 3 draws.
The probability that it is selected in the sample is given by
P(it is selected in 1st draw) + P(it is not selected in 1st draw).P(it is selected in 2nd draw) + P(it is not selected in 1st draw & 2nd draw).P(it is selected in 3rd
draw)
which becomes
1/30 + (29/30).(1/29) + (29/30). (28/29). (1/28)
which is equal to 3/30 =1/10
Therefore, the probability that each of the 30 observations is selected in the sample is 3/30 =1/10.
This is the required result.
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Hi,
How many mL of FeCl3.H2O solution is required to just dissolve 1 g of copper in 1 hour? Please provide the chemical and mathematical equations too!
With Regards,
Suhas D.
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Almost impossible to answer, since the time of reaction is strongly depending on the surface of copper and concentration of the FeCl3 solution . A simplified approach would be :
Cu + 2 Fe3+ --> Cu2+ + 2 Fe2+
-> 1eq Cu requires a minimum of 2 eq FeCl3 x H2O
1g Cu = 15,7366 mmol
so you will need about 31,4733 mmol of Fe(III)
in the case of FeCl3 x6 H2O (most common hydrate) [ 270,29] this amounts to:
about 8,507 g dissolved in a appropriate amount of water.
Or 31,47 ml of a 1M solution.
Now the time strongly depends on the Cu surface area and Fe(III) concentration the diffusion -> temp. and so on.
I hope this helps.
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I know how to plot a 2D real vector. Let's say I have a vector 'a' represented in a row matrix, a = [1 1]. I can plot it in xy plane and I will be getting a line having the equation x=y.
Similarly, I know how to plot a complex number. Let's say I have a complex number z=a+ib. I can plot in real-imag plane and I will be getting a similar line having the equation x=y.
But I don't know how to plot a complex vector 'c' represented in a row matrix, c = [1+i 1+i].
Kindly guide in plotting other alternate complex vectors such as [1+i 1-i], [1 i], [i 1]
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Dear Hakeem,
V = ( a+ib, c+id,e+if)= (a,c,e)+i(b,d,f):
Any complex component corresponds to a point in R^2
A vector of 2 complex components requires a representation
in R^2 X R^2 which is homeomorphic to R^4.
A vector of 3 complex components requires a representation
in R^2 X R^2 XR^2 which is homeomorphic to R^6.
The geometry of R^4 or R^6 is not attainable in general as simple as R^3 ,
but we can imagine their projections.
For physics and to tackle some problems in physics as electromagnetics
when dealing with ( sinusoidal field), the American physicists J.Willard Gibss, (1880), invented the idea of bi-vector, where the complex vector splits into two real vectors as the following: the complex vector
V = ( a+ib, c+id,e+if)= (a,c,e)+i(b,d,f)
where the real part of V=Re(V)=(a,c,e)
and the imaginary part of V = Im(V) = (b,d,f)
( following your question V = ( a+ib, c+id) (a,c)+i(b,d) )
and applying this definition, it is easily proved that :
"all multilinear identities valid for real vectors are also valid for
complex vectors"
The geometry and algebra of such representation are available in the attached paper, hope you find it useful in your research.
Best regards
PS.
The suggested presentation is not unique, we can use the tools of differential geometry to tackle such complex vectors based on the mathematical model under consideration.
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Hi everyone,
Is there some suitable mathematical or empirical law that allow us to get the stress drop of an earthquake and the corner frequency; using the seismic moment?
thank you all
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Thank you very much, it's very helpful,
thank you.
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Do you know if there is a mathematical approach (or any publication that came out with something similar) that state the age cut-off between the [(206/238)/(207/206)], and [(206/238)/(207/235)] discordancy degree calculation?
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Several papers have touched on this recently, including:
In my opinion you need to look at your own data to inform this decision.
Nick
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Is there a quantitive measurement of how equilateral a triangle? Such as the following:
Triangle A(2,3,4)
Triangle B(3,3,3)
Triangle C(10,10,1)
Is there a measurement such that 0 is a triangle that doesn't satisfy the triangle inequality theorem and 1 is a perfect equilateral triangle, assuming that a triangle's side length range is not infinity but rather constrained between (0,c].
Therefore I should get:
Triangle A = some value between 0 - 1
Triangle B = 1
Triangle C = value close to 0
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Dear Juan Gerardo Alcazar I think you are right, but you need some measure which is invariant when you apply homothetic transformation on the triangle, otherwise similar triangles would yield different results. If you do this you will see that the proposed answers are really different.
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The Monod equation is a mathematical model for the growth of microorganisms. But the mushrooms do not follow this trend as they have a phase where spawn running is carried out. Also, the biomass increase is differed from other microbes.
The attached images shows the difference.
Please tell me can we still use Monod equation to to express specific growth rate of mushrooms and substrate utilization?
or which model will be more suitable in my case?
Thanks
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Respected Mirosław Grzesik Sir,
Is it possible to derive a new model in my case, as all mushroom species follow the trends as given in the image above?
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Relativistic gamma can only be positive, in the time dilation equation.Hence , modulus of relativistic gamma has to be applied. If this error is taken into prudent account, cosmic speed of particles greater than 1kg and 1s is one-third the speed of light.Hence only meagre, kinetic relativistic effects are possible in nature.
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It is not really a mistake, you add that you only consider the positive branch of the square root so that you avoid things like when v = 0, x = - x' and things like that.
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For shell elements, is the elasticity tensor for linear-elastic & isotropic materials the same in a local curve-linear (convected) system vs. a local Cartesian system?
I wonder because intuitively, for a shell element & linear-elastic isotropic material, the only direction that matters (material-property wise) is the z direction. And in this case, the local z axis is aligned with the curve-linear coordinate system. But how do we mathematically show it?
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Let's wait the author's reply.
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If we have a matrix with both zeros and ones, in Matlab we just 'find' command to find the indexes of those nonzero elements. But how can we find it mathematically . can anyone help me with that.
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Is 1+1=0?
Is it worth to do a computation (especially for large matrices) if Mathlab finds all your 1s quickly?
If your answers are "yes", simply add the n by n matrix full of 1 to the yours. The result b_ij=0 says that a_ij=1 in the original matrix, and vice versa.
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Suppose I find 1000,00(one lakh) 2x2 matrix responding to eogenvalues : e1,e2
Then which one I will accept and which 99999 matrices to reject.
Give yoir views. My findings are mathematically correct.
B.Rath
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@Preter Breuer
In the question e1=/= e2 .
Then suggest your answer.
B.Rath
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I have been struggling to get endorsement for putting preprint in arXiv, but I a unable to get it. What is the best method to get endorsement in arXiv for physics or mathematics?
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The arXiv started the endorsement requirement for some highly demanded areas (like physics-hep) some years ago, due to the insistence of lots of cranks wanting to publish their "papers" there. The endorsement works as follows: you must look for someone who is actively uploading papers in the arXiv and has the "Endorser" flag. When you look for a preprint in the arXiv, you will notice at the bottom of the page a link like that:
Which authors of this paper are endorsers?
By clicking on it you will see who can endorse you. Look for some person who knows you or your work, then ask this person to endorse you. If she agrees, then try to submit your paper. You will receive the "need for endorsement" message, asking you to provide the mail of one possible endorser. Then, after you give the name of your endorser, she will receive an email saying:
"XYZ requests your endorsement to submit an article to the ABC section of arXiv. To tell us that you would (or would not) like to endorse this person, please visit the following URL:
The endorser will click on the link and will be asked for a code which is available in the mail. That's all, you have been endorsed.
The endorser will be reminded that she is NOT asked to judge the quality of the work, just to make a statement about her confidence in your status as a working scientist. But, of course, the first one that should be convinced about the quality of your work is yourself, because someone will have to raise her hand to support you.
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The state [uud] is given. The transposition (12) is a symmetry of this state e.g. (12)[uud]=[uud]
Let us calculate the result under acting of the cycle (132):
(132)[uud]=[duu]
But (132)=(23)(12), so
(132)[uud]=(23)(12)[uud]=
=(23)[uud]=[udu].
Where is the mistake?
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Во-первых, я никакой ни дохтур.Дорогая Ева, вы не ответили
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У вас есть сообщество почитателей Яноша Больяи?
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Если этого нет, то я буду вторым, после вас.
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First, I am not a doctor. Dear Eve, you did not answer ---------- Do you have a community of admirers of Janos Bolyai? ----- If not, then I will be the second, after you.
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FYI: "Is mathematics an effective way to describe the world?",
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Even inductive logic is ultimately deductive. One can say if A then B and if B then C, therefore if A then C. However, the first two statements are deductions as one can never be certain that if A then it is always B. the first two statements are deductive and therefore something we have found in the physical world. But that is the conclusion that our brains have come up. our brain evolved in a certain environment and was shaped by it through natural selection to function in a way that increased our chances of survival in that environment. this is the reason we do not see the blind spot as it is "filled in" by the brain to create a continuous picture of our environment. it is presumptuous to conclude that our brains would have evolved exactly the same way in another environment. this means, symbolic logic is the result of our brain evolving in a certain environment and is not something that is Absolute. This in turn means that our languages and our mathematics are the result of the evolution of our brain in a particular environment. I included mathematics because it is based on inductive logic and as we see there is really no inductive logic, there is only deductive logic and that is dependent on how our brain evolved. thanks.