Mathematics - Science topic

Dr. Juan Weisz, that's very useful. Could you elaborate more on the game. The psychological aspect of it to be specific. Thank you.

Dear Upaka Rathnayake

This article might help you

Please follow this discussion https://www.researchgate.net/post/How_to_train_Neural_Network_with_different_input_and_output_sample_size#view=5efc9cc96fe63d251d01e592

I am not in this area. Please remove me from your list.

I am not in this area. Please remove me from you list.

📷Preston Guynn. added a reply on June 19, 2019:

Force, mass, and energy are a parallel set of descriptions of the effects of special relativistic Thomas Precession. All matter and space, and their interactions are described with distance in three dimensions, time, and their derivatives.

Newton's first law of motion is , "Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it."

Yet the concept of motion requires at least two objects, and if there are two objects, then there is always an external force, which is gravitation.

So the idea of rewriting Newton's laws without force (or mass or energy) is good, but it should be extended to incorporate the most basic non-linear effects of motion in space time, which are special relativity and Thomas Precession.

See my article describing the recent discovery of the effects of Thomas Precession the particle and galactic scales.

Article Thomas Precession is the Basis for the Structure of Matter and Space

Recommended / Share

Please read this useful paper:

You could use MathCityMap@home (www.mathcitymap.eu). You can create a learning path with hints and immediate solution check and chat synchronously with the students in the Digital Classroom!

When is an integral well defined? First, if the integrating function is integrable (in this case it is); second, if the domain of integration makes sense and is non-contradictory, then the final answer is that it depends on domains A1 and A2. What I do not understand is what the two additional integration variables mean, therefore I suppose that in the domains A1 and A2 the limits for z and η are included. If not, it is a meaningless integral.

It seem like, only few studies are talking about problem-solving skills, especially in Africa. Busy trying to find more articles but its hectic.

@Anton: Thanks for sharing your comment with me. To round e using exp to say 3 digits we would type round(exp(1),3). Instead if e is defined in MATLAB by en, say, then we would type round(en,3). The former requires two function calls while the latter would require only one call. In terms of speed, the latter is reasonably faster.

@Colin: Good point. That’s why I suggest to define e as a constant instead. In most common floating-point systems, one typically use double-precision floating point representations; thus working with about 16 significant digits—with the last digit being a random junk digit in certain computations. So, defining e by this finite range of digits is very practical.

@Emad: Salam Alaikom my deer friend, colleague, and one of my favorite teachers who ever taught me. I feel so delighted that you shared your comment here in this forum. You have a point indeed that this would be a kind of redundancy. But it remains important to ask: why should we evaluate exp at x=1 when e is a very known value? In almost all algorithms I developed in my career so far, I frequently use constant parameter inputs defined as double-precision numbers, i.e. are represented by 16 significant digits. In double-precision floating-point systems, this is typically the case. So why should we ask MATLAB to compute exp at x=1 when we can use its 16 significant digits representation instead. This would be faster and computationally more efficient. How about other important constants like the golden ratio which does not occur redundant with other functions? Why should we calculate them when their values are very known values? One of the reasons MATLAB Developers are proud of is that they have a huge library of functions that can help programmers and users to do certain tasks with minimal programming efforts, but they fail to have even a decent library for important mathematical constants. If they define these constants, we could use them directly in our works without having to calculate them using other functions or formulas. To calculate an expression like sin(exp(1)*x)+3*exp(1), why should we ask MATLAB to calculate the exponential function twice at x=1, when we could easily define exp(1) as a constant, say en, and type sin(en*x)+3*en; this would be faster and computationally cost effective indeed. Of course, if one needs more accuracy than 15 or 16 significant digits, we can then ask MATLAB to evaluate the exp function at x=1. But I, as a computational mathematician, never used more than 16 significant digits in all my previous works except when I wanted to compare my approximations with the exact values of the solution—I typically prefer to use MATHEMATICA in this case. Once again I thank you for sharing your smart comment with us. Stay safe my dear teacher.

This Link Maybe Useful:

Many thanks for engaging with my question and for the links. John Mendy raises an uninteresting idea about contextualising COVID-19 reports so that they tie the science and mathematics to a much more human level of reporting that might help the public connect with the stories rather than switching off from too much technical reporting that doesn't seem to involve real people.

This link maybe useful:

This link maybe useful:

Good Answer Muhammad Ali

Are you asking for a list of references related to technology-based pedagogies in mathematics education? If so, get started with ...

Svela, A., Nouri, J., Viberg, O., & Lechen, Z. (2019). A Systematic Review of Tablet Technology in Mathematics Education. International Journal of Interactive Mobile Technologies, 13(8), 139-158. doi:10.3991/ijim.v13i08.10795

Donnelly-Hermosillo, D. F., Gerard, L. F., & Linn, M. C. (2020). Impact of graph technologies in K-12 science and mathematics education. Computers & Education, 146. doi:10.1016/j.compedu.2019.103748

Cullen, C. J., Hertel, J. T., & Nickels, M. (2020). The Roles of Technology in Mathematics Education. Educational Forum, 84(2), 166-1

Akkan, Y. (2012). VIRTUAL OR PHYSICAL: In-service and Pre-Service Teacher's Beliefs and Preferences on Manipulatives. Turkish Online Journal of Distance Education (TOJDE), 13(4), 167-192.

"Random Seed: Definition" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/random-seed-definition/

Nice question

This link is useful,

https://pdfs.semanticscholar.org/0486/c642bda08a9d5f4ba672e9716cde3be34f30.pdf

The whole field was triggered by Shor's invention of his fameous factoring algorithm for quantum computers. 25 years and billions of $ later, it is still not possible to factor the number 15 by using this algorithm, and there are no visible reasons to believe that this wonderful breakthrough might happen within the next 25 years. This simple FACT gives us an idea of the perspectives for QC

Please see this paper:

This link talked about the importance of Math:

https://www.piday.org/10-reasons-why-math-is-important-in-life/

They can describe surface roughness of materials Mandelbrot

"factor analysis" is the phrase often used when both the observed and latent variables are assumed interval (or metric). It is part of the general latent variable model, and when the observed variables are binary this is usually called item response theory (IRT) or latent trait modeling. So it you are wanting latent variable models with binary observed data see the package I suggested above, mirt.

Please see this useful link:

https://plato.stanford.edu/entries/reasoning-analogy/

I'm not sure why there's any discussion here. The equation of a straight line is y = mx + c. This is an inviolate mathematical formula. The equation itself justifies nothing - it's perfect. Data sets are fitted with an appropriate model which in the case of a linear fit is usually a least squares procedure. The equation itself tells you nothing about the data going into that best fitting procedure. The 'goodness' of the model is assessed by deviations from that model. Here correlation coefficients (e.g. R²) can be employed. So, the equation on its own tells you nothing about whether that model is appropriate or not. How close theory and practice are, however, tells you something about the appropriateness of the model. Be careful with 2 things:

I think, systems dynamics and regression models.

I agree with Hamed Majidian : Results that are textbook knowledge do not necessarily require a reference. And in most cases a reference to the original source would be useless unless you really used that original. Typically, I'd cite rather a comprehensive textbook.

Please be aware: Citations serve two purposes:

I don’t think Scopus advertises the magazines in its database. I have another question Is the list of journals covering the math direction to the scopus database for 2020 approved?

To Salah Mehdi Salih,

Thanks for reply!

Victor Christianto , Nice Topic.

Following.

Paradox is in the contradiction between narrow energetic widths of transmitter and receiver, because of long decay times, and wide spectral width of wave packet, because of short interaction time.

As a possible explanation it can be the consideration the process as a virtual, which expressed the Feynman diagram.

Nice Dear Nik Smidt

Obviously you need to define in detail which parts of the enormous system, that we may call "the logistics network." What do you want to capture with your model?

Also: before you start something new, do you know what parts of this enormous system you would like to provide a model for? You will definitely need to scale down from the global chains of transport and logistics - so what parts are you interested in? What is the purpose of this exercise? Could you, for example, start by reading the recent years of logistics networks papers, so that you can see what the models need, in terms of data, for example? Do you want to collaborate with a logistics partner, in order to obtain real data?

There are lots of questions to be answered, as what model you end up with will determine what questions will be possible to answer. This is not a five-minute exercise, but a PhD project, perhaps with actual partners from logistics.

Nice Topic , Following

Mathematical models will never simulate human behavior precisely.

Different models show different results. So, if some model provides some precise conclusions about some community, it is not necessarily the same for the others.

People's insights, morals, freedom, and responsibility are very complicated to be captured and recorded in exact equations or tables. Some approximated partial results are accepted for making decisions about some phenomenon.

Robert Shour,

No truer words were ever spoken. I am somewhat reminded me of the "Two Cultures of Mathematics" discussions that went on in the wee hours between mathematics graduate students. That is the "problem solvers" vs. the "theory builders." Some subjects lend themselves to problem solvers, say analytic number theory which requires everything including the kitchen sink to be thrown at it and on the other hand algebraic number theory which has volumes theory laid as foundations. Paul Endros was maybe the King of the Problem Solvers and Michael Atiyah the King of the Theory Builders.

Of course most mathematicians are somewhere between and broad theories all start out addressing a problem - often with long historical roots. Which category a mathematician falls in is more a matter of temperament and personality than a choice and most mathematicians most likely move between the two. There are those that focus on a problem and during that focus understand what assumptions can be loosen so that the solution is not just of a specific problem but a theory for a much larger category of problems.

Often times one sets out to develop a theory - hoping to apply it to a larger category of problems just to find the assumptions required in the theory are not satisfied by the candidate problems one is trying to address. This happened in the 1960's in what was termed global analysis where problems in the calculus of variations were to be viewed as critical points of functions on infinite dimensional manifolds - with a broad robust calculus developed to apply to this critical point theory similar to Morse theory for function on finite dimensional space to variational prolems. Smale's condition C, now know as the Palais- Smale compactness condition was required for the functional calculus. After this beautiful theory was developed, it turns out that most of the classic problems in calculus of variations do not satisfy condition C. The utility envisioned for this theory - did not fully materialize.

While those that focus on expanding the tools of theoretical physics often find that they make progress by starting with examples (specific problems) and exploring the commonality. For me the solution of the problem (or a category of similar problems) is the key and I lose interest in working to expand the conditions under which the results still hold. As Gauss says once a problem has been wrestled to the ground and tamed, time to move on the the next challenge. But as you say that is a matter of temperament.

As far the theoretical physicists it is often - their vision needs quite a bit of help wrapping mathematical rigor around it. For example without Maurice Grossman, Einstein would not have able to present his theory of general relativity in a coherent and simple mathematical way. Without Roger Penrose, Steven Hawkins would have suffered in his understanding and explaining of black holes, singularities, big bang, etc., in a robust way. In fact on Hawkins' thesis defense, Penrose noted Hawkins' sloppy mathematics. After that the two started working together. It took Stone and von Neumann and later Segal and Bargmann to put quantum mechanics and quantum field theory as envisioned by Dirac, Pauli, Feynman, etc. on a firm robust mathematical footing that it enjoys today. So in reality I think theoretical physicists are more of the story tellers who often depend on others to fill in the details to make the story meaningful and to be able to stand up to experimental validation/falsification.

From a physical point of view, Weyl ordering provides a consistent procedure for quantizing polynomial Hamiltonians, but of course this is not enough to be preferred as a quantization method. From a mathematical point of view, its importance lies in the subsequent developments of Weyl's idea by Wigner and Moyal which, ultimately, led to the idea of star products and deformation quantization. It was proved by Kontsevich in the late 90s (in a work that gave him the Fields medal) that any Poisson manifold can be quantized following these ideas. You can see a somewhat cursory description of this line of reasoning in the introduction to a paper of mine: https://arxiv.org/pdf/1110.5700.pdf

Does this work?

One fundamental problem I am facing how to see the frequency components (in ewfd physics, frequency-domain study) in COMSOL other than the excited one( mean by the mode at other frequencies).

A very simple experiment if I take one 500nm width by 30 nm height Si waveguide (2d simulation), and excite it with 193.42 THz at port 1 end, now if I want to see the frequency components at 300 or 200 THz it should appear null or no field components. But how to observe it in COMSOL (the modes or the field components can be seen at 193.42 THz since it's the excited one).

I agree with Abdulrahman Dahash

Dear Mr.Thaisa Jawhly

I sent you a guide that can help you, also this software is open as Mr Som Pal Singh said.

Good luck.

Hi

Please check the following work. It describes the process in details. I believe it will help you.

https://www.researchgate.net/publication/284765876_Approaches_to_qualitative_research_in_mathematics_education_examples_of_methodology_and_methods

Regards

Hi, I think this material is for you:

Dear Vishwaraj B Manur,

First of all, we should separate the concept of Sampling against the concept of Sensing. These two are not interchangeable!

1. Compressed Sensing theory states that it could recover a set of coefficients (which represents in a specific transform domain the useful information from the analyzed signal) from less samples than Nyquist sampling criteria in order to be able to reconstruct a signal (of course as it could be reconstructed from uniform samples by classical Shannon theory).

2. Compressive Sampling theory states that a signal can be sampled by a protocol (non-uniform sampling, random sampling, modulation and sampling, etc.) which will allow later to be reconstructed by means of a Compressed Sensing algorithm which knows about the used sampling protocol.

3. There are at least 4 sampling ways (according to Figure 2 from https://core.ac.uk/download/pdf/34645298.pdf ) to acquire the information from a signal. Take into account that practical CS is a lossy compression, and this is due to the non-ideal process which happens when the sampling process take place.

Manim by Grant Sanderson is the best one out there at the moment.

Have a look at

Radu Bogdan Toma, posiblemente lo decimos/dicen porque se ha convertido en un término "mainstream" que permite "vender el producto" con mucha mayor facilidad.

Sospecho (y es más que una sospecha, de hecho) que este tipo de situaciones se dan con otros muchos otros constructos que se vuelven populares y son utilizados de una forma más o menos gratuíta para justificar algunos trabajos a pesar de que, realmente, no se haga uso esencial de ello.

The answer to this question can be given in different ways. Suppose the function is a linear function or a quadratic function?

the best answer is set(gca,'box','on') but in this situation the you add axis. if you want to change the thickness of axis, therefore

set(gca,'linewidth', 2) 2 can be change to an arbitrary thickness

You can find it in Google Books. D. Booth

Thank you and good luck

Have any mathematical relation for all kind of materials? إyes

see the following link.

The Zeta function is a very important function in mathematics. While it was not created by Riemann, it is named after him because he was able to prove an important relationship between its zeros and the distribution of the prime numbers. His result is critical to the proof of the prime number theorem.

For more details see

https://www.britannica.com/science/Riemann-zeta-function

Yes, I am working on such modelling for the COVID-19, and I am ready to cooperate with you in this hot topic.

Regards,

Emad

Most HEIs will have Language test and an associated test i.e. ELTs. But what is needed is a portfolio of evidence or entrance exam or written and oral tests or a combination of all three. I also know of "bridging weeks" where all tests, up skilling etc are completed as part of a pre-registration induction week

It depends on what is your application of Monte Carlo simulation. You could have different computational time reduction strategy. But generally speaking, to have a good sampling technique will make your Monte Carlo simulation much easier and more efficient. I would suggest the Latin hypercube sampling (LHS) sampling technique, which I used quite often. It will make the distribution of your samples very close to the expected distribution with small number of sample generation.

I suggest you check the following link. Hope it may be helpful. https://stats.stackexchange.com/questions/22569/pca-and-proportion-of-variance-explained

Views differed on induction, so there are those who place it within the direct approach, and there are those who place it within the types of discovery, according to the role of both the teacher and the learner. For you, you can look for a discovery-based induction or a combination of several types of discovery.

Dear Soroush,

Refer the following link and files that helpful for you about PV systems using PSCAD.

SRT is completely erroneous since it is based on the wrong kind of transformations: they have lost the scale factor characterizing the Doppler effect. First, Lorentz considered a more general form of transformations (with a scale factor), but then he, and also Poincare and Einstein equated it 1 without proper grounds. Their form was artificially narrowed, the formulas became incorrect. This led to a logical contradiction of the theory, to unsolvable paradoxes.  Accordingly, GRT is also incorrect.  For more details, see my brochure "Memoir on the Theory of Relativity and Unified Field Theory" (2000):  http://vixra.org/abs/1802.0136

Have a look at: https://arxiv.org/help/endorsement

make them happy or sad

I suggest you read : http://users.isr.ist.utl.pt/~wurmd/Livros/school/Bishop%20-%20Pattern%20Recognition%20And%20Machine%20Learning%20-%20Springer%20%202006.pdf

Dear Ernie,

I suggest you to see links and attached files on topic.

https://www.researchgate.net/publication/264422436_Psychometric_properties_of_an_inventory_to_determine_the_factors_that_affect_students'_attitudes_toward_mathematics

Best regards

Here is the paper, download from above link:

Dear all,

thank you very much for your answers and help.

I would suggest to your administration that this is a poor idea for mathematical and chemical courses at least. In these one size does not fit all.

Best, D. Booth

Mechanics. Newton's first axiom says that, in the absence of an external force, a body either is at rest or moves with constant velocity. In fact, this is a statement opposing Aristotle's view that a force is needed to keep a body in motion at any non-zero velocity.

Other than that trivial movment in the absence of a force, one might argue that quantum mechanical zero-point motion is movement without a force.

So there are several places outside music where movement appears without a force. In fact, I doubt the applicability of the same notion of movement as in physics to the "flow of notes". Movement in music is a different concept from that of movement in physics. The same word has different connotations in different fields. I believe, it would be easy to argue that with a similar change of meaning to the word force, you would find that the "flow of notes" does not happen without a force.

There is a tendency of confusing and therefore (often unintentionally) abusing notions having the same name but meaning different things in different contexts. For example, when people speak about energy they gain by meditation, this has nothing to do with an energy that might be describable by a hamiltonian or be subjected to energy conservation.

Dear Dr Kamran Zakaria

Quoting

See the details and visit

Computed Tomography (CT) Scan | Cancer.Net

www.cancer.net › diagnosing-cancer › tests-and-procedures › comput..

The following some useful papers in the topic

Study of techniques of identifying the earthquake precursory anomalies in terms of mathematical modeling

Zun-guo Yan, Jia-dong Qian, Jun-hua Chen, Sheng-le LiJournal:Earthquake ScienceYear:2000

Earthquakes in quasistatic models of fractures in elastic media: formalism and numerical techniques

Chen, Kan, Bhagavatula, Ravi, Jayaprakash, CJournal:Journal of Physics A: Mathematical and General PhysicsYear:1997

Dear Sanjay Kumar,

Convert the original and enhanced images to HSV color space first, and then, use MSE & PSNR to the V-component only.

Mental capabilities are different from one person to another and this must be taken into account by the subject teacher

Hello Masoud Masoumi Moghadam

Hope these articles will help you:

And have a look at these:

Regards

I advise you the following papers

Existence and structure of past asymptotically simple solutions of Einstein's field equations with positive cosmological constant

Helmut FriedrichJournal:Journal of Geometry and PhysicsYear:1986

Asymptotics of Solutions of the Einstein Equations with Positive Cosmological Constant

Alan D. RendallJournal:Annales Henri PoincaréYear:2004

and the books

The Role of Neutrinos, Strings, Gravity, and Variable Cosmological Constant in Particle Physics

KluwerKursunoglu B., et al. (eds.)Year:2002

Theory of the cosmological constant

Coleman.Categories:Physics\\Astronomy: AstrophysicsYear:1988

Good Luck

hi Spvnd Sumalatha ,

If a person is good in mathematics and has command over it, that means he has good logic aptitude and grasping ability. If now he want to do research in Fluid mechanics of course he can. He should start with reading the basic physics books and gradually increase the level to engineering fluid mechanics. Which, at this stage, should be a matter of not more than 6 focused months. after that he will be able to do like masters. Do not run behind paper publication from the start it will a by product of your focused learning and problem solving.

The most interesting, of a large number of tools discovered in 1960 at Ishango, is a bone tool handle called the Ishango Bone (now located on the 19th floor of the Royal Institute for Natural Sciences of Belgium in Brussels, and can only be seen on special demand)

Jack Sarfatti, Everything is wonderful, but I do not perceive it well by ear. Could you write a few words about what is relevant now that excites you and prevents you from thinking about the philosophical question of the origin of nature (the nature of things)?

You want to know the journals that one can talk to regarding which referee will be selected?

Normally that is never a concern for the scientist, as the journal typically has a long list of available referees, and also a database that tells them how quick and good they are, and what special topics they would rather be in service for.

Typically the journal will NOT pick anyone of the ones that you suggest, as they might think that they may be your friends. As an editor myself, I would hesitate picking anyone among the suggested reviewers, unless I know them, and know that they are conscientious.

The change of the imaginary part with concentration is essentially Beer's law:

If you search in Google, for " throughput equation"

https://corporatefinanceinstitute.com/resources/knowledge/finance/throughput/

The relationship between the absorption coefficient alpha and the extinction coefficient k can be expressed by the relation:

alpha= 4 pi f k/ c

f the frequency of the incident wave, and c is the speed of light.

For more details please follow the link: http://www.reading.ac.uk/ir-substrateopticaltheory-absorptionandextinctioncoefficienttheory.aspx

Best wishes

Dear Dagnachew Jenber ,

You are misreading the relation.

It is not x^s = e^sin(x).

It is x^s = e^sln(x).

the power is (s)(ln(x)).

Mostafa Gamal Emam Hussein Your question 'How to calculate mathematically SiO₂ nano particles of 50 nm size thickness on glass substrate?' does not make grammatical sense in English. Using 'Sio2' (which I have corrected in my italics above and PH (should be pH) and a density of 1.2 (no units specified; indeed g/l is a very strange - and low - density) plus a 'volume' of 50nm (50 nm) - 50 nm is a length, not a volume - shows a marked scientific confusion.

What do you want to calculate mathematically?

Only useful comment I can make is that 1000 microliters is about 50 drops.

Thank you so much! Paul Louangrath David Morse

Stay at home. :-)

First and foremost mathematical expressions do not " govern a mechanical phenomenon." The equations describe a relationship between the variables in the equations and how they evolve over time. For utility in the sciences, it is hoped the equations actually are an accurate representation of the physics in this case. The equations are a theory of how the physics behaves. Predictions can be derived from the equations. However, the final piece of the scientific method is to verify or falsify the theory through comparing the prediction to experimental data.

Or to quote Richard Feynman: "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong."

very nice question as you i wait to see the answer

According to an appendix of Matter and Mind of the late Mario Bunge, there are two kinds of truth: Formal truths of logic and mathematics and Factual truths of ordinary knowledge science and technology. Confusion between the two kinds of truth is a source of more confusion if possible. While the first kind of truth is easy to assess, even if some theoretical facts are undecidable the second lacks a well-structured formalism. Possibly you are taking of the second class of truths, so this might be associated to a perhaps neverending debate...

Although there is no direct answer to your question, it might be of interest to reconsider Maxwell's demon and Quantum Biology research.

I do recall that Prof. Capek's research--from our mutual discussions--from Charles University in Prague as he was working on a quantum model of Maxwell's demon.

There is ongoing a lot of research on Quantum Biology. It has a very bright future despite it is not, to the surprise of all, working at the absolute zero temperature as novel quantum computers.

We researchers are becoming more and more aware of the fact that QM approaches can shed light on many so far unsolvable scientific problems including the very foundations of biological functioning.

certainly

Thank you Dr. Mila Ilieva !!

Dear Muhammad Ali

It is a very general question. Distance, space and time, etc. is equivalent to define the suitable manifold structure and atlas charts that are the best to describe the environment (Universe) of your mathematical model. Concerning the question about the set of the fundamentals, say {F} that are needed to study the field or topic P. In general, the essential tools of mathematics like calculus, linear algebra, differential equations, and the undergraduate elementary mathematics are strongly needed in almost all branches of sciences. But for some specific topics, special preliminaries are needed too. Examples: (1) General topology is a prerequisite of Algebraic or differential topology. (2) Multivariable calculus is a prerequisite for optimization theory. (3) Advanced Matrix theory is strongly recommended as a prerequisite to study the dynamical systems and control theory. (4) Group theory is needed to understand Galois theory. (5) Probability theory is a must for decision making. Etc. Best regards

Check Google Scholar:

Muhammad Ali, I am glad that I met a like-minded person here, but I would like to note that mathematical models describe reality (nature) in some cases, and fantasy (invented nature) in others. My goal is to describe moving matter.

Hello Ibrahim,

Here's a resource that gives multiple examples and the implicit equations for most of them: https://www.lexjansen.com/wuss/2006/tutorials/TUT-Suhr.pdf

Good luck with your work.

I"m suggest that a research about the design of a mathematics model to measure the credit capacity of the borrower in the Iraqi environment.

It also suggested that a financial program design associate with commercial credit, accounting and and mobile payment companies