Questions related to Mathematics
I have a background in maths, psychology, and partly neuroscience. My passion and vision for the future is to merge the abstract and clear-cut way of thinking of maths with the empirically proven concepts and theories of psychology to help establishing a theoretical description of brain functioning. Is there a chance to be able to work as a scientist only on this theoretical level, or do I always have to do empirical studies (fMRI etc.) on my own?
Is there any mathematical equation to determine the appropriate number of hidden layers for a sequential model?
In literature two formulae are generally used for evaluating Gravimmetric power density (Pd)
1. Pd (W/Kg) = Energy density (Whr/kg) x 3600/ discharge time (s) and
2. Pd (W/Kg) = [106 x V2]/[4 x ESR (Ohm) x mass (mg)]
But it has been found that each equation gives different result for any known value of current density. What may be the reason for it? Which equation is to be used for determining the power density of two electrode supercapacitor?
I shared the picture of three parameters 1.Change in Temperature, 2. Change in Relative Humidity, 3. Change in Pressure and respective error value for that.
From the attached data(picture and excel file attached), I need to find the Error value for different input parameter.
1.Change in Temperature = 1°C
2. Change in Relative Humidity = 1%
3. Change in Pressure = 1mbar
What is the error value?
1.Change in Temperature = 2°C
2. Change in Relative Humidity = 2%
3. Change in Pressure = 2mbar
What is the error value?
1.Change in Temperature = 4°C
2. Change in Relative Humidity = 3%
3. Change in Pressure = 2mbar
What is the error value?
Is it possible to find the error value by mathematics. Please tell the way to calculate using calculator or python programming.
is there a deeper fundamental property of neutrino oscillations? How does it work at the field level? is there any advanced mathematical connection or is only a physical fact?
I designed and made a rotary atomizer with the help of 3D printing. Now, in order to evaluate its performance, I want to measure the diameter of the produced droplets. According to mathematical calculations and theory, the diameter of the droplets is about 100 microns and I want to measure the diameter experimentally.
Please help me in this way how to experimentally measure the diameter of a drop that is produced continuously.
Maybe a stupid question, but I forgot how to calculate such things. Let's say I have a group of 200 elements (genes). I want to divide this group into n subgroups, each containing 10 elements. However, each element should be present in more than one subgroup. Is there a cool formula to calculate n depending on the number of times each element should be present in independet subgroups?
I'm solving differential equation.
u'(x) = a11(x)*u(x) + a12(x)*v(x)
v'(x) = a21(x)*u(x) + a22(x)*v(x)
or simply, U'=AU.
Given A(or, a11/a12/a21/a22) as a function of x, i want general solution for u & v.
Solution for constant A is already known, using matrix-exponential.
But this case, this is for given matrix A as a function!!!, and I found out that the same approach is not valid by my hand.
Hope any keyword or references to go further....please.
I am conducting research about Students' Perceptions on Face-to-Face and Online Mathematics Learning. One of the statements of the problem in this study is to determine if there is a significant difference on the students' perceptions between face-to-face and online mathematics learning. I will be using the Independent T-test in hypothesis testing. Now, I am struggling on what data should I use especially for the mean and n. My survey questionnaire consists of 20 items (10 items for perceptions on face-to-face learning and 10 items for online learning). I already gathered the data and calculated the weighted as well as the grand mean of both learning mode. Can I use the grand weighted mean as mean for hypothesis testing using Independent T-test? What could be the value I use for n? I have 84 respondents. If I use the weighted mean, the n would be 10 because it would be based from the items (each learning mode) in survey questionnaire. Please help me and thank you for responding!
This is my very first encounter with functional equation of this kind, and methods of series solution and differential equations are of not much help. The solution to this problem, or at least the mathematical prerequisites to understand solution to this problem is asked.
This function is asymptotically zero at both +_ infinity, positive otherwise, and has a peak near zero.
If I am correct, then this is the frequency distribution of numbers fed to the sequence xn+1=a ln (xn2) as long as the sequence generated is chaotic and sufficiently large in number (value of a is usually limited to 0.2 to 1.3, Positive and negative signs of a are essentially immaterial except for the sequence is negated after first term) .The sequence is initiated or seeded with number roughly as the same order of magnitude of 1 in both positive and negative side, except for the values that eventually lead to zero or infinity in the sequence. The sequence is allowed to proceed, and frequency distribution of numbers in the sequence are noted, from which a continuous probability distribution may be numerically guessed but not analytically found. The expression to find out formula of the continuous probability distribution comes to me from the following reasoning
- Suppose, the probability distribution is given by y=f(x). Now, if I consider a "dx" (infinitesimally) thin strip around x, then I come up with f(x) dx fraction of all points required to construct the probability distribution. When this fraction of all points are passed through yet another sequence of transformation through the recurrence xn+1 =a ln (xn)2 , the fraction of points involved must be unchanged. That is, when x is substituted with a ln x2 , the infinitesimal strip area, which changes to f( a ln x^2) d (a ln x^2), must be numerically equal to f(x) dx, thus the functional equation is postulated
- I am not entirely sure about this reasoning, and experts are welcome to point out my fault of reasoning and show the correct equation , if I am mistaken.
Please see my related question https://www.researchgate.net/post/Can-you-figure-out-Chaos-of-the-recurrence-x-n-1lnx-n2 for further details.
Hi everyone. recently I designed a customized semantic segmentation network with 31 layers and SGDM optimation to segment plant leaf regions from complicated backgrounds. can anyone help me how to explain this with mathematical expressions using image processing. thank you
I got confused when I plotted the graph of -(x^2 - x)^(2/3). the graph shows the function achieves its maxima at x =0 and x =1 but when we follow the procedure of derivatives then we get x = 0.5. Please help me in this.
I have the x,y data of two curves (solid red and blue in the attached image) and I want to find out the envelope function of the two (dashed magenta curve in the attached image). Is there a way to do it in Origin or Igor? Or in any other mathematical software for instance?
I want to integrate two carbon fiber materials together and want to model it mathematically considering the processes of joining the materials and the possible stress around the joints due to external loads.
I will appreciate if someone can recommend and the numerical methods which one is better suited for this purpose.
Thank you all in advance
In the recent paper which has been exhibited in the 51th Annual Iranian Mathematics Conference entitled "Notes on maximal subrings of rings of continuous functions" we give some
properties of maximal subrings of some classes of subrings of C(X). However, we could not answer the following two important questions in this context.
1. Is every maximal subring of C(X) unit-free (i.e., whenever R is a maximal subring of C(X) and
f is an element of R with empty zero-set, then f is a unit of R)?
2. Is every maximal subring of C(X) uniformly closed (i.e., closed under uniform topology on C(X))?
I would be very delighted if you could let me your opinion about any ideas towards approaching the answers of these questions.
I recently saw a question regarding the relationship between language and mathematical learning, but am interested in learning more about the opposite.
Can anyone recommend relevant readings that explore the relationship between mathematical ability/maths learning and language acquisition. I am primarily interested in second/foreign language acquisition, but also interest in first language acquisition and the relation to mathematics.
(This question was prompted by something I read in one of Georgette Yakman's papers on STEAM learning (2008, I believe), which suggested something along the lines that understanding of mathematics was integral to understanding language, and am interested in learning more about the topic).
Can you just assume a situation with no figures or data to back it ? Is it reasonable?
#Logic #mathematics #data
As it is well known, Linked Opend Data (LOD) and computational ontologies have great success in the fields of Life Sciences (Biology, Medicine, etc). See e.g. the big LS-cluster at <https://lod-cloud.net/>.
However, I wonder why mathematics are – in comparison – covered only sparsely by ontologies or LOD.
Indicators (to the best of my current knowledge):
- https://lod-cloud.net/datasets?search=mathematics retrieves only one result. This links to http://msc2010.org/mscwork/ which seems outdated and contains several broken (404) links.
- Since http://ksl-web.stanford.edu/knowledge-sharing/papers/engmath.html (Gruber and Olsen) there seems to be no attempt for ontological modelling of mathematics as a whole (or at least a significant portion of it).
- https://www.ebi.ac.uk/ols/ontologies gives only one hit for "math" (in browser search)
- there is no "math*" tag on https://lov.linkeddata.es/dataset/lov/vocabs?&tag_limit=0 (but there is "biology" or "geography" or "geometry")
Probably there is some (machine-processable) formalization of mathematical knowledge but it seems almost disconnected from the "semantic web" and LOD-bubble.
- Why is this?
- Should this be changed?
- If 2., how?
I need to write a MATLAB code that has the ability to process a GIS image in order to extract the coordinates of the grid points within the red region (R) and that are at least distance "d" from its boundary. Each point in the R is given a weight w1 (attached figure). The same procedure is to be made for the green region (G) but w2 is the weight of any point in G. The gathered data are saved in a matrix formed of three rows: row 1 contains the abscissa, row 2 contains the ordinate, and row 3 the weight.
I am looking forward to getting your suggestions...thanks in advance.
Hi everyone! Greetings from Munich!
It appears in my mediation analysis, that X is negatively related to M, and M is positively related to Y. Also, i find a significant negative effect of X on Y through M. But since M is determined as a perceived benefit, i am currently struggling with the interpretation of this indirect effect.
Mathematically, of course, this indirect effect result makes sense since "- x + = -", but can i interpret this by saying the benefit is overridden or is it rather that the benefit "backfires" on Y and thus a negative indirect is found?
Many thanks in advance!
Does anybody know about an mathematical optimization model which combines vendor managed inventory with fixed lot-sizes for production? That is, a model that performs a simultaneous production and delivery (transportation) planning with respect to production and transportation lot sizes.
So the keyfigures should be fixed lot-sizes for production, transportation assets, capacities and costs from vendor to VMI-stock, known demand on customer (retailer) side and inventory restrictions for the VMI-stock.
It will be also helpful if you just know about any paper or similiar which has recognized this problem.
We know many largest numbers as googol number(=10^100), googolplex number(=10^googol), and other unimaginable large numbers.
What is the largest known number that is the result of solving a problem in physics or mathematics?
Are they really practical or just based on conjecture?
using BTE how do we get mobilities and conductivity ,more calculation(mathematics) oriented answers would be helpful.
Question about the loss of hyperbolicity in nonlinear PDE: when complex eigenvalues appear, what is the effect on flow? I understand that we do not have general results on existence in this case, but is it only the mathematical tools that are lacking where can we show physical phenomena of instability?
Most plagiarism checkers don’t work because they cannot check equations and theorems which are the fundamental core of a mathematics article.
Dear Colleagues and Authors,
plenty of problems in mathematics, economics, physics, biology, chemistry, and engineering, e.g., optics, radar, acoustics, communication theory, signal processing, medical imaging, computer vision, geophysics, oceanography, astronomy, remote sensing, natural language processing, machine learning, non-destructive testing, and other disciplines, can be reduced to solving an inverse problem in an abstract space, e.g., in Hilbert and Banach spaces. Inverse problems are called that because they start with the results and then calculate the causes. Solving inverse problems is a non-trivial task that involves many areas of Mathematics and Techniques. In cases where the problem is ill-posed, small errors in the data are greatly amplified in the solution, and therefore, regularization techniques using parameter choice rules with optimal convergence rates are necessary.
Currently, I am editing a special issue on "Numerical Analysis: Inverse Problems – Theory and Applications 2021" with a Switzerland-based "Mathematics" MDPI Journal.
I would like to draw your attention to this possibility of submitting research articles:
Please let me know if you need any help.
Thank you for your kind consideration,
It is known in a input / output feedback linearization control that in a closed loop the physical state of the system is transformed into a linear mathematical state, which we have to stabilize by a linear auxiliary control, this linear mathematical state must be obtained, either by successive derivations of its outputs which is not recommended in case of implementation, or by a Luenberger observer.
In this question we want to know how demonstrate that this stabilizing linear control of the closed loop system can be developed via the physical state estimated by a nonlinear Thau observer.
While calculating channel capacity, I wish to know how path loss directly or indirectly affects the Bandwidth. Is there any mathematical relationship in this regard?
A large number of learners do not wish to study mathematics and have negative attitudes towards mathematics, including students in mathematics departments. In your opinion, what are the reasons?
Conversely, what attributes of the physical universe do attributes of the natural logarithm model?
For example, the exponential function based on the natural logarithm has itself as its derivative. That seems to model aspects of the physical universe.
What are other math-physics correspondences for the natural logarithm?
I am interested in broadening my understanding of the physical assumptions needed to simplify its mathematical description. From these assumptions i will to choose a suitable turbulence model to run the simulation in Ansys.
The problem is fairly basic;
Inlet flow conditions: Velocity in= 44.2 m/s, Mach number inlet = 0.128, atmospheric total pressure and temperature. Turbulent boundary layer thickness @ 4H upstream of the step is 1.9 cm.
Outlet flow conditions: Fully developed flow.
Any advice would be much appreciated
I have a query that
How the flatten layer in deep learning model transform pooled feature matrix into a vector??
What is the mathematical equation for flattened layer?
How can I find out the dependency of two variables from one or multiple equations.
Set 1 -
Set 2 -
How highly ( z1 and x1 ) and ( z2 and x2 ) are related among themselves and can we quantify it?
Which Set's relation/dependency of the variables are stronger in comparison with the other Set ?
How easy will it be to get back x from z from both the Sets ? Which one will be harder and how to express that ?
Creep is a time dependent process whereas MD simulation is restrictive in terms of the time scale. Hence to get appreciable strain in fs/ps time range we have to use a stress of GPa magnitude. Can we correlate this data with real-life service condition where only 10-200 MPa stress is observed. Is there any mathematical way of proving that?
I understand that we can produce that number in MATLAB by evaluating exp(1), or possibly using exp(sym(1)) for the exact representation. But e is a very common constant in mathematics and it is as important as pi to some scholars, so after all these many versions of MATLAB, why haven't they recognize this valuable constant yet and show some appreciation by defining it as an individual constant rather than having to use the exp function for that?
Recently I face some problems with the mathematical ( calculation) on the reference governor and command governor, so I need some help from you all to get which platform or journal can let me understanding the calculation. Thx
- How was the importance of the zeta function discovered ?
- why do zeta function contain so much information ?
- What other areas of mathematics does it relate to ?
- Are there any books on the RH ?
- I've heard something about a connection with quantum physics – what's that about?
- Isn't there a connection with cryptography? Would a proof compromise the security of Internet communications and financial transactions?
- What are the Extended Riemann Hypothesis, Generalised RH?
I have a symmetric airfoil with known equation. Now a sine function passes along the airfoil equation like following figure. I want to find the sine function in (x,y) coordinate system.
Terry Tao blogged about this unfortunate event. Kindly share among Mathematical community and increase awareness.
Any decision-making problem when precisely formulated within the framework of mathematics is posed as an optimization problem. There are so many ways, in fact, I think infinitely many ways one can partition the set of all possible optimization problems into classes of problems.
1. I often hear people label meta-heuristic and heuristic algorithms as general algorithms (I understand what they mean) but I'm thinking about some things, can we apply these algorithms to any arbitrary optimization problems from any class or more precisely can we adjust/re-model any optimization problem in a way that permits us to attack those problems by the algorithms in question?
2. Then I thought well if we assumed that the answer to 1 is yes then by extending the argument I think also we can re-formulate any given problem to be attacked by any algorithm we desire (of-course with a cost) then it is just a useless tautology.
I'm looking foe different insights :)
Teaching Mathematics at school to all students is commonly justified by the opinion that it improves their problem-solving skills and "makes them smarter" (whichever measure is implied by this). I wonder a few things about this:
1) If there is a clear empirical support for this opinion. Does that evidence answer the question of the causality direction between learning maths and cognitive ability? Recommendations on good literature about this would be appreciated too.
2) Do the abilities students develop improve performance for solving problems that are non explicitly mathematical. For example - learning volumes of 3D shapes could improve spatial navigation.
3) And importantly, are these improvements particularly due to teaching maths? E.g. for the previous example - wouldn't learning world maps in a geography class or spatial maze tasks develop spatial navigation more efficiently than learning calculation of volumes?
I came across a term pseudo inverse laplacian/generalized inverse laplacian. What is the impact of pseudo inverse laplacian on the graph, both in directed and undirected graph.
What is the procedure for calculating the orthonormal basis for a matrix which is equivalent to requiring that [(1/sqrt (N)*[N*1 matrix] transpose of orthonormal basis) ] is an orthogonal matrix.
In the reference paper pseudo inverse is calculated for bipartite graph while my case involves directed and undirected graphs both.
Our knowledge of the world begins not with matter, but with perception. There are no physical quantities independent of the observer. All physical quantities used to describe Nature refer to the observer. Moreover, different observers can take into account the same sequence of events in different ways. Consequently, each observer assumes a “stay” in his physical world, which is determined by the context of his own observations.
If mathematics and physics, which describe the surrounding reality, are effective human creations, then we must consider the relationship between human consciousness and reality. Undoubtedly, the existing unprecedented scientific and technological progress will continue. However, if there is a limit to this progress, the rate of discovery will slow down. This remark is especially important for artificial intelligence, which seeks to create a truly super intelligent machine.
My dissertation thesis is Perceptions of mathematical ceonceptions depending on MBTI personalities. It can includes methods of solving, understanding, imaginations of math issues, etc. I would like to know if there is any research connects MBTI with solving university mathematics for example methods of solving depending on MBTI, because I was struggling to find something similar.
EDIT: instead of MBTI I should use BIG FIVE TYPOLOGY!
I am interested in the practical uses of mathematical minimal surfaces in engineering design (such as gyroids, Schwarz surfaces, etc.). Can anyone provide good examples, particularly in art and design (or nature-based design)? I am particularly interested in examples that have been physically created and used for some practical purpose or as art. However, I am having a hard time finding published work on this topic that is not purely computational.
If anyone has published work in this area, please consider sharing it in this thread so we can get a good discussion going.
I wish to develop a peer mentoring model based on the content knowledge and pedagogical content knowledge knowledge in Mathematics and technological skills. Unfortunately I cant find a standardized test/ assessment tool to determine their competence level on each domain. Hopefully some of you can help me find a link or way to find an assessment tool ? Thank you in advance
I am asking to know by you, expert in cybersecurity and mathematics, if Computer virology (the one of Cohen and Andler) is still an active field of research. That research made in France at Inria at 2000-2010 . I do not see any prosecutor and I do not understand if this is a dead branch or not. I am interested in it in order to understand malware and detect behavior.
Thank you very much for your precious help!
I have written two articles about a generalization of Multiple zeta values and Multiple zeta star values. I also presented applications for this generalization including partition identities, polynomial identities, a generalization of the Faulhaber formula, as well as MZV identities. If you are intrested check them out on my profile and give me your opinion.
Math relates numbers to other numbers. But this is insufficient for physics. Physics models which include a cause-and-effect are more useful and result in bettter human understanding. For example, current models are time reversable. If cause-and-effect is part of the calculation, the model would not be time reversable without another equation showing how energy (entropy) is expended. Further, any proposed model that was only mathematical manupliation would not be considered physics.
The parameters are:
1. Stator phase resistance (Rs).
2. Inductances (Ld & Lq).
3. Flux linkage established by magnets (V.s)
4. Inertia (j)
5. Viscous damping coefficient (F).
6. No. of pole pairs
7. Generator speed (wm)
In this link shifted functions are defined as r*(x-o)/100 (where r is the original range)to keep the range between 100. But for optimizing the functions should I generate the values of X between [-100,100] or between [o-100,o+100]? If the function is shifted by o vector then the respective ranges should also change. Because if for 0<-100 or o>100, the global optimum won't fall in the range. And even if I generate the o values between [-100,100] then the function would be shifted in the range rather than being in the range where it is well defined.
- An understanding of theories about how people learn, and the ability to apply these theories in teaching mathematics; It is one of the primary requirements for effective teaching of mathematics, and a large number of scientists have studied mental development and the nature of learning in different ways, and this resulted in various theories of learning.
I would like to invite you to submit both original research and review articles to the Special Issue on "Modern Applications of Numerical Linear Algebra" organised by Mathematics (IF=1.747) ISSN 2227-7390. For more details see https://mdpi.com/si/74727.
Considering the majority of the population, as if, they do not know as to what is their strength. This perhaps is due to their considerably lesser exposure to various possibilities, as a result under exploitation of visible potential indicators being observed perceivably reflective. This is somewhat mathematically to be calculated based on the following generic formula which could further be deepened by incorporating a finer level of referrals and parameters as per the identified essentials during the study.
Average calculated potential vs actual harvested potential vs differential potential = under or over harnessed potential
Over harnessed potential to be analyzed in terms of negative or positive impact in achieving socioeconomic equilibrium, so should be recommended to calculate in case of under harvested potential as well.
The above study should reflect socioeconomic loss vs gain due to under or overutilization of the human resource.
I would highly appreciate your view on the above.
For a function, usually sign of second derivative (and if it is zero, even/odd index of higher order derivative whose numerical value is zero) is enough to detect whether the extreme point is maximum/minimum/saddle point, if first derivative is zero. For a functional (NOT A FUNCTION), Euler-Lagrange equation plays the role of first "derivative" of Functional. However, it the RHS of Euler-Lagrange equation is set to zero and the resultant differential equation is solved, then how to find whether this function (as solution to differential equation) corresponds to minimum, maximum or saddle "point" of functional?
Unfortunately, the nature of extremum of a functional is usually declared to be "beyond the scope" of most preliminary/introductory functional analysis resources (I have not checked all). How difficult is that mathematics and what are the prerequisites to understand the mathematics involved in finding the nature of functional extremum?
Please note my knowledge on variational calculus, integral equations and transformations as well as group theory and advanced differential geometry is rudimentary.
Let T denote the circle group, that is, the multiplicative group of all complex numbers with absolute value 1. Let f : T → T be a (sequentially) continuous map, and such that f(z2 ) = f2 (z) for all z ∈ T. Then there is an integer k such that f(z) = zk for all z ∈ T.
How to predict remaining useful life (RUL) on used aeroengine and its components level?
Any standard mathematical relations for RUL?
I am on a quest to solve how a cell repairs itself through encoding-decoding of proteins. Is there any link to genetic algorithms to solve age old questions such as aging and how we heal?
I have calculated EVI2 using landsat 7 surface reflectance images and I am getting values above 1.25 (mathematical maximum for EVI2 based on the formula) in my study area (heavily vegetated). I get a range between 0.2 and 1.8. Many publications stipulate -1 to 1, especially based on MODIS data. I also did a check with Landsat 7 TOA images, and I get ranges from -1 to 1, as the publications say. Does this mean something is wrong with the Landsat 7 surface reflectance images, or should values above 1.25 still be okay?
Computer Aided Design (Cad) subject deals with the backend mathematical calculation that happens in a 3D design.
I want to ask if I can get good resources that can explain the mathematical approach behind the Adaptive Model Predictive Control AMPC MATLAB toolbox?
am not be able to find the mathematical analysis behind this toolbox even on the MathWorks webpage.
Mathematical programming is the best optimization tool with many years of strong theoretical background. Also, it is demonstrated that it can solve complex optimization problems on the scale of one million design variables, efficiently. Also, the methods are so reliable! Besides, there is mathematical proof for the existence of the solution and the globality of the optimum.
However, in some cases in which there are discontinuities in the objective function, there would be some problems due to non-differentiable problem. Some methods such as sub-gradients are proposed to solve such problems. However, I cannot find many papers in the state-of-the-art of engineering optimization of discontinuous optimization using mathematical programming. Engineers mostly use metaheuristics for such cases.
Can all problems with discontinuities be solved with mathematical programming? Is it easy to implement sub-gradients for large scale industrial problems? Do they work in non-convex problems?
A simple simple example of such a function is attached here.
Problem: 5 minutes of play are worth more than an hour of study
Knowing that: G = Game S = Gtudy 1 hour = 60 min
The mathematical formula that defines the statement is: 5 x G> 60 x S The quantitative ratio of the minutes expressed in the mathematical formula can be simplified: 60: 5 = 12, therefore the simplified mathematical formula is: G> 12 x S
So, 1 minute of play is worth more than 12 minutes of study Or it can be said that: game G is worth more than 12 times than study S.
Therefore, the quantitative value of physical objects (or of spatial and / or temporal quantities) must be calculated differently from the qualitative value of human life experiences.
Explain why it is possible___________________________________________________________________
(Exercise based on Fausto Presutti's Model of PsychoMathematics).
I only have one sample size. I want to find if there is a significance difference between BSED-Math Students' Perceptions on Face-to-Face and Online Mathematics Learning.
If it makes easier, assume that f is continuous on [0,∞).
Specifically, I know that there are discontinuous everywhere solutions f of the given equation. I also know how to prove that, if f is continuous at 0, then f(x)=0 for all x∈ℝ. I don't know what gives the assumption of continuity of f at a non-zero point?
In several discussions, I have often come across a question on the 'mathematical meaning of the various signal processing techniques' such as Fourier transform, short-term fourier transform, stockwell transform, wavelet transform, etc. - as to what is the real reason for choosing one technique over the other for certain applications.
Apparently, the ability of these techniques to overcome the shortcomings of each other in terms of time-frequency resolution, noise immunity, etc. is not the perfect answer.
I would like to know the opinion of experts in this field.
In recent years, many new heuristic algorithms are proposed in the community. However, it seems that they are already following a similar concept and they have similar benefits and drawbacks. Also, for large scale problems, with higher computational cost (real-world problems), it would be inefficient to use an evolutionary algorithm. These algorithms present different designs in single runs. So they look to be unreliable. Besides, heuristics have no mathematical background.
I think that the hybridization of mathematical algorithms and heuristics will help to handle real-world problems. They may be effective in cases in which the analytical gradient is unavailable and the finite difference is the only way to take the gradients (the gradient information may contain noise due to simulation error). So we can benefit from gradient information, while having a global search in the design domain.
There are some hybrid papers in the state-of-the-art. However, some people think that hybridization is the loss of the benefits of both methods. What do you think? Can it be beneficial? Should we improve heuristics with mathematics?
In the lands with ancient plain sediments, the courses of rivers change dramatically over time for easy movement and the arrival of rivers to an advanced geomorphic stage.
Are there mathematical arrays that achieve digital processing such as spectral or spatial improvements or special filters to detect buried historical rivers?
In the definition of a group, several authors include the Closure Axiom but several others drop it. What is the real picture? Does the Closure Axiom still have importance once it is given that 'o' is a binary operation on the set G?
I am considering to send my research about Sophie Germain primes and it´s relation with primes of the form prime(a)+prime(b)+1= prime(c) and prime(b)-prime(a)-1= prime(c)
Mainly you have to send a mathematic research but others science researchs are accepted too. I don´t know the level of the contest but my chance is that my research i´ts have a deep relation with the work of Sophie Germain.
Do you have any recomendation of the form to present my work and the form of write to the responsables of the prize?
For any given function f : [a, b] → R, there exists a sequence of polynomial functions converging to f at each point where f is continuous. (Note that we did not ask the convergence to be uniform).