Science topic

# Function - Science topic

Explore the latest questions and answers in Function, and find Function experts.
Questions related to Function
• asked a question related to Function
Question
Edit: I updated question 1 and added a link in Section 3.1. I also explained the intuition in section 4.4.1.
I have yet to understand amenability and group theory, but the questions in my attachment might be of interest.
I would be glad if all the questions were answered; however, if you wish for a particular question, read section 4 of my paper and the question in section 5.
I want an elegant choice function where, for specific A in 4.4, gives the structure (defined in 4.2) that I'm looking for.
follow
• asked a question related to Function
Question
I'm doing a homework about finding the CpG islands within a gene of our interest. I picked the FXN gene and found 11 possible CpG islands using this website http://dbcat.cgm.ntu.edu.tw/.
I'm also supposed to find out what role do these regions may play in gene regulation and transcription however I'm lost at this point. I know that if there is a CpG island close to the promoter region, it has a role in gene silencing but all of the islands in this gene appear to be located in introns only so they don't overlap with exons either. What kind of a role CpG islands may play if they're on the non-coding sequences?
CpG's in islands located near promotors are usually methylated and play a role in gene regulation (as mentioned) while CpG's in gene regions like introns/exons tend to be unmethylated. Methylation at such sites is usually subject to persistent epigenetic remodeling as part of genome packaging and chromosome structure but tend to become globally hypomethylated with age. I would check if there is any literature on this gene having parental imprinting - a quick search I did found a few articles on the epigenetic silencing of this gene and its involvement in Friedreich's ataxia ( ) which might be relevant to what you're looking at.
• asked a question related to Function
Question
How to linearize any of these surface functions (separately) near the origin?
I have attached the statement of the question, both as a screenshot, and as well as a PDF, for your perusal. Thank you.
It seems the linearization is accomplished by replacing x1, for x1^2. And separately by replacing x2, for x2^2 & x2^4.
In this way, the surface function is linearized about the origin (0,0), it means we can find f1(x1,x2)=a*x1+b*x2, whilst a and b are calculable in terms of the algebraic parameters, k and c.
But my question transforms to another level. How, we can find a compact algebraic expression for f1(x1,x2), and f2(x1,x2), close enough to the origin. This algebraic expression, need NOT be necessarily linear (it could be a nonlinear function).
Question synopsis:
1--How to find another compact analytical expression equivalent to f1(x1,x2), f2(x1,x2)? (with fair accuracy)
2-- Is it possible to find an approximation near the origin (0,0), for f1(x1,x2), f2(x1,x2), as a function of only one of the two variables (either x1, or x2)?
Regarding the second synopsis, I am to cite another ResearchGate question linked below:
However, the gist of the idea in this link is not clear to me.
• asked a question related to Function
Question
Hello,
I established transfer functions with PAST 4.01, and I would like to input some downcore data (lake sediments, diatoms) to reconstruct past environmental change quantitatively using the transfer function.
However, I don't know how to put the data into the transfer function in PAST.
Does anyone know how to do that?
Or I appreciate any other suggestions for methods to build a transfer function and its application.
Thank you very much in advance!
I have attached the past 3 manual to this response; hopefully it its helpful
• asked a question related to Function
Question
Here we discuss about one of the famous unsolved problems in mathematics, the Riemann hypothesis. We construct a vision from a student about this hypothesis, we ask a questions maybe it will give a help for researchers and scientist.
I put together a solution of the RH myself. While it can't be considered a complete proof while not vetted by experts, it presents various strong arguments and a real breakthrough, which is the inversion formula for Dirichlet series. Given any Dirichlet F(s), you know a(n) from F(s). Unfortunately, it's impossible to have an integral representation for a(n) usually, it's a Taylor power series. Please head to my page for the paper.
• asked a question related to Function
Question
I want to perform a checkerboard resolution test of my tomographic inversion. What kind of function do people use to make the checkerboard model of low/high anomalies? Bell-shaped (gaussian) anomalies?
Bruno, did you get an answer to your question. I'm interested in the answer since I'm dealing with the same issue.
• asked a question related to Function
Question
Under what conditions the solution of nonlinear ordinary differential equations belong to the space of continouse functions? Need opinions
The solution of ODE is an Integral function, I think it always belongs to the space of continouse functions.
• asked a question related to Function
Question
Can any body tell me what is difference between 'probability density function' and 'power spectral density function' for random data like wind speed?
The probability density function p(x) is defined by the following relation:
P(x, x+dx)= p(x) dx,
x is the random variable, P(x,x+dx) is the probability to find x between x and x+dx,
dx is the interval over which one calculates the probability.
So, finally
p(x)=P(x, x+dx)/dx
As for the power spectral density it can be defined by the relation:
P(f, f+df) = p(f) df,
where p(f) is the spectral power density, P(f, f+df) is the power contained in the frequency interval df around the frequency f.
So, p(f)=P(f, f+df)/df,
So the spectral power density is the total power contained in a frequency interval df divide by the frequency interval df.
Best wishes
• asked a question related to Function
Question
Hello everyone,
I am thinking how the function should look like in order to generate this kind of curve shown below.
I am guessing the variables should be :
• the radius that increases by "x" after every half-rotation,
• how many rotations should take place before stopping.
Can anyone shed some light on this?
t = 20:0.1:40;
x = t.*cos(t);
y = t.*sin(t)
plot(x,y)
• asked a question related to Function
Question
the predicted ORFs were annotated using Batch CD-Search in NCBI and now I really want to classify their functions like the COG does.
• asked a question related to Function
Question
Hello everyone,
Please I have this transfer function model of numerator order 1 and denominator order 5. I want to reduce this to a numerator order 1 and denominator order 2 or simply a first order system with a coefficient as the numerator. How do I achieve this using MATLAB. I know of the function BALRED. But this function reduces the model to an even order for both numerator and denominator. I also know of MINREAL which is for pole-zero cancellation. This function can only cancel the single order numerator thereby reducing the denominator order by one. I would like to know if there's any function that could help me achieve this or if there's another way to go about this. Thank you!
Thank you @Guillermo Valencia-Palomo
• asked a question related to Function
Question
Hello all I need help please
How to create a function for the Renyi and Shannon formulas?
RENYI=(1/1-alpha).* log2(sum(q .^alpha))
SHANNON=-(sum (q .* log2 (q)))
• asked a question related to Function
Question
Some modular functions, such as the Riemann zeta one, display a fractal behaviour.
Does also the curve of the j-function display power law properties, or a scale free structure?
It it feasible to calculate the j-function's power law slope, or its Lyapunov exponent? Is the j-function somehow correlated with the Feigenbaum constant of logistic plots?
@ Fabio,
It seems very nice example. Did you mean the discriminant of the (Klein's J-function) ? In general, some of modular forms are Fractals.
But not all of them.
Best regards
• asked a question related to Function
Question
Hi. I am intrested in studing the Mittag Leffler type functions. Can any one suggest some book or article that discusses the orthogonality of Mittag Leffler type functions.
Dear Ali,
I would like to suggest the following for your mentioned one:
1. Four orthogonal polynomials connected to a two parameter function of Mittag-Leffler type by R. Rangarajan and P. Shashikala
3. An Introduction to Orthogonal Polynomials by Chihara T. S.
4. Orthogonal Polynomials: Computation and Approximation by Gautchi W.
• asked a question related to Function
Question
Knee locking refers to when the leg gets stuck in one position, making it impossible to bend or straighten it. It may only last a few seconds, it may last longer. It all depends on what is causing it. Most cases fall into one of two categories.
There is true locking caused by a mechanical block where something gets stuck inside the joint, preventing movement. This type most commonly occurs as you move the knee into full extension, i.e. towards being fully straight.
Secondly, there is pseudo locking, caused by severe pain which temporarily limits movement in any direction.
Unclear about the question. Although in the text is described that the locking is mechanical (due to loose bodies or meniscal and ACL tear) when usually the knee locks in flexion or the pseudo-locking, when the knee usually locks in extension, the logic of the question was demonstrated in a clear way. The common reason for pseudo-locking is patello-femoral pathology (degeneration of the articular surface of the patella or the trochlea or in rare conditions the existence of a thick plica, folding of the synovium). Nothing of all this is influenced by the diet, except if the amount of food that is consumed is excessive and is resulting to obesity. This is the only case that diet can influence the knee locking. Dietary habits can influence the uric acid and so the potential gouty synovial reaction and consequently arthritis, but this is another matter.
• asked a question related to Function
Question
Hi everyone, I would like to define a heavy side function in comsol multiphysics (flc2hs) for the variable y giving as follows.
y = '1e-6' (for t<=1e-6) or 'x' (for 1e-6<t<=0.999) or '1' (for t>0.999)
where x is a variable.
How could I do implement that ?
best greetings.
Hi Anass,
You can say it like that. My explanation would be that flc2hs simply is a heavyside funcition. Y(T). So y=0 for T<0 and y=1 for T>0. With your “x2“ you generate an T offset of step of the function.
In your example you substract Tm-T different from my example, so also the sign of the argument is changend. So You will get a function which is 1 for values smaler Tm and 0 for values higher Tm, which is what you wanted.
So normaly it should work. But if you are not sure about your function you can also plot the function to check if your syntax is ok.
Hope I was able to help you again. Seems like you are in the wright way.
Best regards
Thomas
• asked a question related to Function
Question
I have data values and try to find some kind of function that decribes these data as good as possible. The attached files are two examples (simple text files, one value per row, 1498 values). The corresponding x-values are 0, 1, 2, ... 1497.
The data starts at y=0 and the asymptote for x->inf is y = 1. Whatever I tried did not fit the data well, especially not the first 50 or so values.
If someone has fun finding a function that fits these data really well, then try your luck :)
The two data series should follow the same kind of function and should differ only in the parameter values (possibly onle in a single parameter - but I don't know for sure).
Dear all,
I have checked the fits proposed by Joachim and also tries to see if weights according to the differences between subsequent values will improve the fit. I made a figure showing the results. Black: data from "values 1", red: data from "values 2". Upper row: data & fitted curve shown in a double-log plot (1 was added to incluse the value at (0|0). This is only for plotting. The fit was done using the original data. Lower row: the residuals, multiplied by 1000, the x-axis is scaled identically to the upper plots.
The fits are impressively good, I think. They follow the data closely. There is never a larger residual than 0.005. Using equal weights, the residuals at low x are the largest. This is improved using weights proportional to the change. I also tried weights proportional to the squared change, what further improved the residuals at low x but starts having a bad influence on the residuals of large x.
I think this result is pretty good, I am happy with it and I am grateful for all your help and interest. Hoewever, I you fell that you can further improve it or come up with an entierly different model that explains the data better, feel free to let us know.
PS: I did the fit and the plot in R. Fitting was done with optim() using all defaults (method = "Nelder-Mead"). The function that was optimized was the sum of squared residuals. Weights were included as factors on the squared residuals:
# the function to be fitted with 3 parameters:
f <- function(par) 1-1/(1+par[1]*x^par[2])^par[3]
# the loss function to be optimized; y: data, w: weights
optFn <- function(par, y, w=1) sum(w*(y - f(par))^2)
# get the fitted parameters
# par: resonable starting parameters
# y: data, w: weights
optim(par=c(0.25, 0.8, 0.2), fn=optFn, y=y, w=w)
• asked a question related to Function
Question
Mann Kendall sequential test
you can use flipud in matlab, and you can get the opposite sequence.
for example:
clc
clear
cd('F:\PAPER CREAT\MK')
data=w;time=(1900:1990)';U=norminv(1-0.05/2,0,1);
N=size(data,1);n=2;nb=1;nB=2;ri=zeros(N,1);rbi=zeros(N,1);s=0;datac=flipud(data);
SFk=zeros(N,1);SBk=zeros(N,1);UFk=zeros(N,1);UBk=zeros(N,1);%data be limited in column
%in inverse order(RbI,UBK,SBK) & natural order(RI,UFK,SFK)
for n=2:N
ri(n)=sum(double(data(1:n-1)<=data(n)));
rbi(n)=sum(double(datac(1:n-1)<=datac(n)));
SFk(n)=SFk(n-1)+ri(n);
SBk(n)=SBk(n-1)+rbi(n);
UFk(n)=(SFk(n)-n*(n-1)/4)/sqrt(n*(n-1)*(2*n+5)/72);
UBk(N-n+1)=(-(SBk(n)-n*(n-1)/4)/sqrt(n*(n-1)*(2*n+5)/72));
end
• asked a question related to Function
Question
We are looking at GAF and we know that HoNOS has been used for ACT before.
Looking to measure occupational functioning.
To be effective in addictions treatment, outcomes need to be truly individualized; how deeply is the patient's addiction affectting his everyday functioning? Is he able to perform daily hygiene?
Does he need reminders? Is he able to shop and prepare meals? Does he eat 3 meals / day? measured by how much weight has been lost and is it gaining back? Is he able to maintain clean clothing, etc. Break the GAF down to parts that can be evaluated in this manner. You may want to put together a flow sheet that can be individualized. Good luck!! GBH
• asked a question related to Function
Question
Consider a continuous Lipschitz function f of the single variable and an interior point x* in a compact interval of its domain. How to use the fundamental theorem of calculus to describe f(x*) = 0? (The old version of this question was posed for C2 functions. In the current RG project this assumption was relaxed to continuous Lipschitz functions.)
There exist primal and dual characterizations of roots.
• asked a question related to Function
Question
How to take Laplace Transform of functions like sin(f'(t)) or sinh(f'(t)) where f'(t) is the derivative of another function with respect to time.
(p.s1 this information may not be relevant but f'(t) is L(f′(t)) = sL(f(t)) − f(0))
(p.s2 I was thinking of Taylor expansion of the trigonometric function before taking the Laplace transform, but I'm not sure if this is the proper way.)
In such a case, I personally prefer numerical integration of the function (using Laplace integral definition) instead of analytical methods. However, the result will be numeric but not a function. I am not sure it can be useful for your case or not.
• asked a question related to Function
Question
For system in the attachment, this system with uncertain parameter and state-dependent uncertainties, how do I choose lyapunov function for this system?
???
• asked a question related to Function
Question
.
??????????????????????????????????????????????????????????????????????????
• asked a question related to Function
Question
How you describe the functional objectives of EHR & CDSS, if EHR is a platform and CDSS is add? Which modules have to work as a lock and key?
??????????????????????????????????????????????????????????????????????????????
• asked a question related to Function
Question
Hello all! Please give tip how to find Fourier transformation for function S(x)=[Λ(x/2)⨂1/2 comb(x/4) ]rect(x/60)? Symbol ⨂ mean tensor product?. Available from: https://www.researchgate.net/post/Hello_all_Please_give_tip_how_to_find_Fourier_transformation_for_function_SxLx_21_2_combx_4_rectx_60_Symbol_mean_tensor_product [accessed May 20, 2017].
Sorry I am not a mathematician only a physician
• asked a question related to Function
Question
Can someone help me explain how the function in the picture is used in UG\Open?In UG\Open, how can I use this function to get model information and save the structure of each function member in this function?
????
• asked a question related to Function
Question
like snr=p*r^(-a)/(noise power)
you are welcome for any suggestions
• asked a question related to Function
Question
To resize a 2D image, for example in matlab, we use the function "imresize". But, if we use this function for a 3D image on every slice, the distances between voxels, according to Z axis, becomes greater then those distances between voxels according to X axis and Y axis. The resulting voxels become straight pavements not cubes.
Some ones have solution for this problem?
Thanks :)
imresize3 means 3D image resize in all axis
• asked a question related to Function
Question
When choosing th activation function for a MLP neural network want criteria can be used? It depends only on the data?
Dear Bogdan,
Choosing activation functions for MLPs depend on a couple of things as discussed below.
1. The activation function for the output layer would depend on whether you are performing classification or regression. For binary classification (i.e. problems of two classes), the Logistic-Sigmoid function can be used with binomial cross-entropy as the cost function. For multiclass classification (i.e. problems with more than two classes), the softmax function is used with multinomial cross-entropy as the cost function. For regression problems (i.e. real-value outputs), the linear/identity function is used.
2. For hidden layer units, your options would depend on the depth of your model as follows:
(a) For shallow models (1 or 2 hidden layers), the Logistic-Sigmoid, Tangent-Sigmoid or rectified linear function can be used. Here, choosing the most appropriate activation function among the aforementioned would be via experiments.
(b) For deep models (i.e. more than 2 hidden layers), the rectified linear function would become more appropriate to alleviate the problem of vanishing gradients.
I hope this helps.
• asked a question related to Function
Question
I've got a humanized bi-specific monoclonal antibody targeting to PD-1 and CTL-4. how can i verify the function of it? what experiment should be taken?
What is your purpose? First, you could test whether the antibody binds both targets, but further experiments depend on what you want to do with the antibody at the end.
• asked a question related to Function
Question
Thank you Riese, it's very helpful.
• asked a question related to Function
Question
does it mean that the two functions are not antagonists? I have solved the optimization problem using the weighted sum method in MATLAB .
thank you
I guess you are minimizing. My impression is, first of all, that you have dominated (inferior) solutions, so it is nor really a PAreto front, but a set of solutions. For a Pareto front, you should delete all dominated solutions.
Second, although the fron looks straight, my guess is that it is not, and, as usual, it is convex. You are just finding the vertices of the feasible region in the objective space.
If is were straight, there would be no way to find so many solutions...
I hope it helps.
Cheers,
• asked a question related to Function
Question
It is known that the exact eigen-functions of sturm-liouville problem are orthogonal with respect to the weight function. But what happens when the solutions are obtained using approximate analytical method?
Do the approximate analytical solutions obtained using asymptotic techniques or using WKB method orthogonal?
Logically, If the solutions are the same, orthogonality property would still be  valid irrespective of the methods that yielded the solution. However, you can subject each of the equivalent solutions to orthogonality test to be certain.
• asked a question related to Function
Question
If Colombeau's algebras existed, what led to the construction of simplified algebras?
When we are faced with an ordinary or partial differential equation, linear or non-linear, how do I decide to attack the problem by one or the other? How do I decide which one is best for each case?
What function is in the plenums, but is not in the simplified? The space of the continuous functions are not totally immersed in simplified GF?
Is there a differential equation that has a solution in one algebra in the other? Because del-bar is solved in the simplified, can also solve in the plenums?
Caro Paolo,
Best regards,
Antonio Ronaldo.
• asked a question related to Function
Question
I am doing master thesis in which I have to optimise active power flowing through HVDC link and it is installed in parallel to AC line. I need to know how can I make obective function and what would be my constraints for this function?
I have to maximize hvdc transmission power.
• asked a question related to Function
Question
I am studying the GABAA receptor composition and its function. I would like to know the difference between α 1 β 2 γ 2 and α 1 β 3 γ 2.
Dear Junichiro Ono
a specific paper does not exist on this topic but hope those papers you find above will be useful to you!
Cheers
• asked a question related to Function
Question
In my research, i came across different distributions on skew student t distribution which from the density function they are so different. I seriously need a clarification and simplicity of the skew student t distribution i.e. the density function and the cumulative function.
The generalised skewed t distribution is a family of distributions: they will all be different based on the parameters (beta, mu and sigma) that you use. The student t distribution (not 'skewed' student t) is a special case (and also a family in itself) of the skewed t distribution that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.
I hope this helps :)
• asked a question related to Function
Question
if you can added the Reference
The size of the FTIR peaks shows the amount of bond existing in the material. But the peaks in different positions should not compare with each other. You can compare the FTIR peaks of similar materials (as you in your case). If you see peak intensity is increase, then you have more of that particular type of bond. You need to make sure that the peak position is at the sample wavenumber. Any big shift in either direction tends to imply that some interaction has occurred. In addition, If the peak shape is similar, then its pretty much just more of that particular type of bond. However if the peak has broadened, then it could mean that some interaction has occurred (usually hydrogen bonding interaction).
• asked a question related to Function
Question
for dendroclimatic studies
• asked a question related to Function
Question
Is it possible to determine the temporal shape of the laser pulse from
the autocorrelation function?
The autocorrelation gives you an idea of the duration of the pulse but you cannot determine the exact shape of your pulse (several pulse shapes can give you the same autocorrelation trace). Often it is assumed that the pulse coming from a laser has a sech2 shape, and the autocorrelation is fitted based on this assumption. To better determine the temporal shape of the pulse, you need information on its phase. This can be achieved by measuring the FROG trace (Frequency Resolved Optical Gating, which is basically a spectrally resolved autocorrelation with a pulse retrieval algorithm). Other methods such as SPIDER and MIIPS can also provide this information.
• asked a question related to Function
Question
The Landauer limit L(T) = kTln2, k is the Boltzmann constant, means the energy corresponding to erasing a single bit of information. Thus, one can define t(T)=kTln2/h, h - the Planck constant. What might be the physical meaning of the so-defined function t(T) or that of its reverse function T(t)? Furthermore, t can be referred as f=1/t to the frequency of some wave having a certain physical sense.
A few general considerations might be:
1. The Planck constant means the correspondence of a dimensionless physical quantity to the quantity of action. That dimensionless physical quantity can be interpreted as entropy.
2. The Landauer limit means energy per a bit of information (entropy).
3, Action is a function of energy and time and thus, time as temperature can be interpreted as a relation (e.g. ratio) of energy and entropy.
4. Then, the dependence of time and temperature at both Landauer limit and Planck constant for both time and temperature are interpreted only by energy and entropy as above implies both time and temperature to be referred to the same state of affairs from two different viewpoints: (quantum) mechanics for time, and thermodynamics for temperature.
5. That idea (4) implies that energy and entropy in turn can be seen as the same quantity from two different viewpoints, and time and temperature represent the difference between the latter two viewpoints from the former two viewpoints accordingly of (quantum) mechanics and thermodynamics.
6. That quantity described whether as time or as temperature means intuitively the transition "inside - outside", or a little more exact: the transition "inside of a physical system" to "outside of the same system". That transition in (quantum) mechanics is called motion and mathematically described as a function of time. It means that system as a single whole conventionally called "particle", which is moving from the past position ("inside") to the future position ("outside") right now. That transition seems not to be called in thermodynamics (at least, I cannot guess how),but it means the transition from considering the system as consisting of many, many elements (“inside”) to a thermodynamic whole (“outside”).
"Might one inteptret the course of time as that irreversible computer heathing the present moment only in virtue of the course of time?" is an optional problem to demonstrate whether this is profound or not. ;)
• asked a question related to Function
Question
Step function of applied voltage in  dbd  plasma actuator
If I have a function of the type v=,v0 tang (t/tao). What will be the value of tao for v0=2000, 3000, is there any relation between them
• asked a question related to Function
Question
in stroke patient, hand functions is usually affected, I am wondering if you have experienced a good method to evaluate hand functions in stroke patient?
Hello Salameh,
We have the most popular test is a Ashworth Scale / Modified Ashworth Scale.
See the link for description of this test.
Raimondas
• asked a question related to Function
Question
I am starting in the molecular docking field. I would like to have some help about this question. I have generated the grid.cnt, grid.ngr, grid.bmp files but I dont know where can I find or how can I generate the pairwise GB grids and the SA grids to do the calculation of the Zou GB/SA scoring function. I am using the Dock6.7
I would really appreciate all the help that can be provided!  :)
Huge hugs!
Hi Stellamaris,
You can get a grid file by use of /usr/local/dock6/tutorials/solvent_scoring_demo/3_grid/solvent_grid.in.
Then add Zou GB/SA Score Parameters into a dock.in file, modify it, and dock.
• asked a question related to Function
Question
I am working at making a overexpression vector of  SESN1,but its three  variation seem  no recognizable function difference.i have already identfied isform 1 and 2 were  expressed in my cell line .so i hope get more information about these 2 isforms.
Hi Ali Mahmoudpour
• asked a question related to Function
Question
hi
How find centroids vertices using LOF function in highlighted section(Definition 3) in attached file ?
The first letter  -- a --  is a misprint and should be removed.
• asked a question related to Function
Question
Suppose that I have the normal and diseased populations as functions of a variable (x), how can I use them to draw a receiver operator curve (ROC)? Assuming the two functions are normal distribution functions and I know the means and the standard deviations of them, how to calculate the ROC at each value of x?
If you know the formula, it is not hard to implement it on excel or similar. Do you need to draw ROC curve? or sensitivity specificity pairs? FPR and TPR?
By the way, your very question has no clues that you are looking for an app. Rather it is understood that you are looking for the formula or the method. You said "ROC at each point" which did not remind me anything.
• asked a question related to Function
Question
like x or e^x
DearSatnam,
If functions are increasing as powers when x tends to infinity, you can use in the space of tempered distributions (generalized functions). See: Zemanian, A.H. - Generalized Integral Transformation. Interscience, New York.
You also can instead of the Hankel tranform use the Meijer transform that holds even for functions of exponential growth.
• asked a question related to Function
Question
Suppose that f and f′ are continuous functions on R.
If f's limit is zero at infinity, does that imply f' has same limit at infinity?
The zero limit has no effect on the derivative. Take f(t):= \sin(t^2).t^{-1}. Then f'(t)=2\cos(t^2} - sin(t^2}.t^{-2} and the value of f' is 1 at any point t={2\Pi n}^{1/2} with a natural n.
• asked a question related to Function
Question
Dear researchers,
can you explain to me the difference between constraint satisfaction of preferences with fuzzy constraints (knowing that there is no objective function with satisfaction problems) , and constraint optimization ?
In other words, what's the difference between CSP, CSOP, and FCSP formalisms ?
Regards !
Hello Naira.
a) Constraint satisfaction problems (CSPs) are mathematical problems defined as a set of objects whose state must satisfy a number of constraints or limitations.
b) FCSP represent an extension of CSPs by allowing a constraint to have a satisfaction degree from the unit interval, (a continuous variable).
You can represent constraints with fuzzy sets over a particular domain and the amount  of satisfaction of a constraint is the membership degree of its domain value on the fuzzy set that represents it.
c) CSOP are CSP which incorporate some optimization algorithm...
See for instance:
I hope this helps. Best, RICARDO
• asked a question related to Function
Question
Assume two real random vectors from observation such that ${\bf{z_1}}=[x_r(0) x_i(0) x_r(1) x_i(1)...x_r(N/2-1) x_i(N/2-1)]$ and ${\bf{z_2}}=[x_r(T) x_i(T) x_r(T+1) x_i(T+1)...x_r(N/2+T-1) x_i(N/2+T-1)]$. Here $x_r(t)$ and $x_i(t)$ are the real and the imaginary parts of x(t). Due to circularly symmetry assumption, zero mean random variables $x_r(t)$ and $x_i(t)$ are independent and identically distributed (i.i.d). The the correlation coefficient is given as
$\rho = \frac{E[x(t)x(t+T)]}{E[x(t)x^*(t)]}$
More Detail is Given in Image attached. Waiting for comments.
The distribution of the "min" function (as well as the "max" function) acting over random variables is modeled to follow an "extreme value" distribution. With the use of this model, I have estimated means and variances in practical problems. I recommend you to read [Coles, S. (2001). "An Introduction to Statistical Modeling of Extreme Values". Springer Series in Statistics.] where you will find several examples and applications of this distribution, and you will find also the mathematical description of the extreme value distribution.
Best regards,
LM Gato.
• asked a question related to Function
Question
Let A be a subset of R^n then the rearrangement of A denoted by A* is the ball B(0,r) having the same volume with A i.e if  |A| =|B(0,r)|  with respect to the Lebesgue measure then
A*= B(0,r)
Let f be a function from R^n to R and f* its symmetric decreasing rearrangement is the function define for x in  R^n  by
f*(x) = integral0infinity 1{f>t}*(x) dt.
Where 1{f>t}* is the characteristic function of the set {f>t}*= B(0 rt ) on R^n for some rt >0.
The set {f>t} := {x in R^n : f(x)>t} is called t-level set of the function f.
QUESTION: How to show that
{f>t}* = {f*>t}?
This is mentioned to be easy in the book of Elliott Lieb and Loss (Analysis second edition, Graduate Studies in Mathematical,
vol 14, American mathematical Society, providence, RI 2001).
Hint 1: show that if t1 >t2 , then {|f|>t1 }*⊆{|f|>t2 }*.
Hint 2: use this to show that if y is in {|f|>t}*
, then yis in {|f|>s}* for every 0<=s<=t. Notice that this implies that f*(y)>=t by the definition.
Hint 3: use hint 1 again to show that if y is not in {|f|>t}*
,sup{s≥0  |  y is in{|f|>s}*}<= t
this implies in particular f*(y)<=t.
• asked a question related to Function
Question
Ace1 in the insect
You most welcome
Houda
• asked a question related to Function
Question
Hello,
In theory of Nevanlinna, and in the unit disc, an analytic function for which order and lower order are the same is said to be of regular growth, and the function which is not of regular growth is said to be of irregular growth.
I need some examples of functions of irregular growth (it's okay if are entire or analytic in the unit disc),
best regards
The main idea of construction is to build irregularly distributed set of zeros, and after that to build an entire function with this set of zeros, using the canonical product.
See Chapter 2, section 5  "Examples" of the following (really brilliant) Goldberg and Ostrovskii book "Value Distribution of Meromorphic Functions" AMS Translations of Mathematical Monographs, vol. 236
I learned this reference from Anna Vishnyakova
She is a former student of Iossif V. Ostrovskii, so if you have more questions, she can help you.
• asked a question related to Function
Question
Is it possible to do feature normalization with respective to class. EX: 10x10 data matrix with two class. Each class of size 5x5. Now normalize 25 features of class 1 and 25 features of class 2 separately. Is this process acceptable.
Another reason why you can't use class-specific normalization is that if you do, you can normalize one class, say, between -2 and -1 and the other one between 1 and 2 and get perfect results with 100% accuracy on the training data.
• asked a question related to Function
Question
I want convert below function:
f(x)= {1   if  0<=x<0.5
{ -1  if  0.5<=x<1
{ 0    O. w.
If H(x) is your heaviside function with a step from 0 to 1 at x=0, then you will need something like this:
H(x) - 2H(x-0.5) + H(x-1)
Check it
• asked a question related to Function
Question
In the same situation the probability of occurrence of which event is more poisson or uniform?(is it possible to estimate  approximately ?)
What is "the same situation"?
• asked a question related to Function
Question
Lateral, anterior and posterior Fontanelles, which  are gapes in the skull of catfishes, covered by tough membrane, what are the functions of these gaps?
Dear Eman,
About what catfishes are you talking? Some catfishes has two cranial fontanelles, others have only one, others have none.
Regards,
Gloria Arratia
• asked a question related to Function
Question
Good mourning, i used the demostration shown in the figure below to reduce the integral shown to a simple form, the function Psi is an odd function with respect to x independant variable. I just want to check whether it is right or not, could any one help?
Looks good!
• asked a question related to Function
Question
where can I find results dealing with prederivative of non smooth functions ?
Ioffe, A. D. Nonsmooth analysis: differential calculus of nondifferentiable mappings. Trans. Amer. Math. Soc. 266 (1981), no. 1, 1–56.
• asked a question related to Function
Question
How to compute the limit of a complex function below? Thanks.
For $b>a>0$, $x\in(-\infty,-a)$, $r>0$, $s\in\mathbb{R}$, and $i=\sqrt{-1}\,$, let
\begin{equation*}
f_{a,b;s}(x+ir)=
\begin{cases}
\ln\dfrac{(x+ir+b)^s-(x+ir+a)^s}s, & s\ne0;\\
\ln\ln\dfrac{x+ir+b}{x+ir+a}, & s=0.
\end{cases}
\end{equation*}
Compute the limit
\begin{equation*}
\lim_{r\to0^+}f_{a,b;s}(x+ir).
\end{equation*}
Before computing the limit one has to fix the precise meaning of the expression. The functions $g(z) = z^s$ and $h(z) = \ln(z)$ are multi-valued, so the question will be correctly posed only after selecting appropriate branches of all expressions that  include these functions. Outside of this I see no difficulties.
• asked a question related to Function
Question
By giving evidence or reference,
Who first discovered hypergeometic functions?
As per Wikipedia,
The term "hypergeometric series" was first used by John Wallis in his 1655 book Arithmetica Infinitorum.
Hypergeometric series were studied by Leonhard Euler, but the first full systematic treatment was given by Carl Friedrich Gauss (1813).
Studies in the nineteenth century included those of Ernst Kummer (1836), and the fundamental characterisation by Bernhard Riemann (1857) of the hypergeometric function by means of the differential equation it satisfies.
Riemann showed that the second-order differential equation for 2F1(z), examined in the complex plane, could be characterised (on the Riemann sphere) by its three regular singularities.
The cases where the solutions are algebraic functions were found by Hermann Schwarz (Schwarz's list).
• asked a question related to Function
Question
I m asking this for any function means for example If we take
f(x)=sqrt(x); etc;
then how can we proceed for calculating the wavelet coefficients.
Excuse me Dear searchers, I will not answer the question, but I will reminder by:
Conditions of flagging an answer as cited in RG:
Flagging is a way for us to make sure that Q&A remains useful and relevant. Help us out by flagging answers that are offensive, of a commercial nature, or spam.
For those who flag an answer outside those provided in bold, it is shame and reveals of a bad mind and soul.
• asked a question related to Function
Question
Say for a given a function f, there are functions h and g satisfying h leq f leq g. What do we call h and g? I've used upper and lower bounds, which is incorrect. I reckon g could be called a dominant. What is h?
I hope your function is from R-->R. What is the meaning of h <=f <= g? Do you mean, h(x)<=f(x)<=g(x) for all x?
h can be called as subordinate of f, or f is a dominant of h.
Karunakaran (Complex Analysis book Author) uses the word, super-ordinate and subordinate for g and h respectively.
• asked a question related to Function
Question
Respected Sir
I want to solve optimal placement of capacitor for distribution system. So I want a good multi objective function for it.
Pareto gives the whole picture of the optimization, when the approximation is estimated after several intents, some of which give the optimal solution to one of the objective functions.
• asked a question related to Function
Question
Dear Sirs,
I want to invert following set of equations:
Y(i)=a(i)X1+b(i)X2+c(i)X3+d(i)X1X2+e(i)X1X3+f(i)X2X3+g(i)X1^2+h(i)X2^2+i(i)X3^2     i=[1,4]
It consists of four outputs (Y1-Y4), 3 inputs (X1-X3), and (9*4) coeff.
I intend to generate X1,X2,X3=function(Y1,Y2,Y3,Y4).i.e. Equations of X1,X2,X3. We may assume coefficients of your choice to simplify the solution. Please help me with possible guidance.
I don't believe there is general case for the setup of your example problem. MATLAB's fminsearch might be useful in approximating solutions, given an initial solution close to the actual. Given input vectors of the form:
psi = [y1;y2;y3;y4]
and coefficients
A = [a1,b1,c1,d1,e1,f1,g1,h1,i1; ...]
Let:
% x = [x1,x2,x3]
X = @(x) [x(1); x(2); x(3); x(1)*x(2); x(1)*x(3); x(2)*x(3); x(1)^2; x(2)^2; x(3)^2]
Y = @(X) A * X
ferr= @(Y) sum( (psi - Y).^2 )
xbest = fminsearch( @(x) ferr( Y( X( x ) ) ), xi )
Using randomly large signed elements for A and x, fminsearch finds near-exact answers given a suitably close initial. The coefficients of your actual data may warrant useful simplifications, esp. if the initial condition can be approximated via the squares of your domain.
• asked a question related to Function
Question
I am trying to model the combined effect of different customer orders on the manufacturing system. Having difficulty in understanding the application. Is there a tutorial help anywhere to guide me through this? Could someone give me a quick step-by-step procedure for using Array function in a model, please?
Thank you Mithun.
I shall check them out.
• asked a question related to Function
Question
Midconvex functions that are not convex are not Lebesgue measurable
For continuous functions, "midpoint convex" is equivalent to "convex" as Mikkelson's link already noted.   This is very similar to the argument that an additive continuous function has the form f(x)=Ax with discontinuous counterexamples easily constructed in terms of a Hamel base for the reals as a vector space over the rational field.  Indeed, any such an example is also an example here: midpoint convex (with equality!) but not convex.
• asked a question related to Function
Question
I have come across this condition for a function to be continuous and differentiable both but I was wondering in what cases and how it can be useful for us? In context of applicability.
The continuity is related to uniform convergence of sequences (and series) of functions (including Dini's theorem). On the other hand, for the most Borel measures, Luzin's theorem on approximation by continuous compactly supported functions works. On locally compact spaces, for a large class of measures, the subspace of continuous compactly supported functions is dense in L^p, 1<=p<infinity. For these last assertions see W. Rudin, "Real and complex analysis". Moreover, for a moment determinate positive regular Borel measure on a closed (unbounded) subset A in R^n, any nonnegative continuous compactly supported function (with the support contained in A) can be approximated from above by dominating (hence nonnegative on A) polynomials, in L^1 - norm. This result has applications to the multidimensional moment problem. Concerning the role played by C^2-functions, I recall that the theory of free and constrained extrema is usually proved for such functions.
• asked a question related to Function
Question
How can I solve Riccati inequality in Matlab using a modified function "care"? See attachment, please.
Go to page 7 of the document and pages afterwards for matlab code. It shows how to convert Riccati inequality into LMI.
• asked a question related to Function
Question
a function f(x,y) Any suggestion of a function f(x,y) such that the partial derivative with respect to the variable x is ax and with respect to the variable y is bx?
No, the system isn't inconsistent; just do the math: Integrating the first condition gives that f(x,y)=(a/2)x^2 + c(y). From this one obtains an, apparent,  contradiction, since the derivative of this expression wrt y is a function only of y and can't be equal to bx; unless b=0, which means that c(y)=c(0)=c, is a constant.
If one started out by integrating wrt y, one would've found f(x,y)=bxy + d(x); the derivative of this expression wrt x would then give by + d'(x)=ax=>d'(x)=ax-by, which, once more, is consistent only with b=0.
So the only solution is f(x,y)=(a/2)x^2+c. Standard, elementary, exercise in undergraduate calculus. A mystery what it's doing on such a forum...
• asked a question related to Function
Question
I have been wondering about the function of the ventral spine displayed by acanthosomatid bugs. Have there been studies on this topic? Thanks!
Frank
No there are no studies on it!
• asked a question related to Function
Question
I have to make a nested loop function to move from one co-ordinate of the obstruction to another in a nested loop form. I am unable to figure out how can I develop it in FDS/ WFDS software of NIST?
Thanks Chad, I have solved this problem.
• asked a question related to Function
Question
Here is generic method to transform a random set of values to normality:
1. Compute the empirical cumulative distribution function from the observed data (e.g., by using 'ecdf' function in R)
2. Smooth the function using smoothing spline and call in G(x) (e.g., by using the 'smooth.spline' function in R)
3. Now let U=G(X) should approximately be distributed as uniform distribution on [0, 1].
4. Z=Q(U) would then be distributed approximately normal with mean zero and variance 1.
The question is why do we still keep trying various arbitrary transformations (such as log, square-root, Box-Cox etc.)? Can't we simply use the above steps to transform a data (obtained from an arbitrary continuous distribution) to normally distributed?
In fact, here is a set of sample R codes to illustrate the method:
#####Generic Transformation to normality#######################
x=c(rnorm(25,-1.5,0.5),rnorm(75,1,0.5)) #data from mixture of normals
par(mfrow=c(2,2))
hist(x,prob=T) #you will see a bimodal shape
Fn=ecdf(x); fit=smooth.spline(x,Fn(x))
plot(fit,type="l")
u=predict(fit)\$y
hist(u,prob=T) #you will see uniform shape
z=qnorm(u)
hist(z,prob=T) #you will see a normal shape
lines(sort(z),dnorm(sort(z)))
ks.test(z,"pnorm") #formally tests if transformed data is normal
A sample output is attached where the data is generated from a mixture of normal distribution.
Watheq,
"In experimental design and we we want to build an efficient model for prediction, it is essential to obtain normal response distribution." - That's just not correct, in several ways. The distribution of the response does not matter - the distribution of the residuals is the key, and this is tightly linked to the formulation of the model. And the predictions of models assuming normal residuals are BLUE, even when the actual residual distribution is non-normal. The important part here is the estimated uncertainty of the predictions, what depends on how the stochastic part of the model is defined. Note that this does not neccesarily need to be based on the normal distribution!
"In regression modeling, it is necessary some times to obtain normal distribution for the response variable for better fit." - Again it is not the distribution of the response variable that really matters, but the distribution of the residuals. Apart from this I do not see how this is related to the quality of a fit. How do you measure this quality? All "quality" measures I know depend on the scale of the response, so transforming the response also transforms the meaning of these quality measures, and comparing them is like comparing apples and peaches. At best, It is just meaningless.
A good model gives estimates of interpretable effect sizes. Most transformations will render the estimates quite uninterpretable, what I consider a major disadvantage (NB: the log-transformation is somewhat special because it just makes a model estimating multiplicative effects instead of additive effects).
• asked a question related to Function
Question
hello,please show me how to express the dielectric function of hydrogenated graphene ,any guidance
Please check the following publications, where the dielectric function of graphene is worked out on the basis of the so-called tight-binding approximation:
1. Stauber et al., Optical conductivity of graphene in the visible region of the spectrum. Phys Rev B 78, 085432 (2008).
2. Falkovsky LA, Pershoguba SS. Optical far-infrared properties of a graphene monolayer and multilayer. Phys Rev B 76, 153410 (2007).
The presented theory is in very good agreement with available experimental data. Please notice that the REAL part of the dielectric function is guided by the so-called "universal optical conductivity of graphene". Check, for example
3. Kuzmenko et al., Universal optical conductance of graphite. Phys Rev Lett.
100, 117401 (2008).
Hydrogenated graphene on SiC is somewhat special in the sense that its Fermi-level is 0.2 to 0.3 eV below the Dirac point (i.e., it is strongly p-type doped). This influences a parameter called "chemical potential" in the above papers. In our recent publication we have done some estimate of the influence of the chemical potential on the optical conductivity (and thereby on the dielectric function), please check I.G. Ivanov et al., Layer-number determination in graphene on SiC by reflectance mapping, Carbon 77, 492 (2014). Check the text discussing Eqs. (7) and further.
• asked a question related to Function
Question