What is Domain: Definition and 737 Discussions

A domain name is an identification string that defines a realm of administrative autonomy, authority or control within the Internet. Domain names are used in various networking contexts and for application-specific naming and addressing purposes. In general, a domain name identifies a network domain, or it represents an Internet Protocol (IP) resource, such as a personal computer used to access the Internet, a server computer hosting a website, or the web site itself or any other service communicated via the Internet. In 2017, 330.6 million domain names had been registered.Domain names are formed by the rules and procedures of the Domain Name System (DNS). Any name registered in the DNS is a domain name. Domain names are organized in subordinate levels (subdomains) of the DNS root domain, which is nameless. The first-level set of domain names are the top-level domains (TLDs), including the generic top-level domains (gTLDs), such as the prominent domains com, info, net, edu, and org, and the country code top-level domains (ccTLDs). Below these top-level domains in the DNS hierarchy are the second-level and third-level domain names that are typically open for reservation by end-users who wish to connect local area networks to the Internet, create other publicly accessible Internet resources or run web sites.
The registration of these domain names is usually administered by domain name registrars who sell their services to the public.
A fully qualified domain name (FQDN) is a domain name that is completely specified with all labels in the hierarchy of the DNS, having no parts omitted. Traditionally a FQDN ends in a dot (.) to denote the top of the DNS tree. Labels in the Domain Name System are case-insensitive, and may therefore be written in any desired capitalization method, but most commonly domain names are written in lowercase in technical contexts.

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  1. Euge

    POTW A Nonlinear Elliptic PDE on a Bounded Domain

    Let ##D## be a smooth, bounded domain in ##\mathbb{R}^n## and ##f : D \to (0, \infty)## a continuous function. Prove that there exists no ##C^2##-solution ##u## of the nonlinear elliptic problem ##\Delta u^2 = f## in ##D##, ##u = 0## on ##\partial D##.
  2. raminee

    A Editing in Freq domain and applying inverse FFT

    Hello All, I am somewhat familiar with FFT and iFFT and its uses. However I have an issue when I edit in Freq domain and try to get back to time domain . I have an audio signal in time domain that I transform to frequency domain using an FFT routine in block sizes of N points. (in my case 256...
  3. chwala

    Show that ##\mathbb{Z}[\sqrt 3]## is a Unique factorisation domain

    I am studying this now...i just want to check that my reasoning is fine,... ##[1+\sqrt{-3}]## can be factorised to ##[2⋅-1]## and ##-1## is a unit and ##2## is irreducible, therefore ##\mathbb{z}[\sqrt 3]## is a UFD.
  4. C

    Limit on the edge of the domain

    What is the limit of the function as x goes to -5 (e.g. in the graph below) if the domain of the function is only defined on the closed interval [-5,5]? I realize that the right hand limit DOES exist and is equal to 3, but the left hand limit does not exist? So does that mean that the overall...
  5. C

    I Finding domain when using continuity to evaluate a limit

    For this problem, The solution is, However, when I tried finding the domain myself: ## { x | x - 1 ≥ \sqrt{5}} ## (Sorry, for some reason the brackets are not here) ##{ x | x - 1 ≥ -\sqrt{5}} ## and ## { x | x - 1 ≥ \sqrt{5}}## ##{x | x ≥ 1 -\sqrt{5} }## and ## { x | x ≥ \sqrt{5} + 1}##...
  6. C

    Finding the domain of a composite function

    For this problem, The solution is, However, I tried solving this problem by using the definition of composite function ##f(g(x)) = f(\frac{4}{3x -2}) = \frac{5}{\frac{4}{3x - 2} - 1} = \frac{5}{\frac{6 - 3x}{3x - 2}} = \frac {15x - 10}{6 - 3x}## which only gives a domain ##x ≠ 2##. Would some...
  7. D

    What are the implied domain and range of cos(arctan(x))?

    Hi everyone I have the solution to this question, but I'm not sure I understand it. Why is the domain of the composite function and not [0, pi]? Is it because tan^-1 (0 and R+) will always give a value between (-pi/2, pi/2)? I.e. the domain of the composite function refers to x. Is 0...
  8. brotherbobby

    Possible values an expression can take : ##\dfrac{x^2-x-6}{x-3}##

    Problem statement : Let me copy and paste the problem as it appears in the text : Attempt 1 (from text) : The book and me independently could solve this problem. I copy and paste the solution from the book below. Attempt 2 (my own) : The problem should afford a solution using the...
  9. EmmanKR

    Finding the Frequency Domain and Time Domain magnetic field

    I was wondering if anyone could walk me though a better explanation on how to get the given results for these two questions. The solutions posted by my professor aren't really clear to me so if anyone is able to better explain how to get the solution it would be much appreciated!
  10. A

    Domain of definition differential equations

    Hello. Considering this DE; $$ x^7 x' = (x^8-300)t^6 $$ with inital value x(0) = -2 Now the solution for the initial value should be C = -44; And for x(t) I get ; $$x(t) = (-44 e^{\frac{8}{7} t^7} + 300)^{\frac{1}{8}}$$ Now to get the biggest domain of definition I did this; $$ -44...
  11. S

    Subset of the domain for the transformation to be invariant

    I found that the a) invariant points are all points on y-axis b) invariant lines are y-axis and ##y=c## where ##c## is real I am confused what the final answer should be. How to state the answer as "subset of domain"? Is it: $$\{x,y \in \mathbb R^2 | (0, y) , x = 0, y=c\}$$ Thanks
  12. e2m2a

    Python Plotting Domain Dependent Functions

    Is it possible for Python matplotlib to plot in one graph a domain dependent function? For example, suppose there is a function where y=x from 0< x <=5, y = x sq when 5<x<=7 and y=2x+9 when x>7. Is it possible in Python to plot this with one plot on one graph? If so, how would it be done?
  13. I

    Converting an expression of a particular k-mode to the spatial domain

    $$n_\vec{k} = \omega a^2(\vec{k})\tag{1}$$ One way is to write the inverse Fourier transforms of the terms above. So, eqn (1) becomes $$\int\mathrm{d}^3x\ n(\vec{x})e^{-i\vec{k}\cdot\vec{x}} = \omega \int\mathrm{d}^3x^\prime\ a(\vec{x^\prime})e^{-i\vec{k}\cdot\vec{x^\prime}}...
  14. U

    COMSOL: stress on a sensor, how to use infinite element domain?

    At the risk of waiting hours on simulations of a sensor, I was wondering if I could use infinite element domain on COMSOL to simplify it. The first image consists of what I would like to simulate but found out that the simulation time is a huge factor as I have a lot to simulations to conduct...
  15. P

    LTSpice functionalities regarding its Frequency Domain Analysis

    The time domain analysis is easier to plot compared to analyzing the frequency with respect to the phase. But, LTSpice makes it look really easy. So, for a small signal AC analysis, LTSpice does use a AC voltage source for its frequency domain analysis function. This must be a really convenient...
  16. chwala

    Find the domain of the inverse of a function

    This is a textbook problem: now for part a) no issue here, the range of the function is ##-1≤f(x)≤299## now for part b) i got ##x≥-1## but the textbook indicates the solution as ##x≥0## hmmmmm i think, that's not correct...
  17. mcastillo356

    B Advice to obtain the domain of compound functions

    Hi PF I have a quote from Spanish 6th edition of "Calculus", by Robert A. Adams, and some queries. I translate it this way: "The inverse of secondary trigonometric functions can easily be calculated with the reciprocal function. For example DEFINITION 13 The inverse function of secant...
  18. M

    Comsol: Infinite Element Domain module

    Hello folks, I want to simulate a 2D heat transfer process in the subsurface on a region which is infinite on the r-direction. So, as you know, the very basic way to model this is to draw a geometry that is very long in the r direction. I have done this, and the results that I obtain is correct...
  19. karush

    MHB GRE.al.4 Find the domain of \sqrt{x^2-25}

    $\tiny{GRE.al.4}$ Find the domain of $f(x)=\sqrt{x^2-25}$ a. $[x\le-5]U[x\ge 5]$ b. x=5 c. $5 \le x$ d. $x\ne 5$ e. $\textit{all reals}$ well just by observation because of the radical I chose c. but was wondering if imaginary numbers could be part of the domain alto it is not asked for here...
  20. karush

    MHB 5.6.28 find domain of x in ABS

    $\tiny{\textit{5.6.28}}$ Find $x \quad |2x-5|<9$ divide into 2 solution sets $\begin{array}{rl|rl} (2x-5)&=9&-(2x-5)&=9 \\ 2x&=14&-2x&=4 \\ x&=7&x&=-2 \end{array}$ x is $-2<x<7$ kinda maybe...
  21. Poetria

    Domain of multivariable function - definition

    E.g. all real numbers could be a domain but not necessarily, etc. Am I right?
  22. karush

    MHB S5.t.5 Find domain and asymptotes.

    $\tiny{s5.t.5 Kiaser HS}$ Find domain asymptotes. $g(x)=\dfrac{2x^2-14x+24}{x^2+6x-40}$ $\begin{array}{rll} \textsf{factor}&=\dfrac{2(x-3)(x-4)}{(x-4)(x+10)} =\dfrac{2(x-3)\cancel{(x-4)}}{\cancel{(x-4)}(x+10)} =\dfrac{2(x-3)}{x+10}\\...
  23. N

    Domain of a Function

    Ron Larson stated: "The domain of a function can be described explicitly or it can be implied by the expression used to define the function. The implied domain is the set of all real numbers for which the expression is defined." 1. How is a function defined explicitly? 2. How is a function...
  24. tworitdash

    Rotating radar time domain data

    I want to simulate the time domain data for a rotating radar. I assume that the space around the radar is filled up with a very big extended object and it moves with a constant speed in one direction. Picture attached. I don't take range information here. I am only concerned about the...
  25. tworitdash

    MATLAB Creating and recovering a frequency shift in time domain in MATLAB

    I am trying to simulate and process the Doppler signals. My main problem is a little more complex so I am only posting a simple version of it. Task1: I have a time-domain signal with the velocity of the target as mu. I need to change the velocity to mu cos(theta) where theta is a vector from 0...
  26. tworitdash

    MATLAB How to change the frequency values inside a time domain signal phase

    The problem I am having is simple. I have a Gaussian spectrum initially. Like this, Process 1: S = m0/sqrt(2*pi*sigma^2) * exp(-(vel_axis - mu).^2/(2*sigma^2)); Here, mu is the mean velocity (frequency) and sigma is the standard deviation. vel_axis is the axis on which I am calculating this...
  27. C

    Finding a domain for a function

    I am having some trouble find the domain with this function: ##f(x)=\frac{1}{\sqrt{x^2-4x\cos(\theta)+4}}## and ##\theta\in[0,\pi]##. I know that the denominator needs to be greater than 0. So ##\sqrt{x^2-4x\cos(\theta)+4}>0##. I squared both side of the inequality, ##x^2-4x\cos(\theta)+4>0##...
  28. C

    MHB Finding the domain of this function.

    Dear Everyone, I am having some trouble find the domain with this function: $f(x)=\frac{1}{\sqrt{x^2-2x\cos(\theta)+4}}$ and $\theta\in[0,\pi]$. My attempt: I know that the denominator needs to be greater than 0. So $\sqrt{x^2-2x\cos(\theta)+2}>0$. I squared both side of the inequality...
  29. A

    I How can one see the noise in the Fourier Domain (Nyquist Frequency)?

    Say we have a transform of a line profile that extends out to the Nyquist frequency such that you cannot see the noise level, what could you change in your spectrograph arrangement that would allow you to see the noise level in the Fourier domain? My thought is that we can apply a filter, P(s)...
  30. A

    Please verify my answer to this question about the domain

    For n=1 (ln(ln(x))), the domain is the set of all real x>1 ; for n=2, the domain is the set of all real x>e ; for n=3, the domain is the set of all real x>e^e ; for n=4, the domain is the set of all real x>e^(e^e) ...Thus, for a general n the domain is the set of all real x greater than...
  31. S

    MATLAB Turning Fourier coefficients into an interpolated freq domain function

    Hi, I am interested in understanding the relationships between Fourier series and Fourier transform better. My goal is 1) Start with a set of ordered numbers representing Fourier coefficients. I chose to create 70 coefficients and set the first 30 to the value 1 and the remaining to zero. 2)...
  32. S

    Domain of a trig function

    y = 2sin(x) -1≤ sin(x) ≤ 1 -2 ≤ 2sin(x) ≤ 2 so -2 and 2 are the max/min limits but the domain is -π < x ≤ π Do I find the values of x that outputs -2 and 2 and show that they are within the domain ?
  33. S

    I Domain of convolution vs. domain of Fourier transforms

    Convolving two signals, g and h, of lengths X and Y respectively, results in a signal with length X+Y-1. But through convolution theorem, g*h = F^{-1}{ F{g} F{h} }, where F and F^{-1} is the Fourier transform and its inverse, respectively. The Fourier transform is unitary, so the output signal...
  34. sergey_le

    I Find the domain of a function of the form: ln(sin(1/x))

    the solution
  35. fluidistic

    "Old" books are in public domain, what about old textbooks?

    I'm quickly reading at https://boingboing.net/2019/08/01/80pct-pd.html?fbclid=IwAR3pMnu6G0d-M6Ldf_i5muga3g_m0NVkMQ5u6NiE-f_FapGKftJO76_hxbw that about 80% of books published in the US between 1924 and 1963 are in the Public Domain now. Textbooks are known to be very expensive, even when they are...
  36. A

    Domain of definition of the function f(x,y)=x^y

    Good day as said in the title i need the domain of definition of of the function f(x,y)=x^y for me as x^y=expontial (y*ln(x)) so x>0 but the solution said more than that I really don't understand why we consider the case (0,y) in which while should be different from 0, because I will never...
  37. .Scott

    The Fast Fourier Transform is described in the Quantum Domain

    In August, "Quantum Information Processing" published an article describing a full FFT in the quantum domain - a so-called QFFT, not to be confused with the simpler QFT. According to the publication:
  38. F

    A Are topological defects such as domain walls really discontinuous?

    Are topological defects such as domain walls really discontinuous (implying infinite slopes of the fields) or only approximately ?
  39. S

    B Domain of a composite function

    ##f(x)=-x^2 + 3## so ##f^{-1} (x)=- \sqrt{3-x} ~, x \leq 3## ##ff^{-1} = - (- \sqrt{3-x})^2 + 3 = x## and the domain will be ##x \leq 3## ##f^{-1} f = - \sqrt{3-(-x^2+3)} = -x ## and the domain will be ##x \leq 0## My question: ##ff^{-1} (x)## or ##f^{-1} f(x) ## is not always equal to...
  40. A

    Determining the domain and range for the function ##f^{-1}##

    The domain and range of this function will be the same. We can let ##𝑓(𝑥)=\sqrt{x},𝑥≥0## However, ##𝑦=𝑓(𝑥)≥0##, so the domain and range of ##f## are ##[0,+∞)## And since ##f## is a function, ##f^{-1}s## domain is the range of ##f## and ##f^{-1}s## range is ##f’s## domain. In other words...
  41. M

    Phasor to Time Domain Math

    This is a problem about converting from the phasor to time domain. I am having trouble following the math that the textbook is doing. I was thinking the final answer should be: i(d, t) = 0.20 cos(ωt + βd + 159◦) - 0.091 cos(ωt − βd + 185.6◦) emphasize the minus 0.091 instead of plus 0.091 as...
  42. D

    Complex numbers domain

    i have to find such domain z=x+iy , y,x∈ℝ , |y-x|<=2, |x|<=2 i'm confused with |y-x|<=2, how should i proceed ? with abs of x i am ok.
  43. S

    B Confusion about the domain of this logarithmic function

    Should I just follow the original question? If given as ##f(x)=\ln x^4## then the domain is x ∈ ℝ , x ≠ 0 and if given as ##f(x) = 4 \ln x## the domain is x > 0? So for the determination of domain I can not change the original question from ##\ln x^4## to ##4 \ln x## or vice versa? Thanks
  44. karush

    MHB -gre.al.9 absolute value domain

    Solve for y: $\quad |y+3|\le 4$ a.$\quad y \le 1$ b.$\quad y\ge 7$ c.$\quad -7\le y\le1$ d. $\quad -1\le y\le7$ e. $\quad -7\ge y \ge 1$ Ok I think this could be solved by observation but is risky to do so...
  45. M

    MATLAB Plotting a 3D image from a matrix for a complex domain

    Hi PF! Each element of an ##n\times m## matrix is complex valued. In the following code, I call this "domain". There is also an ##n\times m## matrix that is real valued, below I call this "f". I'd like to plot a 3D image where the ##x-y## plane is the complex plain given by the coordinates...
  46. redtree

    I The domain of the Fourier transform

    Given the domain of the integral for the Fourier transform is over the real numbers, how does the Fourier transform transform functions whose independent variable is complex? For example, given \begin{equation} \begin{split} \hat{f}(k_{\mathbb{C}}) &= \int_{\mathbb{R}} f(z_{\mathbb{C}})...
  47. tworitdash

    A Spectral domain double integral with singularities

    The integral looks like Y_{mut, mn} = -j^{m+n}nm \int_{-\infty}^{\infty}\int_{-\infty}^{\infty} \frac{2 ab (k^2 - k_x^2) \sin^2(\frac{k_yb}{2}) \cos^2(\frac{k_xa}{2})}{\omega \mu k_z (\frac{k_yb}{2})^2 [(n\pi)^2 - (k_xa)^2][(m\pi)^2 - (k_xa)^2]} dk_x dk_y Here, k_z = -1j...
  48. S

    [AC Circuit] How do we convert from the time domain to the phasor domain?

    In this example, We need to covert e2 & e5 to a form with imaginary number . we will obtain e2=j10 & e5=20 Can anyone explain how we got this?
  49. E

    B Showing that formulae are invariant for all values in the domain

    I was just thinking about this and couldn't decide whether it was a silly question or not, so naturally I thought I might ask. It was partly prompted by one of the questions asked in the homework section. Every physical law I can think of is "self-correcting" if you substitute negative values...
  50. V

    Python Phase shifting a measured signal directly in time domain

    I need to perform a phase shift for a measured time domain signal. The signal consists of around 1000 points. I wrote an algorithm for this in Python a while ago and it seems to work as intended, but now I noticed that the algorithm is actually unexpectedly slow. Is it so that phase shifting is...