What is Domain: Definition and 741 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. M

    Proving R as a PID: Z ⊂ R ⊂ Q with R as an Integral Domain

    Homework Statement Prove that R is a PID (principal ideal domain) when R is a ring such that Z \subset R \subset Q (Z=integers, Q=rationals) Homework Equations The Attempt at a Solution So I'm not really sure how to start this problem. I know that a principal ideal domain is an...
  2. A

    About domain theory of ferro magnetism

    hi ... i want to ask about domain theory of ferromagnetism... first of all , According to classical electromagnetism, two nearby magnetic dipoles will tend to align in opposite directions, so their magnetic fields will oppose one another and cancel out. how does this happen? after this ...
  3. T

    Domain of the Function f(x): Explained

    The Question is: What is the Domain of the function f(x)= log_{5}(log_{5}(x + 2) My answer is that the Domain is (-2, \infty). However the it is said that the right answer is (-1, \infty) and I am not convinced so can anyone give me an explanation?
  4. M

    Definition of integral domain from Herstein

    Hi, I ran into conflicting definitions of integral domain. Herstein defines a ring where existence of unity for multiplication is NOT assumed. His definition of integral domain is: "A commutative ring R is an integral domain if ab=0 in R implies a=0 or b=0" I looked in 3 other books and...
  5. U

    Domain of f(x) = sqrt(1-sin(x)): Understanding and Calculating

    Homework Statement let f(x) = sqrt(1-sin(x)) Homework Equations What is the domain of f? What is the domain of f'(x)? The Attempt at a Solution I understand that the domain of f is all real numbers not including every increment of 90 degrees, but I am not sure how to state that...
  6. T

    Self adjointness and domain

    Hi together ... I encountered the following statement: Operator A is self adjoint on D(A) then A(t) \equiv \exp(iHt) A \exp(-iHt) is self adjoint on D(A(t)) \equiv \exp(-iHt) D(A). H is self adjoint, so that exp(...) is a unitary transformation. But why does the domain transform this way...
  7. S

    Messing around with a function changes it's domain?

    messing around with a function changes it's domain?? consider a function f(x)= \sqrt[3]{2x^2-x^3} if i take x^3 common from inside the cube root the function becomes f(x)= x*\sqrt[3]{2/x-1} the domain of the orginal function includes all real numbers, but the domain of the "new" function...
  8. X

    Find functions with given domain and range

    1) Find a continuous function f: (0,1)->R with f[(0,1)]=R I couldn't think of any function except tangent, but its domain is NOT (0,1) though? Any suggestions? 2) Find a continuous function f: (0,1)->R with f[(0,1)]=[0,1] I couldn't think of any function that I know. Any suggestions? 3) Find a...
  9. D

    Faraday's Law in the frequency domain

    I'm trying to figure out what faraday's law is in terms of frequency rather than time. I think the equation is V = -N*B*A*2f. Where N is the number of turns in the loop, B is the magnetic field, A is the area and f is the frequency. However I am not totally convinced that my derivation is correct.
  10. silvermane

    Proving a Product of Commutative Rings not an Integral Domain:

    Homework Statement Prove that if we have two commutative rings R and S and form the product R X S, then R X S cannot be an integral domain. The Attempt at a Solution We have that an integral domain is a commutative ring with 1 not= 0 and with non-zero zero-divisors. ==> (1,0)X(0,1)...
  11. T

    How to Solve Laplace-Transformed ODE on Infinite Domain?

    Homework Statement I'm working with a heat equation that requires a Laplace transform. I performed the transform and ended up with a basic ODE with a particular solution. I solved for the particular solution and then realized I was working on an infinite domain in my spatial dimension...
  12. silvermane

    Proving that b is 1 or -1 in an Integral Domain

    Homework Statement Suppose R is an integral domain. Suppose c in R has c^2 = 1. Prove that b must equal either 1 or -1. Also, in Z/12Z, find an element b not equal to -1 or 1, with b^2 = 1 The Attempt at a Solution So for the first part, I'm guessing it would be a good idea to factor...
  13. S

    Domain and Range of f(x,y)=2x^2+3x^2+1: Real Numbers and Minimum Value of 1

    Homework Statement Find the domain and the range f(x,y)=2x2+3x2+1 Homework Equations non The Attempt at a Solution ... i said that x,y are all real #'s and f(x,y)>=1 or z>=1 is there anything wrong with what i has attempted at? if do could you explain... thanks in advance
  14. H

    Modulation of Sinusoids in Matlab (Frequency Domain Problems)

    The Problem Hi, I am trying to modulate two sinusoids in Matlab. I have some and some , where fx and fc are different frequencies. I then modulate them together, using dot multiplication, . I then plot each in the time domain using and I obtained the correct solution. The problem comes with...
  15. S

    The explanation of the domain of two variable function

    can anyone explain that domain or give me any reference about it??
  16. N

    (signal processing)Time domain vs Frequency domain, totally confused

    Hey guys, I am totally lost in the idea why we have to change function in time domain to frequency domain to ease with our calculations. Let me break my question into serveral smaller ones. 1)What is the physical implication of transferring a signal to frequency domain? (I know that in...
  17. S

    What is the relationship between the domain and range of a function?

    Could someone please explain to me what the range and domain of a function is and how to find them? I just don't understand what they mean Thank You
  18. T

    Question about domain of derivatives

    I was thinking how do I differentiate the domain of functions... Suppose I have a function: f(x) = \left\{\begin{matrix} x^2 -1, \;\; |x| \leq 1\\ 1 - x^2, \;\; |x| > 1 \end{matrix}\right. And I need to derive it: f'(x) = \left\{\begin{matrix} 2x, \;\; |x| \leq 1\\ -2x...
  19. E

    Domain and range can't be negative

    Homework Statement Given f:A→B and g:B→C, let h=g(f(a)) If h is injective, then g is injective. Give a counter example. Homework Equations Injection: Let f:A→B For all f(x1)=f(x2) implies x1=x2 The Attempt at a Solution f(a)=\sqrt{a} from [0, infinity]→[0,infinity]...
  20. R

    Domain and range of a function help

    So I'm skipping pre-cal with full intentions of picking up on AP Calc. Our summer course work is taken from a book called preparing for calculus. After giving me some who-dad that I knew already everything changed in an instant. There's a little gap that isn't quiet filled. A function is...
  21. N

    Is it Possible to Find the Domain of a Discretized Function for Minimization?

    Hello! I'm not quite sure where to put this. I'm programming, but my question should be strictly mathematical. However, just for your information, I'm programming with Mathematica. I have a function that will give me points. If I give it inputs, I can get a value out of it. I can take a...
  22. S

    Finding the domain of the inverse function

    Homework Statement Let f(x)=e^(-x)-x ,, x belongs to R Find the domain of f inverse Homework Equations Domain of f inverse = range of f The Attempt at a Solution we have : -inf < x < inf -inf < -x < inf ... (1) 0 < e^(-x) < inf ... (2) By adding (1) and (2) ...
  23. P

    Basic Summation Operations - Manipulating of domain and change of variable

    Homework Statement a) Show that $\sum_{S(j)} a_j + \sum_{R(j)} a_j = \sum_{S(j) and R(j)} a_j + \sum_{S(j) or R(j)} a_j$ is valid for an arbitrary infinite series, provided that 3 out of 4 sums exist. b) Show that $\sum_{R(j)} a_j = \sum_{R(c-j)} a_{c-j} for an arbitrary infinite series where...
  24. L

    Which concepts in algebra/trig. have a domain and range

    In algebra/trig. what kinds of problems have a domain and a range ? Is this true for anything that can be graphed? Because a lot of the time after you finish a problem in precalc. it then asks for the domain or range, so the question becomes, in mathematics, is it possible to find the domain...
  25. N

    Is the Range of a Countable Function also Countable?

    If the domain of a function is countable, then is its range also countable? also if A is countable and B is countable is A(cartersian product)B countable?
  26. H

    Dsp help - impulse response of system in z domain

    Homework Statement I am given an LTI system where I need to obtain the impulse response and difference equation of H(z). H(z) = (1-0.5z^-3) / [(1-0.5z^-1)(1-0.25z^-1)] and |z| > 0.5 Homework Equations The Attempt at a Solution I am pretty lost about what to do. I...
  27. C

    Convert Time Domain to Phasor Domain with Euler's Formula

    how is euler's formula useful? it must have something to do with converting from the time domain to the phasor domain and back, but i can do that without euler's formula
  28. M

    Natural Laws and their domain of validity

    "Natural Laws" and their domain of validity What is the philosophical justification for extending observed phenomena to "laws of nature". For example, Galileo dropped massive objects and saw that they fall at the same rate, but to then say that all massive objects fall at the same rate requires...
  29. J

    Drawing domain of R^2 integral

    \int _1 ^e \int _{1/e} ^{1/y} f dx dy If asked how to sketch the bounds for that: "x starts at x=1/e and ends at x=1/y 1/e is just a constant so that's a straight line and x=1/y is the exact same line as y=1/x" That's a decent enough engineer's explanation right? (no one in university should...
  30. P

    Finding the Domain of f with Restrictions for Range (-2,4)U(4,11)

    Homework Statement For f(x)=((x^(2)-2x-3)/(x-3)), restrict the domain of f(find Dom (f) first) so that Rnage(f)=(-2,4)U(4,11) The Attempt at a Solution I found that when x=3, the function will be undefined. so the domain(f) should be (-infinity,3)U(3,+infinity). I GUESS now I should go...
  31. K

    Domain of solution to Cauchy prob.

    Prove that the solution of the CP y'=-(x+1)y^2+x y(-1)=1 is globally defined on all of \mathbb{R} How would you go about this? I thought about studying the sign of the right member if the equation. But what would I do next?
  32. N

    Characterstic Curves and domain of dependence

    Please give geometrical desciption of what are characterstic curves and domain of dependence of a PDE. Please help. Thanks.
  33. T

    Range & Domain of f & g: Find, Domain & Range

    Homework Statement Given two functions f(x)=\frac{x}{x+1} , g(x)=\frac{x+2}{x} (1) find the domain of f and g so D_f all real x , x\neq -1 D_g is all real x , x\neq 0 (2) Find the composite function gf and state its domain and range g o f = 3+ 2/x , then its domain would...
  34. N

    How to prove the uniqueness theorem in an unbounded domain?

    I read a lot of books on the uniqueness theorem of Poisson equation,but all of them are confined to a bounded domain \Omega ,i.e. "Dirichlet boundary condition: \varphi is well defined at all of the boundary surfaces. Neumann boundary condition: \nabla\varphiis well defined at all of the...
  35. M

    Function & Domain - Math Homework

    hi ,,,, Homework Statement these are the function 1) f(x)=A(x)/B(x) 2) f(x)=√(A(x)) 3) f(x)=√(A(x))/(B(x)) 4) f(x)=(A(x))/√(B(x)) 5) f(x)=√(A(x))/√(B(x)) 6) f(x)=√((A(x))/(B(x))) The Attempt at a Solution the domain are they right 1) { x∈ R : B(x) ≠ 0 } 2)...
  36. O

    Confused about the terminology for the domain pde

    Homework Statement δu/δt+2tδu/δx=1 for t>0,x>0 with u= 0 on x= 0 for t>0, u=1 at t=0 for x≥0 Homework Equations The Attempt at a Solution ((dx)/(dt))=2t x=t²+c x-t²=c the general solution is: u=t+F(x-t²) Now i am...
  37. C

    Find the exact value of c for which f is continuous on its domain

    Homework Statement Let the function f: [1,infinity)-->R f(x)=\left\{ \begin{array}{rcl} \frac{(\sqrt{x}-1+x\sqrt{x-1}}{\sqrt{x^2-1}} & \mbox{,} & x>1 \\ c, x=1 \end{array}\right. Find the EXACT value of c for which f is continuous on its domain. Homework Equations N/A...
  38. S

    Domain Notation: Continuous Function

    Just wondering how to write the domain of where a function similar to this is continuous: using proper domain notation.
  39. R

    Proving R is a Principal Ideal Domain and X^4+1 is Reducible in Z/pZ[X]

    1.Let R be a ring such that Z ⊂ R ⊂ Q. Show that R is a principal ideal domain. We show that Z is a principal ideal domain, so every ideal in Z which is also in R is principal. But I'm not sure how to use that R is contained in Q. 2. Proof that X^4+1 is reducible in Z/pZ [X] for every...
  40. L

    Trouble finding a mobius transformation from a domain to a unit disc

    Homework Statement S = { z | |Im(z)| < 5 }, z is a complex number Homework Equations I am trying to generate a mobius transformation w = f(z) such that it will map S onto a unit disc but I keep running into problems and contradictions. I think there is a big mistake in my attempt but I...
  41. Mentallic

    Weird Graph Behaviour - Analyzing a Root in Domain 2-4

    I came across this weird graph from another thread: y=\left(x^2-6x+8+\sqrt{x^4-12x^3+52x^2-96x+64}\right)^2 It seems that there is a root y=0 for the domain x=[2,4]. I've never seen such weird behaviour on a graph before. How could analysis of this function (or not?) determine that there...
  42. M

    Applicable domain of Stokes Flow

    Hi, I'm working on a calculation of flow through a rectangular duct and I'm assuming I'm in the Stokes' flow regime (Re<<1), but I also want to experiment on this system and I was wondering if anyone knows until what Re-number Stokes' flow is still a good approximation (and how good, i.e. in...
  43. J

    Symmetry breaking domain walls

    Symmetry breaking "domain walls" The only "spontaneously broken symmetry" that I can easily visualize, is cooling down a ferromagnetic material and having the spins randomly choose a direction to align. Since the choice is random, different regions will usually choose different directions...
  44. A

    Function, f, with domain (-infinity, + infinity)

    I was working on the following problem from a textbook. The textbook has no answer. I have included my solution - I am not sure whether it is correct Any ideas and or solutions? (guidance) Question: Suppose that f is any function with domain (-infinity, +infinity) a) Does the function g...
  45. T

    How to find the domain in one dimension

    Homework Statement I am trying to find the domain of the following.. R^2 to R^3 of g(x,y) = (x-y,x+y,3*x) R^3 to R of h(x,y,z) = x/(y+z) Homework Equations The Attempt at a Solution I don't know how to start. I know how to find the domain in one dimension but how...
  46. Chewy0087

    Domain and Range of fg(x) for f(x)= e^{2x} + 3 and g(x) = ln(x-1)

    Homework Statement Find the range for the function; fg(x) and state its range where f(x)= e^{2x} + 3 and g(x) = ln(x-1) The Attempt at a Solution Putting g into f I reach; fg(x) = e^{2ln(x-1)}+3 (1) - here is where I have the problem, now, I know that it simplifies down to fg(x)...
  47. C

    Domain of a Radial Function

    Homework Statement Find the domain of the function. h(x) = \sqrt{4 - x} + \sqrt{x^2 - 1} Homework Equations a2 - b2 = (a - b) (a + b) I think that's all... The Attempt at a Solution For starters, I know we can't have a negative number in the radical. I looked at the 2nd radical first and...
  48. R

    Transient (Time domain) in transmission lines

    Hello. I am watching this video: https://www.youtube.com/watch?v=xIQtnQ9XPbE and he says there: I see that the wave turns into a "normal" sinus in the end, but it's not constant. I think, that even on an unmatched transmission line, the waves should go back and forth, but eventually...
  49. F

    Does the Dirac measure still exist on a complex domain?

    does the Dirac measure still exist with complex variance? The Dirac delta function can be rigorously defined as a measure. See http://en.wikipedia.org/wiki/Dirac_delta_function#As_a_measure For the gaussian form of the Dirac delta function we have, \[ {\rm{\delta (x - x}}_0 ) =...
  50. L

    Domain of logarithmic funtion

    6throute (x-7) -------------- log11(13-x) What is the domain of the function in interval notation. I know to set x-7 > 0, so that gets me x>7 , and I know I have to set 13-x > 0, which gets me x < 13. But the notation that is correct is [7,12)U(12,13). Where do you...
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