What is domains: Definition and 114 Discussions

In molecular biology, a protein domain is a region of a protein's polypeptide chain that is self-stabilizing and that folds independently from the rest. Each domain forms a compact folded three-dimensional structure. Many proteins consist of several domains, and a domain may appear in a variety of different proteins. Molecular evolution uses domains as building blocks and these may be recombined in different arrangements to create proteins with different functions. In general, domains vary in length from between about 50 amino acids up to 250 amino acids in length. The shortest domains, such as zinc fingers, are stabilized by metal ions or disulfide bridges. Domains often form functional units, such as the calcium-binding EF hand domain of calmodulin. Because they are independently stable, domains can be "swapped" by genetic engineering between one protein and another to make chimeric proteins.

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  1. N

    Functions and domains. Please check my answers.

    Homework Statement Question 1: Which of the following define y as a function of x on R (Real number). Explain for each why they are/ are not function. a) 4x^3 + y = 6 b) x - y - square root x = 8 c) x = cos^2 y d) y = (2x + 3) / (x - 1) Question 2: Let g(x) = sin(x) and h(x) = 1/x...
  2. Ygggdrasil

    Are there really three domains of life?

    Most biology textbooks state that life can be classified into three domains: bacteria, eukarotes, and archaea. This classification began from early studies looking at the evolutionary relationship between these three groups of organisms that concluded that all archaea are more similar to...
  3. S

    Why Do Ferro- magnetic/electric Domains Exist?

    In short, what I am asking is what is the reason/cause of the formation of ferro- magnetic/electric domains, and how would one calculate the 'driving energy' in order to predict domain formation? If we consider a dipole system that experience “ferromagnetic” coupling (my question does not...
  4. d1ngell

    Regarding the finding of domains of functions

    First of all, I would like to appologize if I'm posting this in the wrong section, although I believe it to fit this area. I'm usually not convinced when books claim to have found the natural domain of certain functions. For instance, this book I've been reading has defined the natural domain...
  5. B

    Perturbation Theory on Finite Domains

    In this video (from 27.00 - 50.00, which you don't need to watch!) a guy shows how you can solve the general second order ode y'' + P(x)y = 0 using perturbation theory. However he points out that the domain must be finite in order for this to work, I'm wondering how you would phrase a question...
  6. Math Amateur

    MHB Principal Ideals and Bezout Domains - (a,b)

    Just a further (very basic!) question: Is the following argument - working from definitions - correct Does (a) + (b) = (a,b)? --------------------------------------------------------------------------------- By definition (Dummit and Foote page 251) (a, b) = \{r_1a + r_2b \ | \ r_1...
  7. L

    Question about rational expressions and their domains

    Hi there. I am currently taking "College Math 1" at the local CC and I have encountered something that confuses me regarding rational expressions and their domains. The definition given by the textbook for rational expressions is: "the set of real numbers for which an algebraic expression is...
  8. Math Amateur

    MHB Integral Domains and GCDs

    I am reading Dummit and Foote Sections 9.3 Polynomial Rings that are UFDs. I have a problem understanding what D&F say regarding GCDs on page 306 at the end of Section 9.3 (see attached) D&F write: ====================================================================================== "we...
  9. Math Amateur

    MHB Integral Domains and Principal Ideal Domains (PIDs)

    Dummit and Foote, Section 8.2 (Principal Ideal Domains (PIDs) ) - Exercise 4, page 282. Let R be an integral domain. Prove that if the following two conditions hold then R is a Principal Ideal Domain: (i) any two non-zero elements a and b in R have a greatest common divisor which can be...
  10. P

    Numerical methods for nonlinear PDEs in large domains

    Hi all, first post :) I have a system of z-propagated nonlinear PDEs that I solve numerically via a pseudo-spectral method which incorporates adaptive step size control using a Runge-Kutta-Fehlberg technique. This approach is fine over short propagation lengths but computation times don't...
  11. Math Amateur

    MHB Prime elements in integral domains

    In Dummit and Foote, Section 8.3 on Unique Factorization Domains, Proposition 10 reads as follows: Proposition 10: In an integral domain a prime element is always irreducible. The proof reads as follows: =========================================================== Suppose (p) is a non-zero...
  12. E

    Transformations of Double Integrals with Rectangular Domains in the 1st Quadrant

    Suppose we have the double integral of a function f(x,y) with domain of integration being some rectangular region in the 1st quadrant: 0≤a≤x≤b, 0≤c≤y≤d. Would the following transformation generally be acceptable? (I've quickly tried it out several times with arbitrary integrands and domains...
  13. P

    Ring theory- zero divisors and integral domains

    Homework Statement Consider the ring Z/mZ, show that S = {[0], [a], [2a], · · · , [m − a]} forms a (possibly nonunitary) subring of Z/mZ when a divides m. (i.e. show that (S,+, ·) is closed the usual addition and multiplication. (We are not require to find a multiplicative identity)...
  14. C

    Inequalities With Parity-Specific Domains

    When I was working on a rather difficult real-life math problem, I nearly found the solution. What I came up with was two inequalities: ##X≥\frac{2b-2}{2a+1}-1## and ##Y≥\frac{2b}{2a+1}-2## and the fact that ##X>Y##. However, ##X## must be an even integer and ##Y## must be an odd integer. Is...
  15. D

    Astro-Physics: Math Struggles & Domains of Functions

    While my math struggles continue. I find my self asking if this is the right major I want to chose (astrophysics) I'm in precalculus college level lol.. We are doing domains of comp functions.. and I find it all pointless.. I am very good at algebra and trig... Is this fog (x) stuff really...
  16. K

    Complements of Ranges and Domains

    Given is the function of Set V towards Set W where A is a subset of V and B is a subset of W. Questions: Does the range of the complement of A equal the complement of the range of A? Does the domain of the complement of B equal the complement of the domain of B?I am not entirely sure how to...
  17. J

    Homomorphisms of Polynomials Over Integral Domains

    Let A be an integral domain. If c ε A, let h: A[x] → A[x] be defined by h(a(x))=a(cx). Prove that h is an automorphism iff c is invertible. This one really had me stumped. I have a general idea of what the function is doing. Now, assuming that h is an automorphism, we want to show that...
  18. K

    How Do You Solve the Inequality |x-6| > |x^2-5x+9|?

    mod(x-6) > mod(x^2 - 5x + 9) Can anyone tell me about domain fixtures with mods using the above inequation? A real beginner, so have mercy, be elementry .:D
  19. F

    Vertex of Fundamental Domains & Elliptic Points

    Dear Folks: Suppose \Gamma is a discrete subgroup of SL2(R), which acts on the upper half complex plane as Mobius transformation. F is its fundamental domain. If z is a vertex of F which does not lie on the extended real line ( that is R\bigcup\infty ) ,then must x be an elliptic point...
  20. I

    Super-fluid 4He - (two domains)

    Hi PF , I am making a review article which is mainly based on low temperature physics , upon going through my search I have stumbled across the famous " Lambda transition" of super liquid helium. Paraphrasing what some of the books said : " In the He II domain a percentage of atoms in same...
  21. B

    Integrals over different domains

    Folks, When we are evaluating integrals like the following, what are we evaluating in terms of units etc. For example if I integrate Fdx I get an area which represents the energy where F is the force and d is the displacement so the units are Nm etc. 1) Integrals over intervals ...
  22. A

    Is Every Path Connected and Open Set in the Complex Plane Simply Connected?

    Homework Statement http://imageshack.us/photo/my-images/15/unledflsq.png/Homework Equations A simply connected domain D in the complex plane is an open and path connected set such that every simple closed path in D encloses only points of D.The Attempt at a Solution The answers are a,c and d.I...
  23. D

    Integrals on arbitrary (bounded) domains

    Homework Statement Let A = \{(x, y, z) \in \mathbb{R}^n : 0 \lt x \leq 1, 0 \lt y \leq 1 - x^2, 0 \lt z \leq x^2 + y\}. Define f : A \rightarrow \mathbb{R} by f(x, y, z) = y for each (x, y, z) \in A. Accept that Fubini's theorem is applicable here. Find \int_A f. Homework Equations Fubini's...
  24. S

    Having trouble understanding Domains and Multi Variable Functions

    Hey guys, I'm doing some multivariable calculus atm, and I need some help with the Domains of some multivariable functions... 1) f(x,y) = 3x^2 + 2y The problem I'm having here is I basically forget the definition of domain... would it be for all x and y even though there are two whole quadrants...
  25. I

    Optimization problems involving non-compact domains

    I have some understanding of how to solve problems involving compact domains. Set the gradient to zero and solve for x and y, and then try to parameterize if needed to find max/min over the border of the domain. The thing is, my book doesn't go into much detail on how to do optimize functions...
  26. N

    Need help with determing domains of sin, cos, and tan

    Homework Statement Ok, this is not really a problem, but I need help on understanding the basics of sin, cos, tan, and their inverses. i was looking at http://www.analyzemath.com/DomainRange/domain_range_functions.html and it was saying that the domain for sin and cos is (-inf , + inf)...
  27. N

    FInding domains of ln problems

    Homework Statement How do you find the domain of y=ln(6-x) ? The Attempt at a Solution do i have to set 6-x greater than or equal to 0 to then get that x is less than or equal to 6, or is there more to it than that? I'm confused on where the ln part comes in. Please assist.
  28. T

    Notation for Domain Variable Expressions

    If you have an equation with a variable which isn't defined for a given value or values, how do you express this in proper notation? For example: x=1/((y-2)(y-3)) Do I write simply " y<2 or 2<y<3 or 3<y" or is there a better way to express it? Thx
  29. E

    Understanding Domains and Ranges for Inverse Functions - A Noob's Guide

    Supposing I have a function f(x). Let us suppose that f-1(x) has the same equation as f(x). Will the domain and range as defined for f(x) be the same as for the inverse ?
  30. S

    Domains of Rational Functions (standard notation)

    Im preparing for a CLEP test in precalculus. As part of my prep, I need to review identifying domains of functions. I have a question about writing domains in standard notation. I was hoping someone could explain a bit the style. For an example: x-2 / x^2 -2x -35 As a rational...
  31. E

    Factoring in Integral Domains: Can Every Element be Factored into Irreducibles?

    Homework Statement Consider the integral domain a + b \sqrt{10} . Show that every element can be factored into a product of irreducibles, but this factorization need not be unique. Homework Equations The Attempt at a Solution I know that this is not a unique factorization...
  32. E

    Expressing Elements as Products of Irreducibles in Unique Factorization Domains

    I'm having a bit of trouble with some ring theory I've been reading about, specifically unique factorization domains. I'm not really clear on how one would go about showing that an element can be factored into irreducibles Homework Statement Let R be an integral domain such that every prime...
  33. B

    Composition of functions domains

    Is it always true that the domain of f(g(x)) is the intersection of the domains of f(x) and g(x)? I've been having trouble with this and this answer would make me fully understand this concept. Thanks to everyone!
  34. L

    Functions, Domains, And equality

    Homework Statement Given an example of two different functions f and g, both of which have the set of real numbers as their domain, such that f(x)=g(x) for every rational number. 2. The attempt at a solution I have yet to figure a way to approach this problem. Since it appears as...
  35. B

    Domains for relativity vs quantum mechanics

    Popularized treatments of quantum mechanics describe it as applicable to the behavior of submicroscopic particles, while relativity applies to the very large (i.e., astronomical). This seems totally arbitrary to me. Where is the boundary between the 2 domains? Atoms? Neutrons? Quarks? Or is it...
  36. B

    Composite functions and domains

    Homework Statement The forward-back function is f (t) = 2t for 0\leq{t}\leq{3} , f(t)= 12-2t for 3\leq{t}\leq{6}. Graph f(f(t)) and find its four-part formula. First try t = 1.5 and 3. The Attempt at a Solution There are four possible composite functions from the two given...
  37. C

    Finding the sum and quotient of 2 natural domains

    Homework Statement 3. (a) Let f(x) = ln(x^2-1), and [itex]g(x)=\frac{x}{\sqrt{2-x}}[/tex] (i) Find the natural domains of f, g, f + g, \frac{f}{g}, and \frac{g}{f} Homework Equations N/A The Attempt at a Solution I know that the natural domain of f(x) is x belongs to real...
  38. S

    Localization in integral domains

    i'm working through the following text and I think I found an error please let me know if I'm totally wrong. Janusz, Gerald J. Algebraic Number Fields and I'm starting with the 3rd exercise on page 3. It is as following: let R be an integral domain and p a prime ideal of R. Show there...
  39. M

    Mappings, domains, codomains, proof of linearity

    Homework Statement For the following mappings, state the domain and the codomain. Determine whether the mapping is linear by using the definition of linearity: either prove it is linear or give a counterexample to show why it cannot be linear. i.) f(x1,x2,x3)=(2x2, x1−x3) ii.) g(x1, x2) =...
  40. L

    How can I use FindFit with complex domains?

    Hi there Suppose I have data of the format {x,y+i z} where x,y,z is real and i is the imaginary unit. I'm trying to make a FindFit of some nasty model that, suppose for simplification is f(x) = a^b*x^2+exp(a)*b*i*x (domain is real, codomain is complex and a,b are Real) and can be written...
  41. E

    Mathematica  Mathematica ignoring variable domains

    Please Help! Mathematica ignoring variable domains I had to calculate an integral, which involves real as well complex parts. As mathematica takes all variables to be complex by default I used the elements function to define that certain variables were Reals. But it doesn't change the...
  42. H

    Rings, finite groups, and domains

    Homework Statement Let G be a finite group and let p >= 3 be a prime such that p | |G|. Prove that the group ring ZpG is not a domain. Hint: Think about the value of (g − 1)p in ZpG where g in G and where 1 = e in G is the identity element of G. The Attempt at a Solution G is a...
  43. H

    Integral Domains and Fields

    Homework Statement a) show that Q(√5i) = {r +s√5i | r,s in Q} is a subfield of C. b)show that Z(√5i) = {n + m√5i | n,m in Z} is a subring of C and find the units. The Attempt at a Solution a) Let a = r + s√5i, b = r - s√5i for a,b in Q(√5i). a + b = 2r, ab = r^2 + 5s^2, and -a= -r -...
  44. Pythagorean

    Understanding Phasors: Time & Frequency Domains

    what's a phasor? What's the phasor domain? I've worked with them in my courses and I can move from the time domain to the phasor domain, but I still don't quite intuitively get what a phasor is. In physics, we move between the frequency domain and time domain easily, but they're both...
  45. S

    Why Do Magnetic Domains Aligned with a Magnet Increase in Size?

    I have a conceptual question. I have two physics books that say "In a common iron nail, the domains are randomly oriented. When a strong magnet is brought nearby, two effects take place. One is a growth in size of domains that are oriented in the direction of the magnetic field. This growth...
  46. M

    Domains of vector values functions

    Homework Statement r(t)- ln|t-1| i , e^t j , sqrt(t) k find the natural domains. this is a problem as an example in the book. Homework Equations It gives an answer of (-infinity,1) U (1,+infinity), (-infinity,+ininity) and [0, +infinity) and the intersection of these sets are [0,1)...
  47. J

    Understanding Function Equality and Domain Restrictions

    Suppose f(x) = \frac{x^2 - 1}{x-1} . Why do we say that f(x) = \frac{x^2 - 1}{x-1} = x + 1 , if \frac{x^2 - 1}{x-1} isn't defined at x = 1, but (x + 1) is defined at x = 1. I always thought that we say two functions are equal to each other if their equations are the same and their domain...
  48. L

    Q on Riemann Domains: Is P Injective on U?

    If P is the projection map from a Riemann domain M \rightarrow C^n, and U is a connected subset of M with P(U)=B, where B is a ball in C^n, then is P injective on U, so it's a homeomorphism on U? P is locally a homeomorphism by definition. It would be related to B being simply connected...
  49. S

    Simple counterexample for claim about integral domains

    So I'm looking for an example of an infinite integral domain with finite characterestic. That is a infinite integral domain such that there is a prime p such that p copies of any element added together is the additive identity. I'm just looking for a simple counterexample. I'm working...
  50. J

    Fourier transform, domains, ranges, L^p-spaces

    The Schwartz space on \mathbb{R}^d is defined to be S(\mathbb{R}^d) := \{f\in C^{\infty}(\mathbb{R}^d,\mathbb{C})\;|\; \|f\|_{S,N}<\infty\;\forall N\in\{0,1,2,3,\ldots\}\} where \|f\|_{S,N} := \underset{|\alpha|,|\beta|\leq...
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