Domain Definition and 704 Threads

Hey! :o I want to show that an Artinian integral domain is a field. Let $R$ be an Artinian integral domain and $a\in R$ with $a\neq 0$. Can we take then the sequence $(a)\supseteq (a)^2\supseteq (a^3)\supseteq \dots $ ? (Wondering) Since $R$ is an Artinian integral domain we have that...

Homework Statement I'm having issues with a Laplace problem. actually, I have two different boundary problems which I don't know how to solve analytically. I couldn't find anything on this situations and if anybody could point me in the right direction it would be fantastic. It's just Laplace's...

Homework Statement Find the domain of this function and check with your graphing calculator: f(x)=(1+cosx)/(1-cos2x) Homework EquationsThe Attempt at a Solution i get to (1+cosx)/(1+cosx)(1-cosx) which is factored. so then setting each one to zero one at a time i figure out that cosx = -1 and...

How can I specify the domain of a function symbolically? Assume I have a very simple linear function. $f(x)=2x$ If I want to say that the domain of this function is all the real numbers, how would I write this with symbols? Do I need to use set-builder notation? What would the set-builder...

Homework Statement Find the domain of the function: f(x,y) = xy*√(x2+y) Homework Equations The domain is the set of all input values for which the function is defined. The Attempt at a Solution D = {(x,y): xy>0} I plugged the function into Wolfram and it gave the result: D = {(x,y): x2+y ≥...

Given three parameters: $$a= \frac{(k-3)^2 \sqrt{v}}{s}, \ \ b = \frac{v}{s}(w-10s), \ \ c = s \sqrt{v}.$$ which exact values I know (that is, I know $v,s,k$ and $w$ exactly). I need to guarantee that $a<0$ (this is always satisfied in my calculations!) and $$0<b<1.08148a^2$$ For instance, if...

Homework Statement Find domain of f(x, y) = ln ((x2+2x+y2) / (x2−2x+y2)) Homework EquationsThe Attempt at a Solution Because the function is a natural ln, the restriction on the function is that everything inside the brackets has to >0, otherwise the function is undefined. I worked on the...

Please find attached a spreadsheet trying to plot an inductive/resistive circuit in the time domain and show instantaneous power and Volt Amperes. Logic tells me power can not go negative, but I am not sure my power plot is correct. Can someone please review the spreadsheet and chart to tell me...

Homework Statement ƒ(x,y) = √y + √[25-x2-y2] Homework Equations Quadratic The Attempt at a Solution The expression for f(x,y) is defined as long as x2 + y2 ≥ 25 and y ≥ 0 because of the square roots we can't have negative numbers. {(x,y) ∈ ℝ2 : y ≥ 0 and x2 + y2 ≥ 25} I'm not sure how I'd...

Homework Statement Let r be an element of an integral domain R such that r^2 = r. Show that either r = 0_R or 1_R Homework Equations integral domain means no zero divisors. The Attempt at a Solution This is fundamental as 0 and 1 solve r^2 = r and are the only solutions. However, I'm not...

Hi all, I am facing the problem while executing my fortran (77) program. please help me how to fix it. As I understood, the error means that the domain of log function has included zero values or negative values...But I could not understand...In my case... there are no zero or negative...

Homework Statement Wave equation: ytt=yxx Initial conditions: Y(x,0) =f(x) = x (0 ≤ x < 1) 2.5(5-x) (1 ≤ x < 3) 0 (Otherwise) and yt(x,0) = 0 Boundary condition: y(0,t) =0 Semi infinite domain: 0 ≤ x < infinity Homework Equations d'Alembert solution...

How do you find the Domain of \sqrt{(x^2 + 4)/(x^2 - 4)} ?

I have this function: f(x) = √3x + 2Cos(x) I have to find the local maxima and minima,where -π ∠ or equal to x ∠ or equal to 2π. 1: Differentiate the function given. f'(x) = 3/(2√x) -2Sin(x) 2: Find where f'(x) is undefined or = 0 to get critical points. 3: Find f''(x) [The second...

So I have learned that an interaction term in a Lagrangian like: L= kρσ can result in "domain wall" problems between the fields ρ and σ. I imagine this means that it can result in particles spontaneously changing mass, spin, or some other property, violating conservation laws. Is that why this...

Are there any established methods for optimizing across a 2D surface with noise? I am trying to find the maximum across a 2D surface, but the surface is extremely noisy. Ideally, I would numerically optimize a function without resorting to computing the entire surface, filtering the surface...

I think my question is more appropriate here than in the computation section. My question is: (In the context of inverse fast-fourier transforms and fast-fourier transforms) Knowing ifft(fft(x)=x might be trivial as it is almost a definition; associating it with a domain ##t## is perfectly...

Homework Statement $$ y(s) = \frac {s}{(s+1)(2s+1)} u(s) $$ Where ##u(s)## is the step function ##\frac {1}{s}## Find the output at t=0 and t= infinity Homework EquationsThe Attempt at a Solution My question is kind of basic, so I know the final and initial value theorem $$ \lim_{s \to 0}...

How to integrate $$\int_{-0.5}^{0.5} {\bigg({\frac{1}{4-2e^{-j2{\pi}f}}}\bigg)}^2 df$$

Here is the problem: If -1 is a range value for the function f(x) = -6x + 11, find the domain value. thank you for your help

(1+a)n = (1-a)n I tried following: (1+a)n = (1-a)n [(1+a)/(1-a)]n=1 but what can i do next?

Homework Statement Find the domain and range of the following function: f(x, y) = ln(x+y) Homework EquationsThe Attempt at a Solution I know that the natural log ln(x) is only defined when x>0, so does that mean that ln(x+y) is only defined when x+y>0? Also, would the range just be all positive...

How is a general path called instead of being a continuous function from an interval to some topological space, where we replace the domain from an interval to a compact set, is there a name for such a function? Perhaps I should add that the compact set is also convex.

i need help with finding the domain for a function where there is a square root , here is the picture of such questions : http://imgur.com/YcqadOe please see the picture, there are two questions in it, 35 and 37 let's start with question 35, this is how i try to solve it : x^2 - 5x > 0 x...

Homework Statement Hi, I have a problem with the following exercise. Let C={(x,y,z)∈ℝ3 : x2+y2+z2≤1, z≥√(3x2+8y2)} be a subset of ℝ3. Calculate ∫∫∫C z dxdydz.Homework Equations Spherical coordinates, given by x=ρsinΦcosθ, y=ρsinΦsinθ, z=ρcosΦ, and cylindrical coordinates which are x=ρcosα...

What is a frequency domain and how can we understand the same in practical world? How is it related to complex plain sight domain?

I'm supposed to find the domain of this function, I know I'm supposed to set the denominator equal to 0 but I don't know what to do after that, please help! $$f(x)=\frac{1}{x^{2}-x-6}$$ I can't figure out how to make this look like a real fraction but it's supposed to be 1 over x squared minus...

Isn't the domain of the derivative of a function a subset of the domain of the function itself? Does this mean that the domain of an integrand is always a subset of the corresponding indefinite integral?

What is the smallest (most trivial) integral domain? {0,1} is an integral domain but is {0} an integral domain with unity = 0 and zero = 0? If {0} is not an integral domain then why not?

This technically isn't a coursework or homework problem: I have a uniform Joint density function for the lifetimes of two components, let's call them T1 and T2. They have a uniform joint density function, both are positive it follows, and the region is 0<t1<t2<L and L is some positive constant...

I am reading Joseph J.Rotman's book, A First Course in Abstract Algebra. I am currently focused on Section 3. Polynomials I need help with the a statement of Rotman's concerning the definition of a gcd in a general domain ... the definition The relevant section of Rotman's text reads as...

Hello, I'using Matlab to simulate phase shift in frequency domain (FD). I have got real and imaginary parts of the signal after FFT. I'd like to use phase shift in FD. This works: Y=fft(y); YY=Y.exp(-i*2*pi*nk/N*samples_delay); result=ifft(YY); But in my DSP I can't use the formula above and...

Homework Statement Write down Dl/g without first calculating (l/g)(x) Homework Equations g(x)=-(1/2)x-3 l(x)=√(2-x)-3 The Attempt at a Solution g(x)=-(1/2)x-3 Dg = {x∈ℝ} l(x)=√(2-x)-3 Dl = {x∈ℝ:x≤2} Dg/l = {x∈ℝ:x≤2}

I'm trying to get a better understanding of marginal stability and the s domain in general. According to my textbook, a system that is marginally stable has poles that are conjugates of each other on the jω axis, and their magnitude are the resonant frequency for which if a sinusoid of that...

This is a soft question but I think it's a real fact.The Frequency domain has made revolution in the field of Mathematics,Physics,Digital Signal and image Processing etc. Some of concepts which are very difficult to analyse in spatial or time domain can be very easily understood in the frequency...

I need explanation

hey! How do you work out the domain and range of fg(x), do you work out what range of g(x) will fit the domain of f(x)? I have no clue. Thanks

Homework Statement Specify the domain and range of f(x, y) = arccos(y − x2). Indicate whether the domain is (i) open or closed, and (ii) bounded or unbounded. Give a clear reason in each case.Homework EquationsThe Attempt at a Solution y-x2 >= -1 y >= x2 -1 y-x2 <= 1 y <= x2 +1 I sketched it...

**Motivation:** I am studying for an exam over Chapters $1-3$ of *Real Analysis* by Royden and Fitzpatrick, 4th edition. I am stuck on understanding some of Proposition $11$, which I have reproduced below: **Proposition 11:** Let $f$ be a simple function defined on $E.$ Then for each...

Homework Statement Find the domain of the function f(x,y) = 1/sqrt(x^2-y). Sketch the level curves f=1, f=1/2, f=1/3. Homework EquationsThe Attempt at a Solution Domain is rather simple to find: x^2>y AND x^2-y cannot equal 0. Level curves are also simple to find. They are simply parabolas...

Homework Statement Hey guys. So basically I'm doing some Calc I homework and I'm working on the domain of this function: g(x) = √tan(2x+π) Homework Equations Now to determine the domain, I know that the function under the root cannot be negative. The Attempt at a Solution So after...

Hey Try to figure out the way to find domain of the function ascsin (x+y) without using the formula can someone give the clue how I should start ? Always confuse about inverse of trigonometry function. Thanks in advance.

What is the domain of $$y^2-2y=x^2-x-1$$? I don't know how to find it for implicit functions.

A wave function is a function in a Hilbert space of functions. When representing a physical sytem, what are the conventions for defining the domain and codomain of the wave function? For example, is the domain always the scalar variable representing time? Is the codomain a set of finite...

Okay, so if r,s are elements of R and rs = 0 then either r or s has to equal zero. I'm just confused because it seems that if rs = 0 then we can show that both r and s must be zero... I don't know what I'm doing wrong.. rs = 0 r^-1(rs) = r^-1(0) = 0 1s = 0 s = 0 and then: rs = 0 r(ss^-1) =...

Hi all, I would like to know why the Transfre function of the system is represented in S Domain instead of doing all the math in time domain itself. I studied a course on control systems and i wonder why s- domain is taken instead of other domains like Z- domain and others. Please refer belwo...

Hi Folks, I have an article which explains the modulation of 2 signals given by X_1(f) e^{-j 2 \pi f t_i} and X_2(f) e^{-j 2 \pi f t_i} The only difference between the 2 signals is a time delay, however i don't see a phase difference in either expression It states the convolution of these...

I was thinking about a function whose domain and range are absolutely one point , then I'm stuck in finding the domain and range of the following function .. could anyone help $$y=\sqrt{x^2+y^2}$$

Hi! (Smile) Can I justify like that, that $C[x,y,z]/<y-x^2,z-x^3>$ is an integral domain? We show that $ker(\phi)=<y-x^2,z-x^3>$. From the theorem of isomorphism, we have that $C[x,y,z]/<y-x^2,z-x^3> \cong im(\phi)$ $im(\phi)$ is a subring of $\mathbb{C}[x]$ $\mathbb{C}[x]$ is an...

I am reading a graduate-level Abstract Algebra lemma on noetherian integral domain, I am bring it up here hoping for pointers. The original passage is in one big-fat paragraph but I broke it down here for your easy reading. Let me know if I forget to include any underlying lemmas, thank you for...