Example Definition and 879 Threads

Hello! (Smile) It stands that $R[A \cap B] \subset R[A] \cap R[B]$, since: $$y \in R[A \cap B] \rightarrow \exists x \in A \cap B: xRy \rightarrow \exists x(x \in A \wedge xRy) \wedge (x \in B: xRy) \rightarrow y \in R[A] \wedge x \in R[B] \rightarrow y \in R[A] \cap R[B]$$ But, it doesn't...

Hello! (Wave) Let $R$ be a relation and $A$ a set. The restriction of $R$ to $A$ is the set: $$R\restriction A=\{ <x,y>: x \in A \wedge <x,y> \in R\}=\{ <x,y>: x \in A \wedge xRy\}$$ For a relation $R$ and a set $A$, it stands that: $$dom(R \restriction A)=dom(R) \cap A$$ Could you give...

Hi, I have some trouble understanding if linear momentum and angular momentum (and their conservation laws) are completely independent or not. For example, one can calculate the angular momentum of a uniformly moving body with respect to a fixed point in space and show that it is indeed...

Homework Statement This is from Baby Rudin Exercise 2.20- Are closures and interiors of connected sets always connected? (Look at subsets of \mathbb{R}^2 ). Homework Equations The interior is the set of all interior points for a set E that is a subset of a metric space X. A subset Y of a...

Homework Statement Look at the attached file. 1) Why does Griffith simply say that the E-field of the amperian loop is parallel to the axis of the wire? 2) And how come ##\int \vec{E} \cdot d \vec{l} = -E(s) l ## ? Shouldn't it at least be ## E(s) 2l## ? Why the minus sign and ##l## instead...

I have a course next semester on Classical Mechanics (mostly Lagrangian problems), for a second time. I'm ok for the theoretical preparation, but I'm trying to work ahead on problems and exercises, which was badly explained and without much of any resources. So, one of the sources to exercise on...

A few months ago my door broke, so can I say the Entropy of the door is increased? This is because I read that Entropy is wear and tear. So the door broke due to wear and tear.

Hi All, Recently we've been working on the distinction between the Eulerian and Lagrangian approaches in Fluid mechanics. I understand the simpler examples like a running stream of hot water etc. However one example is really tripping me up. So what's confusing me is that in analyzing...

Hi , Can anyone please give me an idea to disprove the following with counter example: A , B & C be sets. If A X C = B X C , the A = B . I tried giving random numbers in venn diagram but didn't work. And, using subset way to prove equal but still couldn't solve it.

Today in class, there was an example where I didn't understand certain justifications. The example goes something like this: A casino runs a game of chance where you toss a coin and they pay $1 if you get heads , and you pay $1 if you get tails. The coin is a fair coin. A gambler starts...

On the surface of a unit sphere two cars are on the equator moving north with velocity v. Their initial separation on the equator is d. I've used the equation of geodesic deviation...

http://i.imgur.com/GP6QorG.jpg I don't follow the integration in it. I'm assuming Fx(x,0) and Fy(1,y) are the partial derivatives of F with respect to x and y, respectively, but given that, I can't seem to get my head around the result where the partial with respect to x is Fx = (x, 0) instead...

In the presence of a magnetic field with vector potential \vec A and an electric field, the Schrodinger equation for a charged particle with charge q and mass m becomes: \frac{1}{2m} (\frac{\hbar}{i} \vec \nabla-q\vec A)^2 \psi =(E-q \phi)\psi Another fact is that, Schrodinger equation...

Hi, okay here's the problem: *find fl(x) for 9.4* and here's how it's done 9.4 in binary is 1001.0110 0110 0110 since 9 = 1001 .4 = .0110 0110 0110... (basically, 0110 repeating) next using Rounding to Nearest Rule (see top on picture) we get what a binary number (boxed in black in the...

I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). I need help with understanding Example 2.1.2 (ii) (page 39) which concerns V = K^n viewed as a module over the polynomial ring K[T]. Example 2.1.2 (ii) (page 39) reads as follows:In...

I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). At present I am focussed on Chapter 2: Direct Sums and Short Exact Sequences. Example 2.1.2 (i) on pages 38-39 reads as follows:https://www.physicsforums.com/attachments/2957 In the...

I can't tell you how many attempts I've had at this. I must be following the current wrong, or something... PLEASE HELP.. this is an example from the chapter! I feel very stupid...

Hello Forum, The 1D harmonic oscillator is an important model of a system that oscillates periodically and sinusoidally about its equilibrium position. The restoring force is linear. There is only one mode with one single frequency omega_0 (which is the resonant frequency). What about the...

This is not a problem, it is just a concept check :shy: What does it mean that something does not impart linear momentum to the rest of the system? For example grain leaking out a train car.

Homework Statement example: S(18 09 12 3d 11 17 38 39) = 5fd25e03 Homework Equations The Attempt at a Solution So I know about DES that you split a 64 bit block into left and right halves 32 bits each. Where even bits are on the left and odd are on the right. Perform the round...

I am reading Section 6.4: Splitting Fields in Beachy and Blair: Abstract Algebra. I am currently studying Example 6.4.2 on page 290 which concerns the splitting field of x^3 - 2 \text{ over } \mathbb{Q} . In Example 6.4.2, B&B show that the splitting field of x^3 - 2 \text{ over }...

I am reading Dummit and Foote, Chapter 13 - Field Theory. I am currently studying Example 4 [pages 515 - 516] I need some help with what D&F call a simple computation. Example 4 on pages 515-516 reads as follows: Now in the above example, D&F write the following: " ... ... In this case, a...

Can you guys give me a concrete example of a completely positive map from M_m → M_n?

Could someone send me some examples of B-spline curve and NURBS curve? Thank you

Hey! :o I have to solve the following system using the method of the characteristics. $$u_t+uu_x+p_x=0$$ $$p_t+up_x+pu_x=0$$ I have done the following: $$A=\begin{bmatrix} u & 1\\ p & u \end{bmatrix}$$ The eigenvalues are: $\lambda=u \pm \sqrt{p}$ - $\lambda=u+\sqrt{p}:$...

Homework Statement I'll be using ≈ as the equivalence symbol. If m and n are integers, define m≈n to mean that m-n is even. Then ≈ is an equivalence on Z. and [0] = {x→Z | x≈0} is the set of even integers [1] = {x→Z | x≈1} is the set of odd integers where the x→Z was used to...

In my physics book the equation for apparent weight is given as FN = mg + ma where FN is the normal force, m is the mass of the object, g is the gravitational acceleration of the object (= 9.8 m/s2) and a is the acceleration of the system. For example the system could be someone standing on a...

Homework Statement Hi,guys I have a example, i understand almost everything but i have problems understanding some steps. Example: 2u't+3u'x=0,x\inR,t>0,u(x,0)=sin(x),u=u(x,y) The Attempt at a Solution I rewrite the example (1)2u't+3u'x=u's (2)u'tt's+u'xx's=u's From comparing (1)...

On the mathworkd website, they have a case example of Kalman filtering here. What is the system and measurement noise covariance in this example?

Here is a example 1.3 from analytical dynamics of Haim Baruh. a particle moves on a path on the xy plane defined by the curve y=3*x^2 , where x varies with the relation x= sin(a). find the radius of curvature of the path and unit vectors in the normal and tangential directions when a=pi/6...

My friend, who is a beginner in college mathematics, recently asked me to teach her linear algebra. She has a good grip on High School math. I am looking for an amusing theorem in linear algebra which can be appreciated by a beginner in college mathematics and at the same time arouse interest...

Homework Statement Give an example of show that no such example exists. A two dimensional subspace of C[0,1] Homework Equations None that I know of. The Attempt at a Solution I know that C[0,1] is a set of continuous functions but I'm not sure where to go after that.

Can you guys give me example for conduction, convection, radiation energies ?

example of "For every b ∈ R7, the system ATx = b is consistent" Homework Statement "For every b ∈ R7, the system ATx = b is consistent" I'm not sure if this is the right place to post this question. There's isn't a subsection known as 'general math' for me to post. What does the...

Hey Guys! I'm stick on this question, I know that the summation of n=0 to infinity for x^n/n! equals e^x In the question it wants me to come up with a corresponding summation for the function x^2(e^(3x^2) - 1) … I don't know how to manipulate it to get the -1. I know i can substitute x for...

Homework Statement Here is the example along with the solution: What I don't get is what happened to the R_E value. So in this model does it neglect this value? It seems like R_E could be anything and you would still get the same model.I have another question, for this same example, it asks...

I am reading Dummit and Foote Section 10.4: Tensor Products of Modules. I would appreciate some help in understanding Example (8) on page 366 concerning viewing the quotient ring R/I as an (R/I, R) -bimodule. Example (8) D&F page 370 reads as follows: (see attachment)...

I am reading Dummit and Foote Section 10.4: Tensor Products of Modules. I would appreciate some help in understanding Example 2 on page 366 concerning viewing the quotient ring R/I as an (R/I, R) -bimodule. Example (2) D&F page 366 reads as follows...

Homework Statement So I'm having some trouble understanding this paragraph from my textbook. I was hoping that maybe someone could explain it to me. For example, we can assume that the ground is an inertial frame provided we can neglect Earth's astronomical motions(such as its rotation)...

I am reading Dummit and Foote, Section 10.4: Tensor Products of Modules. I am currently studying Example 3 on page 369 (see attachment). Example 3 on page 369 reads as follows: (see attachment) ------------------------------------------------------------------------------- In general...

I am reading Dummit and Foote, Section 10.4: Tensor Products of Modules. I am currently studying Example 3 on page 369 (see attachment). Example 3 on page 369 reads as follows: ------------------------------------------------------------------------------- In general, \mathbb{Z} / m...

I am reading Dummit and Foote Section 10.4: Tensor Products of Modules. I am currently studying Example 2, page 363 (see attachment) and I am trying to closely relate the example to Theorem 8 and the D&F text on extension of the scalars preceding Theorem 8 on pages 359-362) In Example 2 (see...

Homework Statement So I have this rather komplex example and I am looking for help. ∇(3(r*a)r)/R5 -a/R5) r=xex+yey+zez a-constant vector R=r1/2 Homework Equations The Attempt at a Solution So the nabla " works" on every member individualy,and i have to careful here:(r*∇a),because...

Please give me example of antipodal set in infinite dimensional?

Hi there, When it sounds like I am hearing the world from underwater for a few hours/few days after a very loud music concert, is that what is called temporary threshold shift? Or is TTS something that occurs only during the exposure to high dB? (Eg. at the loud concert itself). Thank...

I know there are other things that fail about the rutherford atom but as the electron is accelerating and radiating away energy it would fall into the nucleus, my question is how much energy would the electron need to gain so that the classical atom could be stable a hydrogen atom for example

I'm a little unsure about an example of a surface integral I've come across, in which the method of projection is used. The example finds the surface area of a hyperbolic paraboloid given by z=(x2-y2)/2R bounded by a cylindrical surface of radius a, such that x2+y2=<2. The first issue I'm...

I am reading Dummit and Foote, Example 2 of Section 15.4, page 708. Rewriting the assertions of the example as exercise style questions, EXAMPLE 2, reads as follows: ------------------------------------------------------------------------------------- Let R be any commutative ring with 1 and...

Hi, I am trying to learn something about Bayesian Analysis by doing an example. I have a series of 10 matches played between A and B, where each match is the first to 3 points. With an example data set that looks like this: ABBAA BAAA AABBA BBB BABB AAA AABA BAAA AABBB AAA I...

In the definition of smooth manifolds we require that the transition functions between different charts be infinitely differentiable (a circle is an example of such a manifold). Topological manifolds, however, does not require transitions functions to be smooth (or rather no transition functions...