Example Definition and 845 Threads

I am reading Stephen Lovett's book, "Abstract Algebra: Structures and Applications" and am currently focused on Chapter 5 ... I need some help with Example 5.2.1 in Section 5.2: Rings Generated by Elements ... In the Introduction to Section 5.2.1 (see text above) Lovett writes: " ... ... R[S]...

Hello, We should get the length x , when the grabber can just hold the box. I made two moment equations: Then I put them together into one equation: And from that equation I found out x: Unfortunately the result seems to be wrong. Can you please help me? Where I made the mistake?

So I am reading a handout on transfer functions, and I got to this one example that doesn't seem right to me - which usually means I'm missing something. It looks like this: My understanding is that the numerator in H(s) is supposed to be the laplace transform of the input for the...

Hi, I have the following: Let ##\Omega ## be a discrete subgroup of ##C##, the complex plane. If: i) ##\Omega = \{nw_1 | n \in Z\} ##, then ##\Omega ## is isomorphic to ##Z##. ii) ##\Omega = \{nw_1 + mw_2 | m,n \in Z\} ## where ##w_1/w_2 \notin R ## , then ##\Omega## is isomorphic to ##Z## x...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Chapter 1, Section 1.4 Modules ... ... I need help with the proving a statement Bland makes in Example 13 ... ... Example 13 reads as follows:In the above text from Bland, we read the following: " ... If $$N$$ is...

Homework Statement Give the example and show your understanding: [1][/B].Lets define some property of a point of the function: 1. Point is a stationary point 2. Point is a max/min of a function 3. Point is a turning point of a function If possible name a function whose point has properties of...

There a simple math example that I am confused ##(\sqrt {-4})^2## Theres two ways to think 1-##\sqrt {-4}=2i## so ##(2i)^2=4i^2## which its ##-4## 2-##\sqrt {-4}##.##\sqrt {-4}##=##\sqrt {-4.-4}=\sqrt{16} =4## I think second one is wrong but I couldn't prove how, but I think its cause ##\sqrt...

The example: An electron is trapped in a magnetic field. The electron travels along a circle in a clockwise path. It's my understanding that there is a magnetic field around the electron also circulating in a clockwise direction perpendicular to it's path. Now if this electron was in a...

I'm trying to understand image and pre image better but I am having a hard time finding good examples. So here is one I did come across, let's say ##f:\mathbb{R} →\mathbb{R}## defined by ##f(x)=x^{2}##. Suppose also that ##D = [-1,2]## where ##D\subset \mathbb{R}##. If I'm looking for...

Homework Statement Consider the function $$ f(x) := \begin{cases} 0, & if~ x \in (0,1) - \mathbb{Q} \\ \frac{1}{q}, & if~ x = \frac{p}{q} \in (0,1) \cap \mathbb{Q} \mbox{ in lowest terms. } \\ \end{cases} $$ In his Calculus book, Spivak shows us that ##\lim_{x \rightarrow a} f(x) = 0## for...

Ok, so here's another example Morin did in his book: Ok, so the thing that confuses me is when he used the velocity addition equation: Note:4c/5 and 3c/5 are their speeds relative to the ground. Where v2 is the velocity of the S' frame, and v1 is the velocity of the object moving in the...

Suppose we have a product formed by a multiplication of a unitary matrix U and a diagonal matrix A, can we retrieve the inverse of A without knowing either U or A?

Ok, so here's an example from David Morin's book that I seriously don't understand: Two clocks are positioned at the ends of a train of length L (as measured in its own frame). They are synchronized in the train frame. The train travels past you at speed v. It turns out that if you observe the...

Question :- The critical volume of a gas is 0.072 L mol-1. What will be the radius of the molecule in cm ? Answer in the book :- ##V_c = 3b \implies b = 0.024 L mol## ##\therefore## for every molecule ##b = {24 \text{cm}^3\over 6 \times 10^{23}} = 4 \times 10^{-23}\text{cm}^3## per...

Homework Statement Example 5.3 from The Marion Thornton book (fifth edition) of Classical Dynamics states the following problem: Consider a thin uniform circular ring of radius a and mass M. A mass m is placed in the plane of the ring. Find a position of equilibrium and determine whether it...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of Example 1.27... Example 1.27 reads as follows: My questions on Example 1.27...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of Example 1.27... Example 1.27 (including a short preamble and Definition 1.26) reads as follows: My...

I have been trying to show that $$\lim_{U\rightarrow\infty}\int_C \frac{ze^{ikz}}{z^2+a^2}dz = 0 $$ Where $$R>2a$$ and $$k>0$$ And C is the curve, defined by $$C = {x+iU | -R\le x\le R}$$ I have tried by using the fact that $$|\int_C \frac{ze^{ikz}}{z^2+a^2}dz| \le\int_C...

Homework Statement Bead on spoke: constant speed ##u## along spoke it starts at center at ##t=0## angular position is given by ##\theta=\omega t##, where ##\omega## is a constant Homework Equations ## \frac{d\hat r}{dt} = \dot \theta \hat \theta ## (1) ## \frac{d\hat \theta}{dt} = -\dot...

I have seen the implementation of L-BFGS-B by authors in Fortran and ports in several languages. I am trying to implement the algorithm on my own. I am having difficulty grasping a few steps. Is there a worked out example using L-BFGS or L-BFGS-B ? Something similar to...

There is waterpipe with smooth interior wall as shown in the figure.The curve of waterpipe could be describe as function ##q_y=f(q_x)##. A ball going through this pipe was put at ##O## point with zero initial speed.At the point ##(q_x,q_y)##,the speed of the ball could be decomposed as...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.2: Noetherian and Artinian Modules and need some help to fully understand Example 6 on page 109 ... ... Example 6 reads as follows: In the above example Bland asserts that the matrix ring##\begin{pmatrix}...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.2: Noetherian and Artinian Modules and need some help to fully understand Example 6 on page 109 ... ... Example 6 reads as follows:In the above example Bland asserts that the matrix ring $$\begin{pmatrix}...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.2: Noetherian and Artinian Modules and need some help to fully understand Example 4 on page 108 ... ... Example 4 reads as follows: In the above text, I do not understand the proof that $$R$$ is not left...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.2: Noetherian and Artinian Modules and need some help to fully understand Example 4 on page 108 ... ... Example 4 reads as follows: In the above text, I do not understand the proof that ##R## is not left...

I am reading T. Y. Lam's book, "A First Course in Noncommutative Rings" (Second Edition) and am currently focussed on Section 1:Basic Terminology and Examples ... I need help with an aspect of Example 1.14 ... ... Example 1.14 reads as follows: https://www.physicsforums.com/attachments/5984...

I am reading T. Y. Lam's book, "A First Course in Noncommutative Rings" (Second Edition) and am currently focussed on Section 1:Basic Terminology and Examples ... I need help with an aspect of Example 1.14 ... ... Example 1.14 reads as follows: I cannot follow why the results in Table 1.16...

I've been asked to replace a professor for a couple of classes in an undergraduate quantum mechanic course. I have to present some topics on angular momentum, including the addition of angular momentum. I have no problem with the general theory and can present it just fine. But I would like to...

Homework Statement A man of mass 100 kg can pull on a rope with a maximum force equal to two fifths of his own weight. [Take g = 10 ms^2] In a competition, he must pull a block of mass 1600 kg across a smooth horizontal floor, the block being initially at rest. He is able to apply his maximum...

Homework Statement Homework Equations Between Radio Waves and Protons is where my confusion lies; Online I read that Radio waves are non ionizing but if that's the answer then how are protons ionizing? I mean it's no even included in the types of ionizing radiation here...

I am currently self-studying Mathematical Methods for Studying by Weber, Arfken and Harris. In the chapter Matrix Eigenvalue problems, I'm stuck in a particular step in a particular problem. Please look at the Image attached. The expression which is boxed, $$\frac{F_x}{F_y}\neq\frac{x}{y}$$ in...

I am trying to do a calculation using a value of -211dB re uPa/V , are these SI units? i.e. if OCV = -211db re uPa/V and I have RL = 20log(Vrms) - OCV Do I need to convert the OCV to standard units before putting it in the equation? Wiki isn't so clear about this:

I am trying to find and solve the geodesics equation for polar coordinates. If I start by the definition of Christoffel symbols with the following expressions : $$de_{i}=w_{i}^{j}\,de_{j}=\Gamma_{ik}^{j}du^{k}\,de_{j}$$ with $$u^{k}$$ is the k-th component of polar coordinates ($$1$$ is for...

Hi, I am just going through a textbook on electronics and have come across an explanation that uses potential dividers to work out potential values for resistors. I was wondering if anyone is able to explain how the author got the bit after "which can be written as": R1=(4.9/10.1)*R2 How did...

Do I substitute A_\mu + \partial_\mu \lambda everywhere A_\mu appears, then expand out? Do I substitute a contravariant form of the substitution for A^\mu as well? (If so, do I use a metric to convert it first?) I’m new to Ricci calculus; an explanation as to the meaning of raised and lowered...

Youtube vid of an Einstein's Train example: From the perspective of the man on platform, the rear of the train seems to be approaching the front lightning's light at greater than c (train's speed + c). Is this correct? I thought there was a rule against that...

[I apologise for repeating this post ... but I genuinely would like help ... and the post comes from September 2015 ... and so is not an impatient "bump" of an item ... I hope administrators will understand ...] =====================================================I am trying to gain an...

How is in a bicycle puncture, the air flowing out of the puncture constitutes as an example for work done?

What does it mean to treat something as a point mass. Give an example as well. Thank you.

Homework Statement Here's a standard example of special relativity in action: The mean lifetime of the muon as measured in a laboratory is about 2µs (rounded to 1 s.f.). Thus, the typical distance traveled by a muon should be about ##3\times 10^8ms^{-1}\times 2\times 10^6s = 600m##. The...

I don't have much spear time at the moment, but I came across a SMPS diagram in this thread: https://www.physicsforums.com/threads/quick-question-about-inverter-tx-order-wrt-mains.870309/ And I was trying to figure it out, and I don't want to forget about it before I do. So I was wondering if...

Homework Statement Homework Equations A=epsilon*l*c The Attempt at a Solution So I was wondering on how to set up the equations now, since I don't have much information? Which equations should i use to solve the problem?

Hello all. In Morin's classical mechanics book, chapter 12 (relativistic dynamics), in the axample about the relativistic rocket, we have a rocket that propels itself converting mass into photons and firing them back. Here Morin takes dm as a negative quantity, so the instantaneous mass of the...

The normal subgroup of a normal subgroup need not be normal in the original group (normalcy is not transitive). Could somebody provide me with an example of where this is the case? Thanks :D

I am reading Paolo Aluffi's book: Algebra: Chapter 0 ... ... I am currently focussed on Section I.3 Categories ... ... and am trying to understand Example 3.8 which is introduced as a concrete instance of the coslice categories referred to in Example 3.7 ... Examples 3.7 and 3.8 read as...

I am reading Paolo Aluffi's book: Algebra: Chapter 0 ... ... I am currently focussed on Section I.3 Categories ... ... and am trying to understand Example 3.8 which is introduced as a concrete instance of the coslice categories referred to in Example 3.7 ... Examples 3.7 and 3.8 read as...

Homework Statement A simple classical example that demonstrates spontaneous symmetry breaking is described by the Lagrangian for a scalar with a negative mass term: ##\mathcal{L}=-\frac{1}{2}\phi\Box\phi + \frac{1}{2}m^{2}\phi^{2}-\frac{\lambda}{4!}\phi^{4}##. (a) How many constants ##c##...

Hello I have to search for a few solved examples in fortran and understand them so next week i can make a presentation and explain into the other students. It is a homework for everyone and i don't know which programm i should use. there are few homepages which have many examples but they are...

I am reading Bruce N. Coopersteins book: Advanced Linear Algebra (Second Edition) ... ... I am focused on Section 10.3 The Tensor Algebra ... ... I need help in order to get a basic understanding of Example 10.1 in Section 10.3 ...Example 10.1 plus some preliminary definitions reads as...

I am reading Bruce N. Coopersteins book: Advanced Linear Algebra (Second Edition) ... ... I am focused on Section 10.3 The Tensor Algebra ... ... I need help in order to get a basic understanding of Example 10.1 in Section 10.3 ...Example 10.1 plus some preliminary definitions reads as...