Example Definition and 879 Threads

I am reading "Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 7: Field Extensions ... ... I need help with Example 7.2.7 ...Example 7.2.7 reads as follows: In the above example from Lovett, we read the following: " ... ... From our...

Homework Statement If the centripetal force is at the left side of the equation; that means if we move it over to the other side, it'll have a negative sign, which means it is opposite in sense in relation to N and mg. But how is that possible, considering that the centripetal force always...

Hi just curious, What is the computing/networking model for a site with many users, say, as PF? Is it to grant access to each user to a shared drive? Sorry if this is too simple. I mean, I understand that first I login and I have to be first authenticated, then authorized to access certain...

Homework Statement Homework Equations [/B] Definition: A sequence X_1,X_2,\dots of real-valued random variables is said to converge in distribution to a random variable X if \lim_{n\rightarrow \infty}F_{n}(x)=F(x) for all x\in\mathbb{R} at which F is continuous. Here F_n, F are the...

https://www.theguardian.com/society/2016/apr/07/the-sugar-conspiracy-robert-lustig-john-yudkin Lots of important lessons here, for scientists, teachers, and the general public who consumes and often makes personal decisions based on science news.

Hi was reading about differential forms, when I tried to solve the example given in this pdf https://www.rose-hulman.edu/~bryan/lottamath/difform.pdf. According to it, the answer is that on the image above. But when I tried to solve this same example by following the expression for ##w## given...

Homework Statement [/B] Give examples of fixed points of vector fields and maps that are stable in the linear approximation but are nonlinearly unstable Homework EquationsThe Attempt at a Solution [/B] I was able to find an example in a vector field that, when the Jacobian is found and the...

Homework Statement Provide a counter example to the false assertion: Suppose that f and g are functions and f ◦ g is invertible. Then f and g are invertible. Homework Equations Definitions: An invertible function is 1-1 and onto If the image of g is not contained in the domain of f then f ◦...

Hi guys, I have a question to all of you. This question is based on the example which is located here: http://galileo.phys.virginia.edu/classes/252/time_dil.html I understand it but there is one thing is still unclear to me. So, here it is: Again we have Jill on the rocket and poor Jack on the...

Hello. I would like to check my understanding of how you transform the covariant coordinates of a vector between two bases. I worked a simple example in the attached word document. Let me know what you think.

I am ultimately trying to get Mathematica to solve some equations which are related to a tunnelling problem with an oscillating delta potential. I have the coefficients for absorption and emission: $$ T_n = \frac{sm}{i\hbar^2} (T_{n-1} + T_{n+1})$$ $$T_q = \frac{sm}{2ik_q \hbar^2} (T_{q-1}...

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: " ... ...

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 a...

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?