Example Definition and 845 Threads

I am have been searching for the of a tensor product of two vectors, but found seemingly conflicting definitions. For example, one source definition was, roughly, that the tensor product of two vectors was another column vector in a higher dimensional space, and another defined the tensor...

Hi I was trying the gram schmidt process on example 1.3.2 page 43 as shown below u1=(3,0,0), u2=(0,1,2), u3=(0,2,5)v1=u1=(3,0,0) v2=u2-proj_(w1) u2=(0,1,2)-((<0,1,2><3,0,0>)/9)(3,0,0) However the top line inner product gives 0...

This is an example at the beginning of the section on the Fundamental Theorem for Line Integrals. 1. Homework Statement Find the work done by the gravitational field \vec{F}(\vec{x}) = -\frac{mMG}{|\vec{x}|^3}\vec{x} in moving a particle from the point (3,4,12) to (2,2,0) along a piece wise...

example of a varible capacitor input op-amp to voltage level circuit. I'm not sure how to turn reactance to a voltage level using an op-amp? :wink:

Hello all. I have almost finished chapter 4 on energy in Taylor's classical mechanics book. But in the last example in this chapter I got confused. Here it is: "A uniform rigid cylinder of radius R rolls without slipping down a sloping track as shown in Figure 4.23. Use energy conservation to...

http://www.nap.edu.au/verve/_resources/Example_Test_Numeracy_Y9_calc.pdf Question 28 says 46 centimeters in the answers but i got 47.5 centimeters

Homework Statement Hi, I've been working through a practice problem for which I used the fundamental theorem of calculus, or one of its corollaries. The setup is a population changing over time. The population, P(t) at t = 0 is 6 billion. The limiting population as t goes to infinity is given...

Homework Statement I'm struggling to perform a symplectic reduction and don't really understand the process in general. I have a fairly solid understanding of differential equations but am just starting to explore differential geometry. Hopefully somebody will be able to walk me through this...

I am baffled by some aspects of the torus ... I hope someone can help ... I am puzzled by some aspects of Singh's treatment of the torus in Example 2.2.5 ( Tej Bahadur Singh: Elements of Topology, CRC Press, 2013) ... ... Singh's Example 2.2.5 reads as follows: My questions related to the...

I had a discussion with my friend. He took an icecream stick and told me that if the stick was held horizontally the stick would break easily but if you held the stick vertically it would be difficult to break the stick. He said that vertically the moment of inertia is more. My question is that...

Would this example be valid in satisfying a relation that is symmetric and anti-symmetric? The relation R = {(1,1),(2,2)} on the set A = {1,2,3} Also, I'm curious to know since relations can both be neither symmetric and anti-symmetric, would R = {(1,2),(2,1),(2,3)} be an example of such a...

As many, I wondered why FTL communication has problems with causality. Went over many posts here in PF, and wasn't satisfied. And then I read this explanation, by Richard Baker: (2015-4-2, link is still active) http://www.theculture.org/rich/sharpblue/archives/000089.html His explanation is a...

Homework Statement A step in this process of proving Sn: 1+4+7+...+(3n-2) = n(3n-1)/2 confuses me. I hope someone can clarify this for me. I do not require the work done, I need clarification on a step only. Thanks! Homework Equations After assuming n=k, we say Sk: 1+4+7+...+(3k-2) =...

Homework Statement So I'm back to my wonderful computational physics course after a brief hiatus and once again, I am teaching myself the material. This unit we are working on some thermodynamics. We've just used the "Leap Frog" method to determine heat transfer of a 100k bar with both ends...

In Munkres book "Topology" (Second Edition), Munkres proves that a function F is a homeomorphism ... I need help in determining how to find the inverse of $$F$$ ... so that I feel I have a full understanding of all aspects of the example ... Example 5 reads as follows:Wishing to understand...

Hi I am working on a programming assignment that requires me to implement the successive over-relaxation algorithm. We are given the wikipedia page for this: http://en.wikipedia.org/wiki/Successive_over-relaxation. I have read through the wikipedia page for this numerous times but am still...

I am trying to give some context to medical vaporizers in a literature review I am composing and initially decided to give asthma inhalers and nasal inhalers as examples. I realized however, that some sources on-line were referring to these metered dose inhalers as vaporization devices when...

Show that the galois group for (Complex : Reals) is given by {e, y} where y is y: C-->C is the conjugation automorphism defined by y(z) = z~ (Conjugate of z) for all z in C. if o is an element of gal(C:R) and z = a + bi in C, then o(z) = o(a+bi) = o(a)+o(b)o(i) = a+bo(i) but o(i)^2 = o(i^2) =...

Homework Statement The figure gives the electric potential V(x) along a copper wire carrying uniform current, from a point of higher potential Vs = 9.00 μV at x = 0 to a point of zero potential at xs = 3.20 m. The wire has a radius of 1.50 mm, and copper has a resistivity of 1.69 × 10-8 Ω·m...

I'm having trouble figuring out how the term below boxed in red was eliminated on the left side of the equation as shown below. I reviewed properties of exponential functions, and still can't understand how this term was cancelled. 1. Homework Statement Homework Equations Exponential laws...

Hello! (Wave) I am looking at the proposition: If $(A_n)_{n \in \omega}$ is a sequence of sets and $(f_n)_{n \in \omega}$ is a sequence of functions then: for all $n \in \omega, f_n: \omega \overset{\text{ surjective }}{\rightarrow} A_n$ then there is a function $f: \omega \overset{\text{...

I need some help in fully understanding Example 1, section 4.3 Cauchy Sequences, page 73 of Apostol, Mathematical Analysis. Example 1, page 73 reads as follows: https://www.physicsforums.com/attachments/3844 https://www.physicsforums.com/attachments/3845 In the above text, Apostol writes: "...

I am having a problem understanding an example in kolenkow: an introduction to mechanics. The question I have is on page 71/section 2.9 in the red cover edition. The example is telling me to find the acceleration of the end of the rope and how it is related to the acceleration of the block. I...

Hi! (Smile) According to my notes, a set $A$ is called transitive if the elements of its elements are elements of $A$. For example, the set of natural numbers $\omega$ is a transitive set. Also, if $n \in \omega$ then $n$ is a transitive set since $n=\{0,1,2, \dots, n-1 \}$ and if we take a...

Homework Statement A simple RL circuit in series connected to a source with V(t) = 30Cos(3t+75°)V and is delivering 14.12 W of power. I'm also given the power factor which is pf=0.857 and is lagging. Find the values of R and L Homework Equations P=Vm*Im/2 * pf for power theta =...

Homework Statement An Atwood machine consists of two masses, M and m, which are connected by an inelastic cord of negligible mass that passes over a pulley. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses M and m. Homework Equations...

Are there any tutorials that apply stochastic differential equations to the settings of elementary physics problems ? - for example, an object sliding down a not-frictionless ramp. The ramps of everyday life don't have a constant coefficient of friction. A better model for them would be...

Give an example of a function f:R2-->R , continuous in (0,0), with partial derivatives in (0,0), but not differentiable in (0,0). I was thinking in something like f(x,y)=IxyI

I am looking for a local field of positive characteristic, like Q22 was used in this article: http://8pic.ir/images/s9oiiuqqkq989w3posu9.png in fact, i need an another Example of a local field of positive characteristic like Q22 .

I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Section 2.2 on free modules and need help with Example 5 showing a module with two bases ... ... Thanks to Caffeinemachine, I have largely clarified one issue/problem I had with Example 5, but now have a...

OK. We are producing something and then storing it. The first year, "1" is produced, the second year, "1,1" the third 1,12, so that the production capacity increases 10% per year. How do we convert this into a general formula for how much we have produced in total after year x? It is obviously...

I am reading Paul E. Bland's book, "Rings and Their Modules". In Chapter 1: Basic Properties of Rings and Modules, Bland gives endomorphism rings as a basic example of a ring. The example (Example 7) reads as follows:https://www.physicsforums.com/attachments/3572 I do not feel that I fully...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Section 2.2 on free modules and need help with Example 5 showing a module with two bases ... ... Example 5 reads as follows:I am having trouble understanding the notation and meaning of $$M = \bigoplus_{...

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...

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...