Definition Definition and 1000 Threads

Is ##\frac{ \partial f}{\partial n} = \nabla f \cdot \hat n ## a definition? No article that I found said it's a definition. The term ##\frac{ \partial f}{\partial n}## does not make sense to me, what is ##\partial n##? Also is this correct: \int_v\nabla\cdot (v\nabla u)dV=\int_s (v\nabla...

We have many different ways of describing and quantifying 'energy' eg kinetic, potential etc. We also know that mass and energy are equivalent. We intuitively know what it does and we talk about it across many fora but my question is 'What is Energy?'. What is this characteristic of the universe...

Homework Statement Applying the definition of a limit to show that lim ((x^3 * y(y-1) ) / (x^2 + (y-1)^2) = 0 as (x,y) approaches (0,1) The Attempt at a Solution |x| = sqrt(x^2) <= sqrt((x^2 + (y-1)^2)) |y-1|=sqrt((y-1)^2)<= sqrt((x^2 + (y-1)^2)) |y|<= |y-1| + 1 via the...

Hello.The Einstein has following definition (in my course): Gμε = Rμε - 1/2Rgμε. But why don't we just: gμεGμε = gμεRμε - 1/2Rgμεgμε. <=> G = R- 1/2 . R . 4 = R- 2R = -R? Is this wrong or.? Also, what is the meaning of the ricci scalair and tensor?

"Cosmology is the scientific study of the properties of the universe as a whole." That definition seemed concise and straight to the point for both scientist and the public. Everything else cosmology contains seems would be included within that definition. Does anyone here have a better one...

A set x is well-ordered by < if every subset of x has a least element. Here < is assumed a linear ordering, meaning that all members of a set can be compared, unlike with partial ordering. A set x is transitive if it has property \forall y\;(y\in x\to y\subset x). A set \alpha is ordinal, if...

Homework Statement Does the Cauchy Schwarz inequality hold if we define the dot product of two vectors A,B \in V_n by \sum_{k=1}^n |a_ib_i| ? If so, prove it. Homework Equations The Cauchy-Schwarz inequality: (A\cdot B)^2 \leq (A\cdot A)(B\cdot B) . Equality holds iff one of the vectors...

Homework Statement I'm in this self-learning course. I came on this problem I thought of. So, i^2=-1. But, isn't i=sqroot of -1? If so, the product of the two minus -1 and the square root of that should give 1. Am I not getting something? I searched the web with the keywords of my...

Hi, I'm getting a bit confused about the adjoint representation. I learned about Lie algrebras using the book by Howard Georgi (i.e. it is very "physics-like" and we did not distinguish between the abstract approach to group theory and the matrix approach to group theory). He defines the...

Homework Statement Prove the following: lim x2 - x = 0 x→1Homework Equations If 0<|x-a|<δ then |f(x)-L|<ε The Attempt at a Solution Part I - Set up 0<|x-a|<δ |f(x)-L|<ε If 0<|x-1|<δ then |(x^2 - x) - 0|<ε x|x-1|<ε...

Homework Statement so this is my first time learning about integrals , from spivak' calculus Actual quote : the integral \[ \int_{a}^{b} f(x) \, \mathrm{d}x \]was defined only for a<b we now add the definition \[ \int_{a}^{b} f(x) \, \mathrm{d}x \]=-\[ \int_{b}^{a} f(x) \, \mathrm{d}x \] if a>b...

What is the definition of "Engine Load" A lot of things I have read make reference to engine load but it is not clear if there are different meanings. One definition seems to be that the engine load is the amount of air flowing through the engine as a percentage of the theoretical maximum...

Definition of "View Angle of Human Eye"? I've been told (since high school I think) that "view angle" in a 2-dimensional plane is approximately (distance to the object/object's length). The assumption is that I'm viewing an object AB of length L, basically a segment in a 2-dimensional...

Homework Statement From Young and Freedman's University Physics, 9th Ed., Problem 4-49. Two blocks are connected by a heavy uniform rope with a mass of ##4.00## kg. An upward force of ##200## N is applied to the top block, which has a mass of ##6.00## kg. The lower block has a mass of ##5.00##...

Hello guys! I am trying to get a solid grasp of the Precise Definition of a Limit. I am having a particular hard time linking the intuition of the limit I developed a while ago to the Epsilon-Delta definition. I understand the basics: a limit exists/is only true if and only if for every...

Hello, my textbook says that the magnitude of centripetal acceleration is equal to the sum of the forces acting on that object. (this is in regard to an object in a circular path, by a string. See...

I'm trying to make a MATLAB plot with two types of data, i.e. temperature and air flow rate. Since the temperature and air flow rate are on different scales I wanted two y-scales and since there are quite some data sets, I wanted to make the two air flow rates bold. I tried this, but it doesn't...

I look at wikipedia.org/wiki/Bell_state and use the same notations. The article says that there are just 4 Bell states. Is not |\xi^+\rangle = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |+\rangle_B + |1\rangle_A \otimes |-\rangle_B) another maximally entangled state? The Schmidt decomposition...

Homework Statement Hello, I have to prove, using the limit definition, that \lim_{x\to 1^{+}}{\frac{x-3}{x-1}}=-\infty The Attempt at a Solution I've set this unequation \frac{x-3}{x-1} < - M but it doesn't lead to the result 1<x<1+\frac{2}{M+1}, what did I wrong ? Thanks

I was absent to a calculus III lecture last monday. I didn't miss much, and have gone over what I did. I understand the work and know how to do the problems, the only thing I'm having trouble with is actually picturing what an osculating plane is. I just need a simple explanation of what it...

Alright, I need some help with this. an = \frac{1 - 5n^{4}}{n^{4} + 8n^{3}} To find the limit of convergence, use l'Hopital's Rule. The result will come out to L = -5 From my book, "The sequence {an} converges to the number L if for every positive number ε there corresponds an...

Does anyone know what a D-domain is and a D-domain partition?

Is there a definition of quantum dot that everybody agrees? I searched intensively both from google and from web of science, but I couldn't find a formal definition. e.g (wiki says) A quantum dot is a semiconductor whose excitons are confined in all three spatial dimensions. confined but...

Homework Statement The question states True or False: Two lines parallel to a third line are parallel Homework Equations You need to know the difference between skew, parallel and perpendicular The Attempt at a Solution I thought of three parallel planes (which have an infinite...

In the attachment that I added I highlighted the portion I am questioning. I will define L[f(t)](s) to be the laplace transform of the function f(t). f(t) = e^t L[f(t)](s) = 1/(s-1). The laplace transform is defined for all values s≠1. L[f(t)](2) = 1. Question: "What do they mean by...

I've been having some doubts regarding the definition of work in thermodynamics and how it is related to the change of energy in the system. I have tried asking this in physics stack exchange but I was unable to obtain a satisfactory answer; now that I am trying again in this forum I will aim to...

The Schwarzschild Radius of an object is the length such that if the object is shrunk down that small, the escape velocity becomes equal to the speed of light. That being said, however, the escape velocity of any gravitational body matters where it is measured relative to the center of mass...

Greetings and Salutations! Currently I am not enrolled in a physics class but I am researching on my own and I was wondering if there was an algebraic definition of work and what it was if it exists. The only definition of work I know of (cursory knowledge i.e. I saw the following words...

We define time by the rate at which physical processes (i.e. clocks) tick. With atoms for example we can define time by their energy transition rates such as in atomic clocks. But, what before atoms existed? Current cosmology theories make statements such as that '0.5 seconds after the Big...

Homework Statement Verify ##\left[ x^{i} , p_{k}\right] = i \hbar \delta^{i}_{k}## Homework Equations ## p_{j} = -i \hbar \partial_{j}## The Attempt at a Solution Writing it out i get $$ i \hbar \left( \partial_{k} x^{j} - x^{j} \partial_{k} \right)$$ The Kronecker makes perfect sense, it's...

"Let R be a commutative ring. We say that M is an algebra over R, or that M is an R-algebra if M is an R-module that is also a ring (not necessarily commutative), and the ring and module operations are compatible, i.e., r(xy) = (rx)y = x(ry) for all x, y \in M and r \in R." I'm not really...

I am confused about the following points regarding the definition and causes of the Coanda effect: whether the Coanda effect is the same as normal boundary layer attachment to a surface whether the Coanda effect is only defined for convex surfaces over which a jet (of the same state as the...

I'm trashing the template here because I'm not looking for help with how to solve my homework problem. Instead, I'm looking for what my question actually means! I'm given an equation that describes a magnetic field. One of the specs I'm given is that the magnet period is 10cm. What in the...

Lets say a certain chemical reacts with an acid. Does that make that chemical a base always and vice versa? Like in S + NaOH → Na2S + Na2S2O3, Sulfur reacting with a base would it make S an acid? Or do we call it a base or an acid, reacting with the opposite if it's producing water as a...

(PS: this post was also posted at the quantum mechanics/field theory forum, but I did not get any replies there) Often when one speaks about the effective QED coupling one defines it as $$e = \frac{Z_2 Z_3^{1/2}}{Z_1} e_0 \ \ \ \ (*)$$ when ##Z_1 = Z_2## by the Ward identity this...

Often when one speaks about the effective QED coupling one defines it as $$e = \frac{Z_2 Z_3^{1/2}}{Z_1} e_0 \ \ \ \ (*)$$ when ##Z_1 = Z_2## by the Ward identity this turns out to be ##Z_3^{1/2}e_0## and some authors just define the coupling to be this right away. So why do some make a...

Is there conventional terminology to distinguish between scalars that transform between frames and those that don't? For example, energy is a single-component quantity but it isn't the same in every frame, whereas the length of a vector is also a scalar but is the same in every frame. Do we just...

So, I know this stuff is probably very elementary for most of the people on this site, but I have never had physics before, and I just started physics I at college. The professor has asked us to learn a few basic physics terms and I am having a hard time finding clear definitions for some of...

Hi, I'm new to this forum but I've been aware of its existence for a while and it's pretty cool. I finally came up with a question to post so here i am :) I've read a few nice posts on this forum about this topic, but I couldn't find the answer to what I'm looking for. I'm familiar with the...

Hi, could someone help me to define what is transient or in other words short-lived absorbtion? Maybe the general defintion could sound something like: In transient absorbtion the sample is excited with some kind of source(electrons, laser ,x-ray and so on) and then flashed with wide spectra...

I'll go right to the point. I'm trying to get someone interested in physics (and relieve physics of adjectives like boring) . All I'm asking for is a clear, fun and kind of insightful way for looking at physics and how it relates to our daily lives and how it helps us understand our...

From the book of Nakahara "Geometry, Topology and Physics": A diffeomorfism ##f:\mathcal{M}\to \mathcal{M}## is an isometry if it preserves the metric: ## f^{*}g_{f(p)}=g_{p} ## In components this condition becomes: ## \frac{\partial y^{\alpha}}{\partial x^{\mu}}\frac{\partial...

I am trying to find a consistent, non-circular definition of information, which includes quantum information. The two main definitions that recur are the von Neumann entropy and the superposition definition. Let's take the latter; the former is similar. This would mean that any change in the...

Hello i wonder if anyone here can explain to me, why the wavefunction as a function of position is defined like this: $$\Psi(x,t) = \langle{x}|{\Psi(t)}\rangle$$ Why is it wise to use an inner product as a definition?

Hi, I have my exam tomorrow and have been doing the practice questions. However we don't get the answers to these questions so I am lost as to whether I am doing them right, also I am stuck at a few points, particularly with the definition questions. \[ 1.)Prove\ lim_{x \to...

Was wondering if the only required definition for finite groups is closure (maybe associativity as well). It seems that is all that is necessary. The inverse and identity necessarily seem to follow based on the fact that if I multiply any element by itself enough times, I have to repeat back to...

In early physics, i learned a force was simply a push or pull, talked about as a number of Newtons or pounds, such as "the force is 5lbs". Then you learn that a force is really a vector quantity, having both the direction and strength/force, so it should be "5lbs to the east or 15lbs...

Dyadic Cube C_{k,N} = X \in\ \mathbb{R}^{n} \frac{k_{i}}{2^{N}} \leq x_{i} < \frac{k_{i}+1}{2^{N}} for 1 \leq i \leq n Where k = \pmatrix { k_{1} \cr k_{2} \cr \vdots \cr k_{i} \cr } I understand that N is the level of the cubes, but what does k equal? I'm having trouble...

0k i know net force on a body is defined as mass times acceleration of the body w.r.t inertial frame, but how do we define individual forces acting on the body? Eg. Forces acting on a 1kg block are F1=+6¡ And F2=-4¡ So we know net force=2¡, and net acceleration=2 m/s^2 but how do we actually...

Homework Statement Calculate the derivative of f(x) = x^3 - 3x^2 Homework Equations (f(x+h) - f(x))/h The Attempt at a Solution Just wondering if someone can check my solution. (f(x+h)- f(x))/h= ((x+h)^3- 3(x+h)^2- (x^3-3x^2))/h = (x^3+ 3x^2 h+3xh^2+ h^3-3(x^2+ 2xh+ h^2 )-...